MHT-CET 2026 (19 April Shift II), Paper I, Mathematics question paper

1. A.
   $e^{i\frac{\pi}{4}}$
2. B.
   $\dfrac{1}{\sqrt{2}}e^{i\frac{\pi}{4}}$
3. C.
   $e^{i\frac{\pi}{2}}$
4. D.
   $\dfrac{1}{\sqrt{2}}e^{i\frac{\pi}{2}}$

Tap an option to check your answer.

1. A.
   $6\sqrt{3} + \dfrac{5}{2}$
2. B.
   $\dfrac{5\sqrt{3}}{2} - 6$
3. C.
   $\dfrac{5\sqrt{3}}{2} + 6$
4. D.
   $6\sqrt{3} - \dfrac{5}{2}$

Tap an option to check your answer.

1. A.
   $5$ or $11$
2. B.
   $7$ or $14$
3. C.
   $8$ or $15$
4. D.
   $6$ or $13$

Tap an option to check your answer.

1. A.
   $(4, 3)$
2. B.
   $\left(\dfrac{1}{2}, \dfrac{1}{3}\right)$
3. C.
   $\left(\dfrac{1}{4}, \dfrac{1}{3}\right)$
4. D.
   $\left(\dfrac{1}{3}, \dfrac{1}{2}\right)$

Tap an option to check your answer.

1. A.
   $\dfrac{\sqrt{3} - 1}{\sqrt{3} + 1}$
2. B.
   $\dfrac{1 + \sqrt{3}}{1 - \sqrt{3}}$
3. C.
   $\dfrac{\sqrt{3} + 1}{\sqrt{3} - 1}$
4. D.
   $\dfrac{\sqrt{3} + 1}{2}$

Tap an option to check your answer.

1. A.
   $5$
2. B.
   $5\sqrt{2}$
3. C.
   $\dfrac{5}{\sqrt{2}}$
4. D.
   $\dfrac{5}{2}$

Tap an option to check your answer.

1. A.
   $\left(-\dfrac{1}{2}, -\dfrac{5}{2}\right)$
2. B.
   $\left(\dfrac{1}{2}, -\dfrac{5}{2}\right)$
3. C.
   $\left(\dfrac{1}{2}, \dfrac{5}{4}\right)$
4. D.
   $\left(-\dfrac{1}{2}, \dfrac{5}{4}\right)$

Tap an option to check your answer.

1. A.
   $\dfrac{3}{4}$
2. B.
   $\dfrac{\sqrt{7}}{4}$
3. C.
   $\dfrac{1}{2}$
4. D.
   $\dfrac{3}{8}$

Tap an option to check your answer.

1. A.
   $2$
2. B.
   $1$
3. C.
   $-1$
4. D.
   $-2$

Tap an option to check your answer.

1. A.
   Truth value of $p \to q$ is False
2. B.
   Truth value of $p \to r$ is False.
3. C.
   Truth value of $(\sim q) \to p$ is False.
4. D.
   The truth value of $(\sim p) \wedge r$ is False.

Tap an option to check your answer.

1. A.
   $[q \wedge (p \to q)] \to p$
2. B.
   $(p \wedge q) \to (q \vee \sim p)$
3. C.
   $[(\sim p \vee q) \wedge \sim r] \leftrightarrow p$
4. D.
   $(p \wedge q) \vee (\sim q \vee r)$

Tap an option to check your answer.

1. A.
   $(T, F, T)$
2. B.
   $(F, T, F)$
3. C.
   $(F, F, T)$
4. D.
   $(F, T, T)$

Tap an option to check your answer.

1. A.
   $60^\circ$ or $120^\circ$
2. B.
   $30^\circ$ or $150^\circ$
3. C.
   $45^\circ$ or $135^\circ$
4. D.
   $30^\circ$ or $90^\circ$

Tap an option to check your answer.

1. A.
   $\dfrac{3}{4\Delta}$
2. B.
   $\left(\dfrac{3}{4\Delta}\right)^2$
3. C.
   $\dfrac{45}{4\Delta}$
4. D.
   $\left(\dfrac{45}{4\Delta}\right)^2$

Tap an option to check your answer.

1. A.
   $1013$
2. B.
   $2026$
3. C.
   $3039$
4. D.
   $6078$

Tap an option to check your answer.

1. A.
   $1$
2. B.
   $-1$
3. C.
   $2$
4. D.
   $-2$

Tap an option to check your answer.

