Power, Indices and Surds Questions for Competitive Exams

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 350, 440, 530 and 620 is
a) 350
b) 440
c) 530
d) 620

Show Answer
Ans : b) 440
350 =(35)10 = (243)10
440 = (44)10=(256)10
530 = (53)10 = (125)10
620 = (62)10 = (36)10

Q.2: The greatest number among the following is \frac 49, \sqrt{\frac {9}{49}}, 0.47, (0.7)^2
a) \frac 49
b) \sqrt{\frac {9}{49}}
c) 0.47
d) (0.7)^2

Show Answer
Ans : d) (0.7)^2
\frac 49 =0.44
\sqrt{\frac {9}{49}} = \frac37 = 0.43
(0.7)^2 = 0.49

Q.3: Arranging the following in descending order:
\sqrt[3]{4}, \sqrt 2,  \sqrt[6]{3}, \sqrt[4]{5},
a) \sqrt[3]{4} > \sqrt[4]{5} > \sqrt 2 > \sqrt[6]{3}
b) \sqrt[3]{4} > \sqrt 2 > \sqrt[6]{3}>\sqrt[4]{5}
c) \sqrt 2 >\sqrt[3]{4} > \sqrt[6]{3}> \sqrt[4]{5}
d) \sqrt[6]{3} >\sqrt[4]{5} >\sqrt[3]{4}> \sqrt 2

Show Answer
Ans : a) \sqrt[3]{4} > \sqrt[4]{5} > \sqrt 2 > \sqrt[6]{3}
\sqrt[3]{4} = 4^\frac13 = (4^4) = (256)^\frac {1}{12}
\sqrt 2 = 2^\frac{1}{12} =(64)^\frac{1}{12}
\sqrt [6]3 = 3^\frac{1}{6} = (3^2)^\frac {1}{12} = (9)^\frac {1}{12}
\sqrt[4] 5 =5^{\frac14}= (5^3)^{ \frac{1}{12}} =(125)^\frac{1}{12}

Q.4: The smallest among the numbers 2250, 3150, 5100, 4200 is
a) 2250
b) 3150
c) 5100
d) 4200

Show Answer
Ans : c) 5100
2250 =(25)50 =(32)50
3150 = (33)50 = (27)50
5100 = (52)50 =(25)50
4200 = (44)50 = (256)50

Q.5: Which is greater \sqrt[3]2 or \sqrt3  ?
a) \sqrt[3]2
b) \sqrt3
c) Equal
d) Can not be compared

Show Answer
Ans : \sqrt3
Cube of both the numbers are
(\sqrt[3]2)^3 =2  \: \text {and} \: (\sqrt3)^3 = 3 \sqrt3

Q.6: The smallest among \sqrt[6]{12}, \sqrt[3]4, \sqrt[4]5, \sqrt3 is
a) \sqrt[6]{12}
b) \sqrt[3]4
c) \sqrt[4]5
d) \sqrt3

Show Answer
Ans : c) \sqrt[4]5
LCM of 2,3,4 and 6 is 12
\sqrt[6]{12} =(12)1/6 =(12)2/12 = (122)1/12 = (144)1/12
\sqrt[3]4 = (256)1/12
\sqrt[4]5 = (125)1/12
\sqrt3 = (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 \sqrt {33} =5.745, \text {than the value of} \sqrt {\frac {3}{11}} is approximately.
a) 1
b) 0.5223
c) 6.32
d) 2.035

Show Answer
Ans : b) 0.5223
\sqrt {\frac {3}{11}} =  \sqrt {\frac {3\times 11}{11 \times 11}} = \frac {1}{11} \sqrt {33} = \frac{5.745}{11} = 0.5223

Q.9: If \sqrt 2 = 1.4142...... is given, then the value of \dfrac {7} {(3+\sqrt2)} 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
\frac {7} {(3+\sqrt2)} = \frac {7} {(3+\sqrt2)} \times \frac {3-\sqrt2}{3-\sqrt2} = \frac {21-7\sqrt2}{9-2} =3-\sqrt2 = 3-1.4142 =1.59

