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Solved Examples(Set 1) - Surds and Indices

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

Answer: Option B

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. 4.5B. 4
C. 3.5D. 3
Discuss
answer with explanation

Answer: Option A

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. 3B. 1
C. 2D. 4
Discuss
answer with explanation

Answer: Option D

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. 125B. 25
C. 3125D. 625
Discuss
answer with explanation

Answer: Option C

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. 2B. 4
C. 1D. 6
Discuss
answer with explanation

Answer: Option A

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

Comments(4)

profileHarpreet
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.
like 0 dislike 0 reply
profilepooja
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..........
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profileS.Sathiyendraan
2013-11-25 07:04:03 
It is a very useful to my PGD Entrance Exam
like 0 dislike 0 reply
profilePrabha
2013-07-25 11:35:55 
This page is very useful for my MBA entrance exam :)
like 0 dislike 0 reply

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