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
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
a)
b)
c) 0.47
d)
Show Answer
![Rendered by QuickLaTeX.com (0.7)^2](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-c0eac09c72e0edd517e95369e09ac179_l3.png)
![Rendered by QuickLaTeX.com \frac 49](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-5ae575bb041462d44d29e5d38e7d9056_l3.png)
![Rendered by QuickLaTeX.com \sqrt{\frac {9}{49}} = \frac37 = 0.43](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-89503bc10d8beddb3374e9f7de84dbd0_l3.png)
![Rendered by QuickLaTeX.com (0.7)^2 = 0.49](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-61a42fcefde5a0b0764030dabd20772d_l3.png)
Q.3: Arranging the following in descending order:
a)
b)
c)
d)
Show Answer
![Rendered by QuickLaTeX.com \sqrt[3]{4} > \sqrt[4]{5} > \sqrt 2 > \sqrt[6]{3}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-7864db7bac5c67de9384bc1f83ce0781_l3.png)
![Rendered by QuickLaTeX.com \sqrt[3]{4} = 4^\frac13 = (4^4) = (256)^\frac {1}{12}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-6b741b1686464e4f4d71a3ee9934563b_l3.png)
![Rendered by QuickLaTeX.com \sqrt 2 = 2^\frac{1}{12} =(64)^\frac{1}{12}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-d05cc342c498369a37103b1ed555aef4_l3.png)
![Rendered by QuickLaTeX.com \sqrt [6]3 = 3^\frac{1}{6} = (3^2)^\frac {1}{12} = (9)^\frac {1}{12}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-3c74afdb07e314a94e9fe0ef16d6be9b_l3.png)
![Rendered by QuickLaTeX.com \sqrt[4] 5 =5^{\frac14}= (5^3)^{ \frac{1}{12}} =(125)^\frac{1}{12}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-61996699208612b62c24b523dcf64b11_l3.png)
Q.4: The smallest among the numbers 2250, 3150, 5100, 4200 is
a) 2250
b) 3150
c) 5100
d) 4200
Show Answer
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 or
?
a)
b)
c) Equal
d) Can not be compared
Show Answer
![Rendered by QuickLaTeX.com \sqrt3](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-ea0751b97d69ad1fd9af33b4945121e8_l3.png)
Cube of both the numbers are
![Rendered by QuickLaTeX.com (\sqrt[3]2)^3 =2 \: \text {and} \: (\sqrt3)^3 = 3 \sqrt3](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-6fb66eb3f9b0689c0c2be173fb703f06_l3.png)
Q.6: The smallest among is
a)
b)
c)
d)
Show Answer
![Rendered by QuickLaTeX.com \sqrt[4]5](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-6176005729c63e5360ace648e8a3c9bf_l3.png)
LCM of 2,3,4 and 6 is 12
![Rendered by QuickLaTeX.com \sqrt[6]{12}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-66de1351cd6ad3cfcb3e09656f634799_l3.png)
![Rendered by QuickLaTeX.com \sqrt[3]4](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-2d406c544cb9e655892b46d45cb34194_l3.png)
![Rendered by QuickLaTeX.com \sqrt[4]5](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-6176005729c63e5360ace648e8a3c9bf_l3.png)
![Rendered by QuickLaTeX.com \sqrt3](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-ea0751b97d69ad1fd9af33b4945121e8_l3.png)
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
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
![Rendered by QuickLaTeX.com \sqrt {\frac {3}{11}} = \sqrt {\frac {3\times 11}{11 \times 11}} = \frac {1}{11} \sqrt {33} = \frac{5.745}{11} = 0.5223](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-ae7e693579de0718726da03c3328a351_l3.png)
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
![Rendered by QuickLaTeX.com \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](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-2b2c2ebd465081d9eb69ba4b910e5760_l3.png)
Q.10: Evaluate :
a) 3.46
b) 10.38
c) 13.84
d) 24.22
Show Answer
![Rendered by QuickLaTeX.com 16\sqrt {\frac{3\times 4} {4\times4} } - 9\sqrt {\frac {4\times3}{3\times 3}}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-aff62788561613f50b39ae1a9b3ee78d_l3.png)
=
![Rendered by QuickLaTeX.com \frac {16}{4}\sqrt{12}-\frac 93 \sqrt {12}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-c944ff539274700274abd6e2b7950807_l3.png)
=
![Rendered by QuickLaTeX.com 4 \sqrt{12} -3\sqrt{12} = \sqrt {12} = 3.46](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-9e4a222a8121ff249a8eaee6f969ceff_l3.png)
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
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
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 is
a)
b) 3
c) -3
d)
Show Answer
![Rendered by QuickLaTeX.com \sqrt 3](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-95e02b0b7917e6a24d9dd92e9f4bfbbf_l3.png)
![Rendered by QuickLaTeX.com 3 \sqrt3 \times \sqrt3](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-f52c9aec4be8593224239f43ad98f94b_l3.png)
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
Q.15: If 3x+8 = 272x+1 , then the value of x is :
a) 7
b) 3
c) -2
d) 1
Show Answer
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)
d)
Show Answer
![Rendered by QuickLaTeX.com \sqrt[3]{6}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-58f86a3a7093d13f916e8ab8a686eba8_l3.png)
(36)1/6 = (62)1/6 = 61/3 =
![Rendered by QuickLaTeX.com \sqrt[3]{6}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-58f86a3a7093d13f916e8ab8a686eba8_l3.png)
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
Let
![Rendered by QuickLaTeX.com \sqrt {6+\sqrt {6+\sqrt{6+ ...........}}} = x](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-0f9b1c16ad8263dd53d1cfa12d51636c_l3.png)
Squaring both side
![Rendered by QuickLaTeX.com 6 + \sqrt {6+\sqrt {6+\sqrt{6+ ...........}}} = x^2](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-0cd91b506842e1463945496f6b3d9d55_l3.png)
=
![Rendered by QuickLaTeX.com x^2 = 6+x](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-0d5d6c3795e4de28ba993f6a25c672e4_l3.png)
=
![Rendered by QuickLaTeX.com x^2 - 3x +2x -6 = 0](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-e34b32fc1b31bac787c0f00b867f472c_l3.png)
=
![Rendered by QuickLaTeX.com (x-3)(x-2) = 0](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-4a9cc02e0a51f831ad23c3a92f16d4de_l3.png)
=
![Rendered by QuickLaTeX.com x = 3](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-e2c4e122462fb25369bbf71c27252ddb_l3.png)
Q.18: = ?
a) 4
b) 2
c) 8
d)
Show Answer
![Rendered by QuickLaTeX.com \dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ \sqrt{154+ 15}}}}} {2}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-2cc05282b56fcb3ad91f2a03a09d230c_l3.png)
=
![Rendered by QuickLaTeX.com \dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ \sqrt{169}}}}} {2}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-cffd047c6ba4696d7af653172d4f2b46_l3.png)
=
![Rendered by QuickLaTeX.com \dfrac {\sqrt{10+ \sqrt{25+ \sqrt{108+ 13}}}} {2}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-79188f962602e702b1c7459faf77d18d_l3.png)
=
![Rendered by QuickLaTeX.com \dfrac {\sqrt{10+ \sqrt{25+ 11}}} {2}](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-c9d7859957d1eada1adb08a6cd747645_l3.png)
=
![Rendered by QuickLaTeX.com \dfrac {\sqrt{10+ 6}} {2} = \dfrac 42 = 2](https://nrastudy.com/wp-content/ql-cache/quicklatex.com-b488841f29fba3813949eca44ffeff29_l3.png)
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