PYQ Vault

MHT-CET 2026 (11 April Shift I), 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 A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\}, then which of the following statements is not true?

    Tap an option to check your answer.

  2. 2
    If −1+−3=reiθ-1 + \sqrt{-3} = re^{i\theta}, then the value of θ\theta is

    Tap an option to check your answer.

  3. 3
    There are 55 boys and 33 girls seated in a row for a photograph. The number of ways in which a photograph can be taken if the girls occupy only odd places is...

    Tap an option to check your answer.

  4. 4
    The value of the expression tan⁡(x−9π)\tan(x - 9\pi) is equal to:

    Tap an option to check your answer.

  5. 5
    The principal solutions of csc⁡(θ)=−2\mathrm{\csc}(\theta) = -2 are...

    Tap an option to check your answer.

  6. 6
    The equation of a line passing through the point of the intersection of the lines x−y+1=0x - y + 1 = 0 and 2x+3y−8=02x + 3y - 8 = 0 and having x intercept 33 is

    Tap an option to check your answer.

  7. 7
    If the equation x2−ky2−4x+6y−5=0x^2 - ky^2 - 4x + 6y - 5 = 0 represents a pair of straight lines, then their point of intersection is

    Tap an option to check your answer.

  8. 8
    The equation of a circle which passes through the points (2,3)(2, 3) and (4,5)(4, 5) and whose center lies on the straight line y−4x+3=0y - 4x + 3 = 0 is

    Tap an option to check your answer.

  9. 9
    The value of lim⁡x→3[x]−3x−3\lim_{x \to 3}\dfrac{[x] - 3}{x - 3}, where [⋅][\cdot] denotes the greatest integer function, 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 \vee q) \wedge (q \to r) \wedge (\sim r)] \to (p \wedge q) is False then the truth values of p→qp \to q and q→pq \to p are respectively......

    Tap an option to check your answer.

  11. 11
    The statement pattern (p∨q)→∼r(p \vee q) \to \sim r is logically equivalent to

    Tap an option to check your answer.

  12. 12
    In △ABC\triangle ABC, with usual notations, if cos⁡A=12,a=3,∠B=πc6\cos A = \dfrac{1}{2}, a = 3, \angle B = \dfrac{\pi^c}{6}, then the values of bb and cc are.....

    Tap an option to check your answer.

  13. 13
    If A=12[−1−33−1]A = \dfrac{1}{2}\begin{bmatrix} -1 & -\sqrt{3} \\ \sqrt{3} & -1 \end{bmatrix} then A−1−A2A^{-1} - A^2 is not

    Tap an option to check your answer.

  14. 14
    If A=[2ii3i21]A = \begin{bmatrix} 2i & i^3 \\ i^2 & 1 \end{bmatrix}, then A−1A^{-1} is equal to

    Tap an option to check your answer.

  15. 15
    The minimum value of (sin⁡−1x)2+(cos⁡−1x)2(\sin^{-1}x)^2 + (\cos^{-1}x)^2 is...........

    Tap an option to check your answer.

  16. 16
    If tan⁡−1(1)+tan⁡−1(3)+tan⁡−1(5)+tan⁡−1(14)=π+tan⁡−1(α2)\tan^{-1}(1) + \tan^{-1}(3) + \tan^{-1}(5) + \tan^{-1}\left(\dfrac{1}{4}\right) = \pi + \tan^{-1}\left(\dfrac{\alpha}{2}\right), then the value of α\alpha is...

    Tap an option to check your answer.

  17. 17
    The domain of the function f(x)=x−1+3−xf(x) = \sqrt{x - 1} + \sqrt{3 - x} is ...

    Tap an option to check your answer.

  18. 18
    Let the function f(x)f(x) be defined as: f(x)={[tan⁡(π4+x)]1x,x≠0k,x=0f(x) = \begin{cases} \left[\tan\left(\dfrac{\pi}{4} + x\right)\right]^{\frac{1}{x}}, & x \neq 0 \\ k, & x = 0 \end{cases} If f(x)f(x) is continuous at x=0x = 0, then the value of kk is...

    Tap an option to check your answer.

