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CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 5 Determinants Ex 5(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Exercise 5(b)

Question 1.
Write the number of solutions of the following system of equations.
(i) x – 2y = 0
Solution:
No solution

(ii) x – y = 0 and 2x – 2y = 1
Solution:
Infinite

(iii) 2x + y = 2 and -x – 1/2y = 3
Solution:
No solution

(iv) 3x + 2y = 1 and x + 5y = 6
Solution:
One

(v) 2x + 3y + 1 = 0 and x – 3y – 4 = 0
Solution:
One

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

(vi) x + y + z = 1
x + y + z = 2
2x + 3y + z = 0
Solution:
No solution

(vii) x + 4y – z = 0
3x – 4y – z = 0
x – 3y + z = 0
Solution:
One

(viii) x + y – z = 0
3x – y + z = 0
x – 3y + z = 0
Solution:
One

(ix) a1x + b1y + c1z = 0
a2x + b2y + c2z = 0
a3x + b3y + c3z = 0
and \left|\begin{array}{lll} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array}\right| = 0
Solution:
Infinite solutions as Δ = Δ1 = Δ2 = Δ3 = 0

Question 2.
Show that the following system is inconsistent.
(a – b)x + (b – c)y + (c – a)z = 0
(b – c)x + (c – a)y + (a – b)z = 0
(c – a)x + (a – b)y + (b – c)z =1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.2

Question 3.
(i) The system of equations
x + 2y + 3z = 4
2x + 3y + 4z = 5
3x + 4y + 5z = 6 has
(a) infinitely many solutions
(b) no solution
(c) a unique solution
(d) none of the three
Solution:
(a) infinitely many solutions

(ii) If the system of equations
2x + 5y + 8z = 0
x + 4y + 7z = 0
6x + 9y – z = 0
has a nontrivial solution, then is equal to
(a) 12
(b) -12
(c) 0
(d) none of the three
Solution:
(b) -12

(iii) The system of linear equations
x + y + z = 2
2x + y – z = 3
3x +2y + kz = 4
has a unique solution if
(a) k ≠ 0
(b) -1 < k < 1
(c) -2 < k < 2
(d) k = 0
Solution:
(a) k ≠ 0

(iv) The equations
x + y + z = 6
x + 2y + 3z = 10
x + 2y + mz = n
give infinite number of values of the triplet (x, y, z) if
(a) m = 3, n ∈ R
(b) m = 3, n ≠ 10
(c) m = 3, n = 10
(d) none of the three
Solution:
(c) m = 3, n = 10

(v) The system of equations
2x – y + z = 0
x – 2y + z = 0
x – y + 2z = 0
has infinite number of nontrivial solutions for
(a) = 1
(b) = 5
(c) = -5
(d) no real value of
Solution:
(c) = -5

(vi) The system of equations
a1x + b1y + c1z = 0
a2x + b2y + c2z = 0
a3x + b3y + c3z =0
with has
(a) more than two solutions
(b) one trivial and one nontrivial solutions
(c) No solution
(d) only trivial solutions
Solution:
(a) more than two solutions

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 4.
Can the inverses of the following matrices be found?
(i) \left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]
Solution:
|A| = 0
∴ A-1 can not be found.

(ii) \left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right]
Solution:
∴ |A| = 4 – 6 = -2 ≠ 0
∴ A-1 exists.

(iii) \left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]
Solution:
|A| = \left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right] = 1 – 1 = 0
∴ A-1 does not exist.

(iv) \left[\begin{array}{ll} 1 & 2 \\ 2 & 4 \end{array}\right]
Solution:
|A| = \left[\begin{array}{ll} 1 & 2 \\ 2 & 4 \end{array}\right] = 4 – 4 = 0
∴ A-1 does not exist.

(v) \left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]
Solution:
|A| = \left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] = 1 ≠ 0
∴ A-1 exists.

Question 5.
Find the inverse of the following:
(i) \left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(1)

(ii) \left[\begin{array}{cc} 2 & -1 \\ 1 & 3 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(2)

(iii) \left[\begin{array}{cc} 4 & -2 \\ 3 & 1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(3)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

(iv) \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(4)

(v) \left[\begin{array}{cc} 1 & 0 \\ 2 & -3 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(5)

(vi) \left[\begin{array}{cc} 1 & 0 \\ 0 & -1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(6)

(vii) \left[\begin{array}{cc} i & -i \\ i & i \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(7)

(viii) \left[\begin{array}{ll} x & -x \\ x & x^2 \end{array}\right], x ≠ 0, x ≠ -1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.5(8)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 6.
Find the adjoint of the following matrices.
(i) \left[\begin{array}{ccc} 1 & 1 & -1 \\ 2 & -1 & 2 \\ 1 & 3 & -2 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.6(1)

(ii) \left[\begin{array}{ccc} -2 & 2 & 3 \\ 1 & 4 & 2 \\ -2 & -3 & 1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.6(2)

(iii) \left[\begin{array}{lll} 2 & 1 & 2 \\ 2 & 2 & 1 \\ 1 & 2 & 2 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.6(3)

(iv) \left[\begin{array}{ccc} 1 & 3 & 0 \\ 2 & -1 & 6 \\ 5 & -3 & 1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.6(4)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 7.
Which of the following matrices are invertible?
(i) \left[\begin{array}{ccc} 1 & 0 & 0 \\ 1 & 1 & 1 \\ 2 & -1 & 1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.7(1)

(ii) \left[\begin{array}{ccc} 2 & 1 & -2 \\ 1 & 2 & 1 \\ 3 & 6 & 4 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.7(2)

(iii) \left[\begin{array}{ccc} -1 & -2 & 3 \\ 2 & 1 & -4 \\ -1 & 0 & 2 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.7(3)

(iv) \left[\begin{array}{ccc} 1 & 0 & 1 \\ 2 & -2 & 1 \\ 3 & 2 & 4 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.7(4)

Question 8.
Examining consistency and solvability, solve the following equations by matrix method.
(i) x – y + z = 4
2x + y – 3z = 0
x + y + z = 2
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(1)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(1.1)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(1.2)

(ii) x + 2y – 3z = 4
2x + 4y – 5z = 12
3x – y + z = 3
Solution:
Let
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(2)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(2.1)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

(iii) 2x – y + z = 4
x + 3y + 2z = 12
3x + 2y + 3z = 16
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(3)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(3.1)

(iv) x + y + z = 4
2x + 5y – 2x = 3
x + 7y – 7z = 5
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(4)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(4.2)

(v) x + y + z = 4
2x – y + 3z = 1
3x + 2y – z = 1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(5)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(5.1)

(vi) x + y – z = 6
2x – 3y + z = 1
2x – 4y + 2z = 1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(6)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(6.1)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

(vii) x – 2y = 3
3x + 4y – z = -2
5x – 3z = -1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(7)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(7.1)

(viii) x + 2y + 3z = 14
2x – y + 5z = 15
2y + 4z – 3x = 13
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(8)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(8.1)

(ix) 2x + 3y +z = 11
x + y + z = 6
5x – y + 10z = 34
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(9)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.8(9.1)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 9.
Given the matrices
A = \left[\begin{array}{ccc} 1 & 2 & 3 \\ 3 & -2 & 1 \\ 4 & 2 & 1 \end{array}\right], X = \left[\begin{array}{l} x \\ y \\ z \end{array}\right] and C = \left[\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right]
write down the linear equations given by AX = C and solve it for x, y, z by matrix method.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.9
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.9.1

Question 10.
Find X, if \left[\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 & -1 \\ 2 & 1 & -1 \end{array}\right] X = \left[\begin{array}{l} 6 \\ 0 \\ 1 \end{array}\right] where X = \left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.10
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.10.1

Question 11.
Answer the following:
(i) If every element of a third order matrix is multiplied by 5, then how many times its determinant value becomes?
Solution:
125

(ii) What is the value of x if \left|\begin{array}{ll} 4 & 1 \\ 2 & 1 \end{array}\right|^2=,\left|\begin{array}{ll} 3 & 2 \\ 1 & x \end{array}\right|-\left|\begin{array}{cc} x & 3 \\ -2 & 1 \end{array}\right| ?
Solution:
x = 6

(iii) What are the values of x and y if \left|\begin{array}{ll} x & y \\ 1 & 1 \end{array}\right|=2,\left|\begin{array}{ll} x & 3 \\ y & 2 \end{array}\right|=1 ?
Solution:
x = 5, y = 3

(iv) What is the value of x if \left|\begin{array}{ccc} x+1 & 1 & 1 \\ 1 & 1 & -1 \\ -1 & 1 & 1 \end{array}\right| = 4?
Solution:
x = 0

(v) What is the value of \left|\begin{array}{ccc} \mathbf{o} & -\mathbf{h} & -\mathbf{g} \\ \mathbf{h} & \mathbf{0} & -\mathbf{f} \\ \mathbf{g} & \mathbf{f} & \mathbf{0} \end{array}\right|?
Solution:
0

(vi) What is the value of \left|\begin{array}{l} \frac{1}{a} 1 \mathrm{bc} \\ \frac{1}{b} 1 c a \\ \frac{1}{c} 1 a b \end{array}\right|
Solution:
0

(vii) What is the co-factor of 4 in the determinant \left|\begin{array}{rrr} 1 & 2 & -3 \\ 4 & 5 & 0 \\ 2 & 0 & 1 \end{array}\right|
Solution:
-2

(viii)In which interval does the determinant \left|\begin{array}{ccc} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{array}\right| lie?
Solution:
[2, 4]

(ix) Ifx + y + z = n, what is the value of Δ = \left|\begin{array}{ccc} \sin (x+y+z) & \sin B & \cos C \\ -\sin B & 0 & \tan A \\ \cos (A+B) & -\tan A & 0 \end{array}\right| Where A, B, C are the angles of triangle.
Solution:
0
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.11

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 12.
Evaluate the following determinants:
(i) \left|\begin{array}{ccc} 14 & 3 & 28 \\ 17 & 9 & 34 \\ 25 & 9 & 50 \end{array}\right|
Solution:
\left|\begin{array}{ccc} 14 & 3 & 28 \\ 17 & 9 & 34 \\ 25 & 9 & 50 \end{array}\right|
= 2\left|\begin{array}{ccc} 14 & 3 & 28 \\ 17 & 9 & 34 \\ 25 & 9 & 50 \end{array}\right| = 0
(C1 = C3)

(ii) \left|\begin{array}{ccc} 16 & 19 & 13 \\ 15 & 18 & 12 \\ 14 & 17 & 11 \end{array}\right|
Solution:
\left|\begin{array}{ccc} 16 & 19 & 13 \\ 15 & 18 & 12 \\ 14 & 17 & 11 \end{array}\right| = \left|\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 14 & 17 & 11 \end{array}\right|
( R1 = R1 – R2, R2 = R2 – R3)
= 0 ( R1 = R2)

(iii) \left|\begin{array}{ccc} 224 & 777 & 32 \\ 735 & 888 & 105 \\ 812 & 999 & 116 \end{array}\right|
Solution:
\left|\begin{array}{ccc} 224 & 777 & 32 \\ 735 & 888 & 105 \\ 812 & 999 & 116 \end{array}\right|
= 7\left|\begin{array}{ccc} 32 & 777 & 32 \\ 105 & 888 & 105 \\ 116 & 999 & 116 \end{array}\right| = 0
(C1 = C2)

(iv) \left|\begin{array}{lll} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 3 & 4 & 6 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.12(4)

(v) \left|\begin{array}{ccc} 1 & 2 & 3 \\ 3 & 5 & 7 \\ 8 & 14 & 20 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.12(5)

(vi) \left|\begin{array}{ccc} 1^2 & 2^2 & 3^2 \\ 2^2 & 3^2 & 4^2 \\ 3^2 & 4^2 & 5^2 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.12(6)
= 225 – 256 – 4(100 – 144) + 9(64 – 81)
= -31 – 4(-44) + 9(-17)
= -31 + 176 – 153 = -184 + 176
= -8

(vii) \left|\begin{array}{ccc} 1 & 0 & -5863 \\ -7361 & 2 & 7361 \\ 1 & 0 & 4137 \end{array}\right|
Solution:
\left|\begin{array}{ccc} 1 & 0 & -5863 \\ -7361 & 2 & 7361 \\ 1 & 0 & 4137 \end{array}\right|
= 2\left|\begin{array}{cc} 1 & -5863 \\ 1 & 4137 \end{array}\right|
(expanding along 2nd column)
= 2(4137 + 5863)
= 2 × 10000 = 20000

(viii) \left|\begin{array}{lll} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.12(8)

(ix) \left|\begin{array}{ccc} 0 & a^2 & b \\ b^2 & 0 & a^2 \\ a & b^2 & 0 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.12(9)
= -a2 (0 –  a2) + b (b4 –  0) = a5 + b5

(x) \left|\begin{array}{ccc} a-b & b-c & c-a \\ \boldsymbol{x}-\boldsymbol{y} & \boldsymbol{y}-\boldsymbol{z} & z-\boldsymbol{x} \\ \boldsymbol{p}-\boldsymbol{q} & \boldsymbol{q}-\boldsymbol{r} & \boldsymbol{r}-\boldsymbol{p} \end{array}\right|
Solution:
\left|\begin{array}{lll} a-b & b-c & c-a \\ x-y & y-z & z-x \\ p-q & q-r & r-p \end{array}\right|
= \left|\begin{array}{lll} 0 & b-c & c-a \\ 0 & y-z & z-x \\ 0 & q-r & r-p \end{array}\right| (C1 = C1 + C2 + C3)
= 0 ( C1 = 0)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

(xi) \left|\begin{array}{lll} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{array}\right|
Solution:
\left|\begin{array}{lll} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{array}\right|
= \left|\begin{array}{lll} 0 & b-c & c-a \\ 0 & c-a & a-b \\ 0 & a-b & b-c \end{array}\right| (C1 = C1 + C2 + C3)
= 0

(xii) \left|\begin{array}{ccc} -\cos ^2 \theta & \sec ^2 \theta & -0.2 \\ \cot ^2 \theta & -\tan ^2 \theta & 1.2 \\ -1 & 1 & 1 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.12(12)
(Expanding along 3rd row)
= (-cos2 θ + sec2 θ) (-tan2 θ – 1.2) – (sec2 θ + 0.2) (cot2 θ – tan2 θ)
= sin2 θ – 1.2 cos2 θ – sec2 θ tan2 θ – 1.2 sec2 θ – cosec2 θ +  sec2 θ tan2 θ – 0.2 cot2 θ + 0.2 tan2 θ
= sin2 θ – cosec2 θ + 1.2 (cos2 θ – sec2 θ) + 0.2 (tan2 θ – cot2 θ) ≠ 0
The question seems to be wrong.

Question 13.
If \left|\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{array}\right| = 0 what are x and y?
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.13
or, xy – 0 = 0 ⇒ xy = 0, ⇒ x = 0, or y = 0

Question 14.
For what value of x \left|\begin{array}{ccc} 2 x & 0 & 0 \\ 0 & 1 & 2 \\ -1 & 2 & 0 \end{array}\right| = \left|\begin{array}{lll} 1 & 0 & 0 \\ 2 & 3 & 4 \\ 0 & 3 & 5 \end{array}\right|?
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.14

Question 15.
Solve \left|\begin{array}{ccc} x+a & 0 & 0 \\ a & x+b & 0 \\ a & 0 & x+c \end{array}\right| = 0
Solution:
\left|\begin{array}{ccc} x+a & 0 & 0 \\ a & x+b & 0 \\ a & 0 & x+c \end{array}\right| = 0
or, (x – a) \left|\begin{array}{cc} x+b & 0 \\ 0 & x+c \end{array}\right| = 0
or, (x + a) (x + b) (x + c) = 0
x = -a, x = -b, x = -c

Question 16.
Solve \left|\begin{array}{lll} a+x & a-x & a-x \\ a-x & a+x & a-x \\ a-x & a-x & a+x \end{array}\right| = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.16

Question 17.
Solve \left|\begin{array}{ccc} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{array}\right| = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.17

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 18.
Show that x = 2 is a root of \left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right| = 0 Solve this completely.
Solution:
Putting x = 2,
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.18
= (x – 1) (-15x + 30 – 5x2 + 10x)
= (x – 1) (-5x2 – 5x + 30)
= -5(x – 1) (x2 + x – 6)
= -5(x – 1) (x + 3) (x – 2) = 0
⇒ x = 1 or, -3 or 2.

Question 19.
Evaluate \left|\begin{array}{ccc} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{array}\right|\left|\begin{array}{lll} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.19
= (a – b) (b – c) [(-a + c) – (b + c – a – b)]
= (a – b) (b – c) (-a + c – c + a) = 0

Question 20.
\left|\begin{array}{lll} a & a^2-b c & 1 \\ b & b^2-a c & 1 \\ c & c^2-a b & 1 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.20

Question21.
For what value of X the system of equations
x + y + z = 6, 4x + λy – λz = 0, 3x + 2y – 4z = -5 does not possess a solution?
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.21
= 24 – 6λ – 2λ = 24 – 8λ
when Δ = 0
We have 24 – 8λ, = 0 or, λ = 3
The system of equations does not posses solution for λ = 3.

Question 22.
If A is a 3 × 3 matrix and |A| = 2, then which matrix is represented by A × adj A?
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.22

Question 23.
If A = \left[\begin{array}{cc} 0 & -\tan \frac{\alpha}{2} \\ \tan \frac{\alpha}{2} & 0 \end{array}\right]
show that (I + A) (I – A)-1 = \left[\begin{array}{cc} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right] where I = \left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.23
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.23.1

Question 24.
Prove the following:
(i) \left|\begin{array}{ccc} a^2+1 & a b & a c \\ a b & b^2+1 & b c \\ a c & b c & c^2+1 \end{array}\right| = 1 + a2 + b2 + c2
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(1)

(ii) \left|\begin{array}{ccc} 1 & 1 & 1 \\ a & b & c \\ a^3 & b^3 & c^3 \end{array}\right| = (b – c) (c – a) (a – b) (a + b + c)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(2)
= (a – b) (b – c) (b2 + bc + c2 – a2 – ab – b2)
= (a – b) (b- c) (c2 – a2 + bc – ab)
= (a – b) (b – c) {(c – a) (c + a) + b(c – a)}
= (a – b) (b – c) (c – a) (a + b + c) = R.H.S.
(Proved)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

(iii) \left|\begin{array}{lll} \boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b} \end{array}\right| = 3abc – a3 – b3 – c3
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(3)
= (a + b + c) {(b – c) (a – b) – (c – a)2}
= (a + b + c) (a + b + c) (ab – b2 – ca + bc – c2 – a2 + 2ca)
= (a + b + c) (-a2 – b2 – c2 + ab + bc + ca)
= -(a + b + c) (a2 + b2 + c2 – ab – bc – ca)
=- (a3 + b3 + c3 – 3abc)
= 3abc – a3 – b3 – c3

(iv) \left|\begin{array}{lll} b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2 \end{array}\right| = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(4)
= (b2 – a2 + bc – ac) (a – b) {(-a + b) (c – a) – (bc – ac – ab + a2)}
= (b2 – a2 + bc – ac) (a – b) (- ca + a2 + bc – ab – bc + ac + ab – a2)
= (b2 – a2 + bc – ac) (a – b) × 0 = 0
= R.H.S.
(Proved)

(v) \left|\begin{array}{ccc} -a^2 & a b & a c \\ a b & -b^2 & b c \\ a c & b c & -c^2 \end{array}\right| = 4a2b2c2
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(5)

(vi) \left|\begin{array}{lll} (b+c)^2 & a^2 & b c \\ (c+a)^2 & b^2 & c a \\ (a+b)^2 & c^2 & a b \end{array}\right| = (a2 + b2 + c2 ) (a + b + c) (b – c) (c – a) (a – b)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(6)
= (a – b) (b – c) (a2 + b2 + c2) (-a2 – ab + bc + c2)
= (a – b) (b – c) (a2 + b2 + c2) {(c2 – a2) + b(c – a)}
= (a2 + b2 + c2) (a – b) (b – c) (c – a) (c + a + b)

(vii) \left|\begin{array}{lll} b+c & a+b & a \\ c+a & b+c & b \\ a+b & c+a & c \end{array}\right| = a3 + b3 + c3 – 3abc
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(7)
= (a + b +c) {(a – b) (a – c) – (c – b) (b – c)}
= (a + b + c) (a2 – ac – ab + bc – bc + c2 + b2 – bc)
= (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
= (a3 + b3 + c3 – 3abc)

