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MHT-CET 2026 (17 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
    If α\alpha and β\beta are the distinct roots of the equation x2−x+1=0x^2 - x + 1 = 0, then the value of α200+β206+2\alpha^{200} + \beta^{206} + 2 is equal to

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  2. 2
    The number of arrangements of the letters in the word SOLAPUR, so that consonants and vowels are placed alternately is

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  3. 3
    If cos⁡43∘+sin⁡43∘=k3\cos 43^\circ + \sin 43^\circ = k^3, then cos⁡2∘=…\cos 2^\circ = \ldots

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  4. 4
    If the equation sin⁡3θ−cos⁡2θ=14\sin 3\theta - \cos^2\theta = \dfrac{1}{4} and θ∈[0,π]\theta \in [0, \pi], then the number of solutions is...

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  5. 5
    If A(2,−3)A(2, -3) and C(−6,7)C(-6, 7) are opposite vertices of a rhombus ABCD, then the equation of diagonal BD is

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  6. 6
    The measure of the acute angle between the pair of lines 2x2+xy−y2−x+2y−1=02x^2 + xy - y^2 - x + 2y - 1 = 0 is:

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  7. 7
    The joint equation of a pair of lines passing through point (1,4)(1, 4), one of which is parallel to X-axis and the other makes an angle of 45∘45^\circ with the positive direction of X-axis, is

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

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  9. 9
    The equations of the tangents to the ellipse x216+y29=1\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1 making an inclination of 30∘30^\circ with the major axis are

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  10. 10
    If lim⁡x→1sin⁡(3x2−4x+1)−x2+12x3−7x2+ax+b=−2\lim_{x \to 1}\dfrac{\sin(3x^2 - 4x + 1) - x^2 + 1}{2x^3 - 7x^2 + ax + b} = -2, then the quadratic equation having roots aa and bb is

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  11. 11
    If the statements p: If voltage increases then current decreases. q : If voltage does not increase then current does not decrease. r : If current decreases then voltage increases. s : If current does not decrease then voltage does not increase. then which of the following pairs of statements having same meaning

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  12. 12
    If p→(q∨∼r)p \to (q \vee \sim r) is false, then the truth values of (p↔q)∧r(p \leftrightarrow q) \wedge r and ∼p→∼q\sim p \to \sim q are :

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  13. 13
    With usual notations, in △ABC\triangle ABC, if cos⁡C=sin⁡A2sin⁡B\cos C = \dfrac{\sin A}{2\sin B}, then which of the following is true ?

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  14. 14
    In △ABC\triangle ABC, if a=13,b=14,c=15a = 13, b = 14, c = 15, then the value of sin⁡A+cos⁡A\sin A + \cos A is...

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  15. 15
    If the matrix A=[4132]A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix} is expressed as the sum of a symmetric matrix B and a skew symmetric matrix C then which of the following relations is correct?

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  16. 16
    If AA is a non-singular matrix and A2−A+I=0A^2 - A + I = 0, then A−1=…A^{-1} = \ldots

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  17. 17
    The value of 3tan⁡−1(12)=…3\tan^{-1}\left(\dfrac{1}{2}\right) = \ldots

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  18. 18
    If f(x)=x+2x2−3x+1f(x) = \dfrac{x + 2}{x^2 - 3x + 1}, then the values of xx for which f(x)f(x) is not defined are

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  19. 19
    If f:R→Rf : R \to R and g:R→Rg : R \to R are defined as f(x)=2x−∣x∣f(x) = 2x - |x| and g(x)=2x+∣x∣g(x) = 2x + |x|, then

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  20. 20
    Which of the following function is discontinuous at x=0x = 0 ?

