Number Play Class 7 MCQ Maths Chapter 6

Regular revision with Class 7 Maths MCQ with Answers and Ganita Prakash Class 7 Maths Chapter 6 Number Play MCQ improves accuracy in objective exams.

MCQ on Number Play Class 7

Number Play MCQ Class 7

Class 7 Maths Number Play MCQ

Question 1.
Which of the following expressions has odd parity?
(a) 2 + 6
(b) 8 – 4
(c) 7 + 3
(d) 4 + 5
Solution:
(d) 4 + 5
The word parity is used to denote the property
of being even or odd.
Here, 2 + 6 = 8 (Even)
8 – 4 = 4 (Even)
7 + 3 = 10 (Even)
4 + 5 = 9 (Odd)

Question 2.
Which of the following statements is not true?
(a) The parity of the sum of any count of even numbers is even.
(b) The parity of the sum of even count of odd numbers is even.
(c) The parity of the sum of odd count of odd numbers is odd.
(d) If the parity of n is odd, then the parity of n² is even.
Solution:
(d) If the parity of n is odd, then the parity of n² is even.
If n is an odd number, then n1 is also an odd number.
For example, 5 is an odd number, and 5² = 25 is also an odd number.
∴ If the parity of n is odd, then the parity of n² is also odd.
Statement (d) is not true.

Question 3.
Which of the following expressions has odd parity at n = 4?
(a) n²
(b) 2n + 1
(c) 3n
(d) n – 2
Solution:
(b) 2n + 1
At n = 4, n² = 4² = 16 (Even)
At n = 4, 2n + 1 = 2 × 4 + 1 = 9 (Odd)
At n = 4, 3n = 3 × 4 = 12 (Even)
At n = 4, n – 2 = 4 – 2 = 2 (Even)

Question 4.
Which of the following has an even parity?
(a) 3 + 8
(b) 7 – 2
(c) 5²
(d) 5 + 7
Solution:
(d) 5 + 7
The word parity is used to denote the property of being even or odd.
Here, 3 + 8 = 11 (Odd)
7 – 2 = 5 (Odd)
5² = 25 (Odd)
5 + 7 = 12 (Even)

Question 5.
Which of the following has an odd parity?
(a) 8 × 88
(b) 7 × 72
(c) 9²
(d) 82
Solution:
(c) 9²
We know that the parity of the product is odd
if both numbers are odd and the parity of the product of two numbers is even if at least one of them is even.
∴ The parity of both 8 × 88 and 7 × 72 is even.
Also, the parity of n² is the same as the parity of n.
∴ The parity of 9² is odd and the parity of 8² is even.

Question 6.
At what value of n, the expression 3n + 8 has an odd parity?
(a) 9
(b) 8
(c) 4
(d) 0
Solution:
(a) 9
Given expression, 3n + 8
At n = 9, 3 n + 8 = 3 × 9 + 8 = 27 + 8 = 35 (Odd)
At n = 8, 3 n + 8 = 3 × 8 + 8 = 24 + 8 = 32 (Even)
At w = 4, 3n + 8 = 3 × 4 + 8 = 12 + 8 = 20 (Even)
At n = 0, 3n + 8 = 3 × 0 + 8 = 0 + 8 = 8 (Even)
So, the expression has odd parity when n = 9.

Question 7.
Which of the following months has days with odd parity?
(a) April
(b) June
(c) August
(d) November
Solution:
(c) August
Months that have an even number of days show even parity, while those with an odd number of days show odd parity.

April, June, and November each have 30 days, showing even parity, while August, with 31 days, shows odd parity.

Question 8.
If each number in a 3 × 3 magic square is increased by 1, the magic sum will increase by:
(a) 2
(b) 4
(c) 3
(d) 5
Solution:
(c) 3
We know that in a 3 × 3 magic square (using 1 – 9) if we increase each number by n the magic sum increases by 3n.
∴ If each number of a magic square is increased by 1, the magic sum will increase by 3.

Question 9.
What will be the magic sum of a magic square if the central number is 15?
(a) 45
(b) 40
(c) 30
(d) 35
Solution:
(a) 45
Here, central number = 15 = 3 × 5
We know that in a 3 × 3 magic square (using 1-9) if we multiply each number by n the new magic sum becomes 15 × n.
Here, new magic sum =15 × 3 = 45

Question 10.
In how many different ways, number 6 can be written as a sum of Is and 2s?
(a) 12
(b) 13
(c) 14
(d) 15
Solution:
(b) 13
We know that the number of different ways in which number 6 can be written as the sum of Is and 2s is the 6^th element of the Virahanka sequence.
Virahanka sequence is: 1, 2, 3, 5, 8, 13, …
Thus, 6 can be written as sum of Is and 2s in 13 different ways.

