MHT-CET 2025 (26 April Shift II), Paper I, Mathematics question paper

1. A.
   $( \sim q \land p) \land (p \land \sim p)$
2. B.
   $\ (p \land q) \land ( - p \land q)$
3. C.
   $\lbrack( - q) \land p\rbrack \land q$
4. D.
   $( - q \land p) \vee (p \vee \sim p)$

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1. A.
   $\mathbb{R} - \{ 1\}$
2. B.
   $\mathbb{R} - \{ 2\}$
3. C.
   $\mathbb{R}$
4. D.
   $\mathbb{R} - \{ 1,2\}$

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

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1. A.
   $\tan^{- 1}(2)$
2. B.
   $\tan^{- 1}(3)$
3. C.
   $\tan^{- 1}\left( \frac{1}{2} \right)$
4. D.
   $\tan^{- 1}\left( \frac{1}{3} \right)$

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1. A.
   $\frac{1}{2}$
2. B.
   $\frac{1}{12}$
3. C.
   $\frac{1}{8}$
4. D.
   $\frac{1}{16}$

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

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1. A.
   $(p \land \sim r) \vee ( \sim q \land \sim s)$
2. B.
   $(p \vee \sim q) \leftrightarrow ( \sim r \rightarrow s)$
3. C.
   $(p \leftrightarrow q) \land ( \sim p \vee \sim q)$
4. D.
   $(s \vee \sim p) \leftrightarrow ( \sim p \land \sim r)$

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

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1. A.
   $\frac{3}{2}$
2. B.
   $\frac{- 3}{2}$
3. C.
   $\frac{11}{4}$
4. D.
   $\frac{- 11}{2}$

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1. A.
   $100\pi$
2. B.
   $300\pi$
3. C.
   $200\pi$
4. D.
   $\ 150\pi$

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1. A.
   $\frac{A}{24} - \frac{7}{24}I$
2. B.
   $\frac{A}{21} - \frac{7}{21}I$
3. C.
   $\frac{7I}{24} - \frac{1}{24}\text{ }A$
4. D.
   A-3I

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

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1. A.
   $a + b = c$
2. B.
   $b + c = a$
3. C.
   $a + c = b$
4. D.
   $b = c$

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1. A.
   $\cot^{2}\frac{\alpha}{2}$
2. B.
   $\cot\frac{\alpha}{2}$
3. C.
   $\ \tan\frac{\alpha}{2}$
4. D.
   $\tan^{2}\frac{\alpha}{2}$

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1. A.
   $\frac{7}{24}$
2. B.
   $\frac{- 7}{24}$
3. C.
   $\frac{5}{24}$
4. D.
   $\frac{- 5}{24}$

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1. A.
   $\frac{1}{32}$
2. B.
   32
3. C.
   $(32)^{\frac{1}{2}}$
4. D.
   $(32)^{\frac{1}{3}}$

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1. A.
   $\frac{168}{5}$
2. B.
   28
3. C.
   $\frac{31}{4}$
4. D.
   $\frac{35}{4}$

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

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1. A.
   $\frac{\sqrt{34}}{3}$
2. B.
   $\frac{5}{3}$
3. C.
   $\frac{\sqrt{41}}{4}$
4. D.
   $\frac{5}{4}$

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1. A.
   $y(1 + x) = x + {ce}^{x}$, where c is the constant of integration
2. B.
   $y(1 + x) = {ce}^{x}$, where c is the constant of integration
3. C.
   $y(1 - x) = x - {ce}^{x}$, where c is the constant of integration
4. D.
   $y(1 + x) = x$, where c is the constant of integration

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1. A.
   $\tan x + \cot x + c$, where c is the constant of integration.
2. B.
   $\ \tan x - \cot x + c$, where c is the constant of integration.
3. C.
   $\tan x\ \cot x + c$, where c is the constant of integration.
4. D.
   $\tan x - \cot 2x + c$, where c is the constant of integration.

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

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1. A.
   $2,\frac{25}{4}$
2. B.
   $\ - 2,\frac{25}{4}$
3. C.
   $2,\frac{- 25}{4}$
4. D.
   $\ - 2,\frac{- 25}{4}$

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1. A.
   332620
2. B.
   332540
3. C.
   332640
4. D.
   332520

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1. A.
   $x\frac{\text{ }dy}{\text{ }dx} - 2y = 0$
2. B.
   $\frac{dy}{\text{ }dx} + xy = 0$
3. C.
   $x\frac{\text{ }dy}{\text{ }dx} + y = 0$
4. D.
   $x^{2}\frac{\text{ }dy}{dx} + y = 0$

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

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1. A.
   $\frac{1}{7}$
2. B.
   $\frac{6}{7}$
3. C.
   $\frac{2}{7}$
4. D.
   $\frac{5}{7}$

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1. A.
   5950
2. B.
   8000
3. C.
   7950
4. D.
   6950

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1. A.
   5
2. B.
   36
3. C.
   6
4. D.
   25

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1. A.
   $8\sqrt{3}$ sq. units
2. B.
   $\frac{4}{\sqrt{3}}$ sq. units
3. C.
   $4\sqrt{3}$ sq. units
4. D.
   $\sqrt{3}$ sq. units

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1. A.
   intersecting at point $(1, - 1,2)$
2. B.
   intersecting at right angles
3. C.
   do not intersect
4. D.
   intersecting at point $(3,1, - 1)$