(viii) \left|\begin{array}{ccc} a+b+c & -c & -b \\ -c & a+b+c & -a \\ -b & -a & a+b+c \end{array}\right| = 2(b + c) (c + a) (a + b)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(8)
= -2(a + b) (b + c) (-a – b – c + b)
= 2(a + b) (b + c) (c + a)

(ix) \left|\begin{array}{ccc} a x-b y-c z & a y+b x & a z+c x \\ b x+a y & b y-c z-a x & b z+c y \\ c x+a z & a y+b z & c z-a x-b y \end{array}\right| = (a2 + b2 + c2) (ax + by + cz) (x2 + y2 + z2)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(9)
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.24(9.1)

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 25.
If 2s = a + b + c show that \left|\begin{array}{ccc} a^2 & (s-a)^2 & (s-a)^2 \\ (s-b)^2 & b^2 & (s-b)^2 \\ (s-c)^2 & (s-c)^2 & c^2 \end{array}\right| = 2s3 (s – a) (s – b) (s – c)
Solution:
Let s – a = A, s – b = B, s – c = C
A + B + C = 3s – (a + b + c)
= 3s – 2s = s
Also B + C = s – b + s – c = 2s – (b + c)
= (a + b + c) – b + c = a
Similarly C + A = b, A + B = c
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.25
= 2 ABC (A + B + C)2
[Refer Q.No.9 (xii) of Exercise 5(a)]
= 2(s – a) (s – b)(s – c) s3

Question 26.
if \left|\begin{array}{ccc} x & x^2 & x^3-1 \\ y & y^2 & y^3-1 \\ z & z^2 & z^3-1 \end{array}\right| = 0 then prove that xyz =1 when x, y, z are non zero and unequal.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.26
= (x – y) (y – z) (z – x) (xyz – 1)
It is given that
(x – y) (y – z) (z – x) (xyz – 1) = 0
⇒ xyz – 1 (as x ≠ y ≠ z)

Question 27.
Without expanding show that the following determinant is equal to Ax + B where A and B are determinants of order 3 not involving x.
\left|\begin{array}{ccc} x^2+x & x+1 & x-2 \\ 2 x^2+3 x-1 & 3 x & 3 x-3 \\ x^2+2 x+3 & 2 x-1 & 2 x-1 \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.27

Question 28.
If x, y, z are positive and are the pth, qth and rth terms of a G.P. then prove that \left|\begin{array}{lll} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{array}\right| = 0
Solution:
Let the G.P. be
a, aR, aR2, aR3 …..aRn-1
p th term = aRp-1
q th term = aRq-1
r th term = aRr-1
x = aRp-1, y= aRq-1, z = aRr-1
log x = log a + (p – 1) log R,
log y = log a + (q – 1) log R,
log z = log a + (r – 1) log R
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.28

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 29.
If Dj = \left|\begin{array}{ccc} j & a & n(n+2) / 2 \\ j^2 & b & n(n+1)(2 n+1) / 6 \\ j^3 & c & n^2(n+1)^2 / 4 \end{array}\right| then prove that \sum_{j=1}^nDj = 0.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.29

Question 30.
Ifa1, a2,……an are in G.P. and ai > 0 for every i, then find the value of
\left|\begin{array}{ccc} \log a_n & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+1} & \log a_{n+2} & \log a_{n+3} \\ \log a_{n+2} & \log a_{n+3} & \log a_{n+4} \end{array}\right|
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.30

Question 31.
If f(x)= \left|\begin{array}{ccc} 1+\sin ^2 x & \cos ^2 x & 4 \sin ^2 x \\ \sin ^2 x & 1+\cos ^2 x & 4 \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+4 \sin ^2 x \end{array}\right| what is the least value of f(x)?
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.31
As minimum value of sin 2x is 0. So the minimum value of above function f(x) is 2.

Question 32.
If fr(x), gr(x), hr(x), r = 1, 2, 3 are polynomials in x such that fr(a) = gr(a) = hr(a) and
F(x) = \left[\begin{array}{lll} f_1(x) & f_2(x) & f_3(x) \\ g_1(x) & g_2(x) & g_3(x) \\ h_1(x) & h_2(x) & h_3(x) \end{array}\right] find F'(x) at x = a.
Solution:
We have
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.32
[Since f1a) = g1(a) = h1(a), f2(a) = g2(a) = h2(a) and f3(a) = g3(a) = h3(a) So that each determinant is zero due to presence of two identical rows.]

CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b)

Question 33.
If f(x) = \left[\begin{array}{ccc} \cos x & \sin x & \cos x \\ \cos 2 x & \sin 2 x & 2 \cos 2 x \\ \cos 3 x & \sin 3 x & 3 \cos 3 x \end{array}\right] find f'(\frac{\pi}{2}).
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 5 Determinants Ex 5(b) Q.33

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d)

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Exercise 6(d)

Question 1.
State which of the following is the probability distribution of a random variable X with reasons to your answer:
(a)

X = x 0 1 2 3 4
p(x) 0.1 0.2 0.3 0.4 0.1

(b)

X = x 0 1 2 3
p(x) 0.15 0.35 0.25 0.2

(c)

X = x 0 1 2 3 4 5
p(x) 0.4 R 0.6 R2 0.7 0.3

Solution:
(a) As ∑pi = 1.1 > 1, the given distribution is not a probability distribution.
(b) As ∑pi = 0.95 < 1, the given distribution is not a probability distribution.
(c) As the value of R is not known, the given distribution is not a probability distribution.

Question 2.
Find the probability distribution of number of doublets in four throws of a pair of dice. Find also the mean and the variance of the number of doublets.
Solution:
Let the random variable X represents the number of doublets in 4 throws of a pair of dice.
X can take values 0, 1, 2, 3, 4
In a single throw of two dice
X can take values 0, 1, 2, 3, 4
In a single throw of two dice.
P(doublet) = \frac{6}{36}
P(non-doublet) = 1 – P (doublet) = \frac{5}{36}
Clearly the given experiment is a binomial experiment with n = 4,
p = \frac{1}{6}, q = \frac{5}{6}
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.2
N.B. We can use the definition to find mean and variance.

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d)

Question 3.
Four cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Find the probability distribution of the number of aces. Calculate the mean and variance of the number of aces.
Solution:
Let the random variable X denotes the number of aces.
Thus X can take values 0, 1, 2, 3, 4.
Clearly the given experiment is a binomial experiment with n = 4
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.3
N.B. We can use the definition to find mean and variance.

Question 4.
Find the probability distribution of
(a) number of heads in three tosses of a coin.
Solution:
Let the random variable X denotes the number of heads in three tosses of a coin.
X can take values 0, 1, 2, 3
In one toss p(H) = \frac{1}{2}, p(T) = \frac{1}{2}
This experiment is a binomial experiment with n = 3, p = \frac{1}{2} and q = \frac{1}{2}
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.4
(b) number of heads in simultaneous tosses of four coins.
Solution:
When 4 coins tossed simultaneously, let the random variable X denotes the number of heads.
X can take values 0, 1. 2, 3, 4
This experiment is a binomial experiment with n = 4, p = \frac{1}{2} and q = \frac{1}{2}
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.4(1)

Question 5.
A biased coin where the head is twice as likely to occur as the tail is, tossed thrice. Find the probability distribution of number of heads.
Solution:
Let in a toss P(T) = x
According to the question P(H) = 2x
Now 2x + x = 1
⇒ x = \frac{1}{3}
Thus P(T) = \frac{1}{3}, P(H) = \frac{3}{3}
Clearly the given experiment is a binomial experiment with n = 3, p = P(H) = \frac{2}{3}, q = P(T) = \frac{1}{3}
Let the random variable X denotes the number of heads in three throws of that coin.
X can take values 0, 1, 2, 3
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.5

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d)

Question 6.
Find the probability distribution of the number of aces in question no. 3 if the cards are drawn successively without replacement.
Solution:
Total number of cards = 52
Number of aces = 4
Number of cards drawn = 4 (one by one without replacement)
Let X = the random variable of number of aces drawn.
X can take values 0, 1, 2, 3 or 4
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.6

Question 7.
From a box containing 32 bulbs out of which 8 are defective 4 bulbs are drawn at random successively one after another with replacement. Find the probability distribution of the number of defective bulbs.
Solution:
Total number of bulbs = 32
Number of defective bulbs = 8
∴ Number of nondefective bulbs = 24
Number of bulbs drawn = 4 (one after another with replacement)
Clearly the experiment is a binomial experiment with n = 4
p = p ((drawing a defective bulb) = \frac{8}{32} = \frac{1}{4}
q = p (drawing a non defective bulb) = \frac{3}{4}
Let the random variable X denotes the number of defective bulbs.
∴ X can take values 0, 1, 2, 3, 4.
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.7

Question 8.
A random variable X has the following probability distribution.

X = x 0 1 2 3 4 5
p(x) 0 R 2R 3R 3R R

Determine
(a) R
(b) P(X < 4)
(d) P(2 ≤ X ≤ 5)
(c) P(X ≥ 2)
Solution:
(a) Clearly ∑Pi = 1
⇒ R + 2R + 3R + 3R + R = 1
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.8

Question 9.
Find the mean and the variance of the number obtained on a throw of an unbiased coin.
Solution:
When an unbiased coin is tossed we donot get any number.
p(getting a number) = 0
Thus mean = variance = 0
If instead of coin it would be an unbiased die
Then let X = The number obtained in the throw.
X can take values 1, 2, 3, 4, 5 or 6.
P(X = 1) = P(X = 2) = P(X = 3) = P(X = 4)
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.9

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d)

Question 10.
A pair of coins is tossed 7 times. Find the probability of getting
(i) exactly five tails
(ii) at least five tails
(iii) at most five tails
Solution:
Clearly the given experiment is a binomial experiment with
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.10

Question 11.
If a pair of dice is thrown 5 times then find the probability of getting three doublets.
Solution:
In a single through of a pair of dice
p (a doublet) = \frac{6}{36} = \frac{1}{6}
p (a non doublet) = 1 – p (a doublet) = 1 – \frac{1}{6} = \frac{5}{6}
Clearly the given experiment is a binomial experiment with n = 5
p = \frac{1}{6} and q = \frac{5}{6}
p(3 doublets in 5 throw) = 5C3 p3q2
= 10. \left(\frac{1}{6}\right)^3 \left(\frac{5}{6}\right)^2 = \frac{250}{6^5} = \frac{125}{3888}

Question 12.
Four cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that:
(i) all the four cards are diamonds
(ii) only two cards are diamonds
(iii) none of the cards is a diamond.
Solution:
Out of 52 cards there are 13 diamonds. 4 cards are drawn one by one with replacement.
When we draw a card
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.12

Question 13.
In an examination, there are twenty multiple-choice questions each of which is supplied with four possible answers. What is the probability that a candidate would score 80% or more in the answers to these questions?
Solution:
Total number of questions = 20 for each question
p (correct answer) = \frac{1}{4}
p (wrong answer) = \frac{3}{4}
p (the score is > 80%)
= p (no. of correct answer > 16)
= p (16 correct answers)
+ p(17 correct answers)
+ p (18 correct answers)
+ p (19 correct answers)
+ p (20 correct answers)
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.13

Question 14.
A bag contains 7 balls of different colours. If five balls are drawn successively with replacement then what is the probability that none of the balls drawn is white?
Solution:
Total number of balls = 7 (The colours are different)
Number of balls drawn = 5 (one by one with replacement)
Case – 1
(If a white coloured ball is not present)
p(non is white) = 1
Case – 2
(If one ball is white).
In one draw p(white ball) = \frac{1}{7}
p (non white ball) = \frac{6}{7}
When 5 balls are drawn
p (none of the balls drawn is white) = 5C0 \left(\frac{1}{7}\right)^0 \left(\frac{6}{5}\right)^5 = \left(\frac{6}{7}\right)^5

Question 15.
Find the probability ofthrowing at least 3 sixes in 5 throws of a die.
Solution:
In one throw of a die
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.15

Question 16.
The probability that a student securing first division in an examination is . What is the probability that out of 100 students twenty pass in first division?
Solution:
Clearly the given experiment is a binomial experiment with
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.16

CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d)

Question 17.
Sita and Gita throw a die alternatively till one of them gets a 6 to win the game. Find their respective probability of winning if Sita starts first.
Solution:
In one throw of a die
p (getting a 6) = \frac{1}{6}
p (not getting a 6) = \frac{5}{6}
If Sita begins the game she may win in first round or second round or third round, etc.
Thus p(Sita wins)
CHSE Odisha Class 12 Math Solutions Chapter 6 Probability Ex 6(d) Q.17

Question 18.
If a random variable X has a binomial distribution B(8, \frac{1}{2}) then find X for which the outcome is the most likely. [Hint: Find X=x for which P(X = x) is the maximum, x = 0, 1, 2, 3,…….. 8.]
Solution:
Given binomial distribution is B(8, \frac{1}{2})
Thus n = 8, p = \frac{1}{2}, q = \frac{1}{2}
We shall find X which is most likely i.e. for which p(x = r) is maximum where r = 0, 1, 2, ….., 8
As p = q, the probability is maximum when 8Cr is maximum
But 8Cr, r = 0, 1, 2, ….. ,8 is maximum when r = 4.
Thus the most likely outcome is x = 4.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(b)

Question 1.
Differentiate from definition
(i) e3x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Q.1

(ii) 2x2
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Q.2

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b)

(iii) In (3x + 1)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Q.3

(iv) logx5 (Hint : logx5 = \frac{\ln 5}{\ln x})
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Q.4

(v) In sin x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Q.5

(vi) x2 a2x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(b) Q.6

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(f)

Find derivatives of the following functions.
Question 1.
xx
Solution:
Let y = xx
Then In y = x . In x
\frac{d}{d x}(In y) = \frac{d}{d x}(x . In x)
\frac{1}{y}\frac{d y}{d x} = In x + x . \frac{1}{x} = In x + 1 = 1 + In x
\frac{d y}{d x} = y (1 + In x) = xx (1 + In x) = xx In (ex)

Question 2.
\left(1+\frac{1}{x}\right)^x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.2

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f)

Question 3.
xsin x
Solution:
y = xsin x
⇒ In y = sin x . In x
\frac{1}{y}\frac{d y}{d x} = cos x In x + sin x . \frac{1}{x}
\frac{d y}{d x} = xsin x (cos x . In x + \frac{\sin x}{x})

Question 4.
(log x)tan x
Solution:
y = (log x)tan x
⇒ log y = tan x . log (log x)
\frac{1}{y}\frac{d y}{d x} = sec2 x log (log x) + tan x . \frac{1}{\log x} . \frac{1}{x}
\frac{d y}{d x} = (log x)tan x {sec2 x . log log x + \frac{\tan x}{x \log x}}

Question 5.
2^{\left(2^x\right)}
Solution:
y = 2^{\left(2^x\right)}
⇒ In y = 2x . In 2
\frac{1}{y}\frac{d y}{d x} = 2x . In 2 . In 2
\frac{d y}{d x} = 2^{\left(2^x\right)} . 2x . (In 2)2

Question 6.
(1+\sqrt{x})^{x^2}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.6

Question 7.
\left(\sin ^{-1} x\right)^{\sqrt{1-x^2}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.7

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f)

Question 8.
(\tan x)^{\log x^3}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.8

Question 9.
x1/x + (sin x)x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.9

Question 10.
(cos x)x + xcos x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.10

Question 11.
(x2 + 1)2/3 (3x + 1)1/4 √x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.11

Question 12.
\frac{(x+1)(x+2)^2(x+3)^3}{(x-1)(x-2)^2(x-3)^3}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.12

Question 13.
(sin x)x \sqrt{\sin x}\left(1+x^2\right)^{\frac{1}{2}+x}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.13

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f)

Question 14.
(sec x + tan x)cot x
Solution:
y = (sec x + tan x)cot x
⇒ In y = cot x . In (sec x + tan x)
\frac{1}{y}\frac{d y}{d x} = -cosec2 x . In (sec x + tan x) + cot x . \frac{1}{\sec x+\tan x} × (sec x . tan x + sec2 x)
= -cosec2 x . In (sec x + tan x) + cot x . sec x
\frac{d y}{d x} = y {-cosec2 x . In (sec x + tan x) + cosec x}
= (sec x + tan x)cot x {cosec x – cosec2 x . In (sec x + tan x)}

Question 15.
(2√x)1+√x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(f) Q.15

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(e) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(e)

Differentiate the following functions by proper substitution.
Question 1.
sin-1 2x \sqrt{1-x^2}
Solution:
y = sin-1 2x \sqrt{1-x^2}    [Put x = sin θ
= sin-1 (2 sin θ . cos θ)
= sin-1 sin 2θ = 2θ = 2 sin-1 x.
\frac{d y}{d x} = \frac{2}{\sqrt{1-x^2}}

Question 2.
tan-1 \frac{2 x}{1-x^2}
Solution:
y = tan-1 \frac{2 x}{1-x^2}
= tan-1 \frac{2 \tan \theta}{1-\tan ^2 \theta} = tan-1 (tan 2θ)
= 2θ = 2 tan-1 x
\frac{d y}{d x} = \frac{2 x}{1-x^2}

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e)

Question 3.
tan-1 \sqrt{\frac{1-t}{1+t}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e) Q.3

Question 4.
\left[\left(\frac{1+t^2}{1-t^2}\right)^2-1\right]^{\frac{1}{2}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e) Q.4

Question 5.
tan-1 \left(\frac{\sqrt{x}+\sqrt{a}}{1-\sqrt{x a}}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e) Q.5

Question 6.
sin-1 (\frac{2 x}{1+x^2})
Solution:
y = sin-1 \frac{2 x}{1+x^2}  [Put x = tan θ
= sin-1 \frac{2 \tan \theta}{1+\tan ^2 \theta} = sin-1 sin θ
= 2θ = 2 tan-1 x
\frac{d y}{d x} = \frac{2 x}{1+x^2}

Question 7.
sec-1 \left(\frac{\sqrt{a^2+x^2}}{a}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e) Q.7

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e)

Question 8.
sin-1 \left(\frac{2 \sqrt{t^2-1}}{t^2}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(e) Q.8

Question 9.
cos-1 \left(\frac{1-t^2}{1+t^2}\right)
Solution:
y = cos-1 \left(\frac{1-t^2}{1+t^2}\right) [Put t = tan θ
= cos-1 \frac{1-\tan ^2 \theta}{1+\tan ^2 \theta}
= cos-1 cos 2θ = 2 tan-1 t
\frac{d y}{d x} = \frac{2}{1+t^2}

Question 10.
cos-1 (2t2 – 1)
Solution:
y = cos-1 (2t2 – 1) [Put t = tan θ
= cos-1 (2 cos2 θ – 1)
= cos-1 cos 2θ = 2θ = 2 cos-1 t
\frac{d y}{d x} = – \frac{2}{\sqrt{1-t^2}}

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(d)

Question 1.
Prove the formulae (4) to (7).
Solution:
(4) \frac{d}{d x}(cos-1 x) = \frac{-1}{\sqrt{1-x^2}}
Let y = cos-1 x
⇒ x = cos y
\frac{d}{d x} = \frac{1}{\left(\frac{d x}{d y}\right)} = \frac{1}{-\sin y}
But sin y ≥ 0 when
y ∈ [0, π] ( ∵ [0, π] is the principal value branch for cos-1 x)
\frac{d y}{d x} = \frac{-1}{\sqrt{1-\cos ^2 y}} = \frac{-1}{\sqrt{1-x^2}}

(5) Let y = tan-1 x
⇒ x = tan y
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.1

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d)

(6) Let y = cot-1 x
⇒ x = cot y
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.1(1)

(7) Let y = cosec-1 x
⇒ x = cosec y
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.1(2)

Question 2.
Find derivatives of the following functions.
sin-1 2x
Solution:
y = sin-1 2x
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.2

Question 3.
cot-1 √x
Solution:
cot-1 √x
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.3

Question 4.
sec-1 (2x + 1)
Solution:
y = sec-1 (2x + 1)
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.4

Question 5.
cos-1 \sqrt{\frac{1+x}{2}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.5

Question 6.
cos-1 \left(\frac{x-\frac{1}{x}}{x+\frac{1}{x}}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.6

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d)

Question 7.
tan-1 (cos √x)
Solution:
y = tan-1 (cos √x)
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.7

Question 8.
x2 cosec-1 \left(\frac{1}{\ln x}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.8

Question 9.
cot-1 \frac{\sqrt{1-x^2}}{x}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.9

Question 10.
(x sin-1 x)15
Solution:
y = (x sin-1 x)15
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.10

Question 11.
sin-1 \sqrt{\frac{1-x}{1+x}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(d) Q.11

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(c)

