Regular revision with Class 7 Maths MCQ with Answers and Ganita Prakash Class 7 Maths Chapter 4 Expressions using Letter Numbers MCQ improves accuracy in objective exams.
MCQ on Expressions using Letter Numbers Class 7
Expressions using Letter Numbers MCQ Class 7
Class 7 Maths Expressions using Letter Numbers MCQ
Question 1.
The value of the expression 2x – 7, when x = 5, is:
(a) 7
(b) 5
(c) 3
(d) -4
Solution:
(c) 3
Putting x = 5 in the expression 2x – 7, we get
2 × 5 – 7 = 10 – 7 = 3
Question 2.
The value of the expression 4p + 8q – 10, when p = 3 and q = -1, is:
(a) 8
(b) -24
(c) 14
(d) -6
Solution:
(d) -6
Putting p = 3 and q = – 1 in the expression
4p + 8q – 10,
we get 4 × 3 + 8 × (- 1) – 10 = 12 – 8 – 10
= 12 – 18 = – 6
Question 3.
The simplified form of 9x + 2y + 3x – 7y is:
(a) 12x – 5y
(b) 7xy
(c) 11x – 4y
(d) -3xy
Solution:
(a) 12x – 5y
Given, 9x + 2y + 3x – 7y
Here, 9x and 3x are like terms; 2y and -7y are like terms.
So, 9x + 2y + 3x – 7y = 9x + 3x + 2y – 7y
= 12x – 5y
Question 4.
Shown alongside is a BALANCED hanger using circular and triangular cut-outs. The weight of each circular cut-out is 1 unit and of each triangular cut-out is p units.
Which of the following will help in finding the weight of triangular cut-out?
(a) 6p = 7p
(b) 2p + 4 = 5p + 2
(c) 2(p + 4) = 5(p + 2)
(d) 4p + 2 = 2p + 5
Solution:
(b) 2p + 4 = 5p + 2
Left side: 4 circles and 2 triangles
Right side: 2 circles and 5 triangles
Thus, total weight on left side
= 4 × 1 + 2 × p = (4 + 2p) units
And total weight on right side
= 2 × 1 + 5 × p = (2 + 5p) units
Since the hanger is balanced, both sides must have equal weight.
∴ Weight on left side = Weight on right side
⇒ 4 + 2p = 2 + 5p
⇒ 2p + 4 = 5p + 2
Question 5.
Niharika is printing posters for an event using her home printer. It takes 15 seconds to set up the printer before it starts printing. Once it starts, each poster takes 6 seconds to print. Which of the following expressions shows the total time (in seconds) needed to print4p’ posters, assuming the printer is off initially?
(a) 15 + 6 + p
(b) (15 + 6)p
(c) 15 × 6p
(d) 15 + 6p
Solution:
(d) 15 + 6p
Time taken to set up the printer = 15 seconds (this happens only once).
Time taken to print 1 poster = 6 seconds
Therefore, time taken to print ‘p’ posters = 6p seconds
Thus, total time needed to print ‘p’ posters
= Time taken to set up the printer + Time taken to print ‘p’ posters = (15 + 6p) seconds
Question 6.
The simplified form of 5m – 2n – 7m + 10n + 3 is:
(a) 3
(b) 3m + 3n + 3
(c) 2m + 8n
(d) -2m + 8n + 3
Solution:
(d) -2m + 8n + 3
Given, 5m – 2n – 7m + 10n + 3
Here, 5m and -7m are like terms; -2n and 10n are like terms.
So, 5m – 2n – 7m + 10n + 3
= 5m – 7m – 2n + 10n + 3
= -2m + 8n + 3
Question 7.
Shown below is a representation of one of the properties of whole numbers.
Which of the following represents the property shown?
