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 : 36 [SSC CISF Constable 2011]
If 0.42 × $100^k$ = 42, then the value of k is
a) 2
b) 3
c) 1
d) 4
Answer »Answer:(c)
0.42 × $100^k$ = 42
$42/100 × 100^k$ = 42
$100^k={42×100}/42=100^1$
k=1
Question : 37 [SSC DEO 2009]
If $3^{x + y}$ = 81 and $81^{x - y}$ = 3, then the value of x is
a) $15/8$
b) 39
c) $17/8$
d) 42
Answer »Answer:(c)
$3^{x + y}$ = 81 and $81^{x - y}$ = 3
$3^{x + y}$= 81
$3^{x + y} = 3^4$
x + y = 4 ...(i)
and $81^{x - y}$ = 3
$(3^4)^{x - y}$ = 3
$3^{4x - 4y} = 3^1$
4x - 4y = 1 ...(ii)
By equation (i) × 4 + (ii) we have,
4x + 4y = 16…(iii)
4x-4y=1…(iv)
Solving these two equations(iii),(iv)
8x=17 ⇒ $x = 17/8$
Question : 38 [SSC CHSL 2015]
The exponential form of $√{ √{2}×√{3}}$ is :
a) $6^{1/2}$
b) $6^{1/4}$
c) $6^{-1/2}$
d) 6
Answer »Answer:(b)
Expression = $√{ √{2} × √{3}}$
= $(√2 ×√3)^{1/2}=(2^{1/2} × 3^{1/2})^{1/2$
= $(6)^{1/2× 1/2} = (6)^{1/4}$
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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