1. A.
   $\dfrac{2\pi}{3}$
2. B.
   $\dfrac{4\pi}{3}$
3. C.
   $\dfrac{5\pi}{3}$
4. D.
   $\pi$

Tap an option to check your answer.

1. A.
   $x$
2. B.
   $-x$
3. C.
   $\log x$
4. D.
   $-\log x$

Tap an option to check your answer.

1. A.
   $5$
2. B.
   $10$
3. C.
   $15$
4. D.
   $20$

Tap an option to check your answer.

1. A.
   $e^{12}$
2. B.
   $e^6$
3. C.
   $e^3$
4. D.
   $e^{\frac{3}{2}}$

Tap an option to check your answer.

1. A.
   $1$
2. B.
   $2$
3. C.
   $3$
4. D.
   $m$

Tap an option to check your answer.

1. A.
   $-\dfrac{5}{13}$
2. B.
   $\dfrac{5}{13}$
3. C.
   $\dfrac{13}{5}$
4. D.
   $\dfrac{2}{7}$

Tap an option to check your answer.

1. A.
   $\dfrac{1}{1 + e^{g(x)}}$
2. B.
   $\dfrac{e^{g(x)}}{1 + e^{g(x)}}$
3. C.
   $\dfrac{1}{1 + g(x)}$
4. D.
   $e^{g(x)}$

Tap an option to check your answer.

1. A.
   $\dfrac{5}{36}$
2. B.
   $\dfrac{35}{36}$
3. C.
   $\dfrac{25}{36}$
4. D.
   $\dfrac{36}{25}$

Tap an option to check your answer.

1. A.
   $-4$
2. B.
   $4$
3. C.
   $-2$
4. D.
   $2$

Tap an option to check your answer.

1. A.
   $3$ cm
2. B.
   $5$ cm
3. C.
   $6$ cm
4. D.
   $4$ cm

Tap an option to check your answer.

1. A.
   $x^3\sin x + x^2\cos x - 6x\sin x + 6\cos x + c$
2. B.
   $x^3\sin x + 3x^2\sin x - 6x\sin x - 6\cos x + c$
3. C.
   $x^3\sin x + 3x^2\cos x - 6x\sin x - 6\cos x + c$
4. D.
   $x^3\sin x + 3x^2\cos x - 6x\sin x + 6\cos x + c$

Tap an option to check your answer.

1. A.
   $\log uv + c$
2. B.
   $\log\dfrac{u}{v} + c$
3. C.
   $\dfrac{v^2}{2u^2} + c$
4. D.
   $\dfrac{u^2}{2v^2} + c$

Tap an option to check your answer.

1. A.
   $\dfrac{13}{10}$
2. B.
   $\dfrac{9}{10}$
3. C.
   $\dfrac{3}{10}$
4. D.
   $\dfrac{17}{10}$

Tap an option to check your answer.

1. A.
   $\log 2$
2. B.
   $\log\left(\dfrac{2}{e}\right)$
3. C.
   $-\log e$
4. D.
   $\log\left(\dfrac{4}{e}\right)$

Tap an option to check your answer.

1. A.
   $4$
2. B.
   $\dfrac{14}{3}$
3. C.
   $7$
4. D.
   $\dfrac{26}{3}$

Tap an option to check your answer.

1. A.
   $\dfrac{4}{3}$
2. B.
   $\dfrac{8}{3}$
3. C.
   $\dfrac{20}{3}$
4. D.
   $\dfrac{2}{3}$

Tap an option to check your answer.

1. A.
   $\dfrac{8\sqrt{2}}{3} + \dfrac{9\pi}{2} - 2\sqrt{2} - 9\sin^{-1}\dfrac{1}{3}$
2. B.
   $\dfrac{8\sqrt{2}}{3} + \dfrac{9\pi}{2} + 2\sqrt{2} + 9\sin^{-1}\dfrac{1}{3}$
3. C.
   $\dfrac{4\sqrt{2}}{3} + \dfrac{9\pi}{4} - \sqrt{2} - \dfrac{9}{2}\sin^{-1}\dfrac{1}{3}$
4. D.
   $\dfrac{4\sqrt{2}}{3} + \dfrac{9\pi}{4} + \sqrt{2} + \dfrac{9}{2}\sin^{-1}\dfrac{1}{3}$

Tap an option to check your answer.