(a) a(b + c) = a × b + a × c
(b) a + b = b + a
(c) a × (b × c) = a × (b × c)
(d) a + (b + c) = (a + b) + c
Solution:
(a) a(b + c) = a × b + a × c
From figure, we have
Area on left side = Area on right side
⇒ 16 × 8 = 12 × 8 + 4 × 8
[∵ Area of rectangle = Length × Breadth]
⇒ 8 × 16 = 8 × 12 + 8 × 4
⇒ 8 × (12 + 4) = 8 × 12 + 8 × 4
[∵ 16 = 12 + 4]
Suppose a = 8, b = 12 and c = 4, we get
a(b + c) = a × b + a × c
Question 8.
Amit sells cold drinks and sandwiches at a school canteen. One cold drink costs ₹25 and one sandwich costs ₹40.
If m cold drinks and n sandwiches were sold in a day, which of the following expressions shows the total amount earned (in rupees) that day?
(a) 25m + 40n
(b) (25 + 40) × (m + n)
(c) 40m + 25n
(d) (25 + 40) × m + n
Solution:
(a) 25m + 40n
Cost of 1 cold drink = ₹25
Cost of 1 sandwich = ₹40
Money earned from m cold drinks
= 25 × m = 25m
Money earned from n sandwiches
= 40 × n = 40n
Total earnings = 25m + 40M
Question 9.
The formula of the given number machine is:
(a) 2a + b
(b) a × b + 5
(c) a + 5 × b
(d) None of these
Solution:
(b) a × b + 5
We can see,
4 × 1 + 5 = 445 = 9, 7 × 0 + 5 = 0 + 5 = 5,
3 × 2 + 5 = 6 + 5 = 11, 5 × 3 + 5 = 15 + 5 = 20
Here, the rule followed is “5 more than the product of two numbers”.
Thus, if two numbers are a and b, the formula for the given machine is a × b + 5.
Question 10.
Consider the following number machine:
What is the missing input?
(a) 8
(b) 10
(c) 12
(d) 15
Solution:
(a) 8
We can see,
4 × 3 + 2 × 2 = 12 + 4 = 16,
5 × 3 + 2 × 2=15 + 4=19,
7 × 3 + 3 × 2 = 21 + 6 = 27,
9 × 3 + 3 × 2 = 27 + 6 = 33
So, the rule for the given machine in algebraic expression is,
Output = a × 3 + b × 2, where a and b are inputs.
When output = 34 and b = 5,
34 = a × 3 + 5 × 2
⇒ 34 = 3a + 10 ⇒ 3a = 34 – 10 = 24
⇒ a = \(\frac{24}{3}\) = 8 3
Thus, the missing input is 8.
Question 11.
The value of expression 6m – 7n is:
(i) 6, when m = 4 and n = 2.
(ii) 9, when m = 5 and n = 3.
(iii) -9, when m = 2 and n = 3.
(iv) 10, when m = 3 and n = 1.
Choose the correct option from the following:
(a) (i) and (ii)
(b) (ii) and (iii) only
(c) (ii), (iii) and (iv)
(d) (i) and (iv)
Solution:
(b) (ii) and (iii) only
When m = 4 and n = 2;
6m – 7n = 6 × 4 – 7 × 2 = 24 – 14 = 10
When m = 5 and n = 3;
6m – 7n = 6 × 5 – 7 × 3 = 30 – 21 = 9
When m = 2 and n = 3;
6m – 7n = 6 × 2 – 7 × 3 = 12 – 21 = – 9
When m = 3 and n = 1;
6m – 7n = 6 × 3 – 7 × 1 = 18 – 7 = 11
So, (ii) and (iii) are correct.
Question 12.
If p is a number, then which of the following statements are correct?
(i) 2 more than 3 times the number is 2p + 3.
(ii) 4 less than 7 times the number is 7p – 4.
(iii) 4 more than 5 times the number is 5p + 4.
(iv) 8 less than 4 times the number is 8p – 4.
Choose the correct option from the following:
(a) (i) and (ii)
(b) (ii) and (iii) only
(c) (ii), (iii) and (iv)
(d) (i) and (iv)
Solution:
(b) (ii) and (iii) only
(i) 2 more than 3 times the number is 2 + 3 × p
= 3p + 2.
