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

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) $6^20$

Answer: (c)

$3^50 , 4^40, 5^30$ 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) $√^2{8}$

Answer: (d)

$√^2{8}, √^4{13}, √^5{16}, √^10{41}$

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) $2^250$

Answer: (c)

$2^250=(2^5)^50=(32)^50$

$3^150=(3^3)^50=(27)^50$

$5^100=(5^2)^50=(25)^50$

$4^200=(4^4)^50=(256)^50$

∴ 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

Answer: (a)

$(0.5)^2, √{0.49}, √^3{0.008}, 0.23$

$(0.5)^2$=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) $3/5$

Answer: (d)

$√{0.09}, √^3{0.064},$ 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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