model 2 based on simplification Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26

The value of 2 + $√{0.09} - √^3{0.008}$ - 75% of 2.80 is :

a) - 1

b) 0

c) 0.001

d) 0.01

Answer: (b)

2 + $√{0.09} - √^3{0.008}$ - 75% of 2.80

Expression

= $2 + √{0.09} - √^3(0.2)^3 - 75% of 2.80$

= $2 + 0.3 - 02 -75/100 × 2.80$

= 2.3 - 0.2 - 2.1

= 2.3 - 2.3 = 0

Question : 27 [SSC CGL Prelim 1999]

By how much does $√{12} + √{18}$ exceed $√3 + √2$ ?

a) $ √3 + 2√2$

b) 2$(√3 - √2)$

c) $√2 - 4√3$

d) 2$(√3 + √2)$

Answer: (a)

$(√{12} + √{18}) - (√3 + √2)$

$(2√{3} - √{3}) + (3√2 - √2)$

$√{3} + 2√{2}$

Question : 28 [SSC CGL Prelim 2000]

$(0.01024)^{1/5}$ is equal to :

a) 0.4

b) 4.0

c) 0.00004

d) 0.04

Answer: (a)

$(0.01024)^{1/5}$

= $[(0.4)^5]^{1/5} = {0.4}^{5×1/5} = 0.4$

Question : 29

The value of $(√^3{3.5} + √^3{2.5})((√^3{3.5})^2 - √^3{8.75} + (√^3{2.5})^2)$ is :

a) 6

b) 5.375

c) 5

d) 1

Answer: (a)

$(√^3{3.5} + √^3{2.5})((√^3{3.5})^2 - √^3{8.75} + (√^3{2.5})^2)$

Let $√^3{3.5} = a$ and $√^3{2.5} = b$

Expression

= (a + b)$(a^2 - ab + b^2) = a^3 + b^3$

= $(√^3{3.5})^3 + (√^3{2.5})^3$

= 3.5 + 2.5 = 6

Question : 30

The value of $√^3{1372} × √^3{1458} ÷ √^3{343}$ is

a) 13

b) 18

c) 12

d) 15

Answer: (b)

$√^3{1372} × √^3{1458} ÷ √^3{343}$

Expression

= ${√^3{1372}×√^3{1458}}/√^3{343}$

= $√^3{{1372×1458}/343}$

= $√^3{5832}$

= $√^3{18×18×18} = 18$

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