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MHT-CET 2026 (11 April Shift II), 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 roots of the equation x2+x+1=0x^2 + x + 1 = 0 then α2026+β2026=\alpha^{2026} + \beta^{2026} =

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  2. 2
    The number of ways that 8 beads of different colours can be strung to form a necklace is

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  3. 3
    In △ABC\triangle ABC, if ∠A=90∘\angle A = 90^\circ, then sin⁡(B−C)=\sin(B - C) =

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  4. 4
    The value of cos⁡210∘−cos⁡10∘cos⁡50∘+cos⁡250∘\cos^2 10^\circ - \cos 10^\circ\cos 50^\circ + \cos^2 50^\circ is equal to....

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  5. 5
    The general solution of cos⁡4θ=cos⁡3θ\cos 4\theta = \cos 3\theta is θ=\theta =.....

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  6. 6
    The line 2x+y=42x + y = 4 intersects X and Y axes at points A and B respectively. Let C(p,q)C(p, q) be the point such that the lines AC and BC are perpendicular. The distance of point C from the midpoint of segment AB is...

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  7. 7
    If the distance between the lines represented by (x−2y)2+k(x−2y)=0(x - 2y)^2 + k(x - 2y) = 0 is 33 units and k>0k > 0 then the equations of the lines are

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  8. 8
    If the slope of one of the two lines given by x2a+2xyh+y2b=0\dfrac{x^2}{a} + \dfrac{2xy}{h} + \dfrac{y^2}{b} = 0 is twice that of the other, then h2:ab=…h^2 : ab = \ldots

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  9. 9
    If the equation 3x2+(3−p)xy+qy2−2px=8pq3x^2 + (3 - p)xy + qy^2 - 2px = 8pq represents a circle, then the area (in sq. units) of this circle is

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  10. 10
    The ellipse 4x2+9y2=14x^2 + 9y^2 = 1 intersects positive Y-axis at point A. If S and S' are its foci, then the area (in sq. units) of ΔSAS′\Delta SAS' is _____

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  11. 11
    lim⁡x→1[x−2x2−x−1x3−3x2+2x]=\lim_{x \to 1}\left[\dfrac{x - 2}{x^2 - x} - \dfrac{1}{x^3 - 3x^2 + 2x}\right] =

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  12. 12
    If A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\} then which of the following is not true?

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  13. 13
    Consider the following statements rr: If p→qp \to q is false then p∨qp \vee q is false. ss: If p↔qp \leftrightarrow q is false then p∨qp \vee q is false. The truth values of r→sr \to s and s→rs \to r are respectively ____

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  14. 14
    In triangle ABC, with usual notations, if the angles are in Arithmetic Progression and 3c2=2b23c^2 = 2b^2, then the measure of angle A is

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  15. 15
    If A=[00−10−10−100]A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix} then which of the following is true ?

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  16. 16
    If [21−1−1211−12][abc]=[40−2]\begin{bmatrix} 2 & 1 & -1 \\ -1 & 2 & 1 \\ 1 & -1 & 2 \end{bmatrix}\begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} 4 \\ 0 \\ -2 \end{bmatrix} then the distance of point P(a,b,c)P(a, b, c) from the plane 2x+y+2z=102x + y + 2z = 10 is

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  17. 17
    If cot⁡(cos⁡−1x)=sec⁡(tan⁡−1ab2−a2)\cot(\cos^{-1}x) = \sec\left(\tan^{-1}\dfrac{a}{\sqrt{b^2 - a^2}}\right), then the value of xx is

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  18. 18
    If g(x)=x2+x−2g(x) = x^2 + x - 2 and 12(g∘f)(x)=2x2−5x+2\dfrac{1}{2}(g \circ f)(x) = 2x^2 - 5x + 2 then f(x)f(x) is equal to

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  19. 19
    Let the function f be defined by f(x)=x−∣x∣xf(x) = \dfrac{x - |x|}{x}, for x≠0x \neq 0 and f(0)=2f(0) = 2 then f is

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  20. 20
    The derivative of tan⁡−1(1+x2−1x)\tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - 1}{x}\right) with respect to sin⁡−1(2x1+x2)\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) is...

