# model 1 find largest and smallest value Practice Questions Answers Test with Solutions & More Shortcuts

#### power, indices and surds PRACTICE TEST [5 - EXERCISES]

Question : 1 [SSC CGL Tier-II 2015]

The greatest number among \$3^50 , 4^40, 5^30\$ and \$6^20\$ is

a) \$5^30\$

b) \$3^50\$

c) \$4^40\$

d) \$6^20\$

\$3^50 , 4^40, 5^30\$ and \$6^20\$

\$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\$

∴ Largest number =\$4^40\$

Question : 2 [SSC CHSL 2011]

The greatest of the numbers \$√^2{8}, √^4{13}, √^5{16}, √^10{41}\$ is:

a) \$√^10{41}\$

b) \$ √^4{13}\$

c) \$√^5{16}\$

d) \$√^2{8}\$

\$√^2{8}, √^4{13}, √^5{16}, √^10{41}\$

LCM of 2, 4, 5 and 10 = 20

\$√^2{8}=√^20{8^10}; √^4{13}=√^20{13^5}\$

\$√^5{16}=√^20{16^4}; √^10{41}=√^20{41^2}\$

Clearly, \$√^2{8}\$ is the largest.

Question : 3

The smallest among the numbers \$2^250, 3^150, 5^100\$ and \$4^200\$

a) \$3^150\$

b) \$4^200\$

c) \$5^100\$

d) \$2^250\$

\$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\$

∴ The smallest number =\$(5)^100\$

Question : 4

Which of the following number is the least? \$(0.5)^2, √{0.49}, √^3{0.008}, 0.23\$

a) \$√^3{0.008}\$

b) \$(0.5)^2\$

c) \$√{0.49}\$

d) 0.23

\$(0.5)^2, √{0.49}, √^3{0.008}, 0.23\$

\$(0.5)^2\$=0.25

\$√{0.49}\$=0.7

\$√^3{0.008}\$=0.2

0.23 = 0.23

∴ \$√{0.49}>(0.5)^2>0.23>√^3{0.008}\$

Question : 5

The greatest among the numbers \$√{0.09}, √^3{0.064},\$ 0.5 and \$3/5\$ is

a) 0.5

b) \$√{0.09}\$

c) \$√^3{0.064}\$

d) \$3/5\$

\$√{0.09}, √^3{0.064},\$ 0.5 and \$3/5\$

\$√{0.09}=0.3\$

\$√^3{0.064}=0.4\$; 0.5;

\$3/5\$= 0.6

Clearly, \$√{0.09}<√^3{0.064}<0.5<3/5\$

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