PYQ Vault

MHT-CET 2026 (14 May 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 [⋅][\cdot] represents the greatest integer function of less than or equal to type then the solution set of the equation [x]2−5[x]+6=0[x]^2 - 5[x] + 6 = 0 is

    Tap an option to check your answer.

  2. 2
    cos⁡(4A)=\cos(4A) =

    Tap an option to check your answer.

  3. 3
    The general solution of the equation tan⁡x+sec⁡x=2cos⁡x\tan x + \sec x = 2\cos x is

    Tap an option to check your answer.

  4. 4
    In ΔABC\Delta ABC with the usual notations, angles A,B,CA, B, C of are in A.P. and b:c=3:2b : c = \sqrt{3} : \sqrt{2}. The ratio of the largest and the smallest angle of the triangle will be

    Tap an option to check your answer.

  5. 5
    If x=253−4ix = \dfrac{25}{3 - 4i} then 2x3−11x2+44x+27=2x^3 - 11x^2 + 44x + 27 =

    Tap an option to check your answer.

  6. 6
    In a polygon, the number of diagonals is 5454. Then the number of sides of the polygon is

    Tap an option to check your answer.

  7. 7
    If P(a,b)P(a, b) is the midpoint of a line segment intercepted between the coordinate axes, then the equation of the line is

    Tap an option to check your answer.

  8. 8
    The joint equation of pair of lines passing through origin and perpendicular to the lines given by 3x2+4xy−5y2=03x^2 + 4xy - 5y^2 = 0 is

    Tap an option to check your answer.

  9. 9
    The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a3a is

    Tap an option to check your answer.

  10. 10
    If the line 12x−5y+k=012x - 5y + k = 0 is tangent to the hyperbola x2−4y2=100x^2 - 4y^2 = 100, then k=k =

    Tap an option to check your answer.

  11. 11
    If the function f(x)f(x) is defined as below f(x)={(3x+3−x−2)log⁡(1+4x)(1−cos⁡4x)tan⁡(2x),x≠0(log⁡p)rq,x=0f(x) = \begin{cases} \dfrac{(3^x + 3^{-x} - 2)\log(1 + 4x)}{(1 - \cos 4x)\tan(2x)}, & x \neq 0 \\ \dfrac{(\log p)^r}{q}, & x = 0 \end{cases} is continuous at x=0x = 0 then p+q−r=…p + q - r = \ldots

    Tap an option to check your answer.

  12. 12
    If f(x)=ax−35x+7f(x) = \dfrac{ax - 3}{5x + 7} and lim⁡x→0f(x)⋅lim⁡x→∞f(x)=3\lim_{x \to 0}f(x) \cdot \lim_{x \to \infty}f(x) = 3 then a=…a = \ldots

    Tap an option to check your answer.

  13. 13
    A statement logically equivalent to the statement pattern ∼[(p→∼q)∧(∼q∨p)]\sim[(p \to \sim q) \wedge (\sim q \vee p)] is

    Tap an option to check your answer.

  14. 14
    The truth values of logical statements p,q,rp, q, r are T, T and F respectively. If ∗* and #\# are symbolic logical connectives such that (p#r)→(∼q#r)(p \# r) \to (\sim q \# r) is false and (∼p∗q)↔(∼q#r)(\sim p * q) \leftrightarrow (\sim q \# r) is true, then ∗* and #\# are respectively ____

    Tap an option to check your answer.

  15. 15
    If p∧qp \wedge q is F and p→qp \to q is F, then the truth values of pp and qq respectively are

    Tap an option to check your answer.

  16. 16
    2sin⁡−1(35)+tan⁡−1(15)+tan⁡−1(17)=2\sin^{-1}\left(\dfrac{3}{5}\right) + \tan^{-1}\left(\dfrac{1}{5}\right) + \tan^{-1}\left(\dfrac{1}{7}\right) =

    Tap an option to check your answer.

  17. 17
    If sin⁡−1(1−x)−2sin⁡−1x=π2\sin^{-1}(1 - x) - 2\sin^{-1}x = \dfrac{\pi}{2}, then the value of xx is

    Tap an option to check your answer.

  18. 18
    If A=[4521]A = \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}, then A−1=A^{-1} =

    Tap an option to check your answer.

  19. 19
    If A−1=[3−11−156−55−22]A^{-1} = \begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix} and B=[12−2−1300−21]B = \begin{bmatrix} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{bmatrix}, then (AB)−1=(AB)^{-1} =

    Tap an option to check your answer.

  20. 20
    If f(x)=∣sin⁡x+sin⁡2x+sin⁡3xsin⁡2xsin⁡3x3+4sin⁡x34sin⁡x1+sin⁡xsin⁡x1∣f(x) = \begin{vmatrix} \sin x + \sin 2x + \sin 3x & \sin 2x & \sin 3x \\ 3 + 4\sin x & 3 & 4\sin x \\ 1 + \sin x & \sin x & 1 \end{vmatrix}, then ∫0π2f(x) dx=\int_0^{\frac{\pi}{2}}f(x)\,dx =

    Tap an option to check your answer.