Find derivatives of the following functions.
Question 1.
(x2 +5)8
Solution:
y = (x2 +5)8
\frac{d y}{d x} = \frac{d}{d x}(x2 +5)8
= 8(x2 +5)7 × \frac{d}{d x}(x2 +5) by chain rule
= 8(x2 +5)7 . 2x
= 16x (x2 +5)7

Question 2.
\frac{1}{\left(x^3+\sin x\right)^2}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.2

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c)

Question 3.
In (√x+1)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.3

Question 4.
sin 5x + cos 7x
Solution:
sin 5x + cos 7x
\frac{d y}{d x} = \frac{d}{d x}(sin 5x) + \frac{d}{d x}(cos 7x)
= cos 5x . \frac{d}{d x}(5x) – sin 7x . \frac{d}{d x}(7x)
= 5 cos 5x – 7 sin 7x

Question 5.
esin t
Solution:
y = esin t
\frac{d y}{d x} = \frac{d}{d t}(esin t) = esin t . \frac{d}{d t}(sin t)
= esin t . cos t

Question 6.
\sqrt{a x^2+b x+c}
Solution:
y = \sqrt{a x^2+b x+c}
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.6

Question 7.
\left(\frac{x+1}{x^2+3}\right)^{-3}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.7

Question 8.
sec (tan θ)
Solution:
y = sec (tan θ)
\frac{d y}{d θ} = \frac{d}{d θ} {sec (tan θ)}
= sec (tan θ) . tan (tan θ) . \frac{d}{d θ}(tan θ)
= sec (tan θ) . tan (tan θ) . sec2 θ

Question 9.
sin \left(\frac{1-x^2}{1+x^2}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.9

Question 10.
\sqrt{\tan (3 z)}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.10

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c)

Question 11.
tan3 x
Solution:
y = tan3x = (tan x)3
\frac{d y}{d x} = 3(tan x)2. \frac{d}{d x}(tan x)
= 3tan2 x . sec2 x

Question 12.
sin4 x
Solution:
y = sin4x
\frac{d y}{d x} = \frac{d}{d x}(sin4 x)
= 4 (sin x)3 . \frac{d}{d x}(sin x)
= 4 sin3 x . cos x

Question 13.
sin2 x cos2 x
Solution:
y = sin2 x cos2 x = \frac{1}{4}sin2 2x
\frac{d y}{d x} = \frac{1}{4} \frac{d}{d x}(sin 2x)2
= \frac{1}{4}. 2sin 2x . \frac{d}{d x}(sin 2x)
= \frac{1}{2} sin 2x . cos 2x . \frac{d}{d x}(2x)
= \frac{1}{2} sin 2x cos 2x . 2 = sin 2x . cos 2x

Question 14.
sin 5x cos 7x
Solution:
y = sin 5x cos 7x
\frac{d y}{d x} = \frac{d}{d x}(sin 5x) . cos 7x + \frac{d}{d x}sin 5x . (cos 7x)
= cos 5x . \frac{d}{d x}(5x) . cos 7x + sin 5x . (-sin 7x) . \frac{d}{d x}(7x)
= 5 cos 5x . cos 7x – 7 sin 5x . sin 7x

Question 15.
tan x cot 2x
Solution:
y = tan x. cot 2x
\frac{d y}{d x} = \frac{d}{d x}(tan x) . cot 2x + tan x . \frac{d}{d x}(cot 2x)
= sec2 x / cot 2x + tan x . (-cosec2 x) \frac{d}{d x}(2x)
= sec2 x . cot 2x – 2 tan x . cosec2 x

Question 16.
\sqrt{\sin \sqrt{x}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.16

Question 17.
\sqrt{\sec (2 x+1)}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.17

Question 18.
cosec (ax + b)2
Solution:
y = cosec (ax + b)2
\frac{d y}{d x} = – cosec (ax + b)2 cot (ax + b)2 . \frac{d}{d x}(ax + b)2
[ ∵ \frac{d}{d x}(cosec u) = -cosec u . cot u . \frac{d u}{d x}
= – cosec (ax + b)2 . cot (ax + b)2 . 2(ax + b) . \frac{d}{d x}(ax + b)
[ ∵ \frac{d}{d x}(u2) = 2u \frac{d u}{d x}
= – cosec (ax + b)2 . cot (ax + b)2 . 2(ax + b) . a
= – 2a (ax + b) cosec (ax + b)2 cot (ax + b)2

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c)

Question 19.
aIn x
Solution:
y = aIn x . In a . \frac{d}{d x}(In x)
[ ∵ \frac{d}{d x}(au) = au . In a . \frac{d u}{d x}
= aIn x . In a . \frac{1}{x} = \frac{a^{\ln x} \ln a}{x}

Question 20.
a^{x^2} b^{x^3}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.20

Question 21.
In tan x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.21

Question 22.
5^{\sin x^2}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.22

Question 23.
In tan\left(\frac{\pi}{4}+\frac{x}{2}\right)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.23

Question 24.
\sqrt{\left(a^{\sqrt{x}}\right)}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.24

Question 25.
In (enx + e-nx)
Solution:
y = In (enx + e-nx)
\frac{d y}{d x} = \frac{1}{e^{n x}+e^{-n x}} . \frac{d}{d x} (enx + e-nx)
= \frac{n\left(e^{n x}-e^{-n x}\right)}{e^{n x}+e^{-n x}}

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c)

Question 26.
e^{\sqrt{a x}}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.26

Question 27.
\sqrt{\log x}
Solution:
y = \sqrt{\log x}
\frac{d y}{d x} = \frac{1}{2 \sqrt{\log x}} . \frac{d}{d x}(log x)
= \frac{1}{2 \sqrt{\log x}} . \frac{1}{x}

Question 28.
esin x – acos x
Solution:
y = esin x – acos x
\frac{d y}{d x} = \frac{d}{d x}(esin x) – \frac{d}{d x}(acos x)
= esin x . \frac{d}{d x}(sin x) – acos x . In a . \frac{d}{d x}(cos x)
= esin x . cos x + acos x . In a . sin x

Question 29.
\frac{e^{3 x^2}}{\ln \sin x}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.29

Question 30.
Prove that
\frac{d}{d x}\left[\frac{1-\tan x}{1+\tan x}\right]^{\frac{1}{2}} = 1 / \sqrt{\cos 2 x} (cos x + sin x)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(c) Q.30

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Exercise 7(j)

Test differentiability and continuity of the following functions.
Question 1.
\left|1-\frac{1}{x}\right| at x = 1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.1

Question 2.
x2 |x| at x = 0.
Solution:
Let f(x) = x2 |x|
Then f(0) = 0
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.2
As L.H.D.=R.H.D., f(x) is differentiable at x = 0. We know that every differentiable function is continuous. So f(x) is also continuous at x = 0.

Question 3.
f(x) = tan x at x = \frac{\pi}{2}
Solution:
f(x) = tan x
f(\frac{\pi}{2}) = tan \frac{\pi}{2} which does not exist.
So f(x) is neither continuous not differentiable.

Question 4.
f(x) = cot x at x = \frac{\pi}{2}.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.4

Question 5.
f(x) = |sin x| at x = π.
Solution:
Differentiability:
f(x) = |sin x|, x = π
f(π) |sin π| = 0
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.5

Question 6.
f(x) = latex]\frac{x}{1+|x|}[/latex] at x = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.6
As L.H.D. = R.H.D., f(x) is differentiable at x = 0.
Every differentiable function is continuous.
So f(x) is also continuous at x = 0.

Question 7.
f(x) = \begin{cases}x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x=0\end{cases} at x = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.7

Question 8.
f(x) = \begin{cases}\frac{1-e^{-x}}{x}, & x \neq 0 \\ 1 & x=0\end{cases} at x = 0
Solution:
f(0) = 1
CHSE Odisha Class 12 Math Solutions Chapter 7 Continuity and Differentiability Ex 7(j) Q.8
As L.H.D. = R.H.D., f(x) is differentiable at the origin. Again every differentiable function is continuous. So f(x) is continuous at the origin.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Odisha State Board CHSE Odisha Class 12 Invitation to English 2 Solutions Non-Detailed Chapter 1 The Doctor’s Word Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class English Solutions Non-Detailed Chapter 1 The Doctor’s Word

CHSE Odisha Class 12 English The Doctor’s Word Text Book Questions and Answers

Unit I
Gist :
Dr. Raman was a veteran doctor. He was the epitome of truth. Therefore, the patients gave much importance to his opinion. Dr. Raman was averse to giving mere opinion. Instead, he gave his opinion after testing. The patient’s life depended on what he said. He was cool in the treatment of his patients. He did not like to assure them saying soothing words. A glimpse of the least sign of hope made Dr. Raman prepare to work. Once he treated his patient, he never looked back. The patients visited Dr. Raman when they were hopeless. They did not come earlier for the sake of paying him visiting fee of twenty-five rupees.

ସାରମର୍ମ :
ପ୍ରସିଦ୍ଧ ଡାକ୍ତର ରମଣ ସତ୍ୟର ଉପାସକ ଥିଲେ । ସେଥ‌ିପାଇଁ ରୋଗୀମାନେ ତାଙ୍କ କଥା ଉପରେ ଦେବା ସହ ବିଶ୍ଵାସ ମଧ୍ୟ କରୁଥିଲେ । ତାଙ୍କର କଥା ଉପରେ ରୋଗୀର ଜୀବନ ନିର୍ଭର କରୁଥିଲା । ସେ ବହୁତ ଥଣ୍ଡା ମିଜାଜରେ ରୋଗୀମାନଙ୍କ ଚିକିତ୍ସା କରୁଥିଲେ । ସେ ସାର୍ଚ୍ଚନାମୂଳକ କଥା କହି ରୋଗୀମାନଙ୍କୁ ଭରସା ଦେବାକୁ ପସନ୍ଦ କରୁନଥିଲେ । ଶେଷ ଆଶା ଥିଲା ପର୍ଯ୍ୟନ୍ତ ସେ ମଧ୍ଯ ରୋଗୀମାନଙ୍କର ସେବା ଓ ଚିକିତ୍ସା କରୁଥିଲେ । ଚିକିତ୍ସା ପ୍ରକ୍ରିୟା ଆରମ୍ଭ କରିବା ପରେ ସେ ରୋଗୀକୁ ନବଞ୍ଚାଇ ଛାଡୁନଥିଲେ । ଯେତେବେଳେ ରୋଗୀମାନେ ଆଶାହୀନ ହୋଇ ପଡ଼ୁଥିଲେ, ସେମାନେ ଡାକ୍ତର ରମଣଙ୍କ ନିକଟକୁ ଆସୁଥିଲେ । ସେମାନେ ଆଗରୁ ଆସୁ ନ ଥିଲେ ଯେହେତୁ ସାକ୍ଷାତ୍ କରିବାର ଫିସ୍ ୨୫ ଟଙ୍କା ଥିଲା ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Glossary :
on his last legs : weak and likely to collapse(ଶେଷ ଅବସ୍ଥା)
obvious: clear(ପରିଷ୍କାର)
shirk: avoid (ଏଡ଼େଇବା)
ominous: inauspicious(ଅଶୁଭ)
association: companion( ସାହଚର୍ଯ୍ୟ)
quick: fast(ନ ନେଇ ପାରିବା ଅବସ୍ଥା)
wavering: indecision, to be unable to take decision
whitewashing: hiding somebody’s errors or unpleasant facts (ସତ୍ୟ ଲୁଚାଇବା) ସୃଷ୍ଟି କରିଥିଲା
bred: ପୋଷ୍ୟ
curt: short (ସଂକ୍ଷିପ୍ତ)
dope: hope (ଆଶା)
glimpsed: saw faintly
faintest: କ୍ଷୀଣତମ
sign: ଚିହ୍ନ
rolled up his sleeve: prepared to work (କାର୍ଯ୍ୟ କରିବାକୁ ପ୍ରସ୍ତୁତ ହେଉଥିଲେ )
stepped: arrived (ପହଞ୍ଚୁଥିଲେ)
truthfulness: ସତ୍ୟତା
reason: କାରଣ
opinion: ମତାମତ
valued: much attention is paid (ଗୁରୁତ୍ଵ ଦିଆଯାଉଥୁଲା )
mere : କେବଳ
pronounce a verdict: declaring a decision (ରାୟ ଘୋଷଣା କରିବା)
hung : ଝୁଣ୍ଟିବା
unduly: ଅଯଥା
agreeable words: pleasant words(ସୁଖକର କଥା)
arena: ମଞ୍ଚ
withdrew: retreated ( ପଛଘୁଞ୍ଚା ଦେଉଥିଲେ )
wrested: took violently from a person’s grasp (ମଲ୍ଲୟୁଦ୍ଧ)
the prize: (here) life of the patient (ପୁରସ୍କାର)
Yama: Hindu God of departed spirits (ୟାମା)

Think it out:

Question 1.
Why did the patients visit Dr. Raman only when they were hopeless?
Answer:
The patients visited Dr. Raman only when they were in a critical condition. The doctorasked them why they had not come much before. The reasons were not far to seek. The patients were not willing to pay him visiting fee of twenty-five rupees so early. Besides, they did not feel the necessity of going to the doctor unless they found themselves in a hopeless stage. For them, there was something dangerous to be in the presence of Dr. Raman, because he promptly diagonised the patient.

Question 2.
What impression of Dr. Raman do you get from the passage?
Answer:
Dr. Raman is loyal to his profession in word and spirit. He knows well that a patient’s life depends on his words. He diagonises the patients promptly. He was decisive to the core. He doesn’t like to hide anything concerning the patient. Truthfulness is Dr. Raman’s forte. His short, sharp response to the patient’s condition is a case in point. He sticks to human values. He knows that soothing words cannot save the lives of patients. Dr. Raman doesn’t like hide anything from the patients. He waits till his patients recover.

Unit II

Gist :
Dr. Raman felt restless when he found his bosom friend Gopal in a critical condition. He walked down the memory lane. Forty years had elapsed. Their friendship had been kept intact. Family and profession hindered their meetings in a great measure. At times they dined together, went to the cinema and shared each other’s life and activities. Changing times, circumstances and activities had no effect on their friendship. It was excellent one. They had no contact for the last three months now. The sight of Gopal’s son sitting on a bench in the consulting room made him remember his friend. Dr. Raman talked to him and came to know about his friend’s illness.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

ସାରମର୍ମ :
ଯେତେବେଳେ ଡାକ୍ତର ରମଣ ଜାଣିଲେ ଯେ ତାଙ୍କର ଅନ୍ତରଙ୍ଗ ବନ୍ଧୁ ଗୋପାଳ ଗୁରୁତର ଭାବେ ଅସୁସ୍ଥ ହୋଇଛି, ସେତେବେଳେ ସେ ବିଚଳିତ ହୋଇପଡ଼ିଲେ । ସେ ଦୀର୍ଘ ଚାଳିଶ ବର୍ଷର ବନ୍ଧୁତ୍ଵର ଅନ୍ତରଙ୍ଗ ମୁହୂର୍ତ୍ତଗୁଡ଼ିକୁ ମନେ ପକାଇଲେ । ପରିବାର ଓ ବୃତ୍ତି ତାଙ୍କ ମିଳନରେ ବାଧକ ସାଜିଥିଲା । ବେଳେବେଳେ ସେମାନେ ଏକାଠି ଖାଉଥିଲେ, ଏକାଠି ସିନେମା ଯାଉଥୁଲେ ଏବଂ ପରସ୍ପରର ଦୁଃଖ ଓ ସୁଖରେ ଅଂଶୀଦାର ହେଉଥିଲେ । ପରିସ୍ଥିତିର ପରିବର୍ତ୍ତନ ସେମାନଙ୍କ ବନ୍ଧୁତ୍ଵ ଉପରେ କୌଣସି ପ୍ରଭାବ ପକାଇ ପାରି ନଥିଲା । ତିନିମାସ ହେଲା ସେମାନଙ୍କ ମଧ୍ୟରେ କୌଣସି ଯୋଗାଯୋଗ ହୋଇପାରି ନ ଥିଲା । ଗୋପାଳର ପୁଅଠାରୁ ସେ ଗୋପାଳର ଅସୁସ୍ଥତା ବିଷୟରେ ଜାଣିବାକୁ ପାଇଲେ ।

Glossary :
soothing : comforting (ଆଶ୍ୱାସନାଭରା )
lies: falsehood (ମିଛ)
mopped: cleaned ( ସଫା କଲେ/ପୋଛିଲେ )
brow: forehead (କପାଳ)
kerchief: କିର୍ଚିଫ୍
beside: ପାଖରେ
dearest: most imtimate (ଅନ୍ତରଙ୍ଗ)
kindergarten days: ସ୍କୁଲ ଦିନରୁ
of course: ଅବଶ୍ୟ
wrapped: ଗୁଡ଼ାଇ
dine: ଭୋଜନ
classic friendship: excellent friendship (ଉତ୍ତମ ବନ୍ଧୁତା)
untouched: ଅସ୍ପୃଶ୍ୟ
circumstances: ପରିସ୍ଥିତି
crowded: ଭିଡ଼
got up: ଉଠିପଡିଲି
youth: ଯୁବକ
shy: ଲାଜୁଆ

Think it out

Question 1.
How does the writer describe the friendship between Dr. Raman and Gopal?
Answer:
The writer says that the friendship between Dr. Raman and Gopal spans forty years. It goes back to their school days. Family and profession have made their meetings infrequent. At times on a Sunday, Gopal waits patiently for Dr. Raman in the consulting room till the latter is free. They spend the day in dinning, going to the cinema and sharing each other’s life and activities. Their friendship that still remains untouched by changing times, circumstances and activities is an excellent one.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 2.
How did Dr. Raman come to know about Gopal’s illness?
Answer:
Hectic schedule had led Dr. Raman to forget his friend’s failure to call him in for three months. This fact occurred to him when he noticed his friend’s son sitting on a bench in the consulting room. It was one morning packed with patients. At the time moving to the operation room, Dr. Raman enquired of him about the purpose of visit. At that time he came to know about Gopal’s illness.

Unit III

Gist :
Dr. Raman was awfully busy, because it was an operation day. Then the doctor immediately went to his friend’s home and saw Gopal lying in bed. The doctor asked his wife many questions concerning his illness. Dr. Raman wished Gopal’s wife had summoned him earlier. A doctor nearby was treating him. Gopal’s family did not contact Dr. Raman, because they did not want to disturb him unnecessarily. They felt miserable. Dr. Raman started treating his friend without wasting time. He injected Gopal in the presence of the latter’s family members. Dr. Raman sat back in his waiting for the result. Loss of midday meal made him hungry. He went out for his lunch and came back soon. Dr. Raman apprised his friend’s wife of the necessity of operation and sought their son’s assistance. Gopal’s wife felt dizzy.

