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

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

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  1. 1
    A ball is thrown in the air. Its height at any time tt is given by h=3+14t−5t2h = 3 + 14t - 5t^2, then the maximum height it can reach

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  2. 2
    If (1+i)⋅(1+2i)………(1+ni)=x+iy(1 + i)\cdot(1 + 2i)\ldots\ldots\ldots(1 + ni) = x + iy (Where i=−1i = \sqrt{-1} ), then the value of (2)⋅(5)⋅(10)………(1+n2)(2)\cdot(5)\cdot(10)\ldots\ldots\ldots(1 + n^2)

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  3. 3
    The number of arrangements of the numbers strictly between 10 and 1000 formed with the digits 0, 1, 2, 3, 4, 5, 6 without repetition is

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  4. 4
    The value of sin⁡23Asin⁡2A−cos⁡23Acos⁡2A\dfrac{\sin^2 3A}{\sin^2 A} - \dfrac{\cos^2 3A}{\cos^2 A} is

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  5. 5
    If 0≤x≤π20 \le x \le \dfrac{\pi}{2} , then the number of values of xx for which sin⁡x−sin⁡2x+sin⁡3x=0\sin x - \sin 2x + \sin 3x = 0 is

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  6. 6
    The number of lines passing through A (3, 4) and the sum of whose non-zero intercepts is zero is (are)

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  7. 7
    If 4ab=3h24ab = 3h^2, then the ratio of the slopes of the lines represented by ax2+2hxy+by2=0ax^2 + 2hxy + by^2 = 0 is...

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  8. 8
    The equations of the tangent to the curve x2+y2=10x^2 + y^2 = 10, where the tangent is parallel to the line 2x+y−1=02x + y - 1 = 0, are

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  9. 9
    If the line y=2x+λy = 2x + \lambda is a tangent to the hyperbola 36x2−25y2=360036x^2 - 25y^2 = 3600, then λ=\lambda =

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  10. 10
    lim⁡x→0(5x−1)4 csc⁡ (xlog⁡5)tan⁡(xlog⁡5)⋅log⁡(1+x2log⁡25)=……\displaystyle\lim_{x \to 0}\dfrac{(5^x - 1)^4\,\mathrm{\csc}\,(x\log 5)}{\tan(x\log 5)\cdot\log(1 + x^2\log 25)} = \ldots\ldots

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  11. 11
    Simplest form of the following switching circuit is

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  12. 12
    With usual notations in △\triangleABC, if bcos⁡2C2+ccos⁡2B2=3a2b\cos^2\dfrac{C}{2} + c\cos^2\dfrac{B}{2} = \dfrac{3a}{2} then

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  13. 13
    In a triangle ABC, with usual notations a=3+1,b=3−1a = \sqrt{3} + 1, b = \sqrt{3} - 1 and ∠C=60∘\angle C = 60^\circ then the values of ∠A\angle A and ∠B\angle B respectively are

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  14. 14
    Inverse of [3−214]\begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix} is

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  15. 15
    If A=[5a−b32]A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} and A (adj A)=AATA\,(\mathrm{adj}\,A) = AA^T, then 5a+b=5a + b =

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  16. 16
    If y=tan⁡−1[x−1−x2x+1−x2]y = \tan^{-1}\left[\dfrac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}}\right] , then dydx=\dfrac{dy}{dx} =

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  17. 17
    cos⁡(cos⁡−1(−12)+π3)=\cos\left(\cos^{-1}\left(-\dfrac{1}{2}\right) + \dfrac{\pi}{3}\right) =

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  18. 18
    sin⁡−1(1213)+cos⁡−1(45)+tan⁡−1(6316)=\sin^{-1}\left(\dfrac{12}{13}\right) + \cos^{-1}\left(\dfrac{4}{5}\right) + \tan^{-1}\left(\dfrac{63}{16}\right) =

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  19. 19
    If f(x)=4x+36x−4,x≠23f(x) = \dfrac{4x + 3}{6x - 4}, x \neq \dfrac{2}{3} and (fof)(x)=g(x)(x) = g(x) where g:R−{23}→R−{23}g : \mathbb{R} - \left\{\dfrac{2}{3}\right\} \to \mathbb{R} - \left\{\dfrac{2}{3}\right\}, then (g∘g∘g∘g∘g)(3)=(g \circ g \circ g \circ g \circ g)(3) =

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  20. 20
    If the derivative of the function f(x)={ax2+bif x<−1bx2+ax+4if x≥−1f(x) = \begin{cases} ax^2 + b & \text{if } x < -1 \\ bx^2 + ax + 4 & \text{if } x \ge -1 \end{cases} is continuous everywhere then

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  21. 21
    The derivative of log⁡8(log⁡5x)\log_8(\log_5 x) w. r. t. xx is

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  22. 22
    If y1m+y−1m=2xy^{\frac{1}{m}} + y^{\frac{-1}{m}} = 2x , then (x2−1)y12=(x^2 - 1)y_1^2 =

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  23. 23
    A triangle has two fixed vertices A (a,0)(a, 0) and B(0,b)(0, b) . Let its third vertex C is moving along the line x=yx = y. If ss is the area of triangle ABC, then dsdx=\dfrac{ds}{dx} =

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  24. 24
    The function f(x)=tan⁡−1(sin⁡x+cos⁡x)f(x) = \tan^{-1}(\sin x + \cos x) is an increasing function in the interval.....

