MHT-CET 2026 (13 May Shift I), Paper I, Mathematics question paper

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

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1. A.
   $15$
2. B.
   $22.5$
3. C.
   $30$
4. D.
   $60$

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

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

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1. A.
   $1278$
2. B.
   $1728$
3. C.
   $1872$
4. D.
   $1782$

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

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

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1. A.
   $9$ square units.
2. B.
   $18$ square units.
3. C.
   $27$ square units.
4. D.
   $36$ square units.

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1. A.
   $(1, 3)$
2. B.
   $\left(\dfrac{1}{2}, \dfrac{3}{2}\right)$
3. C.
   $\left(\dfrac{3}{2}, \dfrac{1}{2}\right)$
4. D.
   $(0, -1)$

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1. A.
   $(1, 0)$
2. B.
   $(0, -2 + \sqrt{3})$
3. C.
   $(-1, -2)$
4. D.
   $(-\sqrt{3} + 1, -1)$

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

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1. A.
   $x^2 + y^2 - 8y - 9 = 0$
2. B.
   $x^2 + y^2 + 8y - 9 = 0$
3. C.
   $x^2 + y^2 + 8y - 41 = 0$
4. D.
   $x^2 + y^2 - 8y - 41 = 0$

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1. A.
   $0$
2. B.
   $1$
3. C.
   $2$
4. D.
   $\infty$

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

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1. A.
   $p = T, q = F$
2. B.
   both $p$ and $q$ have the same truth value
3. C.
   $p \to \sim q$ is a contradiction
4. D.
   $p = F, q = T$

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1. A.
   Result 1 is true, Result 2 is true
2. B.
   Result 1 is true, Result 2 is false
3. C.
   Result 1 is false, Result 2 is true
4. D.
   Result 1 is false, Result 2 is false

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

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

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1. A.
   $x = 2, y = 1, z = 3$
2. B.
   $x = 3, y = 2, z = 1$
3. C.
   $x = 1, y = 2, z = 3$
4. D.
   $x = 2, y = 3, z = 1$

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

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1. A.
   $(-\infty, 0)$
2. B.
   $(0, \infty)$
3. C.
   $[0, \infty)$
4. D.
   $(0, 1)$

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1. A.
   $-\dfrac{x^2}{y^2}\sqrt{\dfrac{1 - y^6}{1 - x^6}}$
2. B.
   $\dfrac{y^2}{x^2}\sqrt{\dfrac{1 - y^6}{1 - x^6}}$
3. C.
   $\dfrac{x^2}{y^2}\sqrt{\dfrac{1 - y^6}{1 - x^6}}$
4. D.
   $-\dfrac{y^2}{x^2}\sqrt{\dfrac{1 - y^6}{1 - x^6}}$

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

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

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1. A.
   $f(x)$ is increasing in $(-\infty, 0) \cup (2, \infty)$
2. B.
   $f(x)$ is decreasing in $(-\infty, 0) \cup (2, \infty)$
3. C.
   $f(x)$ is increasing in $(0, 2)$
4. D.
   $f(x)$ is decreasing in $(2, \infty)$

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1. A.
   $25\pi\ \mathrm{cm^3/sec}$
2. B.
   $50\pi\ \mathrm{cm^3/sec}$
3. C.
   $100\pi\ \mathrm{cm^3/sec}$
4. D.
   $10\pi\ \mathrm{cm^3/sec}$

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

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

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1. A.
   $\dfrac{1}{\sqrt{13}}\tan^{-1}\left(\dfrac{4\tan x + 1}{\sqrt{13}}\right) + c$
2. B.
   $\dfrac{2}{\sqrt{11}}\tan^{-1}\left(\dfrac{4\tan x + 2}{\sqrt{11}}\right) + c$
3. C.
   $\dfrac{1}{11}\tan^{-1}\left(\dfrac{2\tan x + 1}{11}\right) + c$
4. D.
   $\dfrac{1}{\sqrt{11}}\tan^{-1}\left(\dfrac{4\tan x + 1}{\sqrt{11}}\right) + c$

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1. A.
   $x - 2\log|x + 1| - \dfrac{2}{x + 1} + c$
2. B.
   $x - 2\log|x + 1| + \dfrac{2}{x + 1} + c$
3. C.
   $x + 2\log|x + 1| + c$
4. D.
   $x - 2\log|x + 1| + c$

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

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1. A.
   $\dfrac{1}{2} < a < 2$
2. B.
   $\dfrac{1}{2} \le a \le 2$
3. C.
   $a \le \dfrac{1}{2}$
4. D.
   $a \ge 2$

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1. A.
   $\log\left(\dfrac{34}{21}\right)$
2. B.
   $\log\left(\dfrac{17}{7}\right)$
3. C.
   $\log\left(\dfrac{17}{18}\right)$
4. D.
   $\log\left(\dfrac{68}{63}\right)$

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1. A.
   $12\sqrt{3}$
2. B.
   $6\sqrt{3}$
3. C.
   $8\sqrt{3}$
4. D.
   $4\sqrt{3}$

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

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

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

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1. A.
   $5$
2. B.
   $\dfrac{5\sqrt{3}}{2}$
3. C.
   $2.5$
4. D.
   $16\sqrt{3}$

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1. A.
   $156$
2. B.
   $78$
3. C.
   $39$
4. D.
   $1$

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

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

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1. A.
   $20$
2. B.
   $32$
3. C.
   $48$
4. D.
   $56$

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1. A.
   $(5, -15)$
2. B.
   $(-5, 5)$
3. C.
   $(6, -17)$
4. D.
   $(-6, 7)$

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

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1. A.
   $5$
2. B.
   $9$
3. C.
   $18$
4. D.
   $\sqrt{29}$

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1. A.
   $4 : 3$ internally, $(0, 2, 33)$
2. B.
   $3 : 4$ internally, $(0, 2, 33)$
3. C.
   $3 : 4$ externally, $(0, 2, 33)$
4. D.
   $4 : 3$ externally, $(2, 0, 33)$

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1. A.
   $17$
2. B.
   $18$
3. C.
   $35$
4. D.
   $53$

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

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1. A.
   $\sqrt[3]{6.75}$
2. B.
   $\sqrt[3]{13.5}$
3. C.
   $\sqrt[3]{9}$
4. D.
   $\sqrt[3]{18}$

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

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