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

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

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

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1. A.
   $7!$
2. B.
   $3! \times 4!$
3. C.
   $3! \times 3!$
4. D.
   $6!$

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

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1. A.
   $3$
2. B.
   $4$
3. C.
   $6$
4. D.
   $8$

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

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1. A.
   $6$ square units.
2. B.
   $12$ square units.
3. C.
   $24$ square units.
4. D.
   $48$ square units.

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1. A.
   $2p + q = 0$
2. B.
   $2p + 3q = 0$
3. C.
   $pq = 1$
4. D.
   $pq + 1 = 0$

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1. A.
   $4$ sq. units
2. B.
   $8$ sq. units
3. C.
   $12$ sq. units
4. D.
   $16$ sq. units

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1. A.
   $\dfrac{3\sqrt{2}}{2}$
2. B.
   $\dfrac{5\sqrt{2}}{2}$
3. C.
   $0$
4. D.
   $\sqrt{2}$

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1. A.
   $\dfrac{1}{8}$
2. B.
   $\dfrac{1}{32}$
3. C.
   $\dfrac{1}{16}$
4. D.
   $0$

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1. A.
   Circuit A
2. B.
   Circuit B
3. C.
   Circuit C
4. D.
   Circuit D

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1. A.
   $p \wedge \sim q$
2. B.
   $\sim p \wedge q$
3. C.
   $p \wedge q$
4. D.
   $\sim p \vee \sim q$

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

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1. A.
   $4 : 3 : 14$
2. B.
   $14 : 4 : 3$
3. C.
   $3 : 4 : 14$
4. D.
   $4 : 14 : 3$

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1. A.
   $\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
2. B.
   $\begin{bmatrix} 1 & 0 & -1 \\ 0 & 0 & 0 \\ -1 & 0 & 1 \end{bmatrix}$
3. C.
   $\begin{bmatrix} 0 & 1 & 0 \\ 1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
4. D.
   $\begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$

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1. A.
   $\begin{bmatrix} 1 + pq & p & 0 \\ q & 1 + pq & p \\ 0 & q & 1 \end{bmatrix}$
2. B.
   $\begin{bmatrix} 1 & p & p^2 \\ q & 1 + pq & p + p^2q \\ q^2 & q + pq^2 & 1 + pq + p^2q^2 \end{bmatrix}$
3. C.
   $\begin{bmatrix} 1 & -p & p^2 \\ -q & 1 + pq & -(p + p^2q) \\ q^2 & -(q + pq^2) & 1 + pq + p^2q^2 \end{bmatrix}$
4. D.
   $\begin{bmatrix} 1 & -p & p^2 \\ -q & 1 + pq & p + p^2q \\ q^2 & q + pq^2 & 1 + pq + p^2q^2 \end{bmatrix}$

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1. A.
   $-\dfrac{\pi}{4}$
2. B.
   $0$
3. C.
   $\dfrac{\pi}{4}$
4. D.
   $\dfrac{\pi}{2}$

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1. A.
   $x^2 - x - 6 = 0$
2. B.
   $x^2 - x - 12 = 0$
3. C.
   $x^2 + x - 12 = 0$
4. D.
   $x^2 + x - 6 = 0$

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1. A.
   $2$
2. B.
   $5$
3. C.
   $9$
4. D.
   $10$

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

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

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

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1. A.
   $-\log_{10}x^2$
2. B.
   $-(\log_{10}x)^2$
3. C.
   $(\log_x 10)^2$
4. D.
   $\dfrac{x^2}{100}$

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1. A.
   Rs. $1100$
2. B.
   Rs. $2200$
3. C.
   Rs. $3300$
4. D.
   Rs. $4400$

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1. A.
   $-128$ ft/sec
2. B.
   $128$ ft/sec
3. C.
   $0$ ft/sec
4. D.
   $256$ ft/sec

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1. A.
   $0$
2. B.
   $1$
3. C.
   $\dfrac{1}{2}$
4. D.
   $-1$

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1. A.
   $\dfrac{-1}{2\tan x} + \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$
2. B.
   $\dfrac{-1}{2\tan x} - \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$
3. C.
   $\dfrac{1}{2\tan x} - \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$
4. D.
   $\dfrac{1}{2\tan x} + \dfrac{1}{2\sqrt{2}}\tan^{-1}\left(\dfrac{\tan x}{\sqrt{2}}\right) + c$

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1. A.
   $\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) + \dfrac{2}{9}\right] + c$
2. B.
   $\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) - \dfrac{2}{9}\right] + c$
3. C.
   $\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) + \dfrac{2}{3}\right] + c$
4. D.
   $\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) - \dfrac{2}{3}\right] + c$

