PYQ Vault

MHT-CET 2026 (13 May 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 f(x)=1x,g(x)=3−2x−x2f(x) = \dfrac{1}{\sqrt{x}}, g(x) = 3 - 2x - x^2 then ∫[(f∘g)(ex)]⋅ex dx=⋅s⋅s⋅s\displaystyle\int[(f \circ g)(e^x)] \cdot e^x\,dx = \cdot s\cdot s\cdot s

    Tap an option to check your answer.

  2. 2
    If f(x)=sin⁡−1[log⁡1/2(x22)]f(x) = \sin^{-1}\left[\log_{1/2}\left(\dfrac{x^2}{2}\right)\right], then the domain of the function f(x)f(x) is:

    Tap an option to check your answer.

  3. 3
    The value of expression tan⁡9∘−tan⁡27∘−tan⁡63∘+tan⁡81∘\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ is....

    Tap an option to check your answer.

  4. 4
    The general solution of the equation 2sin⁡2x+sin⁡22x=22\sin^2 x + \sin^2 2x = 2 is x=(2n+1)αx = (2n + 1)\alpha or x=mπ±β,m,n∈Zx = m\pi \pm \beta, m, n \in \mathbb{Z}, then α\alpha and β\beta are the roots of the quadratic equation ______

    Tap an option to check your answer.

  5. 5
    If in a triangle ABCABC, cos⁡Aa=cos⁡Bb=cos⁡Cc\dfrac{\cos A}{a} = \dfrac{\cos B}{b} = \dfrac{\cos C}{c} and the side a=2a = 2, then the area of the triangle is:

    Tap an option to check your answer.

  6. 6
    In △ABC\triangle ABC, with usual notations, the value of csc⁡⁡(A2)csc⁡⁡(B2)csc⁡⁡(C2)\operatorname{\csc}\left(\dfrac{A}{2}\right)\operatorname{\csc}\left(\dfrac{B}{2}\right)\operatorname{\csc}\left(\dfrac{C}{2}\right) is:

    Tap an option to check your answer.

  7. 7
    If z1=3⋅e5π12iz_1 = 3 \cdot e^{\frac{5\pi}{12}i} and z2=4⋅eπ12iz_2 = 4 \cdot e^{\frac{\pi}{12}i} then z1⋅z2=⋅s⋅sz_1 \cdot z_2 = \cdot s\cdot s

    Tap an option to check your answer.

  8. 8
    The sum of the greatest values of 15Cr{}^{15}C_r and 12Cr{}^{12}C_r is equal to

    Tap an option to check your answer.

  9. 9
    The points on the line x+y−4=0x + y - 4 = 0 which are at one unit distance from the line 4x+3y−10=04x + 3y - 10 = 0 are...

    Tap an option to check your answer.

  10. 10
    The polar coordinates of point PP are (2,π4)\left(\sqrt{2}, \dfrac{\pi}{4}\right). If QQ is the image of PP about yy axis, then the polar coordinates of QQ are ______

    Tap an option to check your answer.

  11. 11
    The coordinates of the foot of the perpendicular from the point (2,3)(2, 3) on the line y=3x+4y = 3x + 4 is given by ...

    Tap an option to check your answer.

  12. 12
    If two lines represented by the equation x2+bcy2=(b+c)xyx^2 + bcy^2 = (b + c)xy are coincident, then ____

    Tap an option to check your answer.

  13. 13
    If the tangent to the circle x2+y2=5x^2 + y^2 = 5 at point (1,−2)(1, -2) also touches the circle x2+y2−8x+6y+k=0x^2 + y^2 - 8x + 6y + k = 0, then k5=⋅s⋅s⋅s\dfrac{k}{5} = \cdot s\cdot s\cdot s

    Tap an option to check your answer.

  14. 14
    The equation of the hyperbola formed by the locus of the point of intersection of the lines 5x−y−25μ=0\sqrt{5}x - y - 2\sqrt{5}\mu = 0, and 5μx+μy−25=0\sqrt{5}\mu x + \mu y - 2\sqrt{5} = 0, where μ\mu is a variable parameter, is...

    Tap an option to check your answer.

  15. 15
    lim⁡x→01−cos⁡(1−cos⁡x)x4=\lim_{x \to 0}\dfrac{1 - \cos(1 - \cos x)}{x^4} =

    Tap an option to check your answer.

  16. 16
    The compound statement [∼(p→q)∨∼(p∧r)]∧p[\sim(p \to q) \vee \sim(p \wedge r)] \wedge p is logically equivalent to:

    Tap an option to check your answer.