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  21. 21
    If y=x⋅7xy = x \cdot 7^x, then the value of dxdy\dfrac{dx}{dy} when x=1x = 1 is

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  22. 22
    If y=[(x+1)(2x+1)(3x+1)……(nx+1)]4y = [(x + 1)(2x + 1)(3x + 1)\ldots\ldots(nx + 1)]^4, where n∈Nn \in N and dydx\dfrac{dy}{dx} at x=0x = 0 is 2k2k, then the value of kk is

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  23. 23
    If f(x)=cos⁡xcos⁡2xcos⁡4xcos⁡8xcos⁡16xf(x) = \cos x\cos 2x\cos 4x\cos 8x\cos 16x, then f′(π4)f'\left(\dfrac{\pi}{4}\right) is equal to

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  24. 24
    The derivative of the function f(x)=cos⁡4x+sin⁡4x, 0≤x≤2πf(x) = \cos^4 x + \sin^4 x,\ 0 \le x \le 2\pi is positive for

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  25. 25
    The tangent to the curve intersects the Y-axis at point P. A line drawn through point P is perpendicular to this tangent and passes through another point (1,0)(1, 0). The differential equation of the curve is...

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  26. 26
    The function f(x)=∫x+3x2−9x+20 dxf(x) = \int\dfrac{x + 3}{x^2 - 9x + 20}\,dx, then f(x)f(x) is

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  27. 27
    If f(x)=log⁡(1+x)−x1+xf(x) = \log(1 + x) - \dfrac{x}{1 + x}, then the values of xx for which f(x)f(x) is monotonically increasing and monotonically decreasing are respectively.....

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  28. 28
    The number 28 is divided into two positive parts such that the sum of the cube of one part and the square of the other part is minimum, then the absolute difference between the two parts is

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  29. 29
    The value of ∫sin⁡3x(cos⁡4x+3cos⁡2x+1)tan⁡−1(sec⁡x+cos⁡x) dx\displaystyle\int\dfrac{\sin^3 x}{(\cos^4 x + 3\cos^2 x + 1)\tan^{-1}(\sec x + \cos x)}\,dx is

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  30. 30
    The value of ∫2x13sin⁡x23 dx\displaystyle\int 2x^{\frac{1}{3}}\sin\sqrt[3]{x^2}\,dx is

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  31. 31
    ∫x3log⁡x dx=\displaystyle\int x^3\log x\,dx =

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  32. 32
    If f′(x)=(x+1)exxf'(x) = \dfrac{(\sqrt{x} + 1)e^{\sqrt{x}}}{\sqrt{x}} and f(0)=ef(0) = e then f(1)=…………f(1) = \ldots\ldots\ldots\ldots

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  33. 33
    The value of ∫0π11+2cos⁡x dx\int_0^\pi\dfrac{1}{1 + 2^{\cos x}}\,dx is ____

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  34. 34
    If In=∫1e(log⁡ex)n dxI_n = \int_1^e(\log_e x)^n\,dx where n∈Z+n \in Z^+ and Im+mI2026=eI_m + mI_{2026} = e, then m=m =

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  35. 35
    The area of the region bounded by the lines 2x−y+1=0, y=−1, y=32x - y + 1 = 0,\ y = -1,\ y = 3 and the y-axis is ____

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  36. 36
    Area enclosed by curve y=2x2y = 2x^2 and lines x≥1, y≤4x \ge 1,\ y \le 4 is ..... sq. units

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  37. 37
    If y=e−mxy = e^{-mx} is a solution of the differential equation d2ydx2+4dydx+3y=0\dfrac{d^2y}{dx^2} + 4\dfrac{dy}{dx} + 3y = 0, then the values of mm are

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  38. 38
    For the differential equation (x2+y2) dy=xy dx(x^2 + y^2)\,dy = xy\,dx, it is given that y(1)=1y(1) = 1 and y(x0)=ey(x_0) = e, then the value of x0x_0 is ____

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  39. 39
    In △OAB, O(0,0,0), A(6,2,−3)\triangle OAB,\ O(0, 0, 0),\ A(6, 2, -3) and B(4,0,3)B(4, 0, 3) are the vertices. Let a⃗\vec{a} and b⃗\vec{b} be position vectors of points AA and BB respectively and OMOM is the projection of a⃗\vec{a} on b⃗\vec{b} then l(AM)l(AM) is equal to...

