model 1 find largest and smallest value Section-Wise Topic Notes With Detailed Explanation And Example Questions

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, $√{0.09}<√^3{0.064}<0.5<3/5$

Answer: (c)

$2^60, 3^48, 4^36$ 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

Answer: (c)

$(2.89)^{0.5}, 2 - (0.5)^2, √3$ and $√^3{0.008}$

$(2.89)^{0.5} = (2.89)^{1/2}$ =1.7,

$2 - (0.5)^2$= 2 - 0.25 = 1.75,

$√3$= 1.732 and

$√^3{0.008}= √^3{0.2 ×0.2 ×0.2}$=0.2

Obviously,

0.2 < 1.7 < 1.732 < 1.75

$√^3{0.008}<(2.89)^{0.5}<√3<2 - (0.5)^2$

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 =$(5)^100$

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.

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 =$4^40$