Question

If x is so small that its two and higher power can be neglected and $(1 - 2x)^{- 1/2}(1 - 4x)^{- 5/2}$ =$1 + kx$ then k =

• A. 1
• B. – 2
• C. 10
• D. 11

Answer 1

Answer: (C)

10

Answer 2

$(1 - 2x)^{- 1/2}(1 - 4x)^{- 5/2} = 1 + kx$

$\left\lbrack 1 + \frac{( - 5/2)( - 4x)}{1!} + \frac{( - 5/2)( - 7/2)( - 4x)^{2}}{2!} + ...... \right\rbrack = 1 + kx$Higher power can be neglected.

Then $\left\lbrack 1 + \frac{x}{1!} \right\rbrack\left\lbrack 1 + \frac{10x}{1!} \right\rbrack = 1 + kx$; $1 + 10x + x = 1 + kx$; $k = 11$