Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

If \( \Large a^{x} = b \), \( \Large b^{y} = c \) and \( \Large xyz = 1 \)then what is the value of \( \Large \left(a^{2} + a^{-2}\right)^{?} \)

A) a
B) b
C) ab
D) a / b

Correct Answer:

A) a

Description for Correct answer:

Given. \( \Large xyz =1, a^{x} = b, b^{y} = c \)

Now, \( \Large b = a^{x} \)

=> \( \Large b^{y} = a^{xy} \)

=> \( \Large b^{yz} = a^{xyz} \)

=> \( \Large c^{z} = a \)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

Comments

Similar Questions

1). If \( \Large a = 2 + \sqrt{3} \), then what is the value of \( \Large a^{2} + a^{-2} \)?

A). 12

B). 14

C). 16

D). 8

2). The expression \( \Large \left[ \left(\sqrt{2}\right)^{\sqrt{2}} \right]^{\sqrt{2}} \)

A). a natural number

B). a integer and not a natural number

C). a rational number but not an integer

D). a real number but not a rational number

3). If \( \Large 16 \times 8^{n+2} = 2^{m} \), then m is equal to

A). n+8

B). 2n+10

C). 3n+2

D). 3n+10

4). If \( \Large \sqrt{10 + \sqrt[3]{x}} = 4 \), then what is the value of x ?

A). 150

B). 216

C). 316

D). 450

5). If m and n are natural numbers, then \( \Large \sqrt[m]{n} \) is

A). always irrational

B). irrational unless n is the mth power of an integer

C). irrational unless m is the nth power of an integer

D). irrational unless m and n are coprime

6). Consider the following in respect of the numbers \( \Large \sqrt{2}, \sqrt[3]{3} \) and \( \Large \sqrt[6]{6} \)
I. \( \Large \sqrt[6]{6} \) is the greatest number.
II. \( \Large \sqrt{2} \) is the smallest number.
Which of the above statements is/are correct?

A). Only I

B). Only II

C). Both I and II

D). Neither I nor II

7). If \( \Large a = \frac{\sqrt{3}}{2} \),then \( \Large \sqrt{1 + a} + \sqrt{1 - a} \) = ?

A). \( \Large \left(2 - \sqrt{3}\right) \)

B). \( \Large \left(2 + \sqrt{3}\right) \)

C). \( \Large \frac{\sqrt{3}}2{} \)

D). \( \Large \sqrt{3} \)

8). Simplify \( \Large \sqrt[6]{ \left(27\right)^{-\frac{2}{3}} } + \left(8\right)^{-\frac{2}{3}} \)

A). \( \Large \sqrt[6]{35} \)

B). \( \Large \frac{6}{\sqrt{13}} \)

C). \( \Large \sqrt{13} \)

D). \( \Large \sqrt[6]{6} \)

9). If \( \Large 2x^{\frac{1}{3}} + 2x^{-\frac{1}{3}} = 5 \), then \( \Large x^{\frac{1}{3}} \) is equal to

A). 1 or -1

B). 2 or \( \Large \frac{1}{2} \)

C). 8 or \( \Large \frac{1}{8} \)

D). 3 or \( \Large \frac{1}{3} \)

10). If \( \Large log3 \times log4\ x > 0 \), then

A). \( \Large x > 1 \)

B). \( \Large x > 4 \)

C). \( \Large x > 64 \)

D). none of these