## Case Study Questions for Class 9 Maths Chapter 1 Real Numbers

**Case Study Questions:**

**Question 1:**

Himanshu has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.

**(i) For what value of n, 4 ^{n} ends in 0?**

(a) 10

(b) when n is even

(c) when n is odd

(d) no value of n

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Answer: (d)**(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n,Â aÂ is a rational number?**

(a) when n is any even integer

(b) when n is any odd integer

(c) for all n > 1

(d) only when n=0

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Answer: (c)**(iii) If x and y are two odd positive integers, then which of the following is true?**

(a)Â x^{2}+y^{2}Â is even

(b)Â x^{2}+y^{2}Â is not divisible by 4

(c)Â x^{2}+y^{2}Â is odd

(d) both (a) and (b)

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Answer: (d)**(iv) The statement â€˜One of every three consecutive positive integers is divisible by 3â€™ is**

(a) always true

(b) always false

(c) sometimes true

(d) None of these

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Answer: (a)**(v) If n is any odd integer, then n ^{2} â€“ 1 is divisible by**

(a) 22

(b) 55

(c) 88

(d) 8