Number System MCQs

Question 1

If n is a natural number and n = $${p_1}^{{x_1}}$$ $${p_2}^{{x_2}}$$ $${p_3}^{{x_3}}$$ where p 1 , p 2 , p 3 are distinct prime factors, then the number of prime factors for n is :

Accepted Answer

$${x_1} 	imes {x_2} 	imes {x_3}$$

Answer

$${x_1} + {x_2} + {x_3}$$

Answer

$$\left( {{x_1} + 1} \right)\left( {{x_2} + 1} \right)\left( {{x_3} + 1} \right)$$

Answer

None of these

Question 2

If a + b + c = 6 and ab + bc + ca = 10, then value of a 3 + b 3 + c 3 - 3abc is :

Accepted Answer

36

Answer

48

Answer

42

Answer

40

Question 3

If m and n are positive integers and (m - n) is an even number, then (m 2 - n 2 ) will always be divisible by :

Accepted Answer

4

Answer

6

Answer

8

Answer

12

Question 4

Consider the following statements :
1. If x and y are composite numbers, then x + y is always composite.
2. There does not exist a natural number which is neither prime nor composite.
Which of the above statements is/are correct ?

Accepted Answer

Neither 1 nor 2

Answer

1 only

Answer

2 only

Answer

Both 1 and 2

Question 5

The number of prime factors in the expressions 6 4 × 8 6 × 10 8 × 12 10 is:

Accepted Answer

72

Answer

80

Answer

64

Answer

48

Question 6

Find the remainder when 54 124 is divided by 17.

Accepted Answer

13

Answer

8

Answer

16

Answer

9

Question 7

If a + b + c = 0, (a + b) (b + c) (c + a) equals

Accepted Answer

- abc

Answer

ab (a + b)

Answer

(a + b + c) 2

Answer

a 2 + b 2 + c 2

Question 8

If x + y + z = 0, then x 3 + y 3 + z 3 is equal to :

Accepted Answer

3xyz

Answer

0

Answer

$$\frac{{{	ext{xy}} + {	ext{yz}} + {	ext{zx}}}}{{{	ext{xyz}}}}$$

Answer

xyz(xy + yz + zx)

Question 9

For the integer n, if n 3 is odd, then which of the following statements are true ? I. n is odd II. n 2 is odd III. n 2 is even

Accepted Answer

I and II only

Answer

I only

Answer

II only

Answer

I and III only