Q.10: Evaluate : 16\sqrt {\frac34} - 9\sqrt \frac 34 \: \: \: \text {if} \: \sqrt {12} = 3.46
a) 3.46
b) 10.38
c) 13.84
d) 24.22

Show Answer
Ans : a) 3.46
16\sqrt {\frac{3\times 4} {4\times4} } - 9\sqrt {\frac {4\times3}{3\times 3}}
=\frac {16}{4}\sqrt{12}-\frac 93 \sqrt {12}
= 4 \sqrt{12} -3\sqrt{12} = \sqrt {12} = 3.46

Rationalising or Prime Factor

Q.11: The number of prime factors in 6333 x 7222 x 8111
a) 1221
b) 1222
c) 1111
d) 1211

Show Answer
Ans : a) 1221
6333 x 7222 x 8111 = (2×3)333 x 7222 x (23)111 = 2333 x 3333 x 7222 x 2333
Total Prime Factor = 333+333+222+333= 1221

Q.12: The total number of prime factors in 410 x 73 x 162 x 11 x 102 is
a) 34
b) 35
c) 36
d) 37

Show Answer
Ans : c) 36
410 x 73 x 162 x 11 x 102
= (22)10 x 73 x (24)2 x 11 x (5×2)2
= 220 x 73 x 28 x 11 x 52 x22
=230 x 52 x 73 x 11
Total Prime Factors = 30+2+3+1 = 36

Q.13: The rationalizing factor of 3 \sqrt3 is
a) \frac 13
b) 3
c) -3
d) \sqrt 3

Show Answer
Ans : d) \sqrt 3
3 \sqrt3 \times \sqrt3 = 3 x 3 =9

Positive and Negative Exponent

Q.14: The quotient when 10100 is divided by 575 is
a) 225 x 1075
b) 1025
c) 275
d) 275 x 1025

Show Answer
Ans : d) 275 x 1025

Q.15: If 3x+8 = 272x+1 , then the value of x is :
a) 7
b) 3
c) -2
d) 1

Show Answer
Ans : d) 1
3x+8 = 272x+1 = (33)2x+1 =36x+3
x+8 =6x + 3
5x = 5, x=1

Q.16: (36)1/6 is equal to
a) 1
b) 6
c) \sqrt 6
d) \sqrt[3]{6}

Show Answer
Ans : \sqrt[3]{6}
(36)1/6 = (62)1/6 = 61/3 = \sqrt[3]{6}

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

Q.17: The value of the expression is :
\sqrt {6+\sqrt {6+\sqrt{6+ ...........}}}
a) 5
b) 3
c) 2
d) 30

Show Answer
Ans : b) 3
Let \sqrt {6+\sqrt {6+\sqrt{6+ ...........}}} = x
Squaring both side
6 + \sqrt {6+\sqrt {6+\sqrt{6+ ...........}}} = x^2
= x^2 = 6+x
= x^2 - 3x +2x -6 = 0
= (x-3)(x-2) = 0
= x = 3

Q.18: \dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ \sqrt{154+ \sqrt{225}}}}}} {\sqrt[3]8} = ?
a) 4
b) 2
c) 8
d) \frac12

Show Answer
Ans : b) 2
\dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ \sqrt{154+ 15}}}}} {2}

= \dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ \sqrt{169}}}}} {2}

= \dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ 13}}}} {2}

= \dfrac {\sqrt{10+ \sqrt{25+ 11}}} {2}

= \dfrac {\sqrt{10+ 6}} {2} = \dfrac 42 = 2

Power, Indices and Surds Questions in Hindi – NRA STUDY




Leave a Comment

Your email address will not be published. Required fields are marked *

error: Content is protected !!