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This mock test of Test: Number Systems - 2 for Class 9 helps you for every Class 9 entrance exam.
This contains 25 Multiple Choice Questions for Class 9 Test: Number Systems - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

How many prime number are there between 0 and 30 :-

Solution:

There are 10 prime numbers between 0 and 30 which are: 2,3,5,7,11,13,17,19,23,29

QUESTION: 2

Two irrational numbers between 2 and 2.5 are :-

Solution:

Irrational number between 2 and 2.5 = √2*2.5 = √5

As it is clear now that,

2 < √5 < 2.5

We know that √5 is an irrational number.

So, √5 is the required irrational number between 2 and 2.5.

QUESTION: 3

The exponential form of is :-

Solution:

(√2×√3)½ = (2×3)½×½ = (6)¼

QUESTION: 4

The rational form of –25.6875 is :-

Solution:

QUESTION: 5

The rational form of is :-

Solution:

As the bar is under two digits multiply with 100

100x = 2.7435*100

100x = 274.35

now subtract with x terms

that gives

99x = 274.35 - 2.7435

99 x = 271.60

x = 271.60/99

x = 2716/9900

QUESTION: 6

The value of is :-

Solution:

QUESTION: 7

Which of the following is not a rational number :-

Solution:

√4 = 2, √9 = 3, √16 = 4 but √2 = 1.414 it is a non-terminating and non-repeating number and such numbers are called irrational numbers. So, √2 is not a rational number.

QUESTION: 8

(2√3 +√3) is equal to

Solution:

(2√3 +√3) = 3√3 ( By addition of like terms )

So option C is correct answer.

QUESTION: 9

The number is :-

Solution:

If this number is rationalised then 3-√3×3-√3/3+√3×3-√3

=(3-√3)^{2/3}^2+√3^{2}

=9+3-6√3/6

=12-6√3/6

=2-√3 this is an irrational number.

QUESTION: 10

Find the remainder when 67^{99} is divided bt 7

Solution:

63 is divisible by 7 for any power, so required remainder will depend on the power of 4

Required remainder

QUESTION: 11

The value of 5. :-

Solution:

QUESTION: 12

The sum of the digits of a number is subtracted from the number, the resulting number is always divisible by which of the following numbers?

Solution:

The resulting number is always divisible by 9. e.g.,

Consider 47.

Sum of its digits is 4+7=11

So,47−11=36 which is exactly divisible by 9

QUESTION: 13

The value of is :-

Solution:

(1 - 10)/(9 + (-3))

=-9/6 = -3/2

QUESTION: 14

If 2^{x} = 4^{y} = 8^{z} and = 4, then the value of x is :-

Solution:

QUESTION: 15

If 9^{x-1} = 3^{2x-1} – 486 then the value of x is :-

Solution:

QUESTION: 16

If a = 1/ (3-2√2) & b = 1/ ( 3+2√2) then the value of a^{2} +b^{2} is :-

Solution:

a = 1/ (3-2√2)

b = 1/ ( 3+2√2)

∴ ab = 1/(3-2√2) * 1/ (3+2√2)

=> 1/ (9-8)

=> 1

We know;

(a+b)^{2} = a^{2} + b^{2 }+ 2ab

And, a^{2}+ b^{2} = (a+b)^{2} - 2ab

=> [ 1/(3-2√2) + 1/(3+2√2) ]^{2} -2*1

=> [3+2√2+3-2√2 / 1]^2 -2

=> (6)^{2} - 2

=> 36 - 2

=> 34

QUESTION: 17

is equal to :-

Solution:

QUESTION: 18

If 2^{2x-y} = 32 and 2^{x+y} = 16 then x^{2} + y^{2} :-

Solution:

QUESTION: 19

The value of is :-

Solution:

QUESTION: 20

The value of

Solution:

QUESTION: 21

Solution:

[(x)^2]^{1/3]1/4}

= [(x^{2})^{1/12}]

= x^{1/6}

QUESTION: 22

The value of 4√3 – 3 √12 + 2 √75 on simplifying is :-

Solution:

QUESTION: 23

If √3 = 1.732, √5 = 2.236, then the value of is :-

Solution:

QUESTION: 24

The product of 4 √6 and 3√24 is :-

Solution:

4√6*3√24=4√6*3√2*√2*√*2*√3

=4√6*6√6

4*6*√6*√6=4*6*6=24*6=144

QUESTION: 25

If a = , b = , then the value of a + b is :-

Solution:

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