Number System - Exercise 1

1. If (32) ^ (x-2) = 64 / (8^x). Find the value of x.

(a) - 2
(b) 3
(c) 2
(d) - 3

2. The largest number that always divides the product of 3 consecutive multiples of 2 is.

(a) 8
(b) 16
(c) 24
(d) 48

3. By what smallest number, 21600 must be divided or multiplies in order to make it a perfect square.

(a) 6
(b) 5
(c) 8
(d) 10

4. How many numbers are there between 500 & 600 in which 9 occurs only once?

(a) 19
(b) 20
(c) 21
(d) 18

5. How many even integers n, where 100<=n<=200 are divisible neither by 7 nor by 9.

(a) 40
(b) 37
(c) 39
(d) 38

6. What is the total number of positive integer solutions that satisfy the equation 4x + 3y = 120?

(a) 9
(b) 10
(c) 8
(d) None of these

7. How many 2-digit natural numbers are there so that ten’s digit is never less than the unit’s digit?

(a) 44
(b) 55
(c) 54
(d) None of these

8. If P is a prime number, then the LCM of P & (P+1) is.

(a) P (P+1)
(b) (P+2) P
(c) (P+1)(P-1)
(d) None of these

9. What is the remainder when 17^23 is divided by 16?

(a) 0
(b) 1
(c) 2
(d) 3

10. The product of two numbers is 16200. If their LCM is 216, find their HCF.

(a) 75
(b) 70
(c) 80
(d) Data Inconsistent

11. The LCM of two numbers is 72 & their HCF is 12. If one of the numbers is 24, what is the other number?

(a) 38
(b) 26
(c) 36
(d) 42

12. Dividing by 3/8 and then multiplying by 5/6 is equivalent to dividing by what number?

(a) 5 / 16
(b) 16 / 40
(c) 9 / 20
(d) 40 / 18

13. How many zeros are there at the end of the product 33 x 175 x 180 x 12 x 44 x 80 x 66?

(a) 2
(b) 4
(c) 5
(d) 6

14. Convert 1153 from base 10 to base 15.

(a) 51D
(b) 51E
(c) 51C
(d) None of these

15. What is the highest power of 31 in 1000!

(a) 31
(b) 32
(c) 33
(d) None of these

16. Convert 413 from base 7 to base 8

(a) 613
(b) 361
(c) 316
(d) None of these

17. (9^6) + 1 when divided by 8, would have a remainder

(a) 0
(b) 1
(c) 2
(d) 3

18. What is the highest power of 54 that divides 31! completely?

(a) 0
(b) 1
(c) 4
(d) None of these

19. The positive integer nearest to 1000 & divisible by 2, 3, 4, 5 & 6 is

(a) 1020
(b) 1040
(c) 960
(d) 1030

20. If the operation,^ is defined by the equation x ^ y = 2x + y,what is the value of a in 2 ^ a = a ^ 3

(a) 0
(b) 1
(c) -1
(d) 4

Related Articles :