PYQ Vault

MHT-CET 2025 (25 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 a circle with centre at (−1,1)( - 1,1) touches the line x+2y+4=0x+ 2y+ 4 = 0 then the co-ordinates of the point of contact are

    Tap an option to check your answer.

  2. 2
    A doctor assumes that patient has one of three diseases d1, d2 or d3. Before any test he assumes an equal probability for each disease. He carries out a test that will be positive with probability 0.7 if the patient has disease d1,0.5d1,0.5 if the patient has disease d 2 and 0.8 if the patient has disease d3. Given that the outcome of the test was positive then probability that patient has disease d2 is

    Tap an option to check your answer.

  3. 3
    A particle PP starts from the point Z0=1+2iZ_{0}= 1 + 2i where i=−1i =\sqrt{- 1}. It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive Y -axis by 3 units to reach a point Z1Z_{1}. From Z1Z_{1} the particle moves 2\sqrt{2} units in the direction of vector i^+j^\widehat{i}+\widehat{j} and then it moves through an angle π2\frac{\pi}{2} in anticlockwise direction on a circle with centre at origin to reach at point Z2Z_{2}, then Z2=Z_{2}=

    Tap an option to check your answer.

  4. 4
    lim⁡x→063x−9x−7x+12−1+cos⁡x=\lim_{x\rightarrow 0} \frac{63^{x}-9^{x}-7^{x}+ 1}{\sqrt{2}-\sqrt{1 + \cos x}}=...... .

    Tap an option to check your answer.

  5. 5
    Consider the following three statements (A) If 3+2=73 + 2 = 7 then 4+3=84 + 3 = 8. (B) If 5+2=75 + 2 = 7 then earth is flat. (C) If both (A) and (B) are true then 5+6=115 + 6 = 11. Which of the following statements is correct?

    Tap an option to check your answer.

  6. 6
    If A=[5a−b32]A=\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} and A⋅adjA=AATA\cdot adjA=AA^{T}, then 5a+b=5a+b=

    Tap an option to check your answer.

  7. 7
    The common principal solution of the equations sin⁡θ=−12\sin\theta= -\frac{1}{2} and tan⁡θ=13\tan\theta=\frac{1}{\sqrt{3}} is

    Tap an option to check your answer.

  8. 8
    The slopes of the lines represented by 6x2+2hxy+y2=06x^{2}+ 2hxy+y^{2}= 0 are in the ratio 2:32:3, then h=h =

    Tap an option to check your answer.

  9. 9
    If θ\theta is an obtuse angle between vectors aˉ\bar{a} and b‾\overline{b} such that ∣a‾∣=5,∣ b‾∣=3|\overline{a}| = 5,|\overline{\text{ }b}| = 3 and ∣a‾×b‾∣=55|\overline{a}\times\overline{b}| = 5\sqrt{5} then aˉ⋅bˉ=\bar{a}\cdot\bar{b}=

    Tap an option to check your answer.

  10. 10
    If the plane x2−y3−z5=1\frac{x}{2}-\frac{y}{3}-\frac{z}{5}= 1 cuts the co-ordinate axes in points A,B,CA,B,C respectively, then the area of the triangle ABCABC is

    Tap an option to check your answer.

  11. 11
    The rate of increase of the population of a city is proportional to the population present at that instant. In the period of 40 years the population increased from 30,000 to 40,000. At any time tt the population is (a)(b)t40(a)(b)^{\frac{t}{40}}. Then the values of a and bb are respectively

    Tap an option to check your answer.

  12. 12
    The probability that a student is not a swimmer is 15\frac{1}{5}. The probability that out of 5 students selected at random 4 are swimmers is

    Tap an option to check your answer.

  13. 13
    A player tosses two coins. He wins ₹ 10, if 2 heads appear, ₹ 5, if one head appear and ₹ 2 if no head appears. Then variance of winning amount is

    Tap an option to check your answer.

  14. 14
    Consider the probability distribution
    X=xX = x12345
    P(X=x)P(X = x)KK2K2KK2K^{2}2K2K5K25K^{2}
    Then the value of P(X>2)P(X > 2) is

    Tap an option to check your answer.

  15. 15
    The equation of the curve passing through origin and satisfying (1+x2)dy dx+2xy=4x2\left( 1 +x^{2} \right)\frac{dy}{\text{ }dx}+ 2xy= 4x^{2} is

    Tap an option to check your answer.

  16. 16
    If y=tan⁡−1(12x−64x31−48x2)y=\tan^{- 1}\left( \frac{12x- 64x^{3}}{1 - 48x^{2}} \right), then dydx=\frac{dy}{dx}=

    Tap an option to check your answer.

  17. 17
    The order of the differential equation whose general solution is given by y=(C1+C2)sin⁡(x+C3)−C4ex+C5y=\left( C_{1}+C_{2} \right)\sin\left( x+C_{3} \right)-C_{4}e^{x+C_{5}} is (where C1,C2,C3,C4,C5C_{1},C_{2},C_{3},C_{4},C_{5} are arbitrary constants)

    Tap an option to check your answer.

