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# Solved Examples(Set 1) - Surds and Indices

 1. (132)7 × (132)? = (132)11.5. A. 3 B. 4.5 C. 4 D. 3.5

Explanation:

$a^m.a^n = a^{m+n}$

(132)7 × (132)x = (132)11.5

=> 7 + x = 11.5

=> x = 11.5 - 7 = 4.5

 2. $\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\text{ What is the value of x ?}$ A. 4.5 B. 4 C. 3.5 D. 3

Explanation:

$a^{n} = \dfrac{1}{a^{-n}}$

\begin{align}&\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}\\\\ &\Rightarrow \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{a}{b}\right)^{-(x-7)}\\\\ &\Rightarrow x - 2 = -(x - 7)\\\\ &\Rightarrow x - 2 = -x + 7\\\\ &\Rightarrow x-2 = -x + 7\\\\ &\Rightarrow 2x = 9\\\\ &\Rightarrow x = \dfrac{9}{2} = 4.5 \end{align}

 3. If 7(x - y) = 343 and 7(x + y) = 16807, what is the value of x? A. 3 B. 1 C. 2 D. 4

Explanation:

7(x - y) = 343 = 73

=> x - y = 3 ---------------------------(Equation 1)

7(x + y) = 16807 = 75

=> x + y = 5 ---------------------------(Equation 2)

(Equation 1)+ (Equation 2) => 2x = 3 + 5 = 8

=> x = 82 = 4

 4. (0.04)-2.5 = ? A. 125 B. 25 C. 3125 D. 625

Explanation:

$a^{-n} = \dfrac{1}{a^n}$

\begin{align}&(0.04)^{-2.5} = \left(\dfrac{1}{.04}\right)^{2.5} = \left(\dfrac{100}{4}\right)^{2.5} = \left(25\right)^{2.5} = \left(5^2\right)^{2.5}\\\\ &= \left(5^2\right)^{\left(\dfrac{5}{2}\right)}= 5^5 = 3125\end{align}

 5. (6)6.5 × (36)4.5 ÷ (216)4.5 = (6)? A. 2 B. 4 C. 1 D. 6

Explanation:

(6)6.5 × (36)4.5 ÷ (216)4.5

= (6)6.5 × [(6)2]4.5 ÷ [(6)3]4.5

= (6)6.5 × (6)9 ÷ (6)13.5

= (6)(6.5 + 9 - 13.5)

= (6)2

Harpreet
2015-02-14 09:59:31
Good One !! More chapters like Ratio & Proportions , Sequence & Series and some statistics topics like Central tendency, Dispersion , Correlation & regression should be added.
pooja
2014-03-10 18:35:52
it's very nice method each que.each farmula are used
so that's very good simplification thank you very much..........
S.Sathiyendraan
2013-11-25 07:04:03
It is a very useful to my PGD Entrance Exam