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  40. 40
    Let a⃗=2i^−3j^+k^, b⃗=3i^+2j^+2k^, c⃗=4i^−3j^+k^\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k},\ \vec{b} = 3\hat{i} + 2\hat{j} + 2\hat{k},\ \vec{c} = 4\hat{i} - 3\hat{j} + \hat{k}, then the vectors a⃗, b⃗, c⃗\vec{a},\ \vec{b},\ \vec{c} are

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  41. 41
    Let aˉ=(a1i^+a2j^+a3k^), bˉ=(b1i^+b2j^+b3k^), cˉ=(c1i^+c2j^+c3k^)\bar{a} = (a_1\hat{i} + a_2\hat{j} + a_3\hat{k}),\ \bar{b} = (b_1\hat{i} + b_2\hat{j} + b_3\hat{k}),\ \bar{c} = (c_1\hat{i} + c_2\hat{j} + c_3\hat{k}) be three non-zero vectors such that aˉ\bar{a} is a unit vector perpendicular to both bˉ\bar{b} and cˉ\bar{c}. If the angle between bˉ\bar{b} and cˉ\bar{c} is π3\dfrac{\pi}{3} then ∣a1a2a3b1b2b3c1c2c3∣2=\begin{vmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{vmatrix}^2 =

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  42. 42
    Two adjacent sides of a parallelogram ABCD are given by AB‾=2i^+10j^+11k^\overline{AB} = 2\hat{i} + 10\hat{j} + 11\hat{k} and AD‾=−i^+2j^+2k^\overline{AD} = -\hat{i} + 2\hat{j} + 2\hat{k}. The side AD is rotated by an acute angle α\alpha in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle α\alpha is given by

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  43. 43
    If θ\theta is the angle between the lines x−12=2y+34; z=−2\dfrac{x - 1}{2} = \dfrac{2y + 3}{4};\ z = -2 and x=1; y−12=z+12x = 1;\ \dfrac{y - 1}{2} = \dfrac{z + 1}{2}, then

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  44. 44
    If for some m∈Rm \in \mathbb{R} the lines L1:x+1m=y−m−1=z−11L_1 : \dfrac{x + 1}{m} = \dfrac{y - m}{-1} = \dfrac{z - 1}{1} and L2:x+2−4=y+19=z+11L_2 : \dfrac{x + 2}{-4} = \dfrac{y + 1}{9} = \dfrac{z + 1}{1} are coplanar, then line L1L_1 passes through the point

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  45. 45
    If the lines r⃗=i^+j^−k^+λ(qi^−2j^+k^)\vec{r} = \hat{i} + \hat{j} - \hat{k} + \lambda(q\hat{i} - 2\hat{j} + \hat{k}) and r⃗=pi^−3j^+2k^+μ(i^−2j^+2k^)\vec{r} = p\hat{i} - 3\hat{j} + 2\hat{k} + \mu(\hat{i} - 2\hat{j} + 2\hat{k}) intersect each other and qi^−2j^+k^q\hat{i} - 2\hat{j} + \hat{k} is collinear to 4i^−4j^+2k^4\hat{i} - 4\hat{j} + 2\hat{k}, then the values of pp and qq are

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  46. 46
    The angle between a diagonal and one of its edges of a cube is ..................

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  47. 47
    For the linear programming problem, x+2y≤10, 3x+y≤12, x,y≥0x + 2y \le 10,\ 3x + y \le 12,\ x, y \ge 0, the maximum value of z=5x+10yz = 5x + 10y occurs at every point on the line segment joining the points..

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  48. 48
    The region satisfying the inequalities y−x≥2, x+y≤5, x≥0y - x \ge 2,\ x + y \le 5,\ x \ge 0 and y≥0y \ge 0 is

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  49. 49
    If the mean and the variance of a binomial variate X are 1 and 0.75 respectively, then which of the following is true?

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  50. 50
    A box contains 8 red and N green balls. Two balls are drawn at random from it. If X is the random variable representing the number of green balls drawn and E(X)=1.2E(X) = 1.2, then N=…N = \ldots

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