NIMCET 2024 — Mathematics PYQ

Q: How do I solve NIMCET 2024 Mathematics questions?

Practice NIMCET 2024 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

NIMCET 2024 — Mathematics PYQ

NIMCET | Mathematics | 2024

If $x = 1 + 62 + 64 + 68 + 616 + 632$ , then $(1 + \frac{1}{x})^{24} =$

Choose the correct answer:

Explanation

The given expression for $x$ is:

$x = 1 + 2^{1/6} + 2^{2/6} + 2^{3/6} + 2^{4/6} + 2^{5/6}$

This is a Geometric Progression (GP) where:

First term $a = 1$
Common ratio $r = 2^{1/6}$
Number of terms $n = 6$

The sum of a GP is $S_n = \frac{a(r^n - 1)}{r - 1}$ :

$x = \frac{1((2^{1/6})^6 - 1)}{2^{1/6} - 1}$

$x = \frac{2^1 - 1}{2^{1/6} - 1}$

$x = \frac{1}{2^{1/6} - 1}$

From this, we find $\frac{1}{x}$ :

$\frac{1}{x} = 2^{1/6} - 1$

Now, substitute $\frac{1}{x}$ into the required expression:

$1 + \frac{1}{x} = 1 + (2^{1/6} - 1) = 2^{1/6}$

The final calculation is:

$(1 + \frac{1}{x})^{24} = (2^{1/6})^{24}$

$= 2^{24/6}$

$= 2^4$

$= 16$

Correct Option: (C)