  21. 21
    If y=cos⁡−1xy = \cos^{-1}x, then d2ydx2=\dfrac{d^2y}{dx^2} =

    Tap an option to check your answer.

  22. 22
    If y=xxy = x^{\sqrt{x}}, then dydx=\dfrac{dy}{dx} =

    Tap an option to check your answer.

  23. 23
    If x=em+e−m2x = \dfrac{e^m + e^{-m}}{2} and y=em−e−m2y = \dfrac{e^m - e^{-m}}{2} then dydx=\dfrac{dy}{dx} =

    Tap an option to check your answer.

  24. 24
    If y=4log⁡4(x+2)−log⁡4(x−2)y = 4^{\log_4(x+2) - \log_4(x-2)}, then dydx=\dfrac{dy}{dx} =

    Tap an option to check your answer.

  25. 25
    The value of cc for which the function f(x)=log⁡(x2+65x)f(x) = \log\left(\dfrac{x^2 + 6}{5x}\right) satisfies Rolle's theorem in the interval [2,3][2, 3] is ____

    Tap an option to check your answer.

  26. 26
    The point on the curve y=3x2−9x+8y = 3x^2 - 9x + 8 where the tangent is parallel to x-axis is

    Tap an option to check your answer.

  27. 27
    In the Lagrange's Mean Value Theorem, f(b)−f(a)=(b−a)f′(c);(a<c<b)f(b) - f(a) = (b - a)f'(c); (a < c < b). If a=2,b=4a = 2, b = 4 and f(x)=x2−4f(x) = \sqrt{x^2 - 4}, then the value of cc is

    Tap an option to check your answer.

  28. 28
    ∫1+cos⁡acos⁡xcos⁡a+cos⁡x dx=\displaystyle\int\dfrac{1 + \cos a\cos x}{\cos a + \cos x}\,dx =

    Tap an option to check your answer.

  29. 29
    If ∫ex−1 dx=aex−1+btan⁡−1(ex−1)+c\displaystyle\int\sqrt{e^x - 1}\,dx = a\sqrt{e^x - 1} + b\tan^{-1}(\sqrt{e^x - 1}) + c, then

    Tap an option to check your answer.

  30. 30
    If ∫x3ex dx=ex(px3+qx2+rx+s)+c\displaystyle\int x^3e^x\,dx = e^x(px^3 + qx^2 + rx + s) + c, then the value of p+q+r+sp + q + r + s is

    Tap an option to check your answer.

  31. 31
    ∫f(x) dx=g(x)+c\displaystyle\int f(x)\,dx = g(x) + c, then ∫xf(x2) dx=\displaystyle\int x f(x^2)\,dx =

    Tap an option to check your answer.

  32. 32
    If ∫0xf(t) dt=x+∫x0t⋅f(t) dt\int_0^x f(t)\,dt = x + \int_x^0 t \cdot f(t)\,dt then the value of f(1)=f(1) =

    Tap an option to check your answer.

  33. 33
    If a>4a > 4 and ∫−211x2+4x+a dx=13tan⁡−1(1)\int_{-2}^1\dfrac{1}{x^2 + 4x + a}\,dx = \dfrac{1}{3}\tan^{-1}(1), then the value of aa is

    Tap an option to check your answer.

  34. 34
    The area of the region bounded by the curves y2=9xy^2 = 9x and x2=9yx^2 = 9y

    Tap an option to check your answer.

  35. 35
    The solution of the differential equation dydx+1=ex+y\dfrac{dy}{dx} + 1 = e^{x+y} is

    Tap an option to check your answer.

  36. 36
    Degree of differential equation (dydx)2+53=1+(dxdy)34+(dydx)5\sqrt[3]{\left(\dfrac{dy}{dx}\right)^2 + 5} = \dfrac{1 + \left(\dfrac{dx}{dy}\right)^3}{\sqrt{4 + \left(\dfrac{dy}{dx}\right)^5}} is

    Tap an option to check your answer.

  37. 37
    The differential equation of system of concentric circles with center (1,2)(1, 2) is ____

    Tap an option to check your answer.

  38. 38
    Let a⃗\vec{a} and b⃗\vec{b} be two unit vectors such that their sum is also a unit vector. If u⃗=a⃗+2b⃗\vec{u} = \vec{a} + 2\vec{b} and v⃗=2a⃗+b⃗\vec{v} = 2\vec{a} + \vec{b}, then the angle between u⃗\vec{u} and v⃗\vec{v} is

    Tap an option to check your answer.

