## Chapter 1: Real Numbers

**Q1**. There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students

(a) 52

(b) 56

(c) 48

(d) 63

Answer: a

**2.** For some integer m, every odd integer is of the form

(A) m

(B) m + 1

(C) 2m

(D) 2m + 1

**Answer: D**

**3.** If two positive integers a and b are written as a = p^{3}q^{2} and b = pq^{3}; p, q are prime numbers, then HCF (a, b) is:

(A) pq

(B) pq^{2}

(C) p^{3}q^{3 }

(D) p^{2}q^{2}

**Answer: B**

**4.** The product of a non-zero number and an irrational number is:

(A) always irrational

(B) always rational

(C) rational or irrational

(D) one

**Answer: A**

**5.** If the HCF of 65 and 117 is expressible in the form 65 m – 117, then the value of m is

(A) 4

(B) 2

(C) 1

(D) 3

**Answer: B**

**6.** The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A) 13

(B) 65

(C) 875

(D) 1750

**Answer: A**

**7.** If two positive integers p and q can be expressed as p = ab^{2} and q = a^{3}b; a, b being prime numbers, then LCM (p, q) is

(A) ab

(B) a^{2}b^{2}

(C) a^{3}b^{2}

(D) a^{3}b^{3}

**Answer: C**

**8.** The values of the remainder r, when a positive integer a is divided by 3 are:

(A) 0, 1, 2, 3

(B) 0, 1

(C) 0, 1, 2

(D) 2, 3, 4

**Answer: C**

**Q9**. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet ?

(a) 36 minutes

(b) 18 minutes

(c) 6 minutes

(d) They will not meet

Answer: a

**10.** A rational number in its decimal expansion is 327.7081. What would be the prime factors of q when the number is expressed in the p/q form?

(A) 2 and 3

(B) 3 and 5

(C) 2, 3 and 5

(D) 2 and 5

**Answer: D**

**11.** The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(A) 10

(B) 100

(C) 2060

(D) 2520

**Answer: D**

**12.** n^{2} – 1 is divisible by 8, if n is

(A) an integer

(B) a natural number

(C) an odd integer greater than 1

(D) an even integer

**Answer: C**

**13.** If n is a rational number, then 5^{2n} − 2^{2n} is divisible by

(A) 3

(B) 7

(C) Both 3 and 7

(D) None of these

**Answer: C**

**14.** The H.C.F of 441, 567 and 693 is

(A) 1

(B) 441

(C) 126

(D) 63

**Answer: D**

**15.** On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

(A) 2520 cm

(B) 2525 cm

(C) 2555 cm

(D) 2528 cm

**Answer: A**

**Q16. ****Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.**

(a) 98 kg

(b) 290 kg

(c) 200 kg

(d) 350 kg

**Answer**: a

**Q17. For some integer p, every even integer is of the form**

(a) 2p + 1

(b) 2p

(c) p + 1

(d) p

**Answer**: b

**Q18. For some integer p, every odd integer is of the form**

(a) 2p + 1

(b) 2p

(c) p + 1

(d) p

**Answer**: a

**Q19. m² – 1 is divisible by 8, if m is**

(a) an even integer

(b) an odd integer

(c) a natural number

(d) a whole number

**Ans**: b

**Q20. The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is**

(a) 5

(b) 60

(c) 20

(d) 100

**Ans**: b