model 3 based on positive and negative exponent 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 : 16 [SSC CAPFs SI 2015]
If $3^{2x - y} = 3^{x + y} = √27$, then the value of $3^{x - y}$ will be
a) $1/√3$
b) $1/√27$
c) $√3$
d) 3
Answer »Answer:(c)
$3^{2x - y} = 3^{x + y} = √27 = (3)^{3/2}$
2x - y = $3/2$
4x - 2y = 3 ....(i)
and, $3^{x + y} = (3)^{3/2}$
x + y = $3/2$
2x + 2y = 3 ....(ii)
From equations (i) and (ii)
4x - 2y + 2x + 2y = 3 + 3
6x = 6 ⇒ x = 1
From equation (i),
4 - 2y = 3
2y = 1 ⇒ $y = 1/2$
$3^{x - y} = 3^{1- 1/2}$ = √3$
Question : 17
The value of $(3 +2√2)^{-3}+ (3 -2√2)^{- 3}$ is
a) 180
b) 189
c) 108
d) 198
Answer »Answer:(d)
$(3 +2√2)^{-3}+ (3 -2√2)^{- 3}$
$(3 + 2√2) (3 - 2√ 2)$
= $(3)^2 - (2√2)^2$ = 9 - 8 = 1
$3 + 2√2 = 1/{3 - 2√2}$
$(x + y)^3 + (x - y)^3 = x^3 + y^3 + 3x^2 y + 3 x y^2 + x^3 - y^3 - 3 x^2 y + 3 x y^2$
= $2 x^3 + 6 x y^2$
$(3 + 2√2 )^{ - 3} + (3 - 2√2)^{ - 3}$
= $(1/{3 + 2√2})^3 +(1/{3 -2√2})^3$
= $(3 - 2√2)^3 + (3 + 2√2)^3$
= $2 × (3)^3 + 6 × 3 × (2√2)^2$
= 2 × 27 + 18 × 8
= 54 + 144 = 198
Question : 18 [SSC CPO 2011]
If $(2000)^10 = 1.024 × 10^k$, then the value of k is
a) 30
b) 31
c) 34
d) 33
Answer »Answer:(d)
$(2000)^10 = 1.024 × 10^k$
$(2×10^3)^10=1024/1000×10^k$
$2^10×10^30=1024×10^{k-3}$
$2^10×10^30=2^10×10^{k-3}$
30 = k - 3 ⇒ k = 33
Question : 19
$(8/125)^{-4/3}$ simplifies to :
a) $625/8$
b) $16/625$
c) $625/32$
d) $625/16$
Answer »Answer:(d)
$(8/125)^{-4/3}=(2^3/5^3)^{-4/3}$
=$[(2/5)^3]^{-4/3}=(2/5)^{-4/3×3}$
=$(5/2)^4=625/16$
Question : 20
If $(x + 1/x)$= 2, then the value of $(x^99 +1/x^99-2)$ is :
a) 0
b) 4
c) 2
d) - 2
Answer »Answer:(a)
$x +1/x$= 2
${x^2 +1}/x= 2$
$x^2 + 1 = 2x$
$x^2$ - 2x + 1 = 0
$(x - 1)^2$ = 0
x - 1 = 0
x = 1
$x^99 + 1/x^99 - 2$ = 1 + 1 - 2 = 0
IMPORTANT quantitative aptitude EXERCISES
model 3 based on positive and negative exponent Shortcuts »
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Click to Start..power, indices and surds Shortcuts and Techniques with Examples
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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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