  17. 17
    The negation of the contrapositive of the statement (p∨q)→r(p \vee q) \to r is logically equivalent to..

    Tap an option to check your answer.

  18. 18
    The dual of the statement pattern (p∧q)∧∼(p∨q)(p \wedge q) \wedge \sim(p \vee q) is a:

    Tap an option to check your answer.

  19. 19
    Let A=[2132]A = \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} and B=[−1−111]B = \begin{bmatrix} -1 & -1 \\ 1 & 1 \end{bmatrix}. If the variables xx and yy satisfy the matrix equation (A−1+B)[xy]=[0−2](A^{-1} + B)\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ -2 \end{bmatrix}, then the value of x+3yx + 3y is......

    Tap an option to check your answer.

  20. 20
    If matrix (x1224x−332)\begin{pmatrix} x & 1 & 2 \\ 2 & 4 & x \\ -3 & 3 & 2 \end{pmatrix} is non-invertible matrix and distinct values of xx are aa and bb then 9(a2+b2)=⋅s⋅s⋅s9(a^2 + b^2) = \cdot s\cdot s\cdot s

    Tap an option to check your answer.

  21. 21
    Let y=13x−5y = \dfrac{1}{3x - 5} and if d4ydx4=1944\dfrac{d^4y}{dx^4} = 1944, then the value of xx is

    Tap an option to check your answer.

  22. 22
    If y=2x+(sin⁡x)xy = 2^x + (\sin x)^x, then dydx=\dfrac{dy}{dx} =

    Tap an option to check your answer.

  23. 23
    If y=sin⁡(2sin⁡−1x)y = \sin(2\sin^{-1}x), then dydx=\dfrac{dy}{dx} = ______

    Tap an option to check your answer.

  24. 24
    If xy⋅yx=1x^y \cdot y^x = 1 then the value of dydx\dfrac{dy}{dx} is

    Tap an option to check your answer.

  25. 25
    If f(x)f(x) is a differentiable function of xx, then lim⁡h→0[f(x+h)]2−[f(x)]22h=\lim_{h \to 0}\dfrac{[f(x + h)]^2 - [f(x)]^2}{2h} =

    Tap an option to check your answer.

  26. 26
    A water tank in the house of an inverted cone is being emptied at the rate of 22 cubic feet per second. The height of the cone is 88 feet and the radius is 44 feet, then the rate of change of the water level when the depth is 66 feet.

    Tap an option to check your answer.

  27. 27
    The approximate value of sin⁡−1(0.51)\sin^{-1}(0.51) is ....... [Given π=3.1416\pi = 3.1416, 23=1.1547\dfrac{2}{\sqrt{3}} = 1.1547]

    Tap an option to check your answer.

  28. 28
    The radius of a spherical balloon increases at the rate of 44 cm/sec. The rate at which its surface area increases, when the radius is 55 metres is

    Tap an option to check your answer.

  29. 29
    If f′(x)=k(cos⁡x−sin⁡x),f′(0)=5,f(π2)=19f'(x) = k(\cos x - \sin x), f'(0) = 5, f\left(\dfrac{\pi}{2}\right) = 19, Then f(x)=f(x) =

    Tap an option to check your answer.

  30. 30
    ∫4x+52x+1 dx=\displaystyle\int\dfrac{4x + 5}{2x + 1}\,dx =

    Tap an option to check your answer.

  31. 31
    ∫xsec⁡(x32)tan⁡(x32)dx=\displaystyle\int\sqrt{x}\sec\left(x^{\frac{3}{2}}\right)\tan\left(x^{\frac{3}{2}}\right)dx =

    Tap an option to check your answer.

  32. 32
    If ∫01tan⁡−1[11−x+x2]dx=2k\int_0^1\tan^{-1}\left[\dfrac{1}{1 - x + x^2}\right]dx = 2k, then the value of kk is:

    Tap an option to check your answer.

  33. 33
    If ∫0∞1(x2+1)(x2+16) dx=πk2−9\int_0^\infty\dfrac{1}{(x^2 + 1)(x^2 + 16)}\,dx = \dfrac{\pi}{k^2 - 9}, then k=…k = \ldots

    Tap an option to check your answer.

  34. 34
    If ∫−14f(x)dx=4\int_{-1}^4 f(x)dx = 4 and ∫24(5−f(x))dx=7\int_2^4(5 - f(x))dx = 7 then ∫2−1f(x)dx=\int_2^{-1}f(x)dx =

    Tap an option to check your answer.

  35. 35
    The area between the curves y=1−∣x∣y = 1 - |x| and y=∣x∣−1y = |x| - 1 is ..... square units.