Question 11.
Two consecutive numbers in the Virahanka sequence are 144 and 233. The next number in the sequence is:
(a) 297
(b) 377
(c) 89
(d) 367
Solution:
(b) 377
We know that in Virahanka sequence, a number is the sum of previous two numbers.
∴ Required number = 144 + 233 = 377

Question 12.
If each number of a 3 × 3 magic square (with numbers 1 – 9) is multiplied by 4, the magic sum will increase by:
(a) 8
(b) 60
(c) 45
(d) 30
Solution:
(c) 45
We know that the magic sum of a 3 × 3 magic square filled using numbers 1-9 is 15.
If each number of a magic square is multiplied by 4, the new magic sum will be 15 × 4 = 60.
∴ The magic sum will increase by:
60 – 15 = 45.

Question 13.
What will be the magic sum of a 3 × 3 magic square if the central number is 0?
(a) 3
(b) 2
(c) 1
(d) 0
Solution:
(d) 0
Generalised form of 3 × 3 magic square is:

m + 1	m – 4	m +3
m + 2	m	m – 2
m – 3	m + 4	m – 1

Given, m = 0. The magic square with central number 0 is obtained as:

1	-4	3
2	0	-2
-3	4	-1

Here, magic sum = 1 – 4 + 3 = 0

Question 14.
How many rhythms are there with 7 beats consisting of short syllables and long syllables?
(a) 13
(b) 21
(c) 34
(d) 55
Solution:
(b) 21
The number of rhythms with 7 beats consisting of short syllables and long syllables is the 7^th element of the Virahanka sequence.
Now, Virahanka sequence is: 1, 2, 3, 5, 8, 13, 21,…
As, the 7^th element is 21, there are 21 rythms with 7 beats.

Question 15.
The number of different magic squares which can be formed with numbers 1-9, including reflection and rotation, are:
(a) 3
(b) 4
(c) 7
(d) 8
Solution:
(d) 8
Total 8 magic squares can be formed with numbers 1-9, including reflection and rotation.

Question 16.
The expression n² – 1 has even parity when:
(i) n = 2
(ii) n = 3
(iii) n = 4
(iv) n = 5
Choose the correct option from the following:
(a) (i) and (ii)
(b) (ii) and (in)
(c) (iii) and (iv)
(d) (ii) and (iv)
Solution:
(d) (ii) and (iv)
Given expression: n² – 1
When n = 2, n² – 1 = 2² – 1 = 4 – 1 = 3 (odd)
When n = 3, n² – 1 = 3² – 1 = 9 – 1 = 8 (even)
When n = 4, n² – 1 = 4² – 1 = 16 – 1 = 15 (odd)
When n = 5, n² – 1 = 5² – 1 = 25 – 1 = 24 (even
Thus, the expression n² – 1 has even parity when n is 3 and 5.

Question 17.
Which of the following 3 × 3 grid is a magic square:
(i)

8	1	6
3	5	7
4	9	2

(ii)

8	1	2
3	5	7
6	9	4

(iii)

6	1	8
7	5	3
2	9	4

(iv)

8	9	6
5	3	7
4	1	2

Choose the correct option from the following:
(a) (i) and (iii)
(b) (ii) and (iv)
(c) (i) and (iv)
(d) (ii) and (iii)
Solution:
(a) (i) and (iii)
We know that a 3 × 3 square grid of numbers is called a magic square if each row, each column and each diagonal, add up to the same number. This number is called the magic sum.

In grid (i), the sum of each row, each column and each diagonal is 15.
Thus, it is a magic square.
In grid (ii), the sum of first row (i.e. 8+1+2 = 11) is different from the sum of second row (i.e. 3 + 5 + 7 = 15).
Thus, it is not a magic square.

The grid (iii) is the vertical reflection of the grid (i).
Thus, it is also a magic square as sum of each row, each column and each diagonal is 15.

In grid (iv), the sum of first row (i.e. 8 + 9 + 6 = 23) is different from the sum of second row (i.e. 5 + 3 + 7 = 15).
Thus, it is not a magic square.