ସାରମର୍ମ :
ଡା. ରମଣ ବହୁତ ବ୍ୟସ୍ତ ଥିଲେ କାରଣ ଏହା ଥିଲା ତାଙ୍କର ଏକ ଅସ୍ତ୍ରୋପଚାର କରିବାର ଦିନ । ପରେ ସେ ସାଙ୍ଗେ ସାଙ୍ଗେ ତାଙ୍କ ବନ୍ଧୁଙ୍କ ଘରକୁ ଗଲେ ଏବଂ ଦେଖିଲେ ଯେ ଗୋପାଳ ଶଯ୍ୟାଶାୟୀ । ଡାକ୍ତର ଗୋପାଳଙ୍କ ସ୍ବାସ୍ଥ୍ୟ ସମ୍ପର୍କରେ ତାଙ୍କ ସ୍ତ୍ରୀଙ୍କୁ ଅନେକ ପ୍ରଶ୍ନ ପଚାରିଲେ । ଗୋପାଳଙ୍କର ପରିବାର ତାଙ୍କୁ କାହିଁକି ଆଗରୁ ଡାକିଲେ ନାହିଁ ବୋଲି ସେ ପଚାରିଲେ । ତାଙ୍କୁ ବିନା କାରଣରେ ଅସୁବିଧାରେ ପକାଇବାକୁ ଚାହୁଁ ନ ଥିଲେ ବୋଲି ସେମାନେ କହିଲେ । ସମୟ ନଷ୍ଟ ନ କରି ଡା. ରମଣ ଚିକିତ୍ସା ଆରମ୍ଭ କରିଦେଲେ । ଫଳାଫଳକୁ ଅପେକ୍ଷା କରି ସେ ବସି ରହିଲେ । ଦିନ ସମୟରେ ଖାଇ ନ ଥ‌ିବାରୁ ସେ ଭୋକିଲା ଅନୁଭବ କଲେ ଏବଂ ସେ ମଧ୍ୟାହ୍ନ ଭୋଜନ ଖାଇବାପାଇଁ ଗଲେ ଏବଂ ଖୁବ୍ ଶୀଘ୍ର ଫେରି ଆସିଲେ । ସେ ଗୋପାଳଙ୍କର ସ୍ତ୍ରୀଙ୍କୁ ଅସ୍ତ୍ରୋପଚାର କରିବାର ଆବଶ୍ୟକତା ଅଛି ବୋଲି କହିଲେ । ସେ ତାଙ୍କ ପୁଅଙ୍କ ସାହାଯ୍ୟ ଚାହିଁଲେ । ଗୋପାଳଙ୍କର ସ୍ତ୍ରୀ ଖୁବ୍ ଅସ୍ବସ୍ତି ଅନୁଭବ କଲେ ।

Glossary :
rushed off: ଶୀଘ୍ର ଗଲେ/ ଧାଇଁଗଲେ
lay: ଶଯ୍ୟା
as if in sleep: ଯେପରି ଶୋଇଛି
trouble: ଅସୁବିଧା
apologetic: କ୍ଷମାପ୍ରାର୍ଥନା କରିବା
miserable: sad (ଦୁଃଖ୍)
took off: removed (କାଢ଼ିନେଲେ)
sizzled: boiled (ଫୁଟାଇଲେ)
sterilizer: ନିରୂପଣ
shot in: ଗୁଳି ଚଳାଇଲା
on any account: ଯେକୌଣସି ହିସାବରେ
giddy: dizzy
sank down: ବୁଡ଼ିଗଲା
drug: medicine (ଔଷଧ )
essayed: tried (ଚେଷ୍ଟା କଲେ )
Snapped: କଥାରେ ବାଧା ଦେଲେ
gleamed: ଚିକ୍‌ଚିକ୍ କଲା
perspiration: sweat (ଝୋଳ)
eyelids: ଆଖ୍ୟାତାଗୁଡ଼ିକ
timidly: ଲାଜରେ
fatigue: tiredness (କ୍ଳାନ୍ତି)
famished: hungry (କ୍ଷୁଧାଇଁ)
midday meal: ମଧ୍ୟାହ୍ନ ଭୋଜନ
bear: tolerate (ଧାରଣ କରିବା)
strain: ଟାଣିବା

Think it out

Question 1.
Why didn’t Gopal’s wife call for Dr. Raman earlier?
Answer:
Dr. Raman went to his friend’s house, because the latter was critically ill. He found Gopal lying in bed. Skillful doctor as he was, Dr. Raman calmly enquired of his wife about his friend’s treatment. He learnt that a doctor nearby had been treating her husband. He asked her why she didn’t call him earlier. She failed to do so, lest he should be busy, and so they did not want to bother him unnecessarily. They were sorry about not summoning him earlier. They felt extremely unhappy.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 2.
What steps did the doctor take to save his friend from death?
Answer:
Dr. Raman was smart in the diagnosis of his friend and treated him instantly. He opened his bag and took out an injection tube; the needle sizzled over the stove. He injected the drug into the patient. After watching him for some time Dr. Raman decided to perform an operation and performed the same. These were the steps the doctor took to save his friend from death.

Unit IV

Gist :
It was about eight in the evening. The doctor’s assistant was beside himself with joy to see the patient’s positive response to the treatment. The doctor was worried about his pulse. He advised his assistant to have a clean watch over the patient. The doctor found that the patient’s condition had improved a little. He was in a condition to eat a little food. The family members heaved a sigh of relief. They were full of joy. They expressed their deep gratitude to Dr. Raman who looked fixedly at the patient. Instead of responding to the concern of the patient’s wife, the doctor instructed her to give her husband glucose and brandy every forty minutes. The wife wanted to know if he was out of danger. The doctor’s silence steeled her to elicit the truth from him. Suspense mounted. The patient’s wife could not bear it. She requested Dr. Raman to apprise her of what was happening, but he did not tell her about the seriousness of the patient’s condition. A bitter weeping broke the silence of the house. The patient looked in confusion. Dr. Raman was as calm as ever.

ସାରମର୍ମ :
ଏହା ଥିଲା ସନ୍ଧ୍ୟା ଆଠଟା ସମୟ। ଡାକ୍ତର ଓ ତାଙ୍କ ସହକାରୀ ରୋଗୀର ଅବସ୍ଥାରେ ଉନ୍ନତି ଦେଖ୍ ଖୁସି ହେଲେ । ଡାକ୍ତର ରମଣ ନାଡ଼ିର ଗତି ଦେଖୁ ବ୍ୟସ୍ତ ହୋଇଗଲେ । ରୋଗୀ ଉପରେ ତୀକ୍ଷ୍ଣ ନଜର ରଖିବାପାଇଁ ଡା. ରମଣ ତାଙ୍କ ସହକାରୀଙ୍କୁ ଉପଦେଶ ଦେଲେ । ତାଙ୍କର ଅବସ୍ଥାରେ କିଛି ଉନ୍ନତି ଆସିଲା ଏବଂ ସେ କିଛି ଖାଦ୍ୟ ଖାଇବାର ଅବସ୍ଥାକୁ ଆସିଲେ । ଘରର ସଦସ୍ୟମାନେ ଟିକିଏ ଆଶ୍ୱସ୍ତି ଅନୁଭବ କଲେ । ସେମାନେ ଖୁସି ହୋଇଗଲେ । ଡା. ରମଣଙ୍କୁ କୃତଜ୍ଞତା ଜ୍ଞାପନ କଲେ । ଡା. ରମଣ ଗୋପାଳଙ୍କର ସ୍ତ୍ରୀଙ୍କୁ ଉପଦେଶ ଦେଲେ ପ୍ରତି ଚାଳିଶ ମିନିଟ୍‌ରେ ଥରେ ଲେଖାଁଏ ଗ୍ଲୁକୋଜ୍ ଓ ବ୍ରାଣ୍ଡି ଦେବାପାଇଁ । ତାଙ୍କ ସ୍ତ୍ରୀ ଜାଣିବାକୁ ଚାହିଁଲେ ସେ ବର୍ତ୍ତମାନ ବିପଦମୁକ୍ତ ନା ନାହିଁ । ଡାକ୍ତର ନୀରବତା ଗୋପାଳଙ୍କ ସ୍ତ୍ରୀ ମନରେ ସନ୍ଦେହ ସୃଷ୍ଟି କଲା । ସେ ରୋଗୀର ଅବସ୍ଥା ବିଷୟରେ ଜାଣିବାକୁ ଚାହିଁଲେ । ଏକ ଦୁଃଖଦ କାନ୍ଦଣା ଘରର ନିର୍ଜନତାକୁ ଭାଙ୍ଗିଦେଲା । ରୋଗୀ ଦ୍ବନ୍ଦ୍ବରେ ଚାହିଁଲେ । ଡାକ୍ତର ଆଗଭଳି ଧୀରସ୍ଥିର ହୋଇ ରହିଥିଲେ ।

Glossary :
stirred: moved (ହଲଚଲ ହେଲା)
slightly: a little (ଟିକିଏ|ସାମାନ୍ୟ) ଅତ୍ୟଧ୍ଵ ଖୁସି ହେଲେ
overjoyed: ଅତ୍ୟଧିକ ଆନନ୍ଦିତ
exclaimed: ଚିତ୍କାର କଲା
enthusiastically: ଉତ୍ସାହର ସହିତ
pull through: recover from illness( ଆରୋଗ୍ୟ ହେବା)
whispered: said in a low voice (ସ୍ବରରେ କହିଲେ)
pulse: ନାଡ
trust: ବିଶ୍ବାସ କରିବା
flash-up: a sudden ray of hope (ଆଶାର ସଙ୍କେତ)
ruminated: ଚିନ୍ତା କଲେ
keep up: maintain (ରକ୍ଷା କଲେ)
relief: ରିଲିଫ୍
swarmed: ବହୁ ସଂଖ୍ୟାରେ
poured out: ଫୋପାଡ଼ିଦେଲା
gratitude: କୃତଜ୍ଞତା
felt restless: ଅଶାନ୍ତ ଅନୁଭବ କଲେ
evasive: avoiding a straight, honest answer (ଅପହଞ୍ଚ)
unbearable: ଅସହ୍ୟ
beckoned: called somebody by a movement of the hand (ଇଶାରା କରି ଡାକିଲେ )
excited: ଉତ୍ଫୁଲ୍ଲିତ
terror: ଆତଙ୍କରାଜ
clasped hands: ହାତ ଯୋଡ଼ିଲେ
implored: requested (ପ୍ରାର୍ଥନା କଲେ)
terrible: ଭୟଙ୍କର
wailing: bitter weeping (କାନ୍ଦଣା)
still: ନୀରବ
bewilderment : confusion (ଭ୍ରମଗ୍ରସ୍ତ ବ୍ୟକ୍ତି)
securely: ଭଲ ଭାବରେ
shut off: ବନ୍ଦ କରିଦେଲେ

Think it out

Question 1.
What was Dr. Raman’s reaction when his assistant said “Sir, he will pull through?”
Answer:
When his assistant said “Sir, he will pull through”, the doctor reacted in an unenthusiastic fashion. The doctor was apprehensive of the patient’s recovery from terrible heart attack. Despite an improvement in pulse rate, the patient was not out of danger. In the doctor’s opinion, it was a sign of false recovery. He pondered for a while on his friend’s condition. Uncertainty still lingered in Dr. Raman’s mind.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 2.
What was Dr. Raman’s response when Gopal’s wife asked about his condition?
Answer:
Gopal’s wife asked Dr. Raman if her husband was out of danger. The doctor’s response to it was usually calm. He advised her to give Gopal glucose and brandy every forty minutes. Gopal’s wife felt restless. She could not bear the suspense. She again enquired of the doctor about her husband’s present condition. He instructed her not to get excited. The doctor was not ready to respond to her query. He was averse to tell the bitter truth.

Unit V

Gist :
Gopal was in a dying state. His mental condition was getting from bad to worse. He kept asking Dr. Raman if he was going to survive. The doctor knew how serious his friend’s condition was. He was feared for his frankness. Dr. Raman advised not to tire himself, but the former’s advice fell flat. Gopal was anxious about signing the will. Dr. Raman wanted him to go away without answering the question. The patient held his waist and expressed his unflinching trust in his word. Gopal requested a truthful prognosis in order to settle his will and avoid “endless misery for his wife and children” than an unsettled will would entail, realistic eventuality with which Dr. Raman concerned. Yet if the doctor revealed his pessimistic opinion, that Gopal would not survive that night, then it would virtually signify a death sentence and put an end to the slimmest chance of the patient’s survival. Dr. Raman did a piece of acting’ and assured his friend and patient that he would live. Gopal accepted his words with gratitude.

ସାରମର୍ମ :
ଗୋପାଳ ମୂମୂର୍ଷୁ ଅବସ୍ଥାରେ ଥିଲା । ତାଙ୍କର ମାନସିକ ଅବସ୍ଥା ଖରାପରୁ ଅତି ଖରାପ ହେଉଥିଲା । ସେ ବଞ୍ଚେ କି ନାହିଁ ବୋଲି ବାରମ୍ବାର ଡାକ୍ତର ରମଣଙ୍କୁ ପଚାରୁଥିଲେ । ଡାକ୍ତର ଜାଣିଥିଲେ ତାଙ୍କର ବନ୍ଧୁଙ୍କର ଅବସ୍ଥା ସଙ୍କଟାପନ୍ନ । ସେ ତାଙ୍କର ଚିରାଚରିତ ଢଙ୍ଗରେ ସତ୍ୟର ପ୍ରକଟ କରିବା ପାଇଁ ଡରିଯାଇଥିଲେ । ଡାକ୍ତର ରମଣ ତାଙ୍କୁ କ୍ଳାନ୍ତ ନ ହେବାପାଇଁ ଉପଦେଶ ଦେଲେ । ଗୋପାଳ ତାଙ୍କ ସ୍ତ୍ରୀ ପିଲାଙ୍କର ଅସରନ୍ତି ଦୁଃଖର ଅନ୍ତ ଘଟାଇବା ପାଇଁ ମୃତ୍ୟୁ ପୂର୍ବରୁ ଇଚ୍ଛାପତ୍ର ପ୍ରସ୍ତୁତ କରିବାକୁ ଚାହୁଁଥିଲେ । ତେଣୁ ସେ ଡାକ୍ତରଙ୍କଠାରୁ ସେ ବଞ୍ଚେ କି ନାହିଁ ଜାଣିବାକୁ ଚାହୁଁଥିଲେ । ଯଦି ଡାକ୍ତର ତାଙ୍କର ବିଷାଦପୂର୍ଣ୍ଣ କଥାକୁ ଶୁଣାଇଦେବେ, ତେବେ ଗୋପାଳ ନିଶ୍ଚିତରୂପେ ସେହି ରାତିରେ ଶେଷ ନିଃଶ୍ବାସ ତ୍ୟାଗ କରିବେ । ଡାକ୍ତରଙ୍କର ସତ୍ୟ କଥା ହିଁ ଗୋପାଳର ମୃତ୍ୟୁର କାରଣ ହୋଇଯିବ ଏବଂ ରୋଗୀର ବଞ୍ଚିବାର କ୍ଷୀଣ ଆଶା ମଉଳିଯିବ । ତେଣୁ ଡାକ୍ତର ଅଭିନୟ କଲେ ଏବଂ କହିଲେ ଗୋପାଳ ନିଶ୍ଚୟ ବଞ୍ଚିବେ । ଗୋପାଳ ଏହି କଥାକୁ କୃତଜ୍ଞତାର ସହ ଗ୍ରହଣ କଲେ ।

Glossary :
resumed his seat: ପୁଣିଥରେ ତାଙ୍କ ଆସନ ଆରମ୍ଭ କଲେ
exert: tire (କ୍ଳାନ୍ତ ହେବା)
whitewash: ମିଛ ସାନା ଦେବା
attached: (here) gave (ଦେଉଥିଲେ )
value: ମୂଲ୍ୟ
stole a look: ଲୁକ୍ ଚୋରି କଲା
motioned: ଗତିଶୀଳ
last: survive (ବଞ୍ଚ୍)
witness:ସାକ୍ଷୀ
idiotic: foolish (ନିର୍ବୋଧ )
drop: ବନ୍ଦ କରିଦେବା
clutched: ଜାବୁଡ଼ି ଧରିଲେ
wrist: ହାତଗୋଡ
unsettle: ଅସନ୍ତୁଷ୍ଟ
endless: ଅସରନ୍ତି
reflected: thought deeply (ଗଭୀରଭାବେ ଚିନ୍ତା କଲେ)
midnight :ମଧ୍ୟରାତ୍ରି
will: ଇଚ୍ଛାପତ୍ର
felt the pulse: ନାଡ଼ି ଚିପିଲେ : ଉତ୍ତେଜିତ ହେଲେ
agitated : ଉତ୍ତେଜିତ
deprecating: expressing disapproval (ବାରଣସୂଚକ)
mess: ଅପ୍ରୀତିକର ପରିସ୍ଥିତି|ବିଶୃଙ୍ଖଳା
virtually: ଆପାତତଃ
death sentence: ମୃତ୍ୟୁଦଣ୍ଡ
survival: ବଞ୍ଚିବା
got down: ଓହ୍ଲାଇଲେ
appealingly: ନିନ୍ଦା କଲେ
damned: ଦୋଷୀ
simulate: ଅନୁକରଣ କରନ୍ତୁ
conceal: hide (ଲୁଚେଇବା)
judgement: ବିଚାର/ରାୟ
stooped over: ଆଉଜି ପଡ଼ିଲା
deliberate: intentional (ଇଚ୍ଛାକୃତ)
emphasis: stress (ଗୁରୁତ୍ଵ)
absolutely: ସମ୍ପୂର୍ଣ୍ଣ ଭାବରେ
glow: ଆଲୋକ
suffused: spread slowly slowly over(ଖେଳିଗଲା)
soundly: ଆରାମରେ

Think it out

Question 1.
Why did Gopal ask Dr. Raman “Am I going?” What was he anxious about?
Answer:
Dr. Raman found his friend and patient in a critical condition; the latter’s wife was crying. The doctor felt his pulse and remained silent. The patient’s anxiety soared. He movingly appealed to the doctor not to avoid anything from him. Dr. Raman still remained unmoved. Gopal was determined to know how long he was going to survive. He was anxious about signing the will which was ready.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 2.
Was Dr. Raman upset at this question? Give your reasons.
Answer:
Gopal’s question, “Am I going” upset Dr. Raman, but he never gave vent to his concern for his friend’s condition. This was the most precarious situation he had ever faced in his life. By nature, he was a realist to the core. He knew that he was a doctor, on whose word the life of a patient depended. He did a piece of acting before his friend.

Question 3.
Why did Dr. Raman decide to tell a lie?
Answer:
Gopal insisted Dr. Raman on telling the truth about his condition. He was keen in signing the will that had already been prepared. Gopal was very sick (dying in Dr. Raman’s judgement) and requested a truthful prognosis to settle his will and avoid the never-ending misery for his wife and children than an unsettled will would entail. If the doctor would reveal his critical opinion, Gopal would not survive that night, then it would virtually signify a death sentence and put an end to the slimmest chance of the patient’s survival. Therefore, Dr. Raman decided to tell a lie.

Question 4.
How did he answer Gopal’js question?
Answer:
Dr. Raman could not remain silent in the face of Gopal’s question how long he was going to survive. His patient and friend was bent on signing the will before his death. Dr. Raman did a piece of acting and assured him that he was improving every second. He advised Gopal to sleep in peace and avoid exertion. In other words, the doctor assured him of his survival.

Question 5.
How did Gopal accept Dr. Raman’s words?
Answer:
Dr. Raman assured his patient of recovery. He said again that his friend’s heart was completely fine. Gopal accepted Dr. Raman’s words with great trust and hope. His statement “If it comes from your lips it must be true” is a case in point. There was a ring of relief about Gopal’s tone. He was a picture of gratitude. He slept in peace.

Unit VI

Gist:
A patient’s life hangs on a doctor’s word. It was true in case of Dr. Raman. The way he handled the serious condition of his friend was a case in point. He was smart. He was calm. He instructed his assistant to attend the patient with a tube and give it, in case of any eventuality. Nothing happened. The patient recovered satisfactorily. Dr. Raman had a last check. Then he informed the sick man’s wife about his brilliant heart. His friend would live till ninety. The doctor was sure of it. His friend had passed the most critical phase in heart-attack. His survival would be a source of constant puzzle to Dr. Raman.

Glossary :
for a moment : ମୁହୂର୍ତ୍ତକ ପାଇଁ
collapse:ଭୁଶୁଡ଼ିବା
tube: ନଳି
struggle: ସଂଘର୍ଷ
made a dash: ଏକ ଡ୍ୟାସ୍ ତିଆରି କଲା
awake: ଜାଗ୍ରତ
bet on it: ଏହା ଉପରେ ବାଜି ଲଗାନ୍ତୁ
turned the comer: ଆସିଲା
puzzle: ପଜଲ୍

Think it out
Question 1.
Did Dr. Raman believe that his patient would recover that night? Why do you think so?
Answer:
Dr. Raman did not believe that his patient would recover that night. He expressed his pessimistic opinion to his assistant. His statement “You might expect the collapse any second now” is a case in point. Dr. Raman instructed his assistant to hurry to the patient with a tube and give it in case of any eventuality.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 2.
“Don’t look so unhappy, lady” – why does Dr. Raman say so?
Answer:
Raman says so to his friend Gopal’s wife when Dr. Raman sees her husband in a state of miraculous recovery from a serious heart attack. The patient was conscious and looked extremely fine. The assistant informed the doctor about his satisfactory pulse. Putting the tube at the patient’s heart, he lends his ears to it for a while and pronounces the final judgement to his wife with assurance, “Don’t look so unhappy lady.” Her husband will survive till ninety. He has stood the critical state of attack.

Question 3.
Does human life hang on a doctor’s word? Give a reasoned answer.
Answer:
Yes, human life hangs on a doctor’s word. The way Dr. Raman saved his friend, Gopal from the verge of death splendidly exemplifies this point.