  18. 18
    In L.P.P., the maximum value of objective function Z=6x+3yZ = 6x+ 3y subject to constraints x+y≤5,x+2y≥4,4x+y≤12,x,y≥0x+y\leq 5,x+ 2y\geq 4,4x+y\leq 12,x,y\geq 0 is

    Tap an option to check your answer.

  19. 19
    If the lines x=ay−1=z−2x=ay- 1 =z- 2 and x=3y−2=bz−2(ab≠0)x= 3y- 2 = bz - 2(ab \neq 0) are coplanar, then

    Tap an option to check your answer.

  20. 20
    If (tan⁡−1x)2+(cot⁡−1x)2=5π28\left( \tan^{- 1}x \right)^{2}+\left( \cot^{- 1}x \right)^{2}=\frac{5\pi^{2}}{8}, then x2+1=x^{2}+ 1 =

    Tap an option to check your answer.

  21. 21
    If p≡p\equiv The switch S1S_{1} is closed, q≡q\equiv The switch S2S_{2} is closed, r≡r \equiv switch S3S_{3} is closed, then symbolic form of following switching circuit is equivalent to

    Tap an option to check your answer.

  22. 22
    Let f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} is differentiable function having f(3)=3,f′(3)=127f(3) = 3,f^{'}(3) =\frac{1}{27} and g(x)={∫3f(x)3t2x−3dt, if x≠3 K, if x=3g(x) =\left\{ \begin{matrix} \int_{3}^{f(x)} \frac{3t^{2}}{x- 3}dt, & \text{~if~}x\neq 3 \\ \text{ }K, & \text{~if~}x= 3 \end{matrix} \right. is continuous at x=3x= 3, then K=K =

    Tap an option to check your answer.

  23. 23
    The area bounded by the curve y=4x−x2y= 4x-x^{2} and X - axis in square units, is ____\_\_\_\_

    Tap an option to check your answer.

  24. 24
    The Cartesian equation of the plane rˉ=(2i^−3j^)+λ(i^+2j^−k^)+μ(2i^+3j^+k^)\bar{r}= (2\widehat{i}- 3\widehat{j}) +\lambda(\widehat{i}+ 2\widehat{j}-\widehat{k}) +\mu(2\widehat{i}+ 3\widehat{j}+\widehat{k}) is

    Tap an option to check your answer.

  25. 25
    If the line x−32=y+5−1=z+22\frac{x- 3}{2}=\frac{y+ 5}{- 1}=\frac{z+ 2}{2} lies in the plane αx+3y−z+β=0\alpha x+ 3y-z+\beta= 0, then values of α\alpha and β\beta respectively are ....

    Tap an option to check your answer.

  26. 26
    ∫log⁡12log⁡2sin⁡(ex−1ex+1)dx=\int_{\log\frac{1}{2}}^{\log2} \sin\left( \frac{e^{x}- 1}{e^{x}+ 1} \right)dx=

    Tap an option to check your answer.

  27. 27
    If the vectors a‾=c(log⁡7x)i^+2j^+3k^\overline{a}= c\left( \log_{7}x \right)\widehat{i}+ 2\widehat{j}+ 3\widehat{k} and b‾=(log⁡7x)i^+3c(log⁡7x)j^−4k^\overline{b}=\left( \log_{7}x \right)\widehat{i}+ 3c\left( \log_{7}x \right)\widehat{j}- 4\widehat{k} make obtuse angle for any x>0x> 0, then c belongs to

    Tap an option to check your answer.

  28. 28
    ∫−π4π4sin⁡−4xdx=\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \sin^{- 4}xdx=

    Tap an option to check your answer.

  29. 29
    The altitude through vertex AA of △ABC\bigtriangleup ABC with position vectors of points A,B,CA,B,C as aˉ,bˉ,cˉ\bar{a},\bar{b},\bar{c} respectively is

    Tap an option to check your answer.

  30. 30
    ∫dx(x+a)97(x−b)57=\int\frac{dx}{(x+a)^{\frac{9}{7}}(x-b)^{\frac{5}{7}}}=

    Tap an option to check your answer.

  31. 31
    The lines rˉ=(i^+j^−k^)+λ(3i^−j^)\bar{r}= (\widehat{i}+\widehat{j}-\widehat{k}) +\lambda(3\widehat{i}-\widehat{j}) and r‾=(4i^−k^)+μ(2i^+3k^)\overline{r}= (4\widehat{i}-\widehat{k}) +\mu(2\widehat{i}+ 3\widehat{k}) are

    Tap an option to check your answer.

  32. 32
    If b‾\overline{b} and c‾\overline{c} are unit vectors and ∣a‾∣=7|\overline{a}| = 7, a‾×(b‾×c‾)+b‾×(c‾×a‾)=12a‾\overline{a}\times (\overline{b}\times\overline{c}) +\overline{b}\times (\overline{c}\times\overline{a}) =\frac{1}{2}\overline{a}, then angle between the vectors aˉ\bar{a} and cˉ\bar{c} and angle between the vectors bˉ\bar{b} and cˉ\bar{c} are respectively

    Tap an option to check your answer.

