model 1 find largest and smallest value Practice Questions Answers Test with Solutions & More Shortcuts
power, indices and surds PRACTICE TEST [5 - EXERCISES]
model 1 find largest and smallest value
model 2 based on simplification
model 3 based on positive and negative exponent
model 4 simplifying roots with values
model 5 simplifying roots of roots
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 »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 »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 »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 »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 »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, $√{0.09}<√^3{0.064}<0.5<3/5$
IMPORTANT quantitative aptitude EXERCISES
power, indices and surds Shortcuts and Techniques with Examples
-
model 1 find largest and smallest value
Defination & Shortcuts … -
model 2 based on simplification
Defination & Shortcuts … -
model 3 based on positive and negative exponent
Defination & Shortcuts … -
model 4 simplifying roots with values
Defination & Shortcuts … -
model 5 simplifying roots of roots
Defination & Shortcuts …
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