CHSE Odisha Class 12 English The Doctor’s Word Important Questions and Answers

Multiple-Choice Questions (MCQs) with Answers

Question 1.
People came to him when the patient was on his last legs. The underlined expression means ___________.
(A) lame
(B) about to be lame
(C) amputated
(D) in a critical condition
Answer:
(D) in a critical condition

Question 2.
“……………..that the time had come to call in Raman”. The underlined expression means _______________.
(A) summon
(B) appeal
(C) visit
(D) all of the above
Answer:
(A) summon

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 3.
Long years of practice of this kind had bred in the doctor a certain curt truthfulness. The underlined expression means ______________.
(A) a sort of diplomacy
(B) blunt truthfulness
(C) boundless truthfulness
(D) completely tactical
Answer:
(B) blunt truthfulness

Question 4.
The patient’s life hung on his word. The underlined expression means ________________.
(A) completely depended
(B) demanded
(C) hanged
(D) none of these
Answer:
(A) completely depended

Question 5.
“………………when he glimpsed the faintest sign of hope, he rolled up his sleeve.” The underlined expression means _________.
(A) consulted
(B) slept
(C) prepared to do his duty
(D) none of these
Answer:
(C) prepared to do his duty

Question 6.
As a doctor, Raman was ______________.
(A) one of the equals
(B) a man with a difference
(C) somewhat fine
(D) held in high esteem
Answer:
(B) a man with a difference

Question 7.
Dr. Raman was _____________.
(A) firmly decisive
(B) moody
(C) bitter
(D) all of the above
Answer:
(A) firmly decisive

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 8.
Dr. Raman’s friendship with Gopal goes back to _____________.
(A) their school days
(B) their nursery school days
(C) more than forty years
(D) all of these
Answer:
(B) their nursery school days

Question 9.
Their friendship was ______________.
(A) excellent
(B) good
(C) very good
(D) strange
Answer:
(A) excellent

Question 10.
Which of the following statements is false?
(A) Dr. Raman and Gopal were close friends.
(B) Their friendship had stood the test of time.
(C) Dr. Raman and Gopal never took dinner together.
(D) Their discussion was wide-ranging
Answer:
(C) Dr. Raman and Gopal never took dinner together.

Question 11.
Dr. Raman was __________.
(A) very punctual
(B) versatile
(C) very busy
(D) quite uncommon
Answer:
(C) very busy

Question 12.
Gopal’s son was ______________.
(A) reticent
(B) bold
(C) nervous
(D) both (A) and (C)
Answer:
(D) both (A) and (C)

Question 13.
Gopal has been confined to bed since ____________.
(A) 46 days
(B) more than two months
(C) a month and a half
(D) long
Answer:
(C) a month and a half

Question 14.
The person to treat Gopal first was _____________.
(A) Dr. Raman
(B) a friend of Gopal’s wife
(C) Gopal’s brother
(D) an unknown doctor
Answer:
(D) an unknown doctor

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 15.
Dr. Raman started his friend’s treatment ______________.
(A) after a careful thought
(B) enthusiastically
(C) bravely
(D) promptly
Answer:
(D) promptly

Question 16.
The word ‘famished’ means ______________.
(A) tired
(B) enthused
(C) excited
(D) hungry
Answer:
(D) hungry

Question 17.
What made Gopal’s wife unbearable was _____________.
(A) Gopal’s critical illness
(B) Dr. Raman’s evasive reply to Gopal’s wife
(C) the doctor’s hunger
(D) his gaze on Gopal
Answer:
(B) Dr. Raman’s evasive reply to Gopal’s wife

Question 18.
“Sir, he will pull through.” What does the underlined expression mean?
(A) forget
(B) improve
(C) recover
(D) pass away
Answer:
(B) improve

Question 19.
Gopal’s slight recovery filled his family with _____________.
(A) relief
(B) delight
(C) gratitude to the doctor
(D) all the above
Answer:
(D) all the above

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 20.
The sick man’s wife asked, “Is he out of danger ?” This indicates his wife’s
(A) stress
(B) nervousness
(C) restlessness
(D) none of these
Answer:
(C) restlessness

Question 21.
To know Gopal’s latest condition was his wife’s __________.
(A) keen determination
(B) hope
(C) wish
(D) interest
Answer:
(A) keen determination

Question 22.
The bitter weeping of Gopal’s wife made Dr. Raman ____________.
(A) anxious
(B) vexed
(C) impatient
(D) confused
Answer:
(D) confused

Question 23.
The doctor advised the patient to _____________.
(A) sleep
(B) sit
(C) relax
(D) get up
Answer:
(C) relax

Question 24.
“Am I going ?” This means ___________.
(A) leaving
(B) interested to go to his house
(C) visiting
(D) facing death
Answer:
(D) facing death

Question 25.
The patient was ___________.
(A) desperate
(B) impatient
(C) panicky
(D) none of these
Answer:
(A) desperate

Question 26.
“It was not in his nature to whitewash.” The underlined word means-
(A) rubbing
(B) cleaning
(C) not to tell a lie
(D) bluff
Answer:
(C) not to tell a lie

Question 27.
Gopal appealed to his friend to _______________.
(A) cure him
(B) save his family’s future
(C) tell the truth
(D) call in his wife
Answer:
(B) save his family’s future

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 28.
He knew too well the family affairs and about those wolves. This means ________________.
(A) wild animals
(B) selfish persons
(C) ruthless people
(D) anti-social elements
Answer:
(D) anti-social elements

Question 29.
Dr. Raman’s act of telling the truth implies his-
(A) commitment to truth
(B) courage
(C) friend’s speedy recovery
(D) friend’s death
Answer:
(D) friend’s death

Question 30.
Dr. Raman resorts to deliberate falsehood ______________.
(A) for the sake of his friend
(B) without any delay
(C) for nothing
(D) none of these
Answer:
(A) for the sake of his friend

Question 31.
What does “on one’s last legs” mean?
(A) Very sick
(B) Weak and about to die
(C) Not in one’s good health
(D) All of the above
Answer:
(B) Weak and about to die

Question 32.
When did people come to Dr. Raman?
(A) When the patient was very sick
(B) When the patient had almost no hope
(C) When the patient collapsed
(D) When the patient had recovered a little
Answer:
(B) When the patient had almost no hope

Question 33.
Why did Dr. Raman often burst out when he found the patient in his last breath?
(A) Why wasn’t he brought to him earlier
(B) Why was he taken to another doctor
(C) Why had the family members treated him wrong
(D) Why was his condition so serious
Answer:
(A) Why wasn’t he brought to him earlier

Question 34.
What was Dr. Raman’s visiting fee?
(A) Twenty rupees
(B) Twenty-five rupees
(C) Thirty rupees
(D) Thirty-five rupees
Answer:
(B) Twenty-five rupees

Question 35.
What fact did people like to avoid?
(A) That the patient had less hope
(B) That the visiting fees of Dr. Raman was high
(C) That Dr. Raman means death sentence
(D) That the patient couldn’t be saved no matter what
Answer:
(A) That the patient had less hope

Question 36.
The patient’s relatives always tried to avoid calling in Dr. Raman; for them there was something ___________ in the very association.
(A) serious
(B) unnecessary
(C) threatening
(D) shirking
Answer:
(C) threatening

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Question 37.
So, when the big man came on the scene it was always__________.
(A) the last moment
(B) critical for the patient
(C) a quick decision to make
(D) late
Answer:
(C) a quick decision to make

Question 38.
What has long years of practice bred in the doctor?
(A) Experience to save lives
(B) A certain manner of rudeness
(C) A certain degree of kindness
(D) A certain curt of truthfulness
Answer:
(D) A certain curt of truthfulness

Question 39.
Why was the doctor’s opinion valued?
(A) For his experience
(B) For his kindness
(C) For him truthfulness
(D) For his expertise
Answer:
(C) For him truthfulness

Question 40.
Dr. Raman was not a mere doctor expressing an opinion but a /an ___________.
(A) judge pronouncing a verdict
(B) kind man helping patients
(C) expert saving lives
(D) experienced consultant
Answer:
(A) judge pronouncing a verdict

Question 41.
What did the patient’s life hang on?
(A) Dr. Raman’s experience
(B) Dr. Raman’s treatment
(C) Dr. Raman’s words
(D) Dr. Raman’s kindness
Answer:
(C) Dr. Raman’s words

Question 42.
What did Dr. Raman never believe?
(A) True words can save life
(B) Mere words can save life
(C) Agreeable words can save life
(D) God’s will can save life
Answer:
(C) Agreeable words can save life

Question 43.
Why did Dr. Raman think that it was not any of his business to provide unnecessary hope to the patients and their family?
(A) Because they would ultimately know the truth in few hours
(B) Because it was none of his business
(C) Because he was not that kind hearted
(D) Because it was not his duty to give people hope
Answer:
(A) Because they would ultimately know the truth in few hours

Question 44.
What would Dr. Raman do if he glimpsed the faintest sign of hope?
(A) Pause all other works and perform operation
(B) Do whatever he could to save the patient
(C) Give hope to the patient and his family
(D) Preapare to fight with death
Answer:
(B) Do whatever he could to save the patient

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

Introducing the Author
R. K. Narayan (1906-2001) is perhaps the most well-known Indian writer in English. Born in Madras, Narayan was educated in Mysore. He started writing in the nineteen thirties. His writing is set in an imaginary town called Malgudi and South Indian family life has seldom been so realistically portrayed as in his novels and short stories. Some of his famous works are Swami and Friends, The Man-Eater ofMalgudi, The Bachelor of Arts, Mr Sampath, The Astrologer’s Day, Waiting for the Mahatma etc. His novel The Guide was selected for the Sahitya Academy Award. Narayan has written a good number of short stories which are noted for their humour, pathos and mild satire. His style is simple and lucid. Walsh aptly remarks, “Narayan ’s fastidious art, blending exact realism, poetic myth, sadness, perception and gaiety are without precedent in literature in English and as far as one can see, without following. It is kind, but unsentimental, mocking but uncynical, profoundly Indian but distinctively individual. Itfascinates by reason of the substantial human nature which it implies and embodies. It carries along with it at every point, a kind of humour strange in English writing which mixes the melancholy and the amusing.”

About the Story
A doctor saves lives both with his skill and with his words. Soothing words of a doctor work wonders for a patient in a critical condition. Dr. Raman, a fictitious physician in the imaginary story, is a classic example. South Indian city of Malgudi is the microcosm for many of Narayansque stories. He is renowned for his diagnostic acumen and “certain curt truthfulness; for that very reason his opinion is valued; he is not a mere doctor expressing an opinion but a judge pronouncing a verdict.” When Dr. Raman is called upon to make a house call and subsequent operation on his dearest friend, Gopal, he faces a very difficult professional ethical dilemma. This story adroitly tackles truthfulness. This story’s concern is not only with professional ethics but also with the tension that often arrives when personal ethics and professional ethics intersect and conflict since it is clear that Dr. Raman violates his usual practice of truth-telling in the interest of his friendship. It is also a commentary on paternalism; Dr. Raman tells the patient’s wife and patient only what he wants them to hear since the truth as he perceives would be damaging to the patient’s outcome, a much censured notion known as “therapeutic privilege”. This story demonstrates the economy and grace with which expertly wrought fiction can capture and present for discussion important issues in (medical) ethics.

ବିଷୟ ସୂଚନା :
ଖରାପ ଅବସ୍ଥାରେ ଜଣେ ରୋଗୀପାଇଁ ଜଣେ ଡାକ୍ତରଙ୍କର ସାନ୍ତନାମୂଳକ କଥାଗୁଡ଼ାକ ଚମତ୍କାର ଭାବେ କାମ କରେ । କାଳ୍ପନିକ କଥାବସ୍ତୁର ଡାକ୍ତର ଚରିତ୍ର ଡା. ରମଣ ହେଉଛନ୍ତି ଏହାର ଏକ ଜୀବନ୍ତ ଉଦାହରଣ । ନାରାୟଣଙ୍କର ଗଳ୍ପଗୁଡ଼ିକର ପୃଷ୍ଠଭୂମି ହେଉଛି ଦକ୍ଷିଣ ଭାରତୀୟ ସହର ମାଲ୍‌ଗୁଡ଼ି । ଡାକ୍ତର ରମଣ ରୋଗର ସଠିକ କାରଣ ନିରୂପଣ କରିବା ଓ ଅପ୍ରିୟ ସତ୍ୟ କଥା କହିବା କାରଣରୁ ପ୍ରସିଦ୍ଧି ଅର୍ଜନ କରିଛନ୍ତି । ସେଥ‌ିପାଇଁ ତାଙ୍କ କଥା ଅଧ୍ଵ ଗୁରୁତ୍ଵ ଦିଆଯାଏ । ସେ ଜଣେ ସାଧାରଣ ଡାକ୍ତରଭାବେ ନିଜର ମତାମତ ଶୁଣାଇନଥା’ନ୍ତି, ବରଂ ଜଣେ ବିଚାରପତିଭାବେ ରାୟ ଶୁଣାଇଥା’ନ୍ତି । ଯେତେବେଳେ ସେ ତାଙ୍କର ଘନିଷ୍ଠ ବନ୍ଧୁ ଗୋପାଳର ଅସ୍ତ୍ରୋପଚାର କରିଛନ୍ତି, ସେ ଏକ ନୈତିକ ଦୃହରେ ପଡ଼ିଛନ୍ତି । ଏହି ଗଳ୍ପରେ ଚତୁରତାର ସହ ସେହି ସତ୍ୟର ପ୍ରକଟନ ଘଟିଛି । ଏଠାରେ ରମଣଙ୍କର ବ୍ୟକ୍ତିଗତ ନୈତିକତା ବୃତ୍ତିଗତ ନୈତିକତା ମଧ୍ୟରେ ଦ୍ବନ୍ଦ୍ବ ଉପୁଜିଛି ଏବଂ ବନ୍ଧୁଙ୍କ ହିତ ପାଇଁ ନିତିଦିନିଆ ସତ କହିବାର ଅଭ୍ୟାସରୁ ସ୍ପଷ୍ଟ ଭାବରେ ବିଚ୍ୟୁତ ହୋଇଛନ୍ତି । ଡାକ୍ତର ରମଣ ରୋଗୀର ସ୍ତ୍ରୀ ଓ ରୋଗୀକୁ କେବଳ ତାଙ୍କ କଥା ଶୁଣିବାକୁ କହିଛନ୍ତି, ଯେହେତୁ ପ୍ରକୃତ ସତ୍ୟ ରୋଗୀର କ୍ଷତି ଘଟାଇପାରେ । ଏହି ଗଳ୍ପରେ ଭେଷଜ ବିଜ୍ଞାନ ସମ୍ବନ୍ଧୀୟ ଅନେକ ତତ୍ତ୍ଵ ନିଖୁଣ ଭାବରେ ଆଲୋଚନା

Summary
In the beginning, the writer, in his characteristic humorous vein, states that the patients visit Dr. Raman when they are hopeless, because of the latter’s visiting fee twenty-five rupees. He has long years of practice behind him. Dr. Raman is renowned for his diagnostic acumen and “certain curt truthfulness”. As a result, his opinion is given great importance. He is not a doctor in an ordinary sense. Dr. Raman is like a sort of judge who delivers a judgement. He saves life with his skill and never likes to say agreeable words. It is because the patient’s will to survive is what matters.

Dr. Raman is keen on saving the lives of his patients when he sees the slightest ray of hope. The writer describes the long-standing relationship between Dr. Raman and Gopal. The doctor comes to know about his friend’s illness from the latter’s son. He is called upon to visit Gopal’s house. The doctor finds his friend and patient in a critical condition. He learns that a “doctor in the next street”, a physician Raman does not know, is ‘ treating the patient. Without wasting time, he administers an injection to his patient. He does not respond to the query of Gopaks wife.

He minutely observes his patient who still remains motionless. He feels worried when he finds his bosom friend in a critical condition, but not hopeless. Skilful doctor as he is, Dr. Raman remains calm in an adverse situation like this. He performs an operation on his dearest friend Gopal. Evening sets in. Raman’s assistant’s joy knows no limit when he sees the patient in a better condition. He is enthusiastic about the patient’s recovery. The doctor gives his assistant a cold response. Although Gopal’s pulse has improved, this is not enough. He suffers from serious heart attack.

Dr. Raman knows that the night is crucial for his patient; he sits beside the latter and notices a slight improvement in his condition. Now the patient is in a state to take a little food. The household heaves a sigh of great relief. Everybody is happy. Overwhelmed with emotion, the family members profusely express their gratitude to the doctor. However, Raman sits silently, intensely looking at the patient’s- face. He is heedless of their words. The doctor’s reaction is evasive. When the wife asks him about her patient’s condition, he remains silent, but she is determined to know the truth. Her patience runs out. She cannot bear the suspense any more. The wife is anxious to know about the condition of her husband.

She requests him to tell the truth. The doctor expresses his inability to talk to her at the moment. His silence on the matter makes her weep bitterly. The patient looks in confusion. Gopal is very sick. He requests the doctor not to hide the truth. He is anxious about signing the will. The doctor’s effort to calm him goes in vain. Gopal requests truthful prognosis in order to settle his will and get rid of the never-ending misery for his wife and children that an unsettled will would entail. The doctor is aware of this realistic eventuality. Dr. Raman faces a very difficult professional dilemma.

He swims between personal ethics and professional ethics. If he reveals his pessimistic opinion, which he does to his assistant: ‘Gopal will not survive the night’, then it will virtually imply a death sentence. The inevitable will happen. His frankness will put an end to the slightest chance of the patient’s survival. Dr. Raman violates his usual practice of truth-telling in the interest of his forty year-old friendship. He does ‘a piece of acting’ and assures his friend and patient that he will survive. Gopal expresses his unflinching trust in the doctor’s statement. His words, “If it comes from your lips, it must be true” is a case in point. Gopal lives and Dr. Raman remarks to his assistant, “How he has survived this attack will be a puzzle to me all life.”

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Doctor’s Word

ସାରାଂଶ :
ଗଳ୍ପର ପ୍ରାରମ୍ଭରେ ଲେଖକ ବ୍ୟଙ୍ଗପୂର୍ଣ୍ଣ ଭାବେ କହିଛନ୍ତି ଯେ ରୋଗୀମାନେ ଆଶାଶୂନ୍ୟ ହେବା ପରେ ହିଁ ଡାକ୍ତର ରମଣଙ୍କ ପାଖକୁ ଆସନ୍ତି, କାରଣ ତାଙ୍କର ରୋଗୀଦେଖା ଫିସ୍ ଥାଏ ୨୫ ଟଙ୍କା । ସେ ଜଣେ ବହୁ ଅନୁଭୂତିସମ୍ପନ୍ନ ଡାକ୍ତର । ତାଙ୍କର ସଠିକ୍ ଭାବେ ରୋଗ ଚିହ୍ନିବାର ଦକ୍ଷତା ଓ ଅପ୍ରିୟ ନିଶ୍ଚିତ ସତ୍ୟ କଥା କହିବା ପାଇଁ ସେ ଖ୍ୟାତି ଅର୍ଜନ କରିଛନ୍ତି । ଫଳରେ ତାଙ୍କର ମନ୍ତବ୍ୟକୁ ଗୁରୁତ୍ଵ ଦିଆଯାଏ । ସେ ଜଣେ ସାଧାରଣ ଡାକ୍ତର ଭଳି ନୁହେଁ, ବରଂ ଜଣେ ବିଚାରପତି ଭଳି ରାୟ ଶୁଣାନ୍ତି । ସେ ନିଜର ଦକ୍ଷତାକୁ ନେଇ ରୋଗୀର ଜୀବନ ବଞ୍ଚାନ୍ତି, ମାତ୍ର ଆଶ୍ଵାସନାବାଣୀ ଶୁଣାଇବାକୁ ଭଲ ପାଆନ୍ତି ନାହିଁ ।

ରୋଗୀଠାରେ ସାମାନ୍ୟ ବଞ୍ଚିବାର ଆଶା ଥିଲେ ସେ ତା’ର ଜୀବନ ବଞ୍ଚାଇବାକୁ ଯତ୍‌ ପରୋନାସ୍ତି ଉଦ୍ୟମ କରନ୍ତି । ଲେଖକ ଏଠାରେ ଡା. ରମଣ ଏବଂ ଗୋପାଳର ବହୁଦିନର ସମ୍ପର୍କକୁ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ଗୋପାଳର ପୁଅଠାରୁ ସେ ଜାଣିବାକୁ ପାଇଛନ୍ତି ଯେ ଗୋପାଳ ରୋଗଦ୍ଵାରା ଆକ୍ରାନ୍ତ ହୋଇଛି । ସେ ଗୋପାଳ ଘରକୁ ବୁଲିବାକୁ ଯାଆନ୍ତି ଏବଂ ଗୋପାଳର ଅବସ୍ଥା ଗୁରୁତର ଥ‌ିବା ଦେଖନ୍ତି ।ସେ ତତ୍‌କ୍ଷଣାତ୍ ରୋଗୀକୁ ଏକ ଇନ୍‌ଜେକ୍‌ସନ୍ ଦିଅନ୍ତି ଏବଂ ଗୋପାଳର ସ୍ତ୍ରୀର ପ୍ରଶ୍ନର ଉତ୍ତର ନ ଦେଇ ରୋଗୀକୁ ତନ୍ନତନ୍ନ ଭାବେ ପରୀକ୍ଷା କରନ୍ତି । ସେ ବ୍ୟସ୍ତ ଓ ବିବ୍ରତ ହୋଇପଡ଼ନ୍ତି ।

