Surds and Indices Aptitude Test Paper 3

Answer: A

Explanation:

Given: 2^x=3^y=6^-z
Let 2^x=3^y=6^-z=k (say)
Then 2 = k^1/x , 3 = k^1/y , 6 = k^-1/z
2 x 3 = 6
k^1/x x k^1/y = k^-1/z ( from above equation)

Equating the powers of above equation because the base is same

Answer: C

Explanation:

Given:

Then p³-3p

Putting the value of 'p' in above equation

By applying (a+b)³ = a³ + b³ + 3ab(a+b)

Answer: C

Explanation:

Given:

Then,

a = k^m, b = kⁿ, c = k^p

abc = 1 (given)

k^m. kⁿ. k^p = k⁰

k^m+n+P = k⁰

m+n+P = 1

Since the base are same

So, m+n+P = 0

Answer: D

Explanation:

By equating the power

5 + 8 = 2x +3
2x = 13 - 3 = 10
X = 10/2 = 5

Answer: D

Explanation:

By equating the powers

x-6 = 1
x = 1+6 = 7