Page 158 - Ganit Kaushal

Subjective/Competency Based Questions
9. Fill the grids below with prime numbers only, so that the product of each row is the number to the
right of the row and the product of each column is the number below the column. (NCERT)
(a) 63 (b) 343

27 66
190 44
45 42 171 28 154 231
10. There are just four natural numbers less than 100 that have exactly three factors. One of them is 25.
What are the other three? What can be said about these numbers?
11. Write two-digit odd numbers whose digit sum is 8.
12. Find the prime factorisation of the following numbers: (NCERT)
(a) 729 (b) 1024 (c) 1331 (d) 1000
13. In each of the following, replace ‘*’ by (a) the smallest digit, (b) the greatest digit, so that the number
formed is divisible by 6.
(i) 2*4706 (ii) 5825*34
Assertion Reason Type Questions.

A statement of assertion (A) is followed by a statement of reason (R). Choose the correct option from the
choices given below for each question:

(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.
1. Assertion (A): 6 × 5 = 30. So, 30 is a multiple of 5 and 6.

Reason(R): If ‘a’ is a factor of ‘c’, then ‘c’ is called a multiple of ‘a’.
2. Assertion (A): 5, 7, 11, 13 and 17 are prime numbers.
Reason (R): The smallest natural number is 1.
3. Assertion (A): 2, 4, 6, 8, and 9 are composite numbers.
Reason (R): A number is said to be a composite number if it has more than two different factors.
4. Assertion (A): 17 and 19 are a pair of twin prime numbers.
Reason (R): A pair of prime numbers with a difference of 2 are called twin prime numbers.
5. Assertion (A): The sum of the only prime triplet is 15.
Reason (R): There exists one and only one prime triplet i.e., 3, 5, and 7.

6. Assertion (A): 24 is a perfect number.
Reason (R): If the sum of all the factors of a number is equal to twice the number, then the number
is called a perfect number.

7. Assertion (A): The number 1,77,056 has 8 as one of its factors.
Reason (R): A number is divisible by 8 if the number formed by its last two digits (units and tens) is
divisible by 8.

8. Assertion (A): The number 14,734 is divisible by 4.
Reason (R): A number is divisible by 4 if the number formed by its last two digits (units and tens) is
divisible by 4.

156 Mathematics-6