କିନ୍ତୁ ଏହିପରି ଗୁରୁତର ଅବସ୍ଥାରେ ସେ ଆଶା ହରାନ୍ତି ନାହିଁ । ସେ ପ୍ରିୟବନ୍ଧୁ ଗୋପାଳ ଶରୀରରେ ଏକ ଅସ୍ତ୍ରୋପଚାର କରନ୍ତି । ସନ୍ଧ୍ୟା ଆଗତ ହୋଇଛି । ଡ. ରମଣଙ୍କର ସହକାରୀଜଣକ ଦେଖନ୍ତି ଯେ ରୋଗୀର ସ୍ଵାସ୍ଥ୍ୟବସ୍ଥାରେ ଉନ୍ନତି ଘଟୁଛି । ତାଙ୍କର ଖୁସିର ସୀମା ରହେ ନାହିଁ । କିନ୍ତୁ ଡା. ରମଣ କହନ୍ତି ଯେ ଯଦିଓ ଗୋପାଳଙ୍କର ନାଡ଼ିର ଗତିରେ ଉନ୍ନତି ଘଟିଛି, ତଥାପି ଏହା ଯଥେଷ୍ଟ ନୁହେଁ । ଡା. ରମଣ ଜାଣିଛନ୍ତି ଯେ ରାତିଟି ତାଙ୍କ ରୋଗୀ ପାଇଁ ଗୁରୁତ୍ଵପୂର୍ଣ୍ଣ କାରଣ ସେ ଗୁରୁତର ହୃଦ୍‌ରୋଗରେ ପୀଡ଼ିତ । ବର୍ତ୍ତମାନ ରୋଗୀଟି କିଛି ଖାଦ୍ୟ ଗ୍ରହଣ କରିବା ଅବସ୍ଥାକୁ ଆସିଛନ୍ତି । ଘରର ଅଥଚ ଡା. ରମଣ ରୋଗୀଙ୍କର ମୁହଁକୁ ଚାହିଁ ଧୀରସ୍ଥିର ହୋଇ ବସିଥାଆନ୍ତି ।

ସେ ଘରର ସଦସ୍ୟମାନଙ୍କର କୃତଜ୍ଞତାର ଚାହାଁନ୍ତି । ସେ ଡାକ୍ତରଙ୍କୁ ସତ୍ୟ କହିବାକୁ ଅନୁରୋଧ କରନ୍ତି । ସେହି ସମୟରେ ଡାକ୍ତରଙ୍କର ନୀରବତା ରୋଗୀର ସ୍ତ୍ରୀଙ୍କ ମନରେ ବହୁତ ଆଘାତ ଦେଇଛି ଏବଂ ସେ ଖୁବ୍ ଜୋର୍‌ରେ କାନ୍ଦିଛନ୍ତି । ରୋଗୀଟି ଦ୍ବନ୍ଦ୍ବରେ ପଡ଼ି ଚାହିଁଛି । ଗୋପାଳ ବହୁତ ଅସୁସ୍ଥ ହୋଇପଡ଼ିଛି । ସେ ଡାକ୍ତରଙ୍କୁ ସତ୍ୟ ହିଁ କହିବାପାଇଁ ଅନୁରୋଧ କରିଛି । ଡାକ୍ତର ତାଙ୍କୁ ସାନ୍ତନା ଦେଇପାରି ନାହାନ୍ତି । ଗୋପାଳ ବାରମ୍ବାର ସତ୍ୟ କହିବା ପାଇଁ ବାଧ୍ୟ କରିଛି ଯାହା ଫଳରେ ସେ ନିଜର ଇଚ୍ଛାପତ୍ର ପ୍ରସ୍ତୁତ କରି ତାଙ୍କ ପରିବାରର ଚିରଦୁଃଖର ଅବସାନ ଘଟାଇପାରିବେ । ଏହି ବାସ୍ତବ ସତ୍ୟ ବିଷୟରେ ଡାକ୍ତର ସଚେତନ ଅଛନ୍ତି ।

ଏଠାରେ ଡାକ୍ତର ଏକ କଷ୍ଟକର ବୃତ୍ତିଗତ ଦ୍ବନ୍ଦ୍ବକୁ କିଭଳି ସାମନା କରିଛନ୍ତି ତାହା ବର୍ଣ୍ଣିତ ହୋଇଛି । ସେ ବ୍ୟକ୍ତିଗତ ନୀତି ଏବଂ ବୃତ୍ତିଗତ ନୀତି ମଧ୍ୟରେ ଦ୍ବନ୍ଦ୍ବରେ ପଡ଼ିଛନ୍ତି । ସେ ଜାଣିଛନ୍ତି ଯେ ସେହି ରାତିରେ ଗୋପାଳ ନିଶ୍ଚିତ ମୃତ୍ୟୁବରଣ କରିବ । ଏହି ଧ୍ରୁବ ସତ୍ୟ ନିଶ୍ଚୟ ଘଟିବ । ସେ ଯଦି ମୁକ୍ତ ଭାବରେ ସତ୍ୟର ପ୍ରକଟ କରିବେ, ତେବେ ରୋଗୀର ବଞ୍ଚିବାର କ୍ଷୀଣ ଆଶାଟିକକ ନଷ୍ଟ ହୋଇଯିବ । ଡାକ୍ତର ତାଙ୍କର ଚାଳିଶ ବର୍ଷର ବନ୍ଧୁଙ୍କର ହିତ ପାଇଁ ଏହିଭଳି ଦୃଢ଼ ଉକ୍ତିକୁ ଗୋପାଳ ପୂର୍ଣ୍ଣ ବିଶ୍ଵାସ କରିଛି । ଶେଷରେ ଗୋପାଳ ବଞ୍ଚିଯାଇଛି । ଡାକ୍ତର ରମଣ ତାଙ୍କର ସହଯୋଗୀଙ୍କୁ କହିଛନ୍ତି, ‘ରୋଗୀ କିପରି ଏହି ହୃଦ୍‌ରୋଗରୁ ବଞ୍ଚିପାରିଲେ, ତାହା ତାଙ୍କ ପାଇଁ ଚିର ରହସ୍ୟମୟ ହୋଇ ରହିବ ।’’

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 2 The Nightingale and the Rose

Odisha State Board CHSE Odisha Class 12 Invitation to English 2 Solutions Non-Detailed Chapter 2 The Nightingale and the Rose Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class English Solutions Non-Detailed Chapter 2 The Nightingale and the Rose

CHSE Odisha Class 12 English The Nightingale and the Rose Text Book Questions and Answers

Unit – I

Gist:
The love-stricken young Student desperately longs for red roses, because the girl promises to dance with him on the condition he brings her these beautiful flowers, but he doesn’t find any red rose. He is sad. In a dance programme given by the Prince, the young Student will become lonely. His heart will bleed. The Nightingale, famous for her enchanting voice, hears him cry for the want of the girl, who is apparently his true love. She shares the feelings of the young Student. She feels the importance of love that comes from within, not from outside. The young man’s longing for a red rose grows intense, but in vain. He has no red rose to give the girl so as to enable her to dance with him. He weeps. A little Green Lizard and a Butterfly laugh at the weeping young Oxford boy. The Nightingale alone understands the mystery of Love.

ସାରମର୍ମ :
ପ୍ରେମପୀଡ଼ିତ ଯୁବ-ଛାତ୍ରଜଣକ ଏକ ଲାଲ୍ ଗୋଲାପ ପାଇଁ ବ୍ୟାକୁଳ ହୋଇଉଠିଛି କାରଣ ତା’ର ପ୍ରେମିକା ପ୍ରତିଜ୍ଞା କରିଛି ଯେ ଯଦି ଯୁବକଜଣକ ତାଙ୍କୁ ଏକ ଲାଲ୍ ଗୋଲାପ ଦିଏ, ତେବେ ସେ ଏହି ପ୍ରେମିକ ଯୁବକଙ୍କ ସହ ନୃତ୍ୟ କରିବେ । ସେ କୌଣସି ଲାଲ୍ ଗୋଲାପ ପାଆନ୍ତି ନାହିଁ । ତେଣୁ ସେ ଦୁଃଖ ହୋଇ ଯାଇଛନ୍ତି । ଯଦି ଯୁବତୀଜଣଙ୍କ ଆଉ କାହା ସହ ନୃତ୍ୟ କରିବେ, ତେବେ ଯୁବ-ଛାତ୍ର ଜଣଙ୍କ ହୃଦୟ ରକ୍ତାକ୍ତ ହୋଇଯିବ । ଆକର୍ଷଣୀୟ ଗୀତ ଓ ସଙ୍ଗୀତ ପାଇଁ ପ୍ରସିଦ୍ଧ ବୁଲ୍‌ବୁଲ୍ ପ୍ରେମିକ ଯୁବକଙ୍କର ଦୁଃଖକୁ ବୁଝିପାରନ୍ତି ଏବଂ ସେହି ଯୁବତୀ ପ୍ରତି ଥ‌ିବା ସଚ୍ଚା ପ୍ରେମକୁ ଜାଣିପାରନ୍ତି । ସେ ସଚ୍ଚା ପ୍ରେମିକର ପ୍ରେମକୁ ବୁଝିପାରନ୍ତି । ସତ୍ ପ୍ରେମ ହୃଦୟ ଭିତରୁ ଆସିଥାଏ, ହୃଦୟ ବାହାରୁ ନୁହେଁ । ଯେହେତୁ ଯୁବ-ଛାତ୍ରଙ୍କ ପାଖରେ ସେହି ଯୁବତୀଙ୍କୁ ଦେବାପାଇଁ ଲାଲ୍ ଗୋଲାପ ନ ଥିଲା, ତେଣୁ ସେ କାନ୍ଦିଛନ୍ତି । ଝିଟିପିଟି ଓ ପ୍ରଜାପତି ଏହି ଭାବକୁ ବୁଝିନପାରି ଥଟ୍ଟା କରନ୍ତି । କିନ୍ତୁ ବୁଲ୍‌ବୁଲ୍ ପ୍ରେମର ଏହି ରହସ୍ୟକୁ ବୁଝିପାରିଛି ।

Glossary :
nest : ବସା
wondered : ଆଶ୍ଚର୍ଯ୍ୟ ହେଲେ
entire: ସମଗ୍ର
wretched: miserable (ଦୁଃଖପୂର୍ଣ୍ଣ)
passion: ଆବେଗ
pale: ମଳିନ
brow: କପାଳ
murmured: ଧୀରେ ଧୀରେ କହିଲା
lean: incline (ଆଉଜିବା)
my heart will break: my sorrow will know no end (ମୋ ହୃଦୟ ବିଦୀର୍ଣ୍ଣ ହେବ)
precious: valuable (ମୂଲ୍ୟବାନ୍)
emerald: ମୋତି
dearer: morecostly ( ଅଧ୍ଵମୂଲ୍ୟବାନ୍)
opal: ରତ୍ନପଥର
pearl: ମୁକ୍ତା
pomegranate: ଡାଳିମ୍ବ
weigh: measure (ମାପିବା)
in exchange of : ବଦଳରେ
play upon: ଉପରେ ଖେଳ
string: ତାର
harp: ବୀଣା
violin: ବେହେଲା
stringed instruments: ବାଦ୍ୟଯନ୍ତ୍ର
lightly: ହାଲୁକା ଭାବରେ
gay: (here) beautiful (ସୁନ୍ଦର)
throng: ଘେରିଯିବେ
Flung: threw (ପକାଇଦେଲା)
buried: ଘୋଡ଼ାଇ ପକାଇଲା
wept: କାନ୍ଦିଲା
fluttering: ଡେଣା ଫଡ଼ଫଡ଼ କରି
sunbeam : ସୂର୍ଯ୍ୟାଲୋକ
ridiculous : ହାସ୍ୟାସ୍ପଦ
secret of sorrow: ଦୁଃଖର ରହସ୍ୟ
mystery of Love: ପ୍ରେମର ରହସ୍ୟ

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Think it out

Question 1.
Why does the young student pine for a red rose?
Answer:
The Professor’s daughter requests specifically a red rose from the love stricken young student for the sake of dancing with him. Only with the flower the girl will respond to his request for love. But the young student finds no red rose in his garden. His happiness is linked with this beautiful flower. Therefore, the young student pines for a red rose.

Question 2.
Why does the nightingale admire the young student?
Answer:
The young student plunges into sorrow, because he does not find a red rose for the Professor’s daughter whom he loves deeply. She requests specifically a red rose from him as a token of true love. But he is hopeless. He visualises a radiant dream of the girl dancing with him, if he brings her red rose. Without it his dream will collapse like a house of cards. He will be lonely. The nightingale understands the feelings of the forlorn lover and therefore, admires the young student.

Question 3.
How does the nightingale wonder at the mystery of love?
Answer:
The nightingale wonders at the mystery of love to see the sight of a weeping young student. He is grief-sticken because he cannot get a red rose for the Professor’s daughter whom he loves deeply. His happiness depends on this beautiful flower. There is no red rose in his garden. Frustrating thoughts flood into his mind. Deprived of a red rose, he visualises a painful picture of his loneliness.

Unit – II

Gist:
Moved by the young student’s sorrow, the nightingale wishes to find a red rose as a gift for him. Suddenly, she flies high into the air and catch sight of a beautiful Rose-treein the centre of a lawn. She asks it for a rose, but in vain, because its garden is full of white roses. Therefore, the Rose-tree instructs her to go to his brother who grows below the student’s window. The nightingale magnificently responds to his advice. She reaches the destination and appeals to the Rose-tree to give her a red rose. To her great sorrow, she learns that the biting winter has destroyed the buds of all red roses, but the Rose-tree growing beneath the student’s door agrees to give her a red rose by singing to him throughout the night with her breast against a thorn. Besides, the thorn should penetrate her heart. At last the life-blood will be in its veins, eventually resulting the birth of red rose. Instead of being disheartened, the nightingale decides to get a red rose at the cost of her life, for she thinks that nothing is so supreme as love. Life loses its luster before it.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

ସାରମର୍ମ :
ଲାଲ୍ ଗୋଲାପ ନ ପାଇ ଦୁଃଖରେ ଭାଙ୍ଗି ପଡ଼ିଥିବା ଯୁବକର ଦୁଃଖଦ୍ଵାରା ବୁଲ୍‌ବୁଲ୍ ଅନୁପ୍ରାଣିତ ହୋଇ ଏକ ସୁନ୍ଦର ଲାଲ୍ ଗୋଲାପର ଅନୁସନ୍ଧାନରେ ଉପରକୁ ଉଡ଼ିଯାଇଛି । ସେ ଏକ ବଗିଚାରେ ଗୋଟିଏ ସୁନ୍ଦର ଗୋଲାପ ଗଛ ଥ‌ିବାର ଦେଖିଛି । କିନ୍ତୁ ଦୁଃଖର ବିଷୟ ସେହି ଗଛରେ କୌଣସି ଲାଲ୍ ଗୋଲାପ ନାହିଁ । ସେଥୁରେ କେବଳ ଧଳା ଗୋଲାପ ଅଛି । ତେଣୁ ସେ ଗଛଟି ବୁଲ୍‌ବୁଲ୍‌କୁ ସେହି ଯୁବକ ରହୁଥ‌ିବା ପ୍ରକୋଷ୍ଠର ଝରକା ତଳେ ଥିବା ତା’ର ଭାଇ ପାଖକୁ ଯାଇ ଲାଲ୍ ଗୋଲାପ ଆଣିବାପାଇଁ ଉପଦେଶ ଦେଇଛି । ବୁଲ୍‌ବୁଲ୍ ସେହି ଅନୁସାରେ କାର୍ଯ୍ୟ କରିଛି । ସେ ସେଠାରେ ପହଞ୍ଚି ଗୋଟିଏ ଲାଲ୍ ଗୋଲାପ ଦେବାପାଇଁ ଗଛକୁ ଅନୁରୋଧ କରିଛି । ସେ ଶୁଣିବାକୁ ପାଇଛି ଯେ ଅସହ୍ୟ ଶୀତ ହେତୁ ସବୁ ଲାଲ୍ ଗୋଲାପର କଢ଼ ନଷ୍ଟ ହୋଇଯାଇଛି । କିନ୍ତୁ ସେହି ଗୋଲାପ ଗଛଟି ଗୋଟିଏ ସର୍ଭରେ ଲାଲ୍ ଗୋଲାପଟିଏ ଦେବାକୁ ରାଜି ହୋଇଛି । ଯଦି ବୁଲ୍‌ବୁଲ୍‌ଟି ସାରା ରାତି ନିଜର ହୃଦୟକୁ ଏକ ଗୋଲାପ କଣ୍ଟାରେ ବିଦ୍ଧ କରି ଗୀତ ଗାଏ, ତେବେ ସେ ଗୋଟିଏ ଲାଲ୍ ଗୋଲାପ ଦେବ । ବୁଲ୍‌ବୁଲ୍‌ର ହୃଦୟରୁ କ୍ଷରିତ ରକ୍ତରେ ଧଳା ଗୋଲାପଟି ଲାଲ୍ ଗୋଲାପରେ ପରିଣତ ହେବ ।ଏଥ‌ିରେ ମଧ୍ୟ ବୁଲ୍‌ବୁଲ୍ ରାଜି ହୋଇଛି । ସେ ଗୋଟିଏ ଲାଲ୍ ଗୋଲାପ ପାଇଁ ନିଜ ଜୀବନକୁ ଉତ୍ସର୍ଗ କରିଛି । କାରଣ ସେ ଭାବିଛି ପ୍ରେମଠାରୁ କିଛି ବି ଅଧିକ ନୁହେଁ । ସଚ୍ଚା ପ୍ରେମ ଆଗରେ ମଧ୍ୟ ଜୀବନ ତା’ର ଗୌରବ ହରାଇ ବସେ ।

Glossary :
wings: ଡେଣା
flight: ଉଡ଼ାଣ
soared: ଉର୍ଦ୍ଧ୍ୱଗାମୀ
spray: a very small branch of a tree (ଗଛର ଏକ ଛୋଟ ଡାଳ)
beneath: ତଳେ
shook head
coral: ପ୍ରବାଳ
redder : ଅଧ୍ଵ ଲାଲ୍
Nipped: destroyed (ନଷ୍ଟ କରିଦେଲା)
bud: କଢ଼ି|କଢ଼
terrible: ଭୟଙ୍କର
dare: ସାହସ କରିବା
stain: paint (ରଙ୍ଗ କରିବା)
price: cost (ମୂଲ୍ୟ)
Yet Love …. Life: The writer gives more importance to Love than Life.

Think it out

Question 1.
What does the nightingale do to get a red rose?
Answer:
The nightingale is moved to pity because of the young student’s sorrow. She wishes to find a red rose as a gift for him. She asks nearly everywhere for this beautiful flower. She flies high and in the course of her flight, the nightingale notices a beautiful Rose-tree in the midst of the lawn. The bird requests him to give her a red rose in exchange of her sweetest song, but in vain, because the roses in the tree are white. Again, in accordance with his suggestion, the nightingale flies over to the Rosetree beneath the student’s window. Here her request for a red rose meets with a tough test.

Question 2.
How does the Rose-tree growing beneath the student’s door agree to give her a red rose?
Answer:
In response to her request for a red rose, the Rose-tree growing beneath the student’s door demands a high price from the nightingale. As winter has destroyed his buds, she should place her heart closer to the thorn. In other words, she is required to pinch her own heart against the thorn of a white rose to turn it red with her own blood. In this way, the Rose-tree growing beneath the student’s door agrees to give her a red rose.

Question 3.
Why does the nightingale decide to pet a red rose at the cost of her life?
Answer:
The Rose-tree agrees to give the nightingale a red rose, provided she sings throughout the night, pressing her heart against the thorn and the white rose will turn red with her own blood. It means her ultimate sacrifice. The nightingale thinks that nothing is as precious as Love and she will pay a heavy price for a red rose. Nevertheless, Love is supreme, Life is inferior to it. The nightingale understands the importance of the love of the young student and hence decides to get it at the cost of her life.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Unit – III

Gist:
The nightingale comes near the miserable young student and promises to bring him a red rose by creating it out of music by moonlight and colouring a white rose into red by using her own blood, but she wants an assurance from him in return that he will a true lover, because to her Love is superior to Philosophy and Power. Her words makes him confused. The young student fails to understand anything. But the oak-tree understands everything. He appeals to the bird to sing him one last melodious song. The bird responds to it in an instant. The nightingale goes on her mission. The oak tree is now lonely and sad. The young student doubts her feelings. He identifies the nightingale with most artists who are stylish, but not sincere. She does not understand the language of sacrifice. Music is her life. Her voice sounds melodious. He expresses pity for the nightingale. Her songs are meaningless. They lack practical value. These are the student’s feelings about the nightingale which he writes in his note-book.