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

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1. A.
   $-\dfrac{1}{16}$
2. B.
   $-\dfrac{25}{16}$
3. C.
   $\dfrac{25}{4}$
4. D.
   $-\dfrac{25}{4}$

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

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1. A.
   $2$
2. B.
   $4$
3. C.
   $6$
4. D.
   $8$

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1. A.
   $\dfrac{\pi}{4}$
2. B.
   $\dfrac{\pi}{6}$
3. C.
   $\dfrac{\pi}{3}$
4. D.
   $\dfrac{\pi}{2}$

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1. A.
   $8\log 2 - \dfrac{14}{3}$
2. B.
   $8\log 2 + \dfrac{7}{3}$
3. C.
   $16\log 2 + \dfrac{7}{3}$
4. D.
   $16\log 2 - \dfrac{14}{3}$

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1. A.
   Circle
2. B.
   Ellipse
3. C.
   Hyperbola
4. D.
   Pair of straight Lines

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1. A.
   $a = c = 0,\ b + d = 0$
2. B.
   $a = c = 0,\ b = d$
3. C.
   $b = d = 0,\ a + c = 0$
4. D.
   $b = d = 0,\ a = c$

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1. A.
   $\dfrac{3\vec{a} + 4\vec{b} + 2\vec{c}}{9}$
2. B.
   $\dfrac{6\vec{a} + 2\vec{b} + \vec{c}}{9}$
3. C.
   $\dfrac{3\vec{a} + 2\vec{b} + 4\vec{c}}{9}$
4. D.
   $\dfrac{6\vec{a} + \vec{b} + 2\vec{c}}{9}$

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1. A.
   $5\sqrt{3}$
2. B.
   $10\sqrt{2}$
3. C.
   $5\sqrt{2}$
4. D.
   $4\sqrt{3}$

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

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1. A.
   $9$
2. B.
   $7$
3. C.
   $0$
4. D.
   cant determine

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1. A.
   $25$
2. B.
   $27$
3. C.
   $29$
4. D.
   $31$

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1. A.
   $\sqrt{29}$
2. B.
   $\sqrt{41}$
3. C.
   $\sqrt{61}$
4. D.
   $\sqrt{51}$

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1. A.
   $\dfrac{x}{a} - \dfrac{y}{b} - \dfrac{z}{c} = 0$
2. B.
   $\dfrac{x}{a} - \dfrac{y}{b} + \dfrac{z}{c} = 0$
3. C.
   $\dfrac{x}{a} + \dfrac{y}{b} - \dfrac{z}{c} = 0$
4. D.
   $\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 0$

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1. A.
   $5$
2. B.
   $20$
3. C.
   $10$
4. D.
   $8$

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1. A.
   $\dfrac{x - a}{b} = y = \dfrac{z - c}{d}$
2. B.
   $\dfrac{x - b}{a} = \dfrac{y - d}{c} = z$
3. C.
   $x = \dfrac{y - a}{b} = \dfrac{z - c}{d}$
4. D.
   $\dfrac{x - b}{a} = y = \dfrac{z - d}{c}$

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1. A.
   $2x + y \ge 2,\ x - y \ge 1,\ x + 2y \le 8,\ x \ge 0,\ y \ge 0$
2. B.
   $x + 2y \ge 2,\ x - y \ge 1,\ x + 2y \le 8,\ x \ge 0,\ y \ge 0$
3. C.
   $2x + y \ge 2,\ x - y \le 1,\ x + 2y \le 8,\ x \ge 0,\ y \ge 0$
4. D.
   $2x + y \ge 2,\ x - y \le 1,\ 2x + y \le 8,\ x \ge 0,\ y \ge 0$

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1. A.
   $0.125$
2. B.
   $0.25$
3. C.
   $0.375$
4. D.
   $0.75$

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1. A.
   $P\left(X < \dfrac{a}{2}\right) = P\left(X > \dfrac{a}{2}\right)$
2. B.
   $P\left(X < \dfrac{a}{2}\right) < P\left(X > \dfrac{3a}{2}\right)$
3. C.
   $P\left(X < \dfrac{a}{2}\right) > P\left(X > \dfrac{3a}{2}\right)$
4. D.
   $P\left(X < \dfrac{a}{2}\right) = P\left(X > \dfrac{3a}{2}\right)$

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1. A.
   $\dfrac{19}{6}$
2. B.
   $-\dfrac{19}{6}$
3. C.
   $\dfrac{3}{2}$
4. D.
   $-\dfrac{3}{2}$

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