PYQ Vault

MHT-CET 2026 (16 April Shift II), Paper I, Mathematics question paper

50 questions · 100 marks · 90 minutes · +2 per correct answer, no negative marking

Every question in the order it was set, free to read. Tap an option to check it, or open the answer and worked solution. Answers open as you go; sign in free to keep opening them.

Sit it as a timed mock
  1. 1
    If nn is a positive integer, then (1+i3)2n+(1−i3)2n(1 + i\sqrt{3})^{2n} + (1 - i\sqrt{3})^{2n} is equal to .........

    Tap an option to check your answer.

  2. 2
    The number of 4-letter words formed from the English alphabet such that there are exactly 2 vowels and 2 consonants and no vowel is repeated, but consonants may be repeated is:

    Tap an option to check your answer.

  3. 3
    The value of cos⁡(60∘−A)⋅cos⁡A⋅cos⁡(60∘+A)\cos(60^\circ - A) \cdot \cos A \cdot \cos(60^\circ + A) is

    Tap an option to check your answer.

  4. 4
    The general solution of the equation cot⁡θ⋅cot⁡2θ=1\cot\theta \cdot \cot 2\theta = 1 is...

    Tap an option to check your answer.

  5. 5
    The line (2+k)x+(1+k)y=5+7k(2 + k)x + (1 + k)y = 5 + 7k passes through the fixed point for different values of k. If 'd' is the distance of a fixed point from the origin, then d2=…d^2 = \ldots

    Tap an option to check your answer.

  6. 6
    If θ\theta is the acute angle between the lines 2x2+7xy+3y2=02x^2 + 7xy + 3y^2 = 0, then the value of 2cos⁡θ−3sin⁡θ4sin⁡θ+5cos⁡θ=…\dfrac{2\cos\theta - 3\sin\theta}{4\sin\theta + 5\cos\theta} = \ldots

    Tap an option to check your answer.

  7. 7
    The combined equation of the pair of lines passing through the origin and making an angle π4\dfrac{\pi}{4} with the line 3x+y−6=03x + y - 6 = 0 is...

    Tap an option to check your answer.

  8. 8
    Line l:x+y=4l : x + y = 4 intersects the circle x2+y2−2x−2y=2x^2 + y^2 - 2x - 2y = 2 at points AA and BB. If C is the center of the circle, then the area of △ABC\triangle ABC is...

    Tap an option to check your answer.

  9. 9
    If lim⁡x→045x−9x−5x+1(kx−1)(3x−1)=2\displaystyle\lim_{x \to 0}\dfrac{45^x - 9^x - 5^x + 1}{(k^x - 1)(3^x - 1)} = 2, then the value of kk is ...

    Tap an option to check your answer.

  10. 10
    If the truth value of the compound statement [(p↔q)∧(q→r)∧∼r]→(p∧∼q)[(p \leftrightarrow q) \wedge (q \to r) \wedge \sim r] \to (p \wedge \sim q) is false, then the truth values of the statement patterns (p→q)↔(q→r)(p \to q) \leftrightarrow (q \to r) and ∼(p∨r)→(q∧p)\sim(p \vee r) \to (q \wedge p) are, respectively ...

    Tap an option to check your answer.

  11. 11
    The negation of the contrapositive of the statement (p∨∼q)→(p∧∼q)(p \vee \sim q) \to (p \wedge \sim q) is

    Tap an option to check your answer.

  12. 12
    In triangle ABC, with usual notations, if a=4,b=5a = 4, b = 5 and c=6c = 6, then angle C is equal to...

    Tap an option to check your answer.

  13. 13
    If A=[235−2],B−1=[152525−15]A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}, B^{-1} = \begin{bmatrix} \frac{1}{5} & \frac{2}{5} \\ \frac{2}{5} & -\frac{1}{5} \end{bmatrix}, then (AB)−1=(AB)^{-1} =

    Tap an option to check your answer.

  14. 14
    If A=[aij]3×3A = [a_{ij}]_{3 \times 3} is a matrix such that aij=∣2i−5j∣a_{ij} = |2i - 5j|, where ∣⋅∣|\cdot| denotes the modulus function, then the element in the 2nd2^{nd} row and 3rd3^{rd} column of A−1A^{-1} is ...

    Tap an option to check your answer.

  15. 15
    If A=[2−102]A = \begin{bmatrix} 2 & -1 \\ 0 & 2 \end{bmatrix} and A2+xA+yI2=O2A^2 + xA + yI_2 = O_2, where I2I_2 and O2O_2 are the identity matrix and null matrix of order 2 respectively, then:

    Tap an option to check your answer.

  16. 16
    The value of cot⁡−1[1−sin⁡x+1+sin⁡x1−sin⁡x−1+sin⁡x]\cot^{-1}\left[\dfrac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} - \sqrt{1 + \sin x}}\right], where x∈(0,π2)x \in \left(0, \dfrac{\pi}{2}\right) is...

    Tap an option to check your answer.