(ii) 4 less than 7 times the number is 7 × p – 4
= 7p – 4.
(iii) 4 more than 5 times the number is 4 + 5 × p
= 5p + 4.
(iv) 8 less than 4 times the number is 4 × p – 8
= 4p – 8.
So, (ii) and (iii) are correct.
Question 13.
The expression 5x – 3y + 4 is equivalent to
(i) 7x – 2y – (2x + y + 2) + 6
(ii) 5x – y + 3 – 2(y + 2x) + 1
(iii) x – y – (2y – 4x) + 4
(iv) 2(2y – x – 2) + 7(1 – y + x) + 1
Choose the correct option from the following:
(a) (i) only
(b) (ii) and (iii) only
(c) (i), (iii) and (iv) only
(d) (i), (ii), (iii) and (iv)
Solution:
(c) (i), (iii) and (iv) only
(i) 7x – 2y – (2x + y + 2) + 6
= 7x – 2y – 2x – y – 2 + 6
= (7x – 2x) + (-2y – y) + 4
= 5x + (-3y) + 4 = 5x – 3y + 4
(ii) 5x – y + 3 – 2(y + 2x) + 1
= 5x – y + 3 – 2y – 4x + 1
= (5x – 4x) + (-y – 2y) + 3 + 1
= x + (-3y) + 4
= x – 3y + 4 ≠ 5x – 3y + 4
(iii) x – y – (2y – 4x) + 4
= x – y – 2y + 4x + 4
= (x + 4x) + (-y – 2y) + 4
= 5x + (-3y) + 4 = 5x – 3y + 4
(iv) 2(2y – x – 2) + 7(1 – y + x) + 1
= 4y – 2x – 4 + 7 – 7y + 7x + 1
= (-2x + 7x) + (4y – 7y) – 4 + 7 + 1
= 5x + (-3y) + 4 = 5x – 3y + 4
So, (i), (iii) and (iv) are correct.
Expressions using Letter Numbers Class 7 Fill in the Blanks
Question 1.
If n is a number, then:
(i) 7 more than the number is _____.
(ii) 3 less than the number is __.
(iii) 5 less than 7 times the number is _________.
(iv) 12 more than 9 times the number is _____.
Solution: n + 7, n – 3, 7n – 5, 9n + 12.
(i) 7 more than the number is n + 7.
(ii) 3 less than the number is n – 3.
(iii) 5 less than 7 times the number is 7n – 5.
(iv) 12 more than 9 times the number is 9n + 12.
Question 2.
If x = – 4, then 5 – x = ____.
Solution: 9
Putting x = – 4 in the expression 5 – x, we get
5 – (-4) = 5 + 4 = 9
∴ If x = – 4, then 5 – x = 9.
Question 3.
If t = 21, then 3t = _______ .
Solution: 63
Putting t = 21 in the expression 31, we get
3 × 21 = 63
∴ If t = 21, then 3t = 63.
Question 4.
If p = 7 and q = – 3, then 3p + 2q = _______.
Solution: 15
Putting p = 7 and q = – 3 in the expression 3p + 2q, we get
3 × 7 + 2 × (- 3) = 21 – 6 = 15 .
∴ If p = 7 and q = – 3, then 3p + 2q = 15.
Question 5.
If x = 12, then 4x + 5 = ______.
Solution: 53
Putting x = 12 in the expression 4x + 5, we get
4 × 12 + 5 = 48 + 5 = 53
∴ If x = 12, then 4x + 5 = 53.
Question 6.
If m = – 4, then 5(m + 1) = _______.
Solution: -15
Putting m = -4 in the expression 5(m + 1), we get
5(- 4 + 1) = 5 × (- 3) = -15
∴ If = -4, then 5(m + 1) = -15.
Question 7.
If p = – 10 and q = 5, then 5p + 10q = ______.
Solution: 0
Putting p = -10 and q = 5 in the expression 5p + 10q, we get
5 × (- 10) + 10 × 5 = – 50 + 50 = 0
∴ If p = – 10 and q = 5 then 5p + 10q = 0.