1. A.
   $\dfrac{d^2y}{dx^2} = 0$
2. B.
   $\dfrac{dy}{dx} = 0$
3. C.
   $\dfrac{dy}{dx} = -\cot\alpha$
4. D.
   $\dfrac{d^2y}{dx^2} = \csc^2\alpha$

Tap an option to check your answer.

1. A.
   $1$
2. B.
   $6$
3. C.
   $4$
4. D.
   $12$

Tap an option to check your answer.

1. A.
   $\cot\left(\dfrac{x + y}{2}\right) = x + c$
2. B.
   $\tan\left(\dfrac{x + y}{2}\right) = x + c$
3. C.
   $-\sin(x + y) = x + c$
4. D.
   $\sec(x - y) + x = c$

Tap an option to check your answer.

1. A.
   $\sqrt{8}$
2. B.
   $8$
3. C.
   $14$
4. D.
   $\sqrt{14}$

Tap an option to check your answer.

1. A.
   $\dfrac{8}{9}$
2. B.
   $\dfrac{\sqrt{17}}{9}$
3. C.
   $\dfrac{1}{9}$
4. D.
   $\dfrac{4\sqrt{5}}{9}$

Tap an option to check your answer.

1. A.
   $\dfrac{1}{\sqrt{2}}$
2. B.
   $\sqrt{2}$
3. C.
   $2$
4. D.
   $2\sqrt{2}$

Tap an option to check your answer.

1. A.
   $-5(\sqrt{2} + 1)$
2. B.
   $5(1 - \sqrt{2})$
3. C.
   $5(\sqrt{2} + 1)$
4. D.
   $5(\sqrt{2} - 1)$

Tap an option to check your answer.

1. A.
   $\dfrac{1}{\sqrt{17}}$
2. B.
   $\dfrac{3}{\sqrt{26}}$
3. C.
   $\dfrac{5}{\sqrt{17}}$
4. D.
   $\dfrac{7}{\sqrt{26}}$

Tap an option to check your answer.

1. A.
   $\dfrac{8}{\sqrt{26}}$
2. B.
   $\dfrac{6}{\sqrt{26}}$
3. C.
   $\dfrac{4}{\sqrt{26}}$
4. D.
   $\dfrac{2}{\sqrt{26}}$

Tap an option to check your answer.

1. A.
   $\dfrac{1}{\sqrt{2}}$
2. B.
   $\dfrac{1}{2}$
3. C.
   $\dfrac{1}{\sqrt{3}}$
4. D.
   $\dfrac{1}{3}$

Tap an option to check your answer.

1. A.
   $b = 13$
2. B.
   $b = 15$
3. C.
   $b = 16$
4. D.
   $b = 18$

Tap an option to check your answer.

1. A.
   $2\sqrt{2}$
2. B.
   $2\sqrt{3}$
3. C.
   $3\sqrt{2}$
4. D.
   $3\sqrt{3}$

Tap an option to check your answer.

1. A.
   Maximize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \le 250, x_1 \le 30, x_2 \le 4x_1, x_1 \ge 0, x_2 \ge 0$.
2. B.
   Minimize $z = 150x_1 + 90x_2$ subject to $x_1 + x_2 \le 250, x_1 \ge 30, x_2 \ge 4x_1, x_1 \ge 0, x_2 \ge 0$.
3. C.
   Minimize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \le 250, x_1 \ge 30, x_2 \ge 4x_1, x_1 \ge 0, x_2 \ge 0$.
4. D.
   Maximize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \le 250, x_1 \ge 30, x_2 \ge 4x_1, x_1 \ge 0, x_2 \ge 0$.

Tap an option to check your answer.

1. A.
   $\left(\dfrac{1}{5}\right)^6$
2. B.
   $1 - \left(\dfrac{1}{5}\right)^6$
3. C.
   $\left(\dfrac{4}{5}\right)^6$
4. D.
   $1 - \left(\dfrac{4}{5}\right)^6$

Tap an option to check your answer.

1. A.
   $2.6$
2. B.
   $3.8$
3. C.
   $3.2$
4. D.
   $3.6$

Tap an option to check your answer.

1. A.
   $\dfrac{20}{64}$
2. B.
   $\dfrac{31}{64}$
3. C.
   $\dfrac{35}{64}$
4. D.
   $\dfrac{32}{64}$

Tap an option to check your answer.

1. A.
   $\dfrac{2\pi}{3}$
2. B.
   $\dfrac{3\pi}{2}$
3. C.
   $\dfrac{\pi}{4}$
4. D.
   $\dfrac{\pi}{2}$

Tap an option to check your answer.