  17. 17
    If (tan⁡−1x)2+(cot⁡−1x)2=5π28(\tan^{-1}x)^2 + (\cot^{-1}x)^2 = \dfrac{5\pi^2}{8}, then the value of xx is equal to...

    Tap an option to check your answer.

  18. 18
    If f(x−1x+1)=x+1f\left(\dfrac{x - 1}{x + 1}\right) = x + 1, then ∫f(x) dx=⋅s\displaystyle\int f(x)\,dx = \cdot s

    Tap an option to check your answer.

  19. 19
    If ex+ef(x)=ee^x + e^{f(x)} = e, then the domain of f(x)f(x) is

    Tap an option to check your answer.

  20. 20
    If the function f is continuous at x=πx = \pi, where f(x)=1−cos⁡[7(x−π)]5(x−π)2f(x) = \dfrac{1 - \cos[7(x - \pi)]}{5(x - \pi)^2}, for x≠πx \neq \pi, then f(π)=f(\pi) =

    Tap an option to check your answer.

  21. 21
    Let f(x) be a twice differentiable function such that f′′(x)=−f(x)f''(x) = -f(x), f′(x)=g(x)f'(x) = g(x) and h(x)={f(x)}2+{g(x)}2h(x) = \{f(x)\}^2 + \{g(x)\}^2. If h(5)=11h(5) = 11, then h(10)h(10) is equal to ...

    Tap an option to check your answer.

  22. 22
    If cot⁡[f(x)]=3x−x31−3x2\cot[f(x)] = \dfrac{3x - x^3}{1 - 3x^2} and sin⁡[g(x)]=1−x21+x2\sin[g(x)] = \dfrac{1 - x^2}{1 + x^2}, then lim⁡x→tf(x)−f(t)g(x)−g(t)=…\displaystyle\lim_{x \to t}\dfrac{f(x) - f(t)}{g(x) - g(t)} = \ldots

    Tap an option to check your answer.

  23. 23
    If y=cos⁡−1(1−4x1+4x)y = \cos^{-1}\left(\dfrac{1 - 4^x}{1 + 4^x}\right), then dydx\dfrac{dy}{dx} at x=1x = 1 is

    Tap an option to check your answer.

  24. 24
    A cylindrical tank without a top lid is being manufactured to hold a fixed volume of 125π125\pi cubic cm. The minimum surface area required to construct this tank is ............square cm

    Tap an option to check your answer.

  25. 25
    A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

    Tap an option to check your answer.

  26. 26
    The equation of tangent to the curves x=1−3t2x = 1 - 3t^2 and y=t−3t3y = t - 3t^3 at the point (−2,2)(-2, 2) is...

    Tap an option to check your answer.

  27. 27
    If f(x)=cos⁡xf(x) = \cos x, then the value of ∫ef(x)(xsin⁡3x+f(x))1−(f(x))2 dx=\displaystyle\int\dfrac{e^{f(x)}(x\sin^3 x + f(x))}{1 - (f(x))^2}\,dx =

    Tap an option to check your answer.

  28. 28
    ∫x4+1x6+1 dx=\displaystyle\int\dfrac{x^4 + 1}{x^6 + 1}\,dx =

    Tap an option to check your answer.

  29. 29
    If a>0,b>0a > 0, b > 0 and ∫1ax2+b dx=16tan⁡−1(2x3)+c\displaystyle\int\dfrac{1}{ax^2 + b}\,dx = \dfrac{1}{\sqrt{6}}\tan^{-1}\left(\dfrac{\sqrt{2}x}{\sqrt{3}}\right) + c, then ∫1bx2+a dx=…\displaystyle\int\dfrac{1}{bx^2 + a}\,dx = \ldots

    Tap an option to check your answer.

  30. 30
    The value of integral ∫01cot⁡−1(1+x2−x) dx\displaystyle\int_0^1\cot^{-1}(1 + x^2 - x)\,dx is...

    Tap an option to check your answer.

  31. 31
    The value of ∫−ππ2x(1+sin⁡x)1+cos⁡2x dx\displaystyle\int_{-\pi}^{\pi}\dfrac{2x(1 + \sin x)}{1 + \cos^2 x}\,dx is...

    Tap an option to check your answer.

  32. 32
    The area of the region enclosed by the lines y=2x,2y=xy = 2x, 2y = x and x=2x = 2 (in sq.units) is...

    Tap an option to check your answer.

  33. 33
    The area of the region common to the parabolas 4y2=9x4y^2 = 9x and 3x2=16y3x^2 = 16y is...

    Tap an option to check your answer.

  34. 34
    For the differential equation d3ydx3+cos⁡(d2ydx2)=0\dfrac{d^3y}{dx^3} + \cos\left(\dfrac{d^2y}{dx^2}\right) = 0, which of the following is true ?

    Tap an option to check your answer.

  35. 35
    If water at 100∘C100^\circ\mathrm{C} cools in 10 minutes to 80∘C80^\circ\mathrm{C} and to 65∘C65^\circ\mathrm{C} in the next 10 minutes, then the room temperature will be ...

    Tap an option to check your answer.