  33. 33
    With usual notations in △ABC\bigtriangleup ABC, if ∠B=π2\angle B =\frac{\pi}{2}, and tan⁡A2,tan⁡C2\tan\frac{A}{2},\tan\frac{C}{2} are roots of equation px2+qx+r=0px^{2}+ qx + r = 0, p≠0p\neq 0, then

    Tap an option to check your answer.

  34. 34
    ∫dxx(x3+1)=\int\frac{dx}{x\left( x^{3}+ 1 \right)}=

    Tap an option to check your answer.

  35. 35
    If tan⁡−1(x+1)+tan⁡−1x+tan⁡−1(x−1)=tan⁡−13\tan^{- 1}(x+ 1) +\tan^{- 1}x+\tan^{- 1}(x- 1) =\tan^{- 1}3, then for x<0x< 0 the value of 500x4+270x2+997=500x^{4}+ 270x^{2}+ 997 =

    Tap an option to check your answer.

  36. 36
    Let f:R−{2}→R−{1}f:\mathbb{R}\mathbf{- \{ 2\} \rightarrow}\mathbb{R}\mathbf{- \{ 1\}} defined by f(x)=x−3x−2f(x) =\frac{x- 3}{x- 2} and g:R→Rg:\mathbb{R}\rightarrow\mathbb{R} defined by g(x)=3x−2g(x) = 3x- 2, then sum of all values of xx for which f−1(x)+g−1(x)=196f^{- 1}(x) +g^{- 1}(x) =\frac{19}{6} is

    Tap an option to check your answer.

  37. 37
    There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is

    Tap an option to check your answer.

  38. 38
    ∫x4cos⁡(tan⁡−1x5)1+x10dx\int\frac{x^{4}\cos\left( \tan^{- 1}x^{5} \right)}{1 +x^{10}}dx equals

    Tap an option to check your answer.

  39. 39
    The length of the perpendicular drawn from the origin on the normal to the curve x2+2xy−3y2=0x^{2}+ 2xy- 3y^{2}= 0 at the point (2,2)(2,2) is

    Tap an option to check your answer.

  40. 40
    If f(x)=log⁡(1+x)−2x2+xf(x) = \log(1 +x) -\frac{2x}{2 +x} then f(x)f(x) is increasing in

    Tap an option to check your answer.

  41. 41
    The angle θ\theta, at which the curves y=3xy=3^{x} and y=7xy=7^{x} intersect, is given by

    Tap an option to check your answer.

  42. 42
    The function f(x)=x3−6x2+ax+bf(x) =x^{3}- 6x^{2}+ax+b satisfies the conditions of Rolle's theorem in [1,3]. Then the values of aa and bb are respectively

    Tap an option to check your answer.

  43. 43
    If y−y−y−........∞=x+x+x+........∞\sqrt{y-\sqrt{y-\sqrt{y- ........\infty}}}=\sqrt{x+\sqrt{x+\sqrt{x+ ........\infty}}} then dy dx=\frac{dy}{\text{ }dx}=

    Tap an option to check your answer.

  44. 44
    If x=sin⁡tx= \sin t and y=sin⁡pty= \sin pt, then the value of (1−x2)d2y dx2−x dy dx+p2y=\left( 1 -x^{2} \right)\frac{d^{2}y}{\text{ }dx^{2}}-x\frac{\text{ }dy}{\text{ }dx}+p^{2}y=

    Tap an option to check your answer.

  45. 45
    Let aˉ=i^+j^−k^\bar{a}=\widehat{i}+\widehat{j}-\widehat{k} and cˉ=5i^−3j^+2k^\bar{c}= 5\widehat{i}- 3\widehat{j}+ 2\widehat{k} and if b‾×c‾=a‾\overline{b}\times\overline{c}=\overline{a} then ∣b‾∣=|\overline{b}| =

    Tap an option to check your answer.

  46. 46
    The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is

    Tap an option to check your answer.

  47. 47
    The eccentricity of the hyperbola which passes through the points (3,0)(3,0) and (32,2)(3\sqrt{2},2) is

    Tap an option to check your answer.

  48. 48
    cos⁡4π8+cos⁡43π8+cos⁡45π8+cos⁡47π8=\cos^{4}\frac{\pi}{8}+\cos^{4}\frac{3\pi}{8}+\cos^{4}\frac{5\pi}{8}+\cos^{4}\frac{7\pi}{8}=

    Tap an option to check your answer.

  49. 49
    The straight line passing through (−3,6)( - 3,6) and midpoint of the line segment joining the points (4,−5)(4, - 5) and (−2,9- 2,9) have inclination

    Tap an option to check your answer.

  50. 50
    The general solution of differential equation (y2−x2)dx=xy dy(x≠0)\left( y^{2}-x^{2} \right)dx=xy\text{ }dy(x\neq 0) 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