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### Q1. In a seminar, the number of participants in English, German and Sanskrit are 45,75 and 135. Find the number of rooms required to house them, if in each room, the same number of participants are to be accommodated and they should be of the same language.

(a) 45

(b) 17

(c) 75

(d) 135

(b) 17

## Q2. Write an irrational number between 2 and 3.

(a) 2.5

(b) 2.001

(c) 2.1333333456…

(d) 2.13

(c) 2.1333333456… non terminating non repeating

## Q3. Which of the following are irrational whose sum and product are both rationals :

(a) v2 + 3,v2 – 3

(b) v2 + v3,v2 – v3

(c) 3 + v2, 3 – v2

(d) v2 + 1,v2 – 1

(c) 3 + v2, 3 – v2 3 + v2 + 3 – v2 = 6 and (3+v2) (3-v2) =7

## Q4. Find the value of x from the following such that x2 is irrational but x4 is rational:

(a) v2

(b) 3v2

(c) 4v2

(d) 2

(c) 4v2 v2 is a irrational number.

## Q5. If HCF (a, b) = 12 and a × b = 1800 then LCM (a, b) is

(a) 3600

(b) 900

(c) 150

(d) 90

(c) 150

## Q6. If mn = 32, where m and n are positive integers, then the value of (n)mn is

(a) 9765625

(b) 9775625

(c) 9785625

(d) 9865625

(a) 9765625

## Q7. The decimal expansion of n is

(a) terminating

(b) non-terminating and non-recurring

(c) non-terminating and recurring

(d) does not exist.

(b) non-terminating and non-recurring

## Q8. If HCF of 55 and 99 is expressible in the form 55 m – 99, then the value of m:

(a) 4

(b) 2

(c) 1

(d) 3

(b) 2

## Q9. Given that LCM of (91, 26) = 182 then HCF (91, 26) is

(a) 13

(b) 26

(c) 7

(d) 9

(a) 13

## Q.10. HCF of 8, 9, 25 is

(a) 8

(b) 9

(c) 25

(d) 1

(d) 1

## Q11. If A = 2n + 13, B = n + 7 where n is a natural number then HCF of A and B

(a) 2

(b) 1

(c) 3

(d) 4

(b) 1

## Q12. (-1)n + (-1)8n = 0 when n is

(a) any positive integer

(b) any odd natural number

(c) any even numeral number

(d) any negative integer

(b) any odd natural number

## Q13. n² – 1 is divisible by 8, if n is

(a) an integer

(b) a natural number

(c) an odd natural number

(d) an even natural number

(c) an odd natural number

## Q14. If n is a natural number, then exactly one of numbers n, n + 2 and n + 1 must be a multiple of

(a) 2

(b) 3

(c) 5

(d) 7

(b) 3

## Q15. The LCM of 2.5, 0.5 and 0.175 is

(a) 2.5

(b) 5

(c) 7.5

(d) 0.875

(d) 0.875

## Q16. The least number, which when divided by 10,14 and 18, leaves remainder 4, is :

a) 630

(b) 634

(c) 252

(d) 496

(b) 634 Required number is the LCM of 10, 14 and 18 (is 630) + 4 = 630 + 4 = 634

## Q17. The greatest number which divides 17, 28 and 34 leaving remainders 2, 3 and 4 respectively is:

(a) 5

(b) 24

(c) 1

(d) 17

(a) 5 Here 17 – 2 = 15, 28 – 3 = 25, 34 – 4 = 30 Required number is the HCF of 15,25 and 30 = 5

## Q18. 72 litres of liquid A and 108 litres of liquid B are to be packed in containers of the same size. The minimum number of containers required are:

a) 36

(b) 18

(c) 5

(d) 10

(c) 5

## Q19. he HCF of two consecutive rational numbers x and x +1 is :

(a) x

(b) x + 1

(c)1

(d) 0

(c)1 HCF of two consecutive numbers is always 1.

## Q20. The HCF of a number which is neither prime nor composite and any other number x is:

(a) x

(b) x + 1

(c) 1

(d) Any number

(c) 1 As, 1 is neither prime nor a composite number, thus, required number is the HCF of 1 and x, which is 1

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