ସାରମର୍ମ :
ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀଟି ଦୁଃଖରେ ଭାଙ୍ଗି ପଡ଼ିଥ‌ିବା ଯୁବ-ଛାତ୍ରଙ୍କ ପାଖକୁ ଆସିଛି ଏବଂ ଗୋଟିଏ ଲାଲ୍ ଗୋଲାପ ଦେବାର ପ୍ରତିଶ୍ରୁତି ଦେଇଛି । ଚନ୍ଦ୍ରବିଧୌତ ରଜନୀରେ ଚମତ୍କାର ସଙ୍ଗୀତ ସୃଷ୍ଟି କରି ନିଜର ରକ୍ତରେ ଧଳା ଗୋଲାପକୁ ଲାଲ୍ କରିଦେବାକୁ ମଧ୍ୟ ସେ ପ୍ରତିଶ୍ରୁତିବଦ୍ଧ ହୋଇଛି ।ଏହା ବଦଳରେ ଯୁବକଜଣକ ଜଣେ ସଚ୍ଚା ପ୍ରେମିକ ହେବା ଆବଶ୍ୟକ, କାରଣ ପ୍ରେମ ହେଉଛି ଦର୍ଶନ ଓ କ୍ଷମତାଠାରୁ ଶ୍ରେଷ୍ଠ । କିନ୍ତୁ ଯୁବକ ପ୍ରେମିକଜଣକ କିଛି ବୁଝିପାରି ନାହାନ୍ତି । ଓଗଛ ପକ୍ଷୀଟିକୁ ଏକ ସଙ୍ଗୀତପୂର୍ଣ୍ଣ ଗୀତ ଗାଇବାପାଇଁ ଅନୁରୋଧ କରିଛି । ସେ ମଧ୍ୟ ତତ୍‌କ୍ଷଣାତ୍ ଗାଇଛି । ଓକ୍ ଗଛ ଦୁଃଖ ପ୍ରକାଶ କରିଛି ଏବଂ ଏକାନ୍ତ ହୋଇଯାଇଛି । ଯୁବ-ଛାତ୍ରଜଣକ ଉତ୍ସର୍ଗର ଭାଷାକୁ ବୁଝିପାରି ନାହାନ୍ତି । ସେ ବୁଲ୍‌ବୁଲ୍ ପାଇଁ ଦୁଃଖ ପ୍ରକାଶ କରିଛନ୍ତି । ସେ କହିଛନ୍ତି ଯେ ତା’ର ଗୀତଗୁଡ଼ିକ ଅର୍ଥହୀନ ଓ ସେଥ‌ିରେ ବାସ୍ତବତାର ମୂଲ୍ୟବୋଧ ନାହିଁ । ବୁଲ୍‌ବୁଲ୍‌ ପ୍ରତି ଏହି ମନୋଭାବକୁ ଯୁବକଜଣକ ତା’ର ଟିପାଖାତାରେ ଲେଖି ରଖିଛନ୍ତି ।

Glossary:
still: ତଥାପି
lying: ପଡ଼ିଥିଲା
you …. rose: The nightingale promises to bring the young student a red rose.
whispered: ଆସ୍ତେ ଆସ୍ତେ କହିବା
lonely : ଏକୁଟିଆ
bubbling: ପାଣି ଫୁଟିବା ଶବ୍ଦ
stain: ବିଦ୍ଧ କରିବା
mightier: more powerful (ଅଧିକ ଶକ୍ତିଶାଳୀ)
heart’s blood: ହୃଦୟର ରକ୍ତ
honey: ମହୁ
pull: ଟାଣି ଆଣିବା
sacrifice: ବଳିଦାନ
fell asleep: ତ୍ୟାଗ କରିବା

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Think it out

Question 1.
What does the nightingale expect from the student in exchange of a red rose?
Answer:
The nightingale is ready to give a red rose to the student, but she wants an assurance from him in exchange: He should be a true lover. The reason is not far to seek. Philosophy, she says, is not as wise as Love, and Love is more forceful than Power.

Question 2.
What does the student write about the nightingale in his notebook?
Answer:
The young student fails to understand anything from the nightingale’s words. He doubts her feelings. He identifies the nightingale with most artists who are stylish, but not sincere. She does not understand the language of sacrifice. Music is her life. Her voice sounds melodious. Her songs are meaningless. They lack practical value. He expresses pity for the nightingale. These are the student’s feelings about the nightingale which he writes in his note-book.

Unit – IV

Gist:
The nightingale flies to the Rose-tree growing beneath the student’s door when the moon shines in heavens. Pinching her own heart against the thorn of the Rose-tree, she keeps on singing throughout the night. As the night advances, the tree appeals to the bird to come closer against the thorn, because the red rose will bloom before the advent of the day. As a believer of true and eternal love, she tries her best to respond the tree’s persistent call to press closer and closer to the thorn. At last, the inevitable happens. The bird turns the white rose red with her own blood. In other words, the red rose appears. The nightingale suffers a lot. She offers her life as an ultimate sacrifice in the name of love that the student feels for the Professor’s daughter.

ସାରମର୍ମ:
ଛାତ୍ରଟିର ଝରକାତଳେ ବଢୁଥିବା ଗୋଲାପ ଗଛ ପାଖକୁ ବୁଲ୍‌ବୁଲ୍‌ଟି ଉଡ଼ିଯାଇଛି । ଆକାଶରେ ଚନ୍ଦ୍ର ଉଦିତ ହୋଇଛି । ଏକ ଧଳା ଗୋଲାପର କଣ୍ଟାରେ ନିଜର ହୃଦୟକୁ ବିଦ୍ଧ କରି ବୁଲ୍‌ବୁଲ୍ ରାତିସାରା ଗୀତ ଗାଇଛି । ରାତି ବଢ଼ିବଢ଼ି ଚାଲିଛି । ଗୋଲାପ ଗଛଟି ବୁଲ୍‌ବୁଲ୍‌କୁ କଣ୍ଟା ଦେହରେ ଅଧ୍ଵ ଚାପି ହୋଇଯିବାକୁ ନିବେଦନ କରିଛି । କାରଣ ଦିନ ହେବା ପୂର୍ବରୁ ଲାଲ୍ ଗୋଲାପ ଫୁଟି ସାରିଥିବା ଦରକାର । ଯେହେତୁ ବୁଲ୍‌ବୁଲ୍ ଚିରନ୍ତନ ପ୍ରେମରେ ବିଶ୍ଵାସ କରେ, ତେଣୁ ସେ ଗୋଲାପ ଗଛର କଥାନୁସାରେ ସେହି କଣ୍ଟା ନିକଟକୁ ଅଧ‌ିକ ଲାଗିଯାଇଛି । ଶେଷରେ ସତ୍ୟର ହିଁ ପ୍ରକଟ ଘଟିଛି । ପକ୍ଷୀଟି ସେହି ଧଳା ଗୋଲାପକୁ ଲାଲ୍ ଗୋଲାପରେ ପରିବର୍ତ୍ତନ କରିଦେଇଛି । ଅର୍ଥାତ୍ ଲାଲ୍ ଗୋଲାପର ଆବିର୍ଭାବ ହୋଇଛି । ବୁଲ୍‌ବୁଲ୍ ବହୁତ ଯନ୍ତ୍ରଣା ପାଇଛି । ପ୍ରେମ ପାଇଁ ସେ ଜୀବନ ଉତ୍ସର୍ଗ କରିଛି।

Glossary:
heavens: ଆକାଶ
ebbed away: finished (ଶେଷ ହୋଇଗଲା)
marvellous: very beautiful ସୁନ୍ଦର )
petal: ପତ୍ରକ
maid: ଝିଅ
delicate:ସୂକ୍ଷ୍ମ
flush: ଝଲକ
press: put pressure (ଚାପ ଦେବା)
bitter: ତୀବ୍ର
thorn: କଣ୍ଟା
Love ….. tomb : Love isdeathless.(ପ୍ରେମର ମୃତ୍ୟୁ ନାହିଁ ।)
fainter: ମୂର୍ଚ୍ଛିତ
choking: ରୁଦ୍ଧ ହୋଇଯିବା
ecstasy: great delight (ପରମ ଆନନ୍ଦ)
the Nightingale .. answer: The nightingale was dead.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Think it out

Question 1.
What does the nightingale do to get a red rose?
Answer:
To get a red rose the nightingale flies to the Rose-tree growing beneath the student’s door when the moon shines in the heavens. She presses her heart closer and closer to the thorn of the Rose-tree, singing throughout the night. As the night advances, the thorn pierces her heart more and more, and her life-blood exists no more.

Question 2.
What kind of songs does the nightingale sing?
Answer:
At first the nightingale sings of the emergence of love in the heart of a boy and a girl. There is no end to her song. With the advancement of night, she sings of the birth of passion that arises in the soul of both man and woman. The last song the nightingale sings is the song of Love that knows no death. In other words, the bird lastly sings the song of Love that defies space and time.

Question 3.
What is the effect of each song?
Answer:
The effect of the nightingale’s song is amazing. At first the nightingale sings of love in the heart of a boy and a girl putting her heart against the thorn and there blossoms a marvellous rose, petal after petal oh the top-most branch of the Rose-tree. When the nightingale sings of the birth of passion that emerges in the soul of man and woman in a louder voice, a delicate flush comes into the leaves of the rose. At last when the nightingale sings the song of Love in a faint voice the marvelous rose becomes crimson.

Unit – V

Gist :
It is noon. To his stunned disbelief the student sees the most beautiful red rose in his life. He hurriedly goes to the Professor’s home with the rose in his hand. Now with the reddest rose in the world at the disposal of the Professor’s daughter, the young student has a radiant vision of the night. They will dance together that night when he will express how deeply he loves her. Here is a dramatic twist in the story. The girl finds the red rose almost insulting, because she prefers jewels and gifts. Moreover, the boy, far from suffering her ingratitude, proves to be ungrateful to himself by tossing the flower aside and declaring that Logic is greater than Love.

ସାରମର୍ମ :
ଏହା ଥିଲା ମଧ୍ୟାହ୍ନ ସମୟ । ନିତାନ୍ତ ଅବିଶ୍ଵାସ୍ୟ ହୋଇଥିଲେ ହେଁ ଯୁବ-ଛାତ୍ରଜଣକ ତାଙ୍କ ଜୀବନରେ ସୁନ୍ଦର ଲାଲ୍‌ରଙ୍ଗର ଗୋଲାପ ଫୁଲଟିଏ ଦେଖିବାକୁ ପାଇଛନ୍ତି । ସେହି ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପ ଫୁଲଟିକୁ ଧରି ସେ ପ୍ରଫେସରଙ୍କ ଝିଅ ନିକଟକୁ ଯାଇଛନ୍ତି । ବର୍ତ୍ତମାନ ପୃଥ‌ିବୀର ସବୁଠାରୁ ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପ ସେହି ତରୁଣୀଙ୍କ ହାତ ପାହନ୍ତାରେ ପହଞ୍ଚିଛି । ଯୁବକଜଣଙ୍କ ମୁଖମଣ୍ଡଳରେ ଏକ ଉଜ୍ଜଳ ହସ ଫୁଟି ଉଠିଛି । ସେ ଯେତେବେଳେ ଏକାଠି ନୃତ୍ୟ କରିବେ ସେ ତା’ର ସଚ୍ଚା ପ୍ରେମକୁ ପ୍ରକାଶ କରିବ ବୋଲି ଭାବିଛି । ମାତ୍ର ନାଟକୀୟ ଢଙ୍ଗରେ ଏଠାରେ ପରିବର୍ତ୍ତନ ଘଟିଛି । ଯୁବତୀଜଣକ ଏହି ଲାଲ୍ ଗୋଲାପକୁ ଅପମାନଜନକ ମନେ କରିଛି । ସେ ଚାହିଁଛି ଅଳଙ୍କାର ଓ ଉପହାର । ଯୁବକଜଣକ ନିଜ ପ୍ରେମିକାକୁ ଅକୃତଜ୍ଞ ମନେ କରିଛନ୍ତି ଏବଂ ଲାଲ୍ ଗୋଲାପକୁ ରାସ୍ତାକୁ ଫୋପାଡ଼ି ଦେଇଛନ୍ତି । ସେ ତର୍କଶାସ୍ତ୍ରକୁ ପ୍ରେମଠାରୁ ଅଧିକ ମହତ୍ତ୍ଵପୂର୍ଣ୍ଣ ବୋଲି ଘୋଷଣା କରିଛନ୍ତି ।

Glossary:
wonderful piece of luck! : ଭାଗ୍ୟର ଅପୂର୍ବ ଅଂଶ
leaned down : ତଳକୁ ଓହ୍ଲାଇଲା
plucked: ତୋଳିଲା
put on : wear (ପିନ୍ଧିବା)
frowned: ରାଗରେ ଗର୍ଜନ କଲା
Ungrateful: ଅକୃତଜ୍ଞ
cart-wheel: ଶଗଡ଼ ଚକ
rude: harsh (ନିର୍ଭୟ)
Logic: ତର୍କଶାସ୍ତ୍ର
dusty: dirty (ମଇଳା)
Metaphysics: ଆଧ୍ୟାତ୍ମିକ ଶାସ୍ତ୍ର

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Think it out

Question 1.
What does the student do with the red rose?
Answer:
The student goes to the Professor’s house with the red rose. He hands over the gift to the Professor’s daughter whom he loves deeply. The student wants the girl to dance with him that night, because in response to her request, he has given her the reddest rose in the world.

Question 2.
How does the Professor’s daughter respond to the student’s gift of the red rose?
Answer:
The Professor’s daughter flatly rejects the student’s gift of the red rose. She finds it almost insulting, since she prefers jewels and gifts. These are more expensive than flowers. The vain daughter of die Professor accuses the student of being harsh and ungrateful. She treats him with contempt. To his shocked disbelief, she rises from the chair and enters the house.

Question 3.
Why does the student return to his books?
Answer:
The Professor’s daughter discards the student’s gift of the red rose. As a result, he is in a rage. He suffers the anguish of the girl’s ingratitude and throws the red rose into the street, with a passing cart run wer it. The student realizes that it was all caprice on his part. He declares that Logic is greater than Love, because the latter is quite deceptive. In his view, in this crude age, to be practical matters most. Hence the student returns to his books.

CHSE Odisha Class 12 English The Nightingale and the Rose Important Questions and Answers

Multiple-Choice Questions (MCQs) with Answers

Question 1.
The student ________ a red rose.
(A) asked for
(B) ran after
(C) scrambled for
(D) panged in
Answer:
(D) panged in

Question 2.
In the student, the nightingale finds a _________.
(A) brilliant scholar
(B) a mad young boy
(C) true lover
(D) all of these
Answer:
(C) true lover

Question 3.
The nightingale sings of love ___________.
(A) off and on
(B) in a state of melancholy
(C) heedless of the external world
(D) for nights together
Answer:
(D) for nights together

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Question 4.
Love is _________.
(A) nice
(B) precious
(C) wonderful
(D) both (B) and (C)
Answer:
(B) precious

Question 5.
The butterfly and lizard __________ the student’s weeping for a red rose.
(A) look down
(B) looked down upon
(C) laughed at
(D) jeered
Answer:
(C) laughed at

Question 6.
The young student’s sorrow moved the nightingale to –
(A) tears
(B) pity
(C) excitement
(D) commitment
Answer:
(A) tears

Question 7.
The response of the first rose-tree to the nightingale’s appeal for a red rose was _________.
(A) negative
(B) positive
(C) ray of hope
(D) evasive
Answer:
(A) negative

Question 8.
The word ‘ nipped’ means ___________.
(A) plucked
(B) cut
(C) destroyed
(D) killed
Answer:
(C) destroyed

Question 9.
The condition set by the rose-tree growing beneath the student’s window to give the nightingale a red rose was ___________.
(A) ridiculous
(B) serious
(C) a very tough
(D) none of these
Answer:
(C) a very tough

Question 10.
The nightingale’s decision to get a red rose sacrificing her life is attributed to _________.
(A) supremacy of love over life
(B) her adoration of love
(C) her sympathy for the student
(D) her attachment to the student
Answer:
(A) supremacy of love over life

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Question 11.
The boy’s beautiful eyes gave a sign of _____________.
(A) hope
(B) strength
(C) sadness
(D) none of these
Answer:
(C) sadness

Question 12.
The tone of the nightingale is one of ___________.
(A) disillusionment
(B) certainty
(C) doubt
(D) assurance
Answer:
(D) assurance

Question 13.
The boy felt that the nightingale’s words are ____________.
(A) pragmatic
(B) absurd
(C) theoretical
(D) emotional
Answer:
(C) theoretical

Question 14.
The nightingale responded to the oak tree’s request for singing her last song for him ___________.
(A) sentimentally
(B) affirmatively
(C) sorrowfully
(D) none of these
Answer:
(B) affirmatively

Question 15.
The student always thinks of __________.
(A) reading books
(B) the nightingale
(C) artists
(D) love
Answer:
(D) love

Question 16.
Which one of the following statements is true?
(A) The nightingale sings for nights.
(B) It is a moon-lit night.
(C) At last, the nightingale sings the origin of love in the heart of a boy and a girl.
(D) Her life-blood becomes thicker
Answer:
(B) It is a moon-lit night.

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Question 17.
Which one of the following statements is false?
(A) The nightingale’s heart is away from the thorn.
(B) She sings on and on.
(C) At first, the rose petal looks pale.
(D) The nightingale obeys the words of the rose-tree.
Answer:
(A) The nightingale’s heart is away from the thorn.

Question 18.
With the nightingale’s song grow louder and louder, her song becomes more and more __________.
(A) melodious
(B) monotonous
(C) about the source of passion in the soul of a man and a maid
(D) none of these
Answer:
(C) about the source of passion in the soul of a man and a maid

Question 19.
The nightingale sings of love that is __________.
(A) timeless
(B) ephemeral
(C) transparent
(D) all of these
Answer:
(A) timeless

Question 20.
The nightingale’s life is marked by ___________.
(A) pain
(B) pleasure
(C) futility
(D) sacrifice
Answer:
(D) sacrifice

Question 21.
The rose the student sees is the most __________.
(A) fragrant
(B) alluring
(C) repulsive
(D) beautiful and the reddest
Answer:
(D) beautiful and the reddest

Question 22.
The Professor’s daughter discarded the student’s gift of red rose _________.
(A) reluctantly
(B) thoughtfully
(C) outright
(D) none of these
Answer:
(C) outright

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Question 23.
She epitomises ___________.
(A) determination
(B) vanity
(C) ingratitude
(D) both (A) and (B)
Answer:
(D) both (A) and (B)

Question 24.
At last, the student realises that love stands for _____________.
(A) all that is beautiful
(B) perfection
(C) foolishness
(D) nobility
Answer:
(C) foolishness

Question 25.
He reconciles himself to life’s __________.
(A) problems
(B) frustration
(C) unfulfillment
(D) reality
Answer:
(D) reality

Introducing the Author :
Oscar Wilde (1854-1900) was a gifted British poet, playwright, novelist and short story writer from Ireland. He associated himself with the literary movement of his time called aestheticism which defined the nature and purpose of art as an independent form free from any moral consideration. ‘Art never expresses anything but itself,’ wrote Wilde and in this view he has had his followers. His own poems, written accordingly, were a mixture of verbal felicity and affected sentiment. His well-known works include the comedy, The Importance of Being Earnest, the novel, The Picture of Dorian Gray, now filmed, and a number of short stories. Wilde was a brilliant conversationalist and his plays abound in smart brilliant dialogue. Today Wilde is best remembered for his short stories, which are available in volumes like The Happy Prince and Other Tales (1888) and A House of pomegranates (1891). Like all other writings of the author, the stories are marked by ‘sparkling wit, an eye for humorous situations, and an insight into human nature’. Among the stories there is a bundle of engaging tales meant for children. They describe in a simple and somewhat fairy tale fashion some meaningful happenings which contain a striking blend of truth and wisdom.