  19. 19
    If y=f(3+2x3−2x)y = f\left(\dfrac{3 + 2x}{3 - 2x}\right), where f(x)=tan⁡(log⁡x)f(x) = \tan(\log x) and dydx=(AB+Cx2)⋅sec⁡2(log⁡(3+2x3−2x))\dfrac{dy}{dx} = \left(\dfrac{A}{B + Cx^2}\right)\cdot\sec^2\left(\log\left(\dfrac{3 + 2x}{3 - 2x}\right)\right), then the respective values of A, B and C are ......

    Tap an option to check your answer.

  20. 20
    If y=x2+8x+3y = \sqrt{x^2 + 8x + 3}, then the value of d2ydx2\dfrac{d^2y}{dx^2} at x=3x = 3 is

    Tap an option to check your answer.

  21. 21
    If y=tan⁡x+tan⁡x+tan⁡x+⋅s⋅s∞y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \cdot s\cdot s\infty}}}, then (dydx)2\left(\dfrac{dy}{dx}\right)^2 at x=π4x = \dfrac{\pi}{4} is

    Tap an option to check your answer.

  22. 22
    If y=x+x2+1y = \sqrt{x + \sqrt{x^2 + 1}}, then the value of dydx\dfrac{dy}{dx} is

    Tap an option to check your answer.

  23. 23
    If y=sin⁡(elog⁡2x)y = \sin(e^{\log 2x}), then the value of dydx\dfrac{dy}{dx} at x=π2x = \dfrac{\pi}{2} is

    Tap an option to check your answer.

  24. 24
    The difference between the local extreme values of the function f(x)=2x3−15x2+36x+40f(x) = 2x^3 - 15x^2 + 36x + 40 is ......

    Tap an option to check your answer.

  25. 25
    A wire of length 6464 m is to be bent to form a rectangle such that its area is maximum, then its area is.....

    Tap an option to check your answer.

  26. 26
    The approximate value of 633\sqrt[3]{63} is

    Tap an option to check your answer.

  27. 27
    The equation of the tangent to the curve y=3x3−3x2+xy = 3x^3 - 3x^2 + x at x=1x = 1 is

    Tap an option to check your answer.

  28. 28
    ∫x+2x2−7x+12 dx\displaystyle\int\dfrac{x + 2}{x^2 - 7x + 12}\,dx is equal to

    Tap an option to check your answer.

  29. 29
    If ∫dx2ax−x2=f(g(x))+c\displaystyle\int\dfrac{dx}{\sqrt{2ax - x^2}} = f(g(x)) + c, where cc is constant of integration, then f(x),g(x)f(x), g(x) are respectively equal to

    Tap an option to check your answer.

  30. 30
    ∫xx+2 dx\displaystyle\int\dfrac{x}{x + 2}\,dx is equal to

    Tap an option to check your answer.

  31. 31
    If [⋅][\cdot] denotes the greatest integer function, then ∫14x[x] dx\displaystyle\int_1^4 x[x]\,dx is equal to

    Tap an option to check your answer.

  32. 32
    If ∫1a(2x+1) dx=5\displaystyle\int_1^a(2x + 1)\,dx = 5, then the sum of the values of aa is..

    Tap an option to check your answer.

  33. 33
    The area of the shaded region is ... sq.units.

    Tap an option to check your answer.

  34. 34
    ∫039−x2 dx=\displaystyle\int_0^3\sqrt{9 - x^2}\,dx =

    Tap an option to check your answer.

  35. 35
    The particular solution of the differential equation xdy+2ydx=0xdy + 2ydx = 0, when x=2x = 2 and y=1y = 1 is

    Tap an option to check your answer.

  36. 36
    The differential equation representing the family of curves xsin⁡x+y3=4axx\sin x + y^3 = 4ax is

    Tap an option to check your answer.

  37. 37
    The order and degree of the differential equation 2+(d2ydx2)3=(d3ydx3)5/2\sqrt{2 + \left(\dfrac{d^2y}{dx^2}\right)^3} = \left(\dfrac{d^3y}{dx^3}\right)^{5/2} respectively are

    Tap an option to check your answer.

