Practice Largest and smallest value - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Out of the numbers 0.3, 0.03, 0.9, 0.09 the number that is nearest to the value of $√{0.9}$ is
(a)
(b)
(c)
(d)
Q-2) The greatest among the numbers $√{0.09}, √^3{0.064},$ 0.5 and $3/5$ is
(a)
(b)
(c)
(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, $√{0.09}<√^3{0.064}<0.5<3/5$
Q-3) The greatest of the following numbers 0.16, $√{0.16}, (0.16)^2$, 0.04 is
(a)
(b)
(c)
(d)
0.16, $√{0.16}, (0.16)^2$, 0.04
$√{0.16}=0.4$
$(0.16)^2=0.0256$
Clearly,
0.0256 < 0.04 < 0.16 < $√{0.16}$
Q-4) The greatest number among $3^50 , 4^40, 5^30$ and $6^20$ is
(a)
(b)
(c)
(d)
$3^50 , 4^40, 5^30$ 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 =$4^40$
Q-5) The greatest number among $2^60, 3^48, 4^36$ and $5^24$ is
(a)
(b)
(c)
(d)
$2^60, 3^48, 4^36$ and $5^24$
$2^60 = (2^5)^12 =(32)^12$
$5^24 = (5^2)^12 =(25)^12$
$2^60 >5^24$
$3^48 =(3^4)^12 =(81)^12$
$3^48 >2^60$
$4^36 =(4^3)^12 = (64)^12$
$3^48$ is the largest number
Q-6) The smallest among the numbers $2^250, 3^150, 5^100$ and $4^200$
(a)
(b)
(c)
(d)
$2^250=(2^5)^50=(32)^50$
$3^150=(3^3)^50=(27)^50$
$5^100=(5^2)^50=(25)^50$
$4^200=(4^4)^50=(256)^50$
∴ The smallest number =$(5)^100$
Q-7) Which one of the following is the least? $√3, √^3{2}, √2$ and $√^3{4}$
(a)
(b)
(c)
(d)
$√3, √^3{2}, √2$ and $√^3{4}$
LCM of 2 and 3 = 6
$√3 = (3)^{1/2}=3^{3/6}=(3^3)^{1/6}=√^6{27}$
$√^3{2} = √^6{2^2} =√^6{4}$
$√{2} = √^6{2^3} =√^6{8}$
$√^3{4} = √^6{4^2} =√^6{16}$
Q-8) The smallest among $√^6{12}, √^3{4}, √^4{5}, √3$ is
(a)
(b)
(c)
(d)
$√^6{12}, √^3{4}, √^4{5}, √3$
LCM of indices of surds
= LCM of 6, 3, 4 and 2 = 12
$√^6{12} =√^12{2^2}=√^12{144}$
$√^3{4} =√^12{4^4}=√^12{256}$
$√^4{5} =√^12{5^3}=√^12{125}$
$√3 =√^12{3^6}=√^12{729}$
The smallest surd = $√^4{5}$
Q-9) The greatest number among $√^3{2}, √3, √^3{5}$ and 1.5 is :
(a)
(b)
(c)
(d)
$√^3{2}, √3, √^3{5}$ and 1.5
LCM of 3 and 2 = 6.
$√^3{2}=√^6{2^2}=√^6{4}$
$√3=√^6{27}$
$√^3{5}=√^6{25}$
1.5 =$√{2.25}=√^6{(2.225)^3}$
Q-10) The least one of $2√3, 2√^4{5}, √8$ and $3√2$ is
(a)
(b)
(c)
(d)
$2√3, 2√^4{5}, √8$ and $3√2$
The orders of the surds are 2, 4, 2 and 2. Their LCM = 4
We convert each surd into a surd of order 4.
$2√3=√{4×3}=√12=√^4(12)^2=√^4{144}$
$2√^4{5}=√^4{2^4×5}=√^4{80}$
$3√2=√18=√^4(18)^2=√^4{324}$
$√8=√^4{64}$
Hence, the least number =$√8$