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MHT-CET 2026 (20 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
    The statement having truth value 'T' from the following is

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  2. 2
    If i=−1i = \sqrt{-1} then [i18+(1i)25]3=\left[i^{18} + \left(\dfrac{1}{i}\right)^{25}\right]^3 =

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  3. 3
    The number of permutations of the letters of the word INSTITUTION are .......

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  4. 4
    If x+y=π4x + y = \dfrac{\pi}{4}, then (1+tan⁡x)(1+tan⁡y)=(1 + \tan x)(1 + \tan y) =

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  5. 5
    A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

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  6. 6
    If the angle made by the lines represented by the equation ax2+2hxy+by2=0ax^2 + 2hxy + by^2 = 0 with X-axis are α\alpha and β\beta, then tan⁡(α+β)\tan(\alpha + \beta) is

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  7. 7
    The equation of a circle whose center lies on x+2y=0x + 2y = 0 and touching the lines 3x−4y+8=03x - 4y + 8 = 0 and 3x−4y−28=03x - 4y - 28 = 0 is

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  8. 8
    If PP be any point on the ellipse 16x2+25y2=40016x^2 + 25y^2 = 400 with foci SS and S′S' and area of △PSS′\triangle PSS' is 9 square units, then the abscissa of point PP is..........

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  9. 9
    The value of lim⁡n→∞[11−n2+21−n2+…+n1−n2]3\lim_{n \to \infty}\left[\dfrac{1}{1 - n^2} + \dfrac{2}{1 - n^2} + \ldots + \dfrac{n}{1 - n^2}\right]^3 is

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  10. 10
    If ∼p∨q\sim p \vee q is false then which of the following is correct?

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  11. 11
    The contrapositive of ∼q→p\sim q \to p is equivalent to

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  12. 12
    The angles of △ABC\triangle ABC are in A.P. and b:c=3:2b : c = \sqrt{3} : \sqrt{2} then ∠A=\angle A =

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  13. 13
    With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

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  14. 14
    If A=[1−5−24]A = \begin{bmatrix} 1 & -5 \\ -2 & 4 \end{bmatrix}, then A−1=A^{-1} =

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  15. 15
    Let A=[312120114]A = \begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & 0 \\ 1 & 1 & 4 \end{bmatrix} and pC11+4C21−5C32=−2pC_{11} + 4C_{21} - 5C_{32} = -2, where CijC_{ij} denotes the cofactor of an element aija_{ij} of matrix AA, then the value of pp is :

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  16. 16
    If 3sin⁡−1(2x1+x2)−4cos⁡−1(1−x21+x2)+2tan⁡−1(2x1−x2)=π33\sin^{-1}\left(\dfrac{2x}{1 + x^2}\right) - 4\cos^{-1}\left(\dfrac{1 - x^2}{1 + x^2}\right) + 2\tan^{-1}\left(\dfrac{2x}{1 - x^2}\right) = \dfrac{\pi}{3} then x=x =?

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  17. 17
    If 2sin⁡−1x−3cos⁡−1x=42\sin^{-1}x - 3\cos^{-1}x = 4, then 2sin⁡−1x+3cos⁡−1x=2\sin^{-1}x + 3\cos^{-1}x =

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  18. 18
    If f(x)=2x−1x+5,x≠−5f(x) = \dfrac{2x - 1}{x + 5}, x \neq -5 then f−1(x)f^{-1}(x) is equal to

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  19. 19
    If the function f(x)f(x) defined by f(x)={ax+1if x≤3bx+3if x>3f(x) = \begin{cases} ax + 1 & \text{if } x \le 3 \\ bx + 3 & \text{if } x > 3 \end{cases} is continuous at x=3x = 3, then (a−b)=(a - b) = ..........

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  20. 20
    If f(x),g(x)f(x), g(x) be twice differentiable functions, satisfying f′′(x)=g′′(x),f′(1)=2g′(1)=4f''(x) = g''(x), f'(1) = 2g'(1) = 4 and f(2)=3g(2)=9f(2) = 3g(2) = 9 then f(x)−g(x)f(x) - g(x) at x=4x = 4 is equal to

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  21. 21
    If y=cos⁡2[cot⁡−1(1−x1+x)]y = \cos^2\left[\cot^{-1}\left(\sqrt{\dfrac{1 - x}{1 + x}}\right)\right] then dydx=\dfrac{dy}{dx} = ........

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  22. 22
    If xy+yx=6\sqrt{\dfrac{x}{y}} + \sqrt{\dfrac{y}{x}} = 6, then dydx=\dfrac{dy}{dx} =

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  23. 23
    If x=4t3+3,y=3t4+4x = 4t^3 + 3, y = 3t^4 + 4 and d2xdy2(dxdy)n\dfrac{\frac{d^2x}{dy^2}}{\left(\frac{dx}{dy}\right)^n} is constant then the value of nn is

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  24. 24
    If x=asin⁡3tx = a\sin^3 t and y=acos⁡3ty = a\cos^3 t, then the value of d2ydx2\dfrac{d^2y}{dx^2} at t=π3t = \dfrac{\pi}{3} is equal to

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  25. 25
    An aeroplane at an altitude of 1 km is flying horizontally at 600 km / hr, passes directly over an observer. Then the rate at which it is approaching the observer when it is 1250 meters away from him is........