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  21. 21
    If the derivative of tan⁡−1(a+bx)\tan^{-1}(a + bx) with respect to x at x=0x = 0 is 1, then a6−b3=a^6 - b^3 =

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  22. 22
    If x3+y3=6x^3 + y^3 = 6 and d2ydx2⋅d2xdy2=m(xy)n\dfrac{d^2y}{dx^2} \cdot \dfrac{d^2x}{dy^2} = \dfrac{m}{(xy)^n}, where m,n∈Rm, n \in R then mn=\dfrac{m}{n} =

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  23. 23
    If x=sin⁡(t),y=cos⁡(pt)x = \sin(t), y = \cos(pt), then (1−x2)d2ydx2−xdydx=(1 - x^2)\dfrac{d^2y}{dx^2} - x\dfrac{dy}{dx} =

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  24. 24
    If the function f(x)=ax3+bx2+11x−6f(x) = ax^3 + bx^2 + 11x - 6, defined on [1,3][1, 3], satisfies all the conditions of Rolle's theorem for c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then

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  25. 25
    The tangent to the curve y2−xy+9=0y^2 - xy + 9 = 0 is vertical when

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  26. 26
    The value of kk such that the function f(x)=sin⁡x−cos⁡x−kx+bf(x) = \sin x - \cos x - kx + b is strictly decreasing for all real xx is

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  27. 27
    ∫sin⁡xsin⁡4x dx=\displaystyle\int\dfrac{\sin x}{\sin 4x}\,dx =

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  28. 28
    ∫4x(4x+4) dx=⋅s\displaystyle\int\sqrt{4^x(4^x + 4)}\,dx = \cdot s

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  29. 29
    The value of ∫1x2−5x+8 dx\displaystyle\int\dfrac{1}{x^2 - 5x + 8}\,dx is equal to...

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  30. 30
    ∫2x4−3x−x2 dx=⋅s\displaystyle\int\dfrac{2x}{4 - 3x - x^2}\,dx = \cdot s

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  31. 31
    If ∫2e[1log⁡x−1(log⁡x)2]dx=a+blog⁡2\displaystyle\int_2^e\left[\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2}\right]dx = a + \dfrac{b}{\log 2}, then values of aa and bb are

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  32. 32
    If ∫0k11+4x dx=log⁡2(43)\displaystyle\int_0^k\dfrac{1}{1 + 4^x}\,dx = \log_2\left(\dfrac{4}{3}\right), then k=k = _____

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  33. 33
    The area bounded by the curve y=x∣sin⁡(x2)∣y = x\left|\sin\left(\dfrac{x}{2}\right)\right| and the X-axis between the lines x=0x = 0 and x=4πx = 4\pi (in square units), is....

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  34. 34
    If the area enclosed between the curves y2=4kxy^2 = 4kx and y=kx,k>0y = kx, k > 0 is 2k3\dfrac{2k}{3} sq. units then k=k =

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  35. 35
    The solution of the differential equation 2xdydx−y=32x\dfrac{dy}{dx} - y = 3 represents a family of

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  36. 36
    The solution of the differential equation xdydx+y=x3y6x\dfrac{dy}{dx} + y = x^3y^6, is...

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  37. 37
    If aˉ=i^+j^+k^,bˉ=i^−j^+2k^\bar{a} = \hat{i} + \hat{j} + \hat{k}, \bar{b} = \hat{i} - \hat{j} + 2\hat{k} and cˉ=xi^+(x−2)j^−k^\bar{c} = x\hat{i} + (x - 2)\hat{j} - \hat{k} are three vectors in which cˉ\bar{c} lies in the plane of aˉ\bar{a} and bˉ\bar{b}, then x=⋅sx = \cdot s

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  38. 38
    If ∣aˉ∣=4,∣bˉ∣=3|\bar{a}| = 4, |\bar{b}| = 3 and aˉ⋅bˉ=8\bar{a}\cdot\bar{b} = 8 then [aˉ  aˉ+bˉ  aˉ×bˉ]=[\bar{a}\ \ \bar{a} + \bar{b}\ \ \bar{a} \times \bar{b}] =