  39. 39
    For two non-zero, non-collinear, non-orthogonal vectors a⃗\vec{a} and b⃗\vec{b} where θ\theta is angle between them, then (a⃗⋅b⃗)2+∣a⃗×b⃗∣2(a⃗⋅b⃗)2−∣a⃗×b⃗∣2=\dfrac{(\vec{a}\cdot\vec{b})^2 + |\vec{a} \times \vec{b}|^2}{(\vec{a}\cdot\vec{b})^2 - |\vec{a} \times \vec{b}|^2} =

    Tap an option to check your answer.

  40. 40
    If aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} are vectors such that [aˉ bˉ cˉ]=3[\bar{a}\ \bar{b}\ \bar{c}] = 3, then [aˉ×bˉ  bˉ×cˉ  cˉ×aˉ]=[\bar{a} \times \bar{b}\ \ \bar{b} \times \bar{c}\ \ \bar{c} \times \bar{a}] =

    Tap an option to check your answer.

  41. 41
    If aˉ=4i^−10j^+(1−p)k^\bar{a} = 4\hat{i} - 10\hat{j} + (1 - p)\hat{k} and bˉ=12i^+(q−10)j^+3k^\bar{b} = 12\hat{i} + (q - 10)\hat{j} + 3\hat{k} satisfy aˉ×bˉ=0ˉ\bar{a} \times \bar{b} = \bar{0}, then the values of pp and qq are respectively

    Tap an option to check your answer.

  42. 42
    If the vectors aˉ=2iˉ+jˉ+3kˉ\bar{a} = 2\bar{i} + \bar{j} + 3\bar{k} and bˉ=piˉ+2jˉ+2kˉ\bar{b} = p\bar{i} + 2\bar{j} + 2\bar{k} are perpendicular to each other, then ...

    Tap an option to check your answer.

  43. 43
    If the angle θ\theta between the line x+11=y−12=z−22\dfrac{x + 1}{1} = \dfrac{y - 1}{2} = \dfrac{z - 2}{2} and the plane 2x−y+kz+4=02x - y + \sqrt{k}z + 4 = 0 is such that cos⁡θ=83\cos\theta = \dfrac{\sqrt{8}}{3}. Then k=k =

    Tap an option to check your answer.

  44. 44
    The acute angle between the line rˉ=2i^+2j^+k^+λ(2i^−3j^+2k^)\bar{r} = 2\hat{i} + 2\hat{j} + \hat{k} + \lambda(2\hat{i} - 3\hat{j} + 2\hat{k}) and the plane rˉ⋅(3i^−2j^+5k^)=4\bar{r}\cdot(3\hat{i} - 2\hat{j} + 5\hat{k}) = 4 is

    Tap an option to check your answer.

  45. 45
    The distance of the point 2i^+j^−k^2\hat{i} + \hat{j} - \hat{k} from the plane rˉ⋅(i^−2j^+4k^)=9\bar{r}\cdot(\hat{i} - 2\hat{j} + 4\hat{k}) = 9, is

    Tap an option to check your answer.

  46. 46
    Let LL be a line x−11=y+23=z−7−1\dfrac{x - 1}{1} = \dfrac{y + 2}{3} = \dfrac{z - 7}{-1} and PP be a plane passing through the midpoint of the segment joining M(−4,2,1)M(-4, 2, 1) and N(2,−4,3)N(2, -4, 3) and perpendicular to segment MN. If the line LL intersects the plane PP at point S(α,β,γ)S(\alpha, \beta, \gamma), then α+β+γ=…\alpha + \beta + \gamma = \ldots

    Tap an option to check your answer.

  47. 47
    The minimum value of z=5x+8yz = 5x + 8y subject to the constraints 0≤x≤4,0≤y≤2,x+y≥50 \le x \le 4, 0 \le y \le 2, x + y \ge 5 is

    Tap an option to check your answer.

  48. 48
    The probability that a person hits a target is 0.60.6. If he fires 55 shots at the target, then the probability that he hits the target at least once is

    Tap an option to check your answer.

  49. 49
    Let X be a random variable with the probability density function defined by f(x)=1x2,1<x<∞f(x) = \dfrac{1}{x^2}, 1 < x < \infty =0= 0 otherwise. If C1={x:1<x<2}C_1 = \{x : 1 < x < 2\} and C2={x:4<x<5}C_2 = \{x : 4 < x < 5\} then P(C1∪C2)=P(C_1 \cup C_2) =

    Tap an option to check your answer.

  50. 50
    Six faces of a die are marked with the numbers −3,−2,−1,0,1,2-3, -2, -1, 0, 1, 2. If such two dice are thrown simultaneously, then the probability of getting the product of the numbers on the uppermost surfaces as ±3\pm 3 or sum of the numbers on the uppermost surfaces is divisible by 22, 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