Surds and Indices Problems with Solution for Competitive Exams
Solutions of Surds and Indices Problems
$$ Q.11.\ The \ value \ of \ (256)^{5\over4} \ is :$$
$$(A) \ 512 $$
$$ (B) \ 984 $$
$$(C) \ 1024 $$
$$ (D)1032 $$
Ans . C
$$(256)^{5\over4} =(4^4)^{5\over4}= 4^\left(4×{5\over4} \right)= 4^5=1024$$
$$ Q.12.\ The \ value \ of \ \left(\sqrt { 8} \ \right)^{1\over3} \ is :$$
$$(A) \ 2 $$
$$ (B) \ 4 \ $$
$$ (C) \ \sqrt { 2} \ \ $$
$$ (D) \ 8 $$
Ans . C
$$\left(\sqrt { 8} \ \right)^{1\over3} \ = \left(8^{{1\over2}} \right)^{1\over3}= 8^\left({1\over2}×{1\over3} \right)$$
$$ =8^{{1\over6}}=(2^3)^{1\over6}=2^\left(3×{1\over6} \right)=2^{1\over2}=\sqrt { 2} \ $$
$$ Q.13.\ The \ value \ of \ \left((10)^{150}÷(10)^{146} \right)\ is :$$
$$(A) \ 1000 $$
$$ (B) \ 10000 $$
$$ (C) \ 100000 $$
$$ (D)10^6 $$
Ans . B
$$(10)^{150}÷(10)^{146}={(10)^{150}\over(10)^{146}}=(10)^{(150-146) }=10^4=10000. $$
$$Q.14.(2.4×10^3)÷(8×10^{-2})=? $$
$$ (A)\ 3×10^{-5}$$
$$ (B) \ 3×10^4 $$
$$ (C)\ 3×10^5 $$
$$ (D) 30 $$
Ans . B
$$(2.4×10^3)÷(8×10^{-2})= {2.4×10^3\over 8×10^{-2}}=(3×10^4) $$
Q.15. If 5a = 3125, then the value of 5(a-3) is :
(A) 25
(B) 125
(C) 625
(D) 1625
Ans . A
If 5a = 3125 ⟺ 5a = 55 ⟺ a = 5
∴ 5(a-3) = 5(5-3) = 52 = 25.
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