NIMCET 2026 — Mathematics PYQ

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Question

NIMCET 2026 — Mathematics PYQ

NIMCET | Mathematics | 2026

The number of solutions of the equation: $tan^{- 1} (3 x) + tan^{- 1} (2 x) = \frac{π}{4}$ is

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:

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