    Tap an option to check your answer.

  36. 36
    The differential equation of all parabolas which have 4a4a as latus rectum and whose axis is parallel to the X-axis is 2ad2ydx2+(dydx)k=02a\dfrac{d^2y}{dx^2} + \left(\dfrac{dy}{dx}\right)^k = 0, then the value of kk is...

    Tap an option to check your answer.

  37. 37
    If the curve y=f(x)y = f(x) passes through the point (1,2)(1, 2) and satisfies the differential equation xdy+(y+x3y2)dx=0xdy + (y + x^3y^2)dx = 0, then the equation of curve is...

    Tap an option to check your answer.

  38. 38
    The differential equation of the equation y=acos⁡(x+b)y = a\cos(x + b) is

    Tap an option to check your answer.

  39. 39
    The cartesian equation of the line passing through the point i^+2j^+3k^\hat{i} + 2\hat{j} + 3\hat{k} and perpendicular to the vectors i^+j^+k^\hat{i} + \hat{j} + \hat{k} and 2i^−j^+k^2\hat{i} - \hat{j} + \hat{k} is

    Tap an option to check your answer.

  40. 40
    If the vector a⃗=xi^−j^+k^\vec{a} = x\hat{i} - \hat{j} + \hat{k} and b⃗=i^+yj^+zk^\vec{b} = \hat{i} + y\hat{j} + z\hat{k} are collinear, then a possible unit vector parallel to the vector i^+yj^+zk^\hat{i} + y\hat{j} + z\hat{k} is...

    Tap an option to check your answer.

  41. 41
    a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} represent three concurrent edges of a rectangular parallelopiped whose lengths are 5,25, 2 and 33 units respectively, then (a⃗+b⃗+c⃗)⋅(a⃗×b⃗+b⃗×c⃗+c⃗×a⃗)=(\vec{a} + \vec{b} + \vec{c}) \cdot (\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}) =

    Tap an option to check your answer.

  42. 42
    If ∣a⃗+b⃗∣=∣a⃗−b⃗∣|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| then the angle between a⃗\vec{a} and b⃗\vec{b} is

    Tap an option to check your answer.

  43. 43
    The vector equation of the plane determined by the lines x=y,z=0x = y, z = 0 and x+y=0,z=0x + y = 0, z = 0 is

    Tap an option to check your answer.

  44. 44
    If the point Q(α,β,γ)Q(\alpha, \beta, \gamma) is the mirror image of P(10,15,20)P(10, 15, 20) in the plane r⃗=k^+λ(−i^+j^)+μ(−i^+k^)\vec{r} = \hat{k} + \lambda(-\hat{i} + \hat{j}) + \mu(-\hat{i} + \hat{k}), λ,μ∈R\lambda, \mu \in \mathbb{R} then the value of 3(α+β+γ)3(\alpha + \beta + \gamma) is

    Tap an option to check your answer.

  45. 45
    If MM is the foot of the perpendicular drawn from A(4,3,2)A(4, 3, 2) on the line joining the points B(2,4,1)B(2, 4, 1) and C(4,5,3)C(4, 5, 3), the co-ordinates of MM are ____

    Tap an option to check your answer.

  46. 46
    Let aa and bb be the distances from the point (2,3,4)(2, 3, 4) to the XY plane and Y-Axis respectively. Then a2+b2=a^2 + b^2 =

    Tap an option to check your answer.

  47. 47
    The minimum value of z=4x+2yz = 4x + 2y subject to the constraints 3x+y≥27,x+y≥21,x+2y≥30,x≥0,y≥03x + y \ge 27, x + y \ge 21, x + 2y \ge 30, x \ge 0, y \ge 0 is

    Tap an option to check your answer.

  48. 48
    Suppose that 60%60\% of all families own a mobile set. If 1111 families are interviewed at random, then the probability that 88 families own a mobile set is..... (Given that (0.6)8=0.0168(0.6)^8 = 0.0168)

    Tap an option to check your answer.

  49. 49
    Let XX be a continuous r. v. with p. d. f. f(x)={kx3,0≤x≤10,otherwisef(x) = \begin{cases} kx^3, & 0 \le x \le 1 \\ 0, & \text{otherwise} \end{cases} then P(X≤34∣X>14)=…P\left(X \le \dfrac{3}{4} \mid X > \dfrac{1}{4}\right) = \ldots

    Tap an option to check your answer.

  50. 50
    If a fair die is thrown, then the odds in favor of getting a perfect square on the uppermost face are:

    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