  38. 38
    The vector aˉ+3bˉ\bar{a} + 3\bar{b} is perpendicular to 7aˉ−5bˉ7\bar{a} - 5\bar{b} and the vector aˉ−4bˉ\bar{a} - 4\bar{b} is perpendicular to 7aˉ−2bˉ7\bar{a} - 2\bar{b}. Then the angle between aˉ\bar{a} and bˉ\bar{b} is

    Tap an option to check your answer.

  39. 39
    If 7j^+10k^,−i^+6j^+6k^7\hat{j} + 10\hat{k}, -\hat{i} + 6\hat{j} + 6\hat{k} and −4i^+9j^+6k^-4\hat{i} + 9\hat{j} + 6\hat{k} are the position vectors of the vertices A, B and C repectively of △ABC\triangle ABC. Then the position vector of the point where the bisector of the angle A meets side BC is

    Tap an option to check your answer.

  40. 40
    If a,b,ca, b, c are distinct non-negative numbers and the vectors ai^+aj^+ck^,i^+k^,ci^+cj^+bk^a\hat{i} + a\hat{j} + c\hat{k}, \hat{i} + \hat{k}, c\hat{i} + c\hat{j} + b\hat{k} lie in the same plane, then the value of cc is...

    Tap an option to check your answer.

  41. 41
    Let A(2,3,0),B(0,3,2)A(2, 3, 0), B(0, 3, 2) and C(4,0,3)C(4, 0, 3) be vertices of a triangle, then the area of the triangle is

    Tap an option to check your answer.

  42. 42
    If D and E are the midpoints of the sides BA and BC of triangle ABC, then AE‾+DC‾=\overline{AE} + \overline{DC} =

    Tap an option to check your answer.

  43. 43
    If the points (1,1,μ)(1, 1, \mu) and (−3,0,1)(-3, 0, 1) are equidistant from the plane r⃗⋅(3i^+4j^−12k^)+13=0\vec{r}\cdot(3\hat{i} + 4\hat{j} - 12\hat{k}) + 13 = 0, then the value of μ\mu are

    Tap an option to check your answer.

  44. 44
    If the lines x−12=y+13=z−14\dfrac{x - 1}{2} = \dfrac{y + 1}{3} = \dfrac{z - 1}{4} and x−21=y+m2=z−21\dfrac{x - 2}{1} = \dfrac{y + m}{2} = \dfrac{z - 2}{1} intersect each other, then the value of mm is....

    Tap an option to check your answer.

  45. 45
    If the lines L1:x−1−3=y−22k=z−32,L2:x−13k=y−51=z−6−5L_1: \dfrac{x - 1}{-3} = \dfrac{y - 2}{2k} = \dfrac{z - 3}{2}, L_2: \dfrac{x - 1}{3k} = \dfrac{y - 5}{1} = \dfrac{z - 6}{-5} are perpendicular to each other, then the equation of a plane containing the line L1L_1 and parallel to the line L2L_2 for the value of kk that satisfies this condition is ...

    Tap an option to check your answer.

  46. 46
    A plane meets the coordinate axes at points A, B and C, such that the centroid of a triangle ABC is (2,−23,12)\left(2, -\dfrac{2}{3}, \dfrac{1}{2}\right). The perpendicular distance from the origin to this plane is...

    Tap an option to check your answer.

  47. 47
    The point at which the maximum value of x+yx + y subject to constraints x+2y≤70x + 2y \le 70 and 2x+y≤95,x≥0,y≥02x + y \le 95, x \ge 0, y \ge 0 is.

    Tap an option to check your answer.

  48. 48
    Let X∼B(n,p)X \sim B(n, p). If E(X)=2E(X) = 2 and Var(X)=1\mathrm{Var}(X) = 1, then the probability of getting at most one success is .....

    Tap an option to check your answer.

  49. 49
    If the following function is probability density function of r.v. X f(x)=kx2(1−x)f(x) = kx^2(1 - x), for 0<x<1=00 < x < 1 = 0, otherwise, then the value of kk is

    Tap an option to check your answer.

  50. 50
    Two cards are drawn at random from a standard pack of 5252 cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...

    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