  36. 36
    The equation of the curve passing through the point (0, 1) and having a slope of the tangent at point P(x,y)P(x, y) is equal to yx+y\dfrac{y}{x + y}, is

    Tap an option to check your answer.

  37. 37
    If f(x)f(x) is a polynomial such that f(x)=[f′(x)]2f(x) = [f'(x)]^2 and f(2)=0f(2) = 0, then f(−2)=…f(-2) = \ldots

    Tap an option to check your answer.

  38. 38
    The equation of a line in cartesian form passing through (0, 0, 0) and (4, 3, c) and parallel to a⃗×b⃗\vec{a} \times \vec{b} where a⃗=2i^+j^+2k^,b⃗=3i^−4j^\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}, \vec{b} = 3\hat{i} - 4\hat{j} is

    Tap an option to check your answer.

  39. 39
    If aˉ=4i^+j^+k^,bˉ=2i^+j^+2k^\bar{a} = 4\hat{i} + \hat{j} + \hat{k}, \bar{b} = 2\hat{i} + \hat{j} + 2\hat{k} and cˉ=3i^+4j^+5k^\bar{c} = 3\hat{i} + 4\hat{j} + 5\hat{k}, then (aˉ+bˉ)⋅(bˉ+cˉ)=(\bar{a} + \bar{b})\cdot(\bar{b} + \bar{c}) =

    Tap an option to check your answer.

  40. 40
    If aˉ=2i^+j^−k^,bˉ=i^+3k^\bar{a} = 2\hat{i} + \hat{j} - \hat{k}, \bar{b} = \hat{i} + 3\hat{k} and cˉ\bar{c} is a unit vector, then the maximum value of the scalar triple product [aˉ bˉ cˉ][\bar{a}\ \bar{b}\ \bar{c}] is

    Tap an option to check your answer.

  41. 41
    Let aˉ,bˉ\bar{a}, \bar{b} and cˉ\bar{c} be three coplanar unit vectors. A unit vector dˉ\bar{d} is perpendicular to them. If (aˉ×bˉ)×(cˉ×dˉ)=326i^−213j^+613k^(\bar{a} \times \bar{b}) \times (\bar{c} \times \bar{d}) = \dfrac{3}{26}\hat{i} - \dfrac{2}{13}\hat{j} + \dfrac{6}{13}\hat{k} and the angle between aˉ\bar{a} and bˉ\bar{b} is 30∘30^\circ, then cˉ\bar{c} is equal to...

    Tap an option to check your answer.

  42. 42
    The volume of a parallelopiped with coterminous edges aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} is 3 cubic units. The volume (in cubic units) of a tetrahedron with coterminous edges (aˉ×bˉ),(aˉ×2cˉ),(bˉ×2cˉ)(\bar{a} \times \bar{b}), (\bar{a} \times 2\bar{c}), (\bar{b} \times 2\bar{c}) is...

    Tap an option to check your answer.

  43. 43
    If the lines 2x=ky=−z2x = ky = -z and 6x=−y=−4z6x = -y = -4z are perpendicular to each other then the value of kk is ...

    Tap an option to check your answer.

  44. 44
    The vector equation of plane in parametric form, passing through the points (-1, 2, 0), (2, 2, -1) and parallel to the line x−11=2y+12=z+1−1\dfrac{x - 1}{1} = \dfrac{2y + 1}{2} = \dfrac{z + 1}{-1} is

    Tap an option to check your answer.

  45. 45
    If dd is the distance of point (2, 5, 10) from the plane containing the lines rˉ=(4j^−k^)+λ(i^+2j^−2k^)\bar{r} = (4\hat{j} - \hat{k}) + \lambda(\hat{i} + 2\hat{j} - 2\hat{k}) and rˉ=(2i^+j^)+μ(i^+2j^−2k^)\bar{r} = (2\hat{i} + \hat{j}) + \mu(\hat{i} + 2\hat{j} - 2\hat{k}), then d2=d^2 =

    Tap an option to check your answer.

  46. 46
    The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5) and (-6, -15, 11) are

    Tap an option to check your answer.

  47. 47
    The minimum value of z=3x+5yz = 3x + 5y, subject to constraints x≤80,y≥60,x+y≤200x \le 80, y \ge 60, x + y \le 200 & x,y≥0x, y \ge 0 occurs at the point...

    Tap an option to check your answer.

  48. 48
    If a fair coin is tossed 8 times, then the probability of getting at most 2 heads is...

    Tap an option to check your answer.

  49. 49
    If a random variable XX has a probability mass function P(x)={kx2,for x=1,2,3,40,otherwiseP(x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3, 4 \\ 0, & \text{otherwise} \end{cases}, then the mean of XX is ...

    Tap an option to check your answer.

  50. 50
    If E1E_1 and E2E_2 are equally likely, mutually exclusive and exhaustive events and P(A∣E1)=0.2P(A|E_1) = 0.2, P(A∣E2)=0.3P(A|E_2) = 0.3, then P(E1∣A)P(E_1|A) equal to...

    Tap an option to check your answer.

Want the real exam feel? Sit this paper with a 90-minute timer and get your score straight away.

Sit it as a timed mock