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Test: Number Systems - 2


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25 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Number Systems - 2

Test: Number Systems - 2 for Class 9 2022 is part of Mathematics (Maths) Class 9 preparation. The Test: Number Systems - 2 questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Number Systems - 2 MCQs are made for Class 9 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Number Systems - 2 below.
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Test: Number Systems - 2 - Question 1

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

Detailed Solution for Test: Number Systems - 2 - Question 1

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

Test: Number Systems - 2 - Question 2

Two irrational numbers between 2 and 2.5 are :-

Detailed Solution for Test: Number Systems - 2 - Question 2

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.

Test: Number Systems - 2 - Question 3

The exponential form of   is :-

Detailed Solution for Test: Number Systems - 2 - Question 3

(√2×√3)½ = (2×3)½×½ = (6)¼

Test: Number Systems - 2 - Question 4

The rational form of –25.6875 is :-

Detailed Solution for Test: Number Systems - 2 - Question 4


Test: Number Systems - 2 - Question 5

The rational form of is :-

Detailed Solution for Test: Number Systems - 2 - Question 5

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

Test: Number Systems - 2 - Question 6

The value of   is :-

Test: Number Systems - 2 - Question 7

Which of the following is not a rational number :-

Detailed Solution for Test: Number Systems - 2 - Question 7

√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.

Test: Number Systems - 2 - Question 8

(2√3 +√3) is equal to

Detailed Solution for Test: Number Systems - 2 - Question 8

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

So option C is correct answer. 

Test: Number Systems - 2 - Question 9

The number  is :-

Detailed Solution for Test: Number Systems - 2 - Question 9

If this number is rationalised then 3-√3×3-√3/3+√3×3-√3
=(3-√3)2/3^2+√32
=9+3-6√3/6
=12-6√3/6
=2-√3 this is an irrational number.

Test: Number Systems - 2 - Question 10

Find the remainder when 6799 is divided bt 7

Detailed Solution for Test: Number Systems - 2 - Question 10

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

Test: Number Systems - 2 - Question 11

The value of 5.  :-

Test: Number Systems - 2 - 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?

Detailed Solution for Test: Number Systems - 2 - Question 12

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

Test: Number Systems - 2 - Question 13

The value of  is  :- 

Detailed Solution for Test: Number Systems - 2 - Question 13

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

=-9/6 = -3/2

Test: Number Systems - 2 - Question 14

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

Test: Number Systems - 2 - Question 15

If 9x-1 = 32x-1 – 486 then the value of x is :-

Test: Number Systems - 2 - Question 16

If  a = 1/ (3-2√2)  &  b =  1/ ( 3+2√2)  then the value of a2 +b2 is :-

Detailed Solution for Test: Number Systems - 2 - Question 16

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 = a2 + b+ 2ab

And, a2+ b2 = (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

Test: Number Systems - 2 - Question 17

  is equal to :-

Test: Number Systems - 2 - Question 18

If 22x-y = 32 and 2x+y = 16 then x2 + y2 :-

Detailed Solution for Test: Number Systems - 2 - Question 18

Test: Number Systems - 2 - Question 19

The value of is :-

Test: Number Systems - 2 - Question 20

The value of  

Test: Number Systems - 2 - Question 21

Detailed Solution for Test: Number Systems - 2 - Question 21

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

= [(x2)1/12]

= x1/6

Test: Number Systems - 2 - Question 22

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

Detailed Solution for Test: Number Systems - 2 - Question 22

Test: Number Systems - 2 - Question 23

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

Test: Number Systems - 2 - Question 24

The product of 4 √6 and 3√24 is :-

Detailed Solution for Test: Number Systems - 2 - Question 24

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

Test: Number Systems - 2 - Question 25

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

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