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  39. 39
    Let aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} be the unit vectors such that aˉ\bar{a} is perpendicular to bˉ\bar{b} and the angle between bˉ\bar{b} and cˉ\bar{c} is 120∘120^\circ. If aˉ+cˉ\bar{a} + \bar{c} is perpendicular to bˉ+cˉ\bar{b} + \bar{c} then

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  40. 40
    Let x0x_0 be the point of local maxima of f(x)=aˉ⋅(bˉ×cˉ)f(x) = \bar{a}\cdot(\bar{b} \times \bar{c}) where aˉ=xi^−2j^+3k^,bˉ=−2i^+xj^−k^\bar{a} = x\hat{i} - 2\hat{j} + 3\hat{k}, \bar{b} = -2\hat{i} + x\hat{j} - \hat{k} and cˉ=7i^−2j^+xk^\bar{c} = 7\hat{i} - 2\hat{j} + x\hat{k} then the value of aˉ⋅cˉ\bar{a}\cdot\bar{c} at x=x0x = x_0 is

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  41. 41
    The parallelopiped is determined by vectors aˉ=−2i^+5j^+3k^,bˉ=i^+3j^−2k^,cˉ=−3i^+j^+4k^\bar{a} = -2\hat{i} + 5\hat{j} + 3\hat{k}, \bar{b} = \hat{i} + 3\hat{j} - 2\hat{k}, \bar{c} = -3\hat{i} + \hat{j} + 4\hat{k}. The altitude of parallelopiped on the parallelogram base determined by vectors bˉ\bar{b} and cˉ\bar{c} is

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  42. 42
    The vector equation of the plane passing through the point A(−2,7,5)A(-2, 7, 5) and parallel to the vectors 4i^−j^+3k^4\hat{i} - \hat{j} + 3\hat{k} and i^+j^+k^\hat{i} + \hat{j} + \hat{k} is ...

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  43. 43
    The point of intersection of the two lines x−33=y−3−1,z−1=0\dfrac{x - 3}{3} = \dfrac{y - 3}{-1}, z - 1 = 0 and x−62=z−13,y−2=0\dfrac{x - 6}{2} = \dfrac{z - 1}{3}, y - 2 = 0 is....

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  44. 44
    If the centroid of a tetrahedron OABCOABC is (1,2,−1)(1, 2, -1), where O is the origin, A(a,2,3),B(1,b,2),C(2,1,c)A(a, 2, 3), B(1, b, 2), C(2, 1, c) are the other vertices, then the distance of the point P(a,b,c)P(a, b, c) from the origin is...

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  45. 45
    If the lines x−12=y+13=z−14\dfrac{x - 1}{2} = \dfrac{y + 1}{3} = \dfrac{z - 1}{4} and x−31=y−c2=z1\dfrac{x - 3}{1} = \dfrac{y - c}{2} = \dfrac{z}{1} intersect, then the radius of circle x2+y2−4x+10y+c=0x^2 + y^2 - 4x + 10y + c = 0 is

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  46. 46
    The corner points of the feasible region determined by a system of linear constraints are (0,3),(1,1)(0, 3), (1, 1) and (3,0)(3, 0). If the objective function is z=px+qyz = px + qy, where p,q>0p, q > 0, then the condition on p and q such that the minimum of z occurs at both (3,0)(3, 0) and (1,1)(1, 1) is _____

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  47. 47
    If X∼B(n,p)X \sim B(n, p), then the value of P(X=k)P(X=k−1)\dfrac{P(X = k)}{P(X = k - 1)} is

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  48. 48
    A player tosses two fair coins, he wins Rs. 55 if two heads appear, Rs. 33 if one head appears and Rs. 22 if no head appears, then the variance of the winning amount is

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  49. 49
    The probability mass function of a random variable X is given by P(X=x)=5Cx25P(X = x) = \dfrac{{}^5C_x}{2^5}, for x=0,1,2,3,4,5x = 0, 1, 2, 3, 4, 5 and =0= 0, otherwise. Then which of the following is correct?

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  50. 50
    If events A and B are such that P(A)=14,P(A∩B)=110P(A) = \dfrac{1}{4}, P(A \cap B) = \dfrac{1}{10} and P(A/B)=2P(B/A)P(A/B) = 2P(B/A) then P(B)=P(B) =...........

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