About the Story :
The main theme of Oscar Wilde’s short story “The Nightingale and the Rose” explores the effects of self-sacrifice in the name of what one truly believes in. As the title suggests, the Nightingale is the main character of the short story. The bird offers her life as an ultimate sacrifice in the name of love, thinking that this would have made a difference in the life of a student. Her sacrifice goes in vain.

“The Nightingale and the Rose” ଗଳ୍ପରେ ଜଣେ ନିଜର ଏକାନ୍ତ ବିଶ୍ଵାସ ନିମନ୍ତେ ଜୀବନ ଉତ୍ସର୍ଗ କରିବାର ଫଳାଫଳ ଉପରେ ଆଲୋକପାତ କରାଯାଇଛି । ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ଏହି ଗଛର ମୁଖ୍ୟ ଚରିତ୍ର । ପ୍ରେମର ଚିରନ୍ତନତାକୁ ବଜାୟ ରଖିବା ପାଇଁ ପକ୍ଷୀଟି ତା’ର ଜୀବନକୁ ଉତ୍ସର୍ଗ କରିଛି । ସେ ଚିନ୍ତା କରିଛି ଯେ ଛାତ୍ରଟିର ଜୀବନରେ ଏହା ଏକ ଭିନ୍ନ ଅବସ୍ଥା ସୃଷ୍ଟି କରିବ । କିନ୍ତୁ ତା’ର ଚରମ ଉତ୍ସର୍ଗ ବିଫଳତାରେ ପର୍ଯ୍ୟବସିତ ହୋଇଛି ।

CHSE Odisha Class 12 English Solutions Non-Detailed Chapter 1 The Nightingale and the Rose

Summary :
The Professor’s daughter is the young Oxford student’s true love. She is ready to dance with him if he brings her a red rose. The Student feels sad, because there is no red rose in the garden. The Nightingale hears the young man’s pine for a red rose. In him the bird sees a ‘true lover’. The young Student visualises his state of loneliness without dancing with the girl he loves. The sight of her darling with others will bring him a deepening frustration.

The absence of a red rose torments him. The young Student’s love makes the Nightingale think how she sings song of love for nights together. She profuses, praises love which is a wonderful thing, more valuable than any other and costlier than fine opals. Love she says, is priceless. The Nightingale admires the young student for his painful love. The sight of the weeping young Student for a red rose has no effect on a little Green Lizard and Butterfly. They don’t share his sorrow.

To them, the student’s eagerness for a red rose appears ridiculous. But the Nightingale understands his secret. She wonders at the mystery of love. The Nightingale is moved to pity by the young Student’s sorrow. She wishes to find a red rose as a gift for him. She leaves the Oak-tree in search of it. While flying higher, she catches sight of a beautiful Rose-tree and requests it to give her a red rose in exchange of her beautiful song.

To the Nightingale’s disappointment, the tree states that its roses are white. But the Nightingale find a ray of hope, when the Rose-tree wants her to go to his brother that grows beneath the student’s window. The bird flies over to the Tree and appeals for a red rose, but in vain. In spite of growing red roses, they have now turned into white ones. The biting winter has destroyed its buds. Storm has wrecked havoc.
The Nightingale still asks the Tree for a red rose. It succumbs to her will. The Tree is ready to give her a red rose, if she sings to it throughout the night with her breast against the thorn. Her life-blood will turn the white rose into a red one. The Nightingale is ready to sacrifice her life for the sake of love.

Brimming with joy, the bird meets the love-stricken young Student and promises him to bring him a red rose. But she wants an assurance from him in return. He will be a true lover. He listens, but cannot make out what the Nightingale is saying. But the Oak-tree understands, feels sad. He wants the bird to sing him one last song, for he will be lonely without her. Soon after the completion of her song, the Student writes about the bird’s music, style, her lack of sincerity and sacrifice for others in his note book.

The Nightingale flies to the Rose-tree growing beneath the Student’s window when the moon shines in the heavens. She believes in true and eternal love. She pinches her own heart against the thorn of the Rose-tree and turns it red with her own blood. She sacrifices her life in the name of love. It is noon. The Student’s delight knows no bound at the sight of a beautiful red rose. He meets the Professor’s daughter with it, but she rejects the rose and in turn, the Student throws the red rose away in the gutter, with a passing cart running over it. The Nightingale’s ultimate sacrifice for the cause of true love goes in vain.

ସାରାଂଶ :
ଅକ୍‌ସଫୋର୍ଡର ଜଣେ ଯୁବ-ଛାତ୍ର ପ୍ରେମ କରନ୍ତି ପ୍ରଫେସରଙ୍କର ଝିଅକୁ । ଯଦି ସେ ପ୍ରେମିକାଙ୍କ ପାଇଁ ଗୋଟିଏ ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପ ଫୁଲ ଆଣିବେ, ତେବେ ତରୁଣୀ ପ୍ରେମିକା ତାଙ୍କ ସଙ୍ଗେ ନୃତ୍ୟ ପରିବେଷଣ କରିବ ବୋଲି ସର୍ଭ ରଖୁଛି ।ରଖୁଛି । ଛାତ୍ରଟି ଦୁଃଖରେ ଭାଙ୍ଗିପଡ଼ିଛି କାରଣ ସେହି ବଗିଚାରେ ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପ ମିଳିନାହିଁ । ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପ ପାଇବାପାଇଁ ଯୁବକର ବ୍ୟାକୁଳତା ଜାଣିପାରେ । ସେହି ଯୁବକଙ୍କଠାରେ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ଦେଖେ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ସଚ୍ଚା ପ୍ରେମିକର ପ୍ରତିମୂର୍ତ୍ତି ।

ନିଜ ପ୍ରେମିକା ଯୁବତୀଙ୍କ ସହିତ ନୃତ୍ୟ କରିନପାରିବାର ଏକାନ୍ତ ନିଃସଙ୍ଗ ଅବସ୍ଥା ବିଷୟରେ ଯୁବଛାତ୍ରଜଣକ ଭାବିଛି । ତାଙ୍କର ପ୍ରିୟ ପ୍ରେୟସୀ ତାଙ୍କୁ ଛାଡ଼ି ଅନ୍ୟ ଜଣଙ୍କ ସହ ନୃତ୍ୟ କରିବା ସେ ଆଦୌ ସହ୍ୟ କରିପାରିବେ ନାହିଁ । ତାଙ୍କର ଜୀବନ ପ୍ରତି ବିତୃଷ୍ଣା ଆସିଯାଏ । ଲାଲ୍ ଗୋଲାପ ନ ପାଇ ସେ ମାନସିକ ଯନ୍ତ୍ରଣା ପାଆନ୍ତି । ଯୁବ-ଛାତ୍ରଙ୍କର ପ୍ରେମକୁ ଦେଖି ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ଭାବେ ସେ କିଭଳି ରାତି ରାତି ଧରି ପ୍ରେମର ଗୀତ ଗାଇଥାଏ । ସେ ଭାବେ ସବୁଠାରୁ ମୂଲ୍ୟବାନ୍ ହେଉଛି ପ୍ରେମ । ପ୍ରେମ ଆଗରେ ସବୁ ଜିନିଷ ତୁଚ୍ଛ । ପ୍ରେମର ମୂଲ୍ୟ କେହି ଦେଇପାରିବେ ନାହିଁ । ଏହି ଯନ୍ତ୍ରଣାଦାୟକ ପ୍ରେମ ପାଇଁ ବୁଲ୍‌ବୁଲ୍ ଯୁବକଙ୍କୁ ପ୍ରଶଂସା କରିଛି । ଏକ ଲାଲ୍ ଗୋଲାପ ଫୁଲ ପାଇବାପାଇଁ ଯୁବ- ଛାତ୍ରଙ୍କର କ୍ରନ୍ଦନର ମୂଲ୍ୟ ଏକ ଛୋଟ ନୀଳବର୍ଣ୍ଣର ଝିଟିପିଟି ପ୍ରଜାପତି କିଛି ବୁଝିପାରନ୍ତି ନାହିଁ । ସେମାନେ ଯୁବକଙ୍କର ଦୁଃଖରେ ଭାଗିଦାର ହୋଇପାରନ୍ତି ନାହିଁ । ଛାତ୍ରଟିର ଲାଲ୍ ଗୋଲାପ ପାଇବାର ଆକାଂକ୍ଷାକୁ ସେମାନେ ପରିହାସ କରନ୍ତି । କିନ୍ତୁ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ବୁଝେ ପ୍ରେମିକ ଯୁବକ ମନରେ ଲୁକ୍‌କାୟିତ ହୋଇଥିବା ପ୍ରେମର ଆସରକୁ । ପ୍ରେମର ରହସ୍ୟକୁ ଦେଖୁ ସେ ଆଶ୍ଚର୍ଯ୍ୟ ହୋଇଯାଏ ।

ଯୁବ-ଛାତ୍ରଙ୍କର ଦୁଃଖରେ ବୁଲ୍‌ବୁଲ୍ ଦୁଃଖ ପ୍ରକାଶ କରେ । ସେ ପ୍ରେମିକ ଯୁବକଙ୍କୁ ଉପହାର ଭାବେ ଏକ ଲାଲ ଗୋଲାପ ଦେବା ପାଇଁ ଇଚ୍ଛା କରେ । ସେ ସେହି ଓକ୍ ବୃକ୍ଷ ଛାଡ଼ି ଲାଲ୍ ଗୋଲାପର ଅନୁସନ୍ଧାନରେ ଚାଲିଯାଏ । ଉପରେ ଉଡ଼ି ଉଡ଼ି ଯାଉଥ‌ିବା ସମୟରେ ସେ ଦେଖେ ଏକ ସୁନ୍ଦର ଗୋଲାପ ଗଛ ଯାହାକୁ ସେ ତା’ର ସୁନ୍ଦର ଗୀତ ବଦଳରେ ଏକ ଲାଲ୍ ଗୋଲାପ ଦେବାପାଇଁ ଅନୁରୋଧ କରେ । କିନ୍ତୁ ଗୋଲାପ ବୃକ୍ଷଟି କହେ ତା’ପାଖରେ କେବଳ ଧଳା ଗୋଲାପ ଅଛି । ଏହା ଶୁଣି ବୁଲ୍‌ବୁଲ୍ ମନ ଦୁଃଖରେ ଭାଙ୍ଗିପଡ଼େ । ପୁନଶ୍ଚ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ମନରେ ଆଶାର ଆଲୋକ ସଞ୍ଚାର ହୁଏ ଯେତେବେଳେ ସେହି ଗୋଲାପ ବୃକ୍ଷଟି କହେ ତା’ର ଭାଇ ଯିଏକି ସେହି ପ୍ରେମିକ ଯୁବକଙ୍କର ଝରକାତଳେ ଅଛି, ତା’ ପାଖରେ ଲାଲ୍ ଗୋଲାପ ଅଛି । ବୁଲ୍‌ବୁଲ୍‌ ସେହି ଗୋଲାପ ଗଛ ପାଖକୁ ଯାଏ ଏବଂ ଏକ ଲାଲ୍ ଗୋଲାପ ଦେବାପାଇଁ ଅନୁରୋଧ କରେ । କିନ୍ତୁ ସଫଳ ହୁଏ ନାହିଁ । ଗୋଲାପ ଗଛଟି କହେ ଯେ ତା’ର ଲାଲ୍ ଗୋଲାପଗୁଡ଼ିକ ବର୍ତ୍ତମାନ ଧଳା ହୋଇଯାଇଛନ୍ତି । ଭୀଷଣ ଥଣ୍ଡା ଏହାର କଢ଼ିଗୁଡ଼ିକୁ ନଷ୍ଟ କରିଦେଇଛି । ଝଡ଼ ସବୁ ଧ୍ବଂସ କରିଦେଇଛି ।

ତଥାପି ମଧ୍ୟ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ଏକ ଲାଲ୍ ଗୋଲାପ ପାଇବାପାଇଁ ଗଛଟିକୁ ଅନୁରୋଧ କରିଛି । ଗଛଟି କହିଛି ଯେ ସେ ଏକ ଲାଲ୍ ଗୋଲାପ ଦେବାପାଇଁ ପ୍ରସ୍ତୁତ; ଯଦି ବୁଲ୍‌ବୁଲ୍ ରାତିସାରା ତା’ର କଣ୍ଟାକୁ ଛାତିରେ ଲଗାଇ ରଖି ଗୀତ ଗାଇବ । ବୁଲ୍‌ବୁଲ୍‌ଠାରୁ ଝରିତ ଲାଲ ରକ୍ତ ସେହି ଧଳା ରଙ୍ଗର ଗୋଲାପକୁ ଲାଲ୍ କରିଦେବ । ବୁଲ୍‌ବୁଲ୍ ସଚ୍ଚା ପ୍ରେମ ପାଇଁ ତା’ର ଜୀବନକୁ ଉତ୍ସର୍ଗ କରିବାପାଇଁ ପ୍ରସ୍ତୁତ ହୋଇଛି ।
ଖୁସିରେ ଆତ୍ମହରା ହୋଇ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ସେହି ପ୍ରେମିକ ଯୁବ-ଛାତ୍ରଙ୍କ ନିକଟକୁ ଯାଇଛି ଏବଂ ତାଙ୍କ ପାଇଁ ଏକ ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପ ଫୁଲ ଆଣିଦେବାପାଇଁ ପ୍ରତିଜ୍ଞା କରିଛି । କିନ୍ତୁ ବୁଲ୍‌ବୁଲ୍ ଚାହେଁ ଯୁବକଜଣକ ଜଣେ ସଚ୍ଚା ପ୍ରେମିକ ହୁଅନ୍ତୁ । ସେ ଶୁଣନ୍ତି, କିନ୍ତୁ ବୁଲ୍‌ବୁଲ୍ କ’ଣ କହୁଛି କିଛି ବୁଝିପାରନ୍ତି ନାହିଁ । ଓକ୍ ବୃକ୍ଷ ଦୁଃଖ ପ୍ରକାଶ କରିଛି । ସେ ଚାହିଁଛି ପକ୍ଷୀଟି ତାଙ୍କ ପାଇଁ ଶେଷ ଗୀତ ଗାଉ, କାରଣ ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀ ବିନା ଓକ୍ ବୃକ୍ଷ ଏକାନ୍ତ ହୋଇଯିବ । ପକ୍ଷୀଟିର ଗୀତର ସମାପ୍ତି ପରେ, ଛାତ୍ରଟି ପକ୍ଷୀର ସଙ୍ଗୀତ ତଥା ଶୈଳୀ ଏବଂ ଅନ୍ୟମାନଙ୍କ ତା’ର ତ୍ୟାଗ ମନୋବୃତ୍ତିର ଅଭାବ ବିଷୟରେ ଟିପ୍‌ପଣୀ ଲେଖୁଛି ।

ଯେତେବେଳେ ଚନ୍ଦ୍ର ଉଦୟ ହୋଇଛି, ବୁଲ୍‌ବୁଲ୍ ପକ୍ଷୀଟି ସେହି ଛାତ୍ରଙ୍କ ଝରକା ତଳେ ଥିବା ଗୋଲାପ ଗଛ ନିକଟକୁ ଉଡ଼ିଯାଇଛି । ସେ ଚିରନ୍ତନ ପ୍ରେମ ଉପରେ ବିଶ୍ଵାସ କରେ । ଏକ ଧଳା ରଙ୍ଗର ଗୋଲାପର କଣ୍ଟା ଉପରେ ସେ ତା’ର ହୃଦୟକୁ ବିଦ୍ଧ କରିଛି ଏବଂ ନିଜର ରକ୍ତରେ ସେହି ଧଳା ରଙ୍ଗର ଗୋଲାପକୁ ରକ୍ତବର୍ଣ୍ଣର ଲାଲ୍ ଗୋଲାପରେ ପରିଣତ କରିପାରିଛି । ଯୁବକର ପ୍ରେମ ପାଇଁ ସେ ତା’ର ଜୀବନକୁ ଉତ୍ସର୍ଗ କରିଦେଇଛି ।

ଏହା ହେଉଛି ମଧ୍ୟାହ୍ନ ସମୟ । ଛାତ୍ରଟି ବଗିଚାରେ ଏକ ଲାଲ୍ ଗୋଲାପ ଫୁଲ ଦେଖ୍ ଖୁବ୍ ଖୁସି ହୋଇଯାଇଛି । ସେ ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପଟିକୁ ସାଙ୍ଗରେ ନେଇ ପ୍ରଫେସରଙ୍କର ଝିଅଙ୍କୁ ସାକ୍ଷାତ୍ କରିଛି, କିନ୍ତୁ ଯୁବତୀଜଣକ ଯୁବକଙ୍କର ପ୍ରେମକୁ ପ୍ରତ୍ୟାଖ୍ୟାନ କରିଛି ଏବଂ ଯୁବକଜଣକ ସେହି ଲାଲ୍ ରଙ୍ଗର ଗୋଲାପଟିକୁ ରାସ୍ତାକୁ ଫୋପାଡ଼ି ଦେଇଛି । ବୁଲ୍‌ବୁଲ୍‌ର ଯୁବକର ପ୍ରେମ ପାଇଁ ଚରମ ଉତ୍ସର୍ଗ ବୃଥା ହୋଇଯାଇଛି ।

CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c)

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Exercise 8(c)

Question 1.
Find the intervals where the following functions are (a) increasing and (b) decreasing.
(i) y = sin x, x ∈ [0, 2π]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.1(1)

(ii) y = In x, x ∈ R+
Solution:
\frac{d y}{d x} = \frac{1}{x} > 0
for all x ∈ R+.
Thus y = In x is increasing in (0, ∞) and decreasing nowhere.

CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c)

(iii) y = ax, a > 0, x ∈ R
Solution:
\frac{d y}{d x} = ax In a > 0 for all x ∈ R provided a > 1.
The function is increasing in (-∞, ∞) is a > 1.
Again \frac{d y}{d x} = ax In a < 0 if 0 < a < 1.
Thus the function is decreasing in (-∞, ∞) if (0 < a < 1)

(iv) y = sin x + cos x, x ∈ [0, 2π]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(a) Q.1(4)

(v) y = 2x3 + 3x2 – 36x – 7
Solution:
\frac{d y}{d x} = 6x2 – 6x – 36
y is increasing if \frac{d y}{d x} > 0
⇒ x2 + x – 6>0
⇒ x2 + 3x – 2x – 6>0
⇒ x (x + 3) -2 (x + 3) > 0
⇒ (x + 3) (x – 2) > 0
for x > 2 or x < -3 and (x + 3 ) (x – 2) < 0 for -3 < x < 2
∴ The function is increasing in (-∞, -3) ∪ (2, ∞) and is decreasing in (-3, 2).

(vi) y = \frac{1}{x-1^{\prime}} x ≠ 1
Solution:
\frac{d y}{d x} = \frac{-1}{(x-1)^2}
The function is increasing if \frac{d y}{d x} > 0
\frac{-1}{(x-1)^2} > 0 which is impossible because \frac{-1}{(x-1)^2} is always -ve for all x ≠ 1. So the function is increasing nowhere. It is decreasing in R – {1}

(vii) y = \left\{\begin{array}{cc} x^2+1, & x \leq-3 \\ x^3-8 x+13, & x>-3 \end{array}\right.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.1(7)

(viii) y = 4x2 + \frac{1}{x}
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.1(8)

CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c)

(ix) y = (x – 1)2 (x + 2)
Solution:
\frac{d y}{d x} = 2 (x – 1) (x + 2) + (x – 1)2
= (x – 1) (2x + 4 + x – 1)
= (x – 1 ) (3x + 3)
= 3 (x – 1) (x + 1 )
The function is increasing if \frac{d y}{d x} > 0.
⇒ (x + 1) (x – 1) > 0
⇒ x < -1 or x > 1
∴ The function is increasing in (-∞, -1) ∪ (1, ∞)
It is decreasing in (-1, 1).

(x) y = \frac{\ln x}{x}, x > 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.1(10)

(xi) y = tan x – 4 (x – 2), x ∈ (-\frac{\pi}{2}, \frac{\pi}{2})
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.1(11)

(xii) y = sin 2x – cos 2x, x ∈ [0, 2π]
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.1(12)

Question 2.
Give a rough sketch of the functions given in question 1.
Solution:
Do yourself.

Question 3.
Show that the function \frac{e^x}{x^p} is strictly increasing for x > p > 0.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.3

CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c)

Question 4.
Show that 2 sin x + tan x ≥ 3x for all x ∈ (0, \frac{\pi}{2}).
Solution:
Let f(x) = 2 sin x + tan x – 3x
Then f(x) = 2 cos x + sec2 x – 3
CHSE Odisha Class 12 Math Solutions Chapter 8 Application of Derivatives Ex 8(c) Q.4