NIMCET 2026 — Mathematics PYQ

Q: How do I solve NIMCET 2026 Mathematics questions?

Practice NIMCET 2026 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 2026 — Mathematics PYQ

NIMCET | Mathematics | 2026

If $tan^{- 1} (3 x) + tan^{- 1} (2 x) = \frac{π}{4}$ , then find the value of $x$ .

Choose the correct answer:

Explanation

To solve the equation $tan^{- 1} (3 x) + tan^{- 1} (2 x) = \frac{π}{4}$ , we use the standard formula for the sum of inverse tangents:

$tan^{- 1} (A) + tan^{- 1} (B) = tan^{- 1} (\frac{A + B}{1 - A B})$

Step 1: Apply the formula

Taking $A = 3 x$ and $B = 2 x$ :

$tan^{- 1} (\frac{3 x + 2 x}{1 - ( 3 x ) ( 2 x )}) = \frac{π}{4}$

$tan^{- 1} (\frac{5 x}{1 - 6 x ^{2}}) = \frac{π}{4}$

Step 2: Solve for $x$

Take the tangent of both sides:

$\frac{5 x}{1 - 6 x ^{2}} = tan (\frac{π}{4})$

Since $tan (\frac{π}{4}) = 1$ :

$\frac{5 x}{1 - 6 x ^{2}} = 1$

$5 x = 1 - 6 x^{2}$

$6 x^{2} + 5 x - 1 = 0$

Step 3: Factor the quadratic equation

$6 x^{2} + 6 x - x - 1 = 0$

$6 x (x + 1) - 1 (x + 1) = 0$

$(6 x - 1) (x + 1) = 0$

Choose the correct answer:

Explore More