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  25. 25
    The minimum value of log⁡xx\dfrac{\log x}{x} in the interval (2,∞)(2, \infty) is

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  26. 26
    ∫(x+1)(x+log⁡x)2x dx=\displaystyle\int\dfrac{(x + 1)(x + \log x)^2}{x}\,dx =

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  27. 27
    ∫cot⁡4x dx\displaystyle\int\cot^4 x\,dx is equal to

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  28. 28
    ∫cos⁡3xsin⁡2x+sin⁡x dx=\displaystyle\int\dfrac{\cos^3 x}{\sin^2 x + \sin x}\,dx =

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  29. 29
    ∫π/6π/3sin⁡x−cos⁡x1+sin⁡xcos⁡x dx=\displaystyle\int_{\pi/6}^{\pi/3}\dfrac{\sin x - \cos x}{1 + \sin x\cos x}\,dx =

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  30. 30
    ∫0log⁡5exex−1ex+3 dx=\displaystyle\int_0^{\log 5}\dfrac{e^x\sqrt{e^x - 1}}{e^x + 3}\,dx =

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  31. 31
    The integrating factor of the differential equation (1+t2)+(x−etan⁡−1t)dtdx=0(1 + t^2) + \left(x - e^{\tan^{-1}t}\right)\dfrac{dt}{dx} = 0 is

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  32. 32
    The degree of the differential equation obtained from the equation (y−a)2=4(x−b)(y - a)^2 = 4(x - b) [where aa and b are arbitrary constants] is

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  33. 33
    The solution of the differential equation (x+2y3)dydx−y=0(x + 2y^3)\dfrac{dy}{dx} - y = 0 is

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  34. 34
    The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

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  35. 35
    If a vector 3i^+4j^−5k^3\hat{i} + 4\hat{j} - 5\hat{k} is rotated through a certain angle about the origin in the anti-clockwise direction, then the components of the new vector are a+1,−3,5a + 1, -3, 5 . The possible values of aa is

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  36. 36
    Let A, B, C, D be the points in the plane with position vectors −2i^−j^,4i^,3i^+3j^-2\hat{i} - \hat{j}, 4\hat{i}, 3\hat{i} + 3\hat{j} and −3i^+2j^-3\hat{i} + 2\hat{j} respectively, then □\squareABCD is

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  37. 37
    Let aˉ=i^+j^,cˉ=i^−j^\bar{a} = \hat{i} + \hat{j}, \bar{c} = \hat{i} - \hat{j} and a vector bˉ\bar{b} be such that aˉ×bˉ=cˉ\bar{a} \times \bar{b} = \bar{c} and aˉ⋅bˉ=3\bar{a}\cdot\bar{b} = 3 then ∣bˉ∣=|\bar{b}| =

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  38. 38
    The acute angle between the vector 2i^+j^−3k^2\hat{i} + \hat{j} - 3\hat{k} and the plane containing the vectors 2i^+3j^−k^2\hat{i} + 3\hat{j} - \hat{k} and i^−j^+2k^\hat{i} - \hat{j} + 2\hat{k} is

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  39. 39
    A parallelogram is constructed on 5aˉ+2bˉ5\bar{a} + 2\bar{b} and aˉ−3bˉ\bar{a} - 3\bar{b} as its adjacent sides, with ∣aˉ∣=22,∣bˉ∣=3|\bar{a}| = 2\sqrt{2}, |\bar{b}| = 3 . The angle between aˉ\bar{a} and bˉ\bar{b} is π4\dfrac{\pi}{4} . Then the length of the diagonals of the parallelogram are

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  40. 40
    The lines x−21=y−31=z−4−k\dfrac{x - 2}{1} = \dfrac{y - 3}{1} = \dfrac{z - 4}{-k} and x−1k=y−42=z−51\dfrac{x - 1}{k} = \dfrac{y - 4}{2} = \dfrac{z - 5}{1} are coplanar if

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  41. 41
    The direction ratios of the normal to the plane passing through (1, 0, 0), (0, 1, 0) which makes an angle of measure 45∘45^\circ with the plane 2x+3y=72x + 3y = 7 are....

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  42. 42
    The lines x−1−1=y+21=z−3−2\dfrac{x - 1}{-1} = \dfrac{y + 2}{1} = \dfrac{z - 3}{-2} and x−11=y+21=z+1−2\dfrac{x - 1}{1} = \dfrac{y + 2}{1} = \dfrac{z + 1}{-2} are

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  43. 43
    If the product of the distances of the point (1, 2, 3) from the origin and the plane 2x−3y+z+k=02x - 3y + z + k = 0 is 7, then the value of k is

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  44. 44
    The vector equation of the line whose cartesian equations are x=2,2y−3z+7=0x = 2, 2y - 3z + 7 = 0

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  45. 45
    The feasible region represented by the constraints y−2x≤4,x+y≥5,x≤4,y≥2,x,y≥0y - 2x \le 4, x + y \ge 5, x \le 4, y \ge 2, x, y \ge 0 is ...........

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  46. 46
    A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number. Let p:P(A)=13p : P(A) = \dfrac{1}{3}, qq : A and B are independent events. Then the truth values of statements pp and qq respectively are.....

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  47. 47
    Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the probability that the exactly two ships arrive safely is

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  48. 48
    A random variable X has the probability distribution
    X=xX = x12345678
    P(X=x)P(X = x)0.230.150.120.100.200.070.080.05
    for the events E = {X is a prime number} and F = {X ≤\le 3}, then P (E∪\cupF)=

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  49. 49
    The probability distribution of a random variable X is given by
    X=xX = x1234
    P(X=x)P(X = x)kk2k2k3k3k4k4k
    Then the c.d.f. of X is given by

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  50. 50
    Two dice are thrown successively 4 times and getting a doublet is called a success. The probability of getting at least 1 success is

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