Number Play Class 7 Assertion and Reason Questions

The following questions are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Question 1.
(A): The parity of 100 × 101 is even.
(R): The parity of the product of two numbers is even when at least one of the numbers is even.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
We know that the parity of the product of two numbers is even when both numbers are even, or when one is even and the other is odd.
Thus, the parity of 100 × 101 is even as 100 is even.
Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Question 2.
(A): The expression 2n + 7 always has an odd parity.
(R): The parity of the sum of an even number and an odd number is odd.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
We know that 2n is an even number.
Also, even number + odd number = odd number
∴ The expression 2n + 7 always has odd parity.
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Question 3.
(A): In a 3 × 3 magic square with numbers 1-9, the first row is [8 5 2],
(R): The magic sum of a 3 × 3 magic square is 15.
Solution:
(d) A is false but R is true.
We know that the magic sum of a 3 × 3 magic square is 15.
Since the number occurring at the centre of a magic square filled using 1-9 must he 5. Hence, the first row cannot be [8 5 2].
∴ Assertion (A) is false, but Reason (R) is true.

Question 4.
(A): The next 3 numbers in the Virahanka sequence: 1, 2, 3, 5, 8, 13,… are 21, 34 and 45.
(R): In Virahanka sequence, a number is the sum of previous two numbers.
Solution:
(d) A is false but R is true.
We know that in Virahanka sequence, a number is the sum of previous two numbers.
∴ The next 3 numbers in the Virahanka sequence: 1, 2, 3, 5, 8, 13, … are 8 + 13 = 21, 21 + 13 = 34 and 34 + 21 = 55.
∴ Assertion (A) is false, but Reason (R) is true.

Number Play Class 7 Fill in the Blanks

Question 1.
The parity of the sum of 99 even numbers is _______.
Solution: even
We know that the parity of sum of any count of even numbers is even.
Therefore, the parity of the sum of 99 even numbers is even.

Question 2.
The parity of the expression n² + n is always ________.
Solution: even
We know that the parity of n is the same as the parity of n.
Also, even number + even number = even number and odd number + odd number = even number.
Therefore, no matter if n is even or odd, the parity of the expression n² + n is always even.

Question 3.
The parity of the sum of numbers from 1 to 20 is ______ .
Solution: even
From 1 to 20, there are 10 even numbers and 10 odd numbers.
We know that the parity of the sum of any count of even numbers is even. So, the sum of 10 even numbers is even.

Also, the parity of the sum of even count of odd numbers is even. So, the sum of 10 odd numbers is even.

Since even number + even number = even number, the parity of the sum of numbers from 1 to 20 is even.

Question 4.
If n is odd, then the parity of n × n × n is __________ .
Solution: odd
We know that,
odd number × odd number = odd number.
∴ If n is odd, then the parity of n ×n × n is odd.

Question 5.
The sum of first 6 numbers in a Virahanka sequence is ______.
Solution: 32
Virahanka sequence is: 1, 2, 3, 5, 8, 13, …
Sum of first 6 numbers = 1 + 2 + 3 + 5 + 8 +13 = 32
Thus, the sum of first 6 numbers in a Virahanka sequence is 32.

Question 6.
The magic sum of a 4 × 4 magic square using numbers 1-16 is _______.
Solution: 34
The sum of numbers from 1 to 16 = 1 + 2 + 3 + …. + 14 + 15 + 16 = 136

We know that in a magic square, each row, each column and each diagonal add up to the same number called the magic sum.
∴ Magic sum = \(\frac{136}{4}\) = 34 [As there are 4 rows and 4 columns in a 4 × 4 magic square]
Thus, the magic sum of a 4 × 4 magic square using numbers 1-16 is 34.

Question 7.
The parity of 6^th element in Virahanka sequence is _______ .
Solution: odd
Virahanka sequence is: 1, 2, 3, 5, 8, 13, …
The 6^th element of Virahanka sequence is 13, which is an odd number.
∴ The parity of 6^th element in Virahanka sequence is odd.

Question 8.
The magic sum of a 4 × 4 magic square using numbers 1-16 is 34. The total of row sum is _______ .
Solution: 136
Given, the magic sum of a 4 × 4 magic square using numbers 1-16 is 34.
Since there are 4 rows, the total of row sum is 4 × 34 = 136.