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

Question : 1 [SSC CPO S.I.2003]

The value of ${(243)^{0.13} × (243)^{0.07}}/{(7)^{0.25} × (49)^{0.075} × (343)^{0.2}}$

a) 1$3/7$

b) $3/7$

c) 2$2/7$

d) $7/3$

Answer: (b)

${(243)^{0.13} × (243)^{0.07}}/{(7)^{0.25} × (49)^{0.075} × (343)^{0.2}}$

Expression

= ${(243)^{0.13+0.07}/{(7)^{0.25} × (7×7)^{0.075} × (7×7×7)^{0.2}}$

= ${(3^5)^{0.2}/{(7)^{0.25} × (7)^{2×0.075} × (7)^{3×0.2}}$

= ${(3)^{5×0.2}/{(7)^{0.25 + 0.15 + 0.6} = 3/7$

Question : 2

$(16^{0.16} × 2^{0.36})$ is equal to

a) 32

b) 2

c) 64

d) 16

Answer: (b)

$(16^{0.16} × 2^{0.36})$

= $(16^{16/100} × 2^{36/100})$

= $(2^{4×16/100} × 2^{36/100})$

= $(2^{64/100 + 36/100}) = (2^{100/100}) = 2$

Question : 3

The value of $√{5 + 2√{6}} - 1/{√{5 + 2√6}}$ is :

a) 1+ $√5$

b) 2$√2$

c) $√5 - 1$

d) 2$√3$

Answer: (b)

$√{5 + 2√{6}}$

= $√{3 + 2 + 2 × √{3} × √{2}}$

= $√{(√{3} + √{2})^2} = √3 + √2$

$1/√{5 + 2√{6}} = √3 - √2$

Hence, Expression

= $√3 + √2 - √3 + √2 = 2√2$

Question : 4 [SSC CGL Prelim 2003]

$√{ √^3{0.004096}}$ is equal to

a) 0.04

b) 4

c) 0.004

d) 0.4

Answer: (d)

$√{ √^3{0.004096}}$

= $(√^3{0.004096})^{1/2}$

= $({0.004096})^{1/3×1/2}$

= $(4096/1000000)^{1/6} = ((4/10)^6)^{1/6}$

= $(4/10)^{6×1/6} = 4/10 =0.4$

Question : 5

The value of : $√{ - √{3} + √{3 + 8√{7 + 4√{3}}}}$ is

a) 3

b) 1

c) 8

d) 2

Answer: (d)

$√{ - √{3} + √{3 + 8√{7 + 4√{3}}}}$

= $√{ - √{3} + √{3 + 8√{4 + 3 + 2 × 2 × √{3}}}}$

= $√{ - √{3} + √{3 + 8√{(2)^2 + (√3)^2 + 2 × 2 × √{3}}}}$

= $√{ - √{3} + √{3 + 8√{(2 × √{3})^2}}}$

= $√{ - √{3} + √{3 + 8(2 × √{3})}}$

= $√{ - √{3} + √{3 + 16 +8√{3}}}$

= $√{-√{3} + √{(√3)^2 + (4)^2 + 2 × 4 √{3}}}$

=$√{-√{3} + √{(4 + √3)^2}}$

= $√{-√{3} + 4 +√{3}} = √4$ = 2

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