MHT-CET 2026 (12 May Shift II), Paper I, Mathematics question paper

1. A.
   $11$
2. B.
   $12$
3. C.
   $13$
4. D.
   $14$

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

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1. A.
   $f(130^\circ) < 0$
2. B.
   $f(220^\circ) > f(320^\circ)$
3. C.
   $f(140^\circ) = f(310^\circ)$
4. D.
   $f(310^\circ) > 0$

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1. A.
   $n\pi + (-1)^n\left(\dfrac{\pi}{3}\right), n \in \mathbb{Z}$
2. B.
   $2n\pi + (-1)^n\left(\dfrac{\pi}{2}\right), n \in \mathbb{Z}$
3. C.
   $n\pi + (-1)^{n+1}\left(\dfrac{\pi}{2}\right), n \in \mathbb{Z}$
4. D.
   $2n\pi + (-1)^n + \left(\dfrac{\pi}{4}\right), n \in \mathbb{Z}$

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

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1. A.
   $2$ and $2\pi/3$
2. B.
   $256$ and $7\pi/3$
3. C.
   $256$ and $2\pi/3$
4. D.
   $64$ and $4\pi/3$

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1. A.
   $60$
2. B.
   $12$
3. C.
   $54$
4. D.
   $18$

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1. A.
   $x + y - 10 = 0$
2. B.
   $x + y + 10 = 0$
3. C.
   $x - y + 10 = 0$
4. D.
   $x - y - 10 = 0$

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

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1. A.
   $6$
2. B.
   $8$
3. C.
   $12$
4. D.
   $16$

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1. A.
   centre is $(-1, 2)$
2. B.
   eccentricity is $\sqrt{\dfrac{19}{3}}$
3. C.
   length of its transverse axis is $4\sqrt{3}$
4. D.
   length of its conjugate axis is $4$

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1. A.
   $\lim_{x \to 2} f(x)$ exists and is equal to $5$
2. B.
   $\lim_{x \to 2} f(x)$ exists but is not equal to $5$
3. C.
   $\lim_{x \to 2} f(x)$ does not exist because $f(2)$ is defined
4. D.
   $\lim_{x \to 2} f(x)$ does not exist because left-hand and right-hand limits are not equal

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1. A.
   Two switches in series
2. B.
   Two switches in parallel
3. C.
   A single switch
4. D.
   The lamp always glows

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1. A.
   She works and she will earn money
2. B.
   She works and she will not earn money
3. C.
   She will earn money and she works.
4. D.
   She will earn money and she does not work.

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

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

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

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1. A.
   $-3$
2. B.
   $3$
3. C.
   $5$
4. D.
   $-5$

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1. A.
   $2p^2 - p + 1$
2. B.
   $4p^2 - p + 1$
3. C.
   $4p^2 - p + 2$
4. D.
   $2p^2 - p + 2$

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

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

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1. A.
   $a = 4, b = 2$
2. B.
   $a = 4, b = -2$
3. C.
   $a = -2, b = 4$
4. D.
   $a = -4, b = 2$

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

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1. A.
   $6, -11$
2. B.
   $6, 11$
3. C.
   $-6, 11$
4. D.
   $-6, -11$

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

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1. A.
   $4$
2. B.
   $-22$
3. C.
   $7$
4. D.
   $0$

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1. A.
   $\sum_{r=0}^{7}(-1)^r x^{7-r} \cdot {}^7P_r$
2. B.
   $\sum_{r=0}^{7} x^{7-r} \cdot {}^7P_r$
3. C.
   $\sum_{r=0}^{7}(-1)^r x^{7-r} \cdot {}^7C_r$
4. D.
   $\sum_{r=0}^{7} x^{7-r} \cdot {}^7C_r$

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1. A.
   $\csc\left(\dfrac{x}{2}\right) + \cot\left(\dfrac{x}{2}\right) + c$
2. B.
   $\sec^2(2x) + \log x + c$
3. C.
   $\log\left|\log\left|\tan\left(\dfrac{\pi}{4} + \dfrac{x}{2}\right)\right|\right| + c$
4. D.
   $\tan\left[\log\left|\sec\left(\dfrac{\pi}{4} + \dfrac{x}{2}\right)\right|\right] + c$

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1. A.
   $\dfrac{1}{2}\log\left|\csc\left(x - \dfrac{\pi}{3}\right) + \cot\left(x - \dfrac{\pi}{3}\right)\right| + c$
2. B.
   $\dfrac{1}{2}\log\left|\csc\left(x - \dfrac{\pi}{3}\right) - \cot\left(x - \dfrac{\pi}{3}\right)\right| + c$
3. C.
   $\dfrac{1}{2}\log\left|\csc\left(x + \dfrac{\pi}{3}\right) - \cot\left(x - \dfrac{\pi}{3}\right)\right| + c$
4. D.
   $\dfrac{1}{2}\log\left|\csc\left(x + \dfrac{\pi}{3}\right) - \cot\left(x + \dfrac{\pi}{3}\right)\right| + c$

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

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

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

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

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

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1. A.
   $5$
2. B.
   $7$
3. C.
   $10$
4. D.
   $-5$

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

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1. A.
   $\dfrac{dy}{dx} + \sqrt{3} = 0$
2. B.
   $\dfrac{dy}{dx} + 1 = 0$
3. C.
   $dx + \sqrt{3}\,dy = 0$
4. D.
   $\dfrac{dy}{dx} = 0$

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1. A.
   $5$
2. B.
   $6$
3. C.
   $8$
4. D.
   $10$

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1. A.
   $5$
2. B.
   $9$
3. C.
   $13$
4. D.
   $18$

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

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1. A.
   $15$
2. B.
   $\pm\dfrac{5}{13}$
3. C.
   $\pm 60$
4. D.
   $\pm 65$

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1. A.
   $3$
2. B.
   $5$
3. C.
   $7$
4. D.
   $9$

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1. A.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(5\hat{i} + 4\hat{j} + 7\hat{k})$
2. B.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})$
3. C.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(3\hat{i} + 7\hat{j} + 13\hat{k})$
4. D.
   $\bar{r} = \hat{i} + 2\hat{j} - 4\hat{k} + \lambda(4\hat{i} + 10\hat{j} + 9\hat{k})$

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1. A.
   $300$
2. B.
   $30$
3. C.
   $360$
4. D.
   $400$

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1. A.
   $10$
2. B.
   $9$
3. C.
   $22$
4. D.
   $32$

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

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1. A.
   $90$ and $190$
2. B.
   $60$ and $180$
3. C.
   $30$ and $120$
4. D.
   $40$ and $220$

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1. A.
   $\dfrac{5}{8}$
2. B.
   $\dfrac{1}{16}$
3. C.
   $\dfrac{5}{16}$
4. D.
   $\dfrac{11}{16}$

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1. A.
   $0$
2. B.
   $1$
3. C.
   $2$
4. D.
   $-1$

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1. A.
   $\dfrac{2}{3}$
2. B.
   $\dfrac{5}{9}$
3. C.
   $\dfrac{3}{8}$
4. D.
   $\dfrac{8}{11}$

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