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1. A.
   $x^{2}\sin x + 2x\cos x - 2\sin x + c$, where c is the constant of integration
2. B.
   $x^{2}\sin x - 2x\cos x - 2\sin x + c$, where $c$ is the constant of integration
3. C.
   $x^{2}\sin x - 2x\cos x + 2\sin x + c$, where c is the constant of integration
4. D.
   $x^{2}\sin x + 2x\cos x + 2\sin x + c$, where c is the constant of integration

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

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1. A.
   $0 < x < \frac{1}{2}$
2. B.
   $1 < x < 2$
3. C.
   $1 \leq x \leq 2$
4. D.
   $- 1 < x < 2$

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

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1. A.
   u
2. B.
   v
3. C.
   $\frac{- 1}{u}$
4. D.
   $\frac{- 1}{v}$

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1. A.
   $\lbrack\overline{r} - (\widehat{i} - 2\widehat{j} + 0\widehat{k})\rbrack \times \left( - \widehat{i} + \frac{1}{2}\widehat{j} - \frac{1}{2}\widehat{k} \right) = \overline{0}$
2. B.
   $\lbrack\overline{r} + (\widehat{i} - 2\widehat{j} + 0\widehat{k})\rbrack \times \left( - \widehat{i} + \frac{1}{2}\widehat{j} + \frac{1}{2}\widehat{k} \right) = \overline{0}$
3. C.
   $\overline{r} = ( - \widehat{i} - 2\widehat{j} + 0\widehat{k}) + \lambda\left( - \widehat{i} + \frac{1}{2}\widehat{j} - \frac{1}{2}\widehat{k} \right)$
4. D.
   $\overline{r} = (\widehat{i} + 2\widehat{j}) + \lambda\left( - \widehat{i} + \frac{1}{2}\widehat{j} - \frac{1}{2}\widehat{k} \right)$

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

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1. A.
   $\frac{44}{2^{13}}$
2. B.
   $\frac{55}{2^{10}}$
3. C.
   $\frac{55}{2^{13}}$
4. D.
   $\frac{44}{2^{10}}$

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1. A.
   $15:14$
2. B.
   $29:13$
3. C.
   $21:16$
4. D.
   $28:9$

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1. A.
   $\frac{25}{2}$ sq. units
2. B.
   25 sq. units
3. C.
   $\frac{25\sqrt{5}}{2}$ sq. units
4. D.
   $25\sqrt{5}$ sq. units

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1. A.
   $\frac{60}{7}$ units
2. B.
   $\frac{7}{60}$ units
3. C.
   $\frac{1}{7}$ units
4. D.
   $\frac{2}{7}$ units

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1. A.
   $\frac{- 2}{\sqrt{101}},\frac{3}{\sqrt{101}},\frac{8}{\sqrt{101}}$
2. B.
   $\frac{- 3}{\sqrt{49}},\frac{2}{\sqrt{49}},\frac{6}{\sqrt{49}}$
3. C.
   $\frac{- 4}{\sqrt{101}},\frac{- 9}{\sqrt{101}},\frac{2}{\sqrt{101}}$
4. D.
   $\frac{4}{22},\frac{- 12}{22},\frac{18}{22}$

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1. A.
   $\pm \left( \frac{3\widehat{i} + \widehat{j} + \widehat{k}}{\sqrt{11}} \right)$
2. B.
   $\pm \left( \frac{- \widehat{i} + 2\widehat{j} + \widehat{k}}{\sqrt{6}} \right)$
3. C.
   $\pm \left( \frac{2\widehat{i} + \widehat{j} + \widehat{k}}{\sqrt{6}} \right)$
4. D.
   $\pm \left( \frac{\widehat{i} + \widehat{j} + \widehat{k}}{\sqrt{3}} \right)$

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1. A.
   $\ 4x - 3y - 2z + 1 = 0$
2. B.
   $\ 3x - 2y + 2z - 3 = 0$
3. C.
   $\ 8x - 5y - 11z + 8 = 0$
4. D.
   $\ 5x - 4y + 2z - 3 = 0$

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1. A.
   Maximize $z = 25x + 18y$ subject to $20x + 15y \leq 640$

   $$5x + 8y\ \geq 500$$

   $$x,y \geq 0$$
2. B.
   Maximize $z = 25x + 18y$ subject to $20x + 15y \leq 640$ 5$\mathcal{x} + 8y \leq 500$

   $$\mathcal{x,}y \geq 0$$
3. C.
   Maximize $z = 25x + 18y$ subject to $20x + 5y \leq 8$ 5$\mathcal{x} + 8y \leq 10$

   $$\mathcal{x,}y \geq 0$$
4. D.
   Maximize $z = 25x + 18y$ subject to $4x + 3y \leq 128$ 5$\mathcal{x} + 8y \geq 500$

   $$\mathcal{x,}y \geq 0$$

Tap an option to check your answer.

1. A.
   $\frac{9}{10}$
2. B.
   $\frac{1}{10}$
3. C.
   $- \frac{9}{10}$
4. D.
   $- \frac{1}{10}$

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1. A.
   $\frac{\pi}{6},\frac{\pi}{3}$
2. B.
   $\frac{\pi}{3},\frac{\pi}{4}$
3. C.
   $\frac{5\pi}{6},\frac{\pi}{2}$
4. D.
   $\frac{2\pi}{3},\frac{\pi}{4}$

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1. A.
   $3x^{2} + 8x + 4$
2. B.
   $3x^{2} + 12x + 12$
3. C.
   $3x^{2} - 12x + 6$
4. D.
   $3x^{2} - 18x + 5$

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1. A.
   $x + y = ab$
2. B.
   $\frac{x}{a} + \frac{y}{b} = 1$
3. C.
   $ax + by = 1$
4. D.
   $x + y = a + b$

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