Power, Indices and Surds Questions for Competitive Exams. Important MCQ, selected from the previous year exam questions papers of SSC CGL, CPO, CHSL, Bank, UPSSSC and other govt jobs examinations for practice. topic wise question and answer of Power, Indices and Surds with solutions are very useful for upcoming competitive Examinations .

## Power, Indices and Surds Questions

### Finding the Largest and Smallest Values

**Q.1: **The greatest number among 3^{50}, 4^{40}, 5^{30} and 6^{20} is

a) 3^{50}

b) 4^{40}

c) 5^{30}

d) 6^{20}

###### Show Answer

**Ans : b) 4**

^{40}3

^{50}=(3

^{5})

^{10}= (243)

^{10}

4

^{40}= (4

^{4})

^{10}=(256)

^{10}

5

^{30}= (5

^{3})

^{10}= (125)

^{10}

6

^{20}= (6

^{2})

^{10}= (36)

^{10}

**Q.2: ** The greatest number among the following is

a)

b)

c) 0.47

d)

###### Show Answer

**Ans : d)**

=0.44

**Q.3: ** Arranging the following in descending order:

a)

b)

c)

d)

###### Show Answer

**Ans : a)**

**Q.4: ** The smallest among the numbers 2^{250}, 3^{150}, 5^{100}, 4^{200} is

a) 2^{250}

b) 3^{150}

c) 5^{100}

d) 4^{200}

###### Show Answer

**Ans : c) 5**

^{100}2

^{250}=(2

^{5})

^{50}=(32)

^{50}

3

^{150}= (3

^{3})

^{50}= (27)

^{50}

5

^{100}= (5

^{2})

^{50}=(25)

^{50}

4

^{200}= (4

^{4})

^{50 }= (256)

^{50}

**Q.5: ** Which is greater or ?

a)

b)

c) Equal

d) Can not be compared

###### Show Answer

**Ans :**

Cube of both the numbers are

**Q.6: ** The smallest among is

a)

b)

c)

d)

###### Show Answer

**Ans : c)**

LCM of 2,3,4 and 6 is 12

=(12)

^{1/6}=(12)

^{2/12}= (12

^{2})

^{1/12}= (144)

^{1/12}

= (256)

^{1/12}

= (125)

^{1/12}

= (729)

^{1/12}

**Q.7: ** If X =(0.25)1\2, Y = (0.4)2, Z=(0.216)1/3, then

a) Y>X>Z

b) X>Y>z

c) Z>X>Y

d) X>Z>Y

###### Show Answer

**Ans : c) Z>X>Y**

X=(0.25)1/2 =0.5

Y= (0.4)2 = 0.16

Z = (0.216) = 0.6

### Simplifying when the Root Values are given

**Q.8: ** If is approximately.

a) 1

b) 0.5223

c) 6.32

d) 2.035

###### Show Answer

**Ans : b) 0.5223**

**Q.9: ** If is given, then the value of correct up to two decimal places is :

a) 1.59

b) 1.60

c) 2.58

d) 2.57

###### Show Answer

**Ans : a) 1.59**

**Q.10: ** Evaluate :

a) 3.46

b) 10.38

c) 13.84

d) 24.22

###### Show Answer

**Ans : a) 3.46**

=

=

### Rationalising or Prime Factor

**Q.11: ** The number of prime factors in 6^{333} x 7^{222} x 8^{111}

a) 1221

b) 1222

c) 1111

d) 1211

###### Show Answer

**Ans : a) 1221**

6

^{333}x 7

^{222}x 8

^{111}= (2×3)

^{333}x 7

^{222}x (2

^{3})

^{111}= 2

^{333}x 3

^{333}x 7

^{222}x 2

^{333}

Total Prime Factor = 333+333+222+333= 1221

**Q.12: ** The total number of prime factors in 4^{10} x 7^{3} x 16^{2} x 11 x 10^{2} is

a) 34

b) 35

c) 36

d) 37

###### Show Answer

**Ans : c) 36**

4

^{10}x 7

^{3}x 16

^{2}x 11 x 10

^{2}

= (2

^{2})

^{10}x 7

^{3}x (2

^{4})

^{2}x 11 x (5×2)

^{2}

= 2

^{20}x 7

^{3}x 2

^{8}x 11 x 5

^{2}x2

^{2}

=2

^{30}x 5

^{2}x 7

^{3}x 11

Total Prime Factors = 30+2+3+1 = 36

**Q.13: ** The rationalizing factor of is

a)

b) 3

c) -3

d)

###### Show Answer

**Ans : d)**

= 3 x 3 =9

### Positive and Negative Exponent

**Q.14: ** The quotient when 10^{100} is divided by 5^{75} is

a) 2^{25} x 10^{75}

b) 10^{25}

c) 2^{75}

d) 2^{75} x 10^{25}

###### Show Answer

**Ans : d) 2**

^{75}x 10^{25} **Q.15: ** If 3^{x+8 }= 27^{2x+1} , then the value of x is :

a) 7

b) 3

c) -2

d) 1

###### Show Answer

**Ans : d) 1**

3

^{x+8 }= 27

^{2x+1}= (3

^{3})

^{2x+1}=3

^{6x+3}

x+8 =6x + 3

5x = 5, x=1

**Q.16: ** (36)^{1/6} is equal to

a) 1

b) 6

c)

d)

###### Show Answer

**Ans :**

(36)

^{1/6}= (6

^{2})

^{1/6}= 6

^{1/3}=

### Based on Square Root Series : Power, Indices and Surds Questions

**Q.17: ** The value of the expression is :

a) 5

b) 3

c) 2

d) 30

###### Show Answer

**Ans : b) 3**

Let

Squaring both side

=

=

=

=

**Q.18: ** = ?

a) 4

b) 2

c) 8

d)

###### Show Answer

**Ans : b) 2**

=

=

=

=

**Power, Indices and Surds Questions in Hindi – NRA STUDY**

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