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  26. 26
    The line x+y=0x + y = 0 touches the curve y2=ax3+by^2 = ax^3 + b at (1,−1)(1, -1) then values of aa and bb respectively are ...........

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  27. 27
    The function f(x)=x(x+3)e−(12)xf(x) = x(x + 3)e^{-\left(\frac{1}{2}\right)x} satisfies all the conditions of Rolle's theorem in [−3,0][-3, 0], then c=c =

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  28. 28
    If ∫f(x) dx=g(x)+c\displaystyle\int f(x)\,dx = g(x) + c then ∫f−1(x) dx=\displaystyle\int f^{-1}(x)\,dx =

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  29. 29
    ∫log⁡x(1+log⁡x)2 dx=\displaystyle\int\dfrac{\log x}{(1 + \log x)^2}\,dx =

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  30. 30
    ∫12x−x2 dx=\displaystyle\int\dfrac{1}{\sqrt{2x - x^2}}\,dx =

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  31. 31
    ∫(x21+x6+x3)(2x18+7x3+14)13 dx=\displaystyle\int(x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{\frac{1}{3}}\,dx =

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  32. 32
    The value of the integral ∫1/ee∣log⁡x∣x2 dx\int_{1/e}^{e}\dfrac{|\log x|}{x^2}\,dx is

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  33. 33
    If ∫−π/2π/2(sin⁡2x+sin⁡3x) dx=k\int_{-\pi/2}^{\pi/2}(\sin^2 x + \sin^3 x)\,dx = k, then the value of kk

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  34. 34
    If In=∫0π/4tan⁡nx dx,n∈NI_n = \int_0^{\pi/4}\tan^n x\,dx, n \in N then In+2+InI_{n+2} + I_n is equal to

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  35. 35
    The area in square units of the region bounded by the curve y=16−x2y = \sqrt{16 - x^2} and lines x=0,x=4x = 0, x = 4 above the X-axis is

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  36. 36
    The general solution of the differential equation dydx+yx=x2+5\dfrac{dy}{dx} + \dfrac{y}{x} = x^2 + 5 is ....

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  37. 37
    The order and degree of the differential equation 1+1(dydx)2=(d2ydx2)32\sqrt{1 + \dfrac{1}{\left(\frac{dy}{dx}\right)^2}} = \left(\dfrac{d^2y}{dx^2}\right)^{\frac{3}{2}}, respectively are

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  38. 38
    Let a⃗=2i^+k^,b⃗=i^+j^+k^\vec{a} = 2\hat{i} + \hat{k}, \vec{b} = \hat{i} + \hat{j} + \hat{k}, and c⃗=4i^−3j^+7k^\vec{c} = 4\hat{i} - 3\hat{j} + 7\hat{k}. If r⃗\vec{r} is a vector such that r⃗×b⃗=c⃗×b⃗\vec{r} \times \vec{b} = \vec{c} \times \vec{b} and r⃗⋅a⃗=0\vec{r}\cdot\vec{a} = 0, Then r⃗⋅c⃗=\vec{r}\cdot\vec{c} =

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  39. 39
    If u⃗=i^+2j^−2k^,v⃗=2i^+k^\vec{u} = \hat{i} + 2\hat{j} - 2\hat{k}, \vec{v} = 2\hat{i} + \hat{k} and w⃗\vec{w} is unit vector then the maximum value of scalar triple product [u⃗ v⃗ w⃗][\vec{u}\,\vec{v}\,\vec{w}] is

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  40. 40
    If a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c} are three non-coplanar vectors and p⃗,q⃗,r⃗\vec{p}, \vec{q}, \vec{r} are defined as p⃗=b⃗×c⃗[a⃗ b⃗ c⃗],q⃗=c⃗×a⃗[a⃗ b⃗ c⃗],r⃗=a⃗×b⃗[a⃗ b⃗ c⃗]\vec{p} = \dfrac{\vec{b} \times \vec{c}}{[\vec{a}\,\vec{b}\,\vec{c}]}, \vec{q} = \dfrac{\vec{c} \times \vec{a}}{[\vec{a}\,\vec{b}\,\vec{c}]}, \vec{r} = \dfrac{\vec{a} \times \vec{b}}{[\vec{a}\,\vec{b}\,\vec{c}]}, then [(a⃗+b⃗)⋅p⃗+(b⃗+c⃗)⋅q⃗+(c⃗+a⃗)⋅r⃗][(\vec{a} + \vec{b})\cdot\vec{p} + (\vec{b} + \vec{c})\cdot\vec{q} + (\vec{c} + \vec{a})\cdot\vec{r}] is equal to

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  41. 41
    The volume of the parallelopiped whose coterminous edges are 2i^+j^−k^,3i^−j^−k^,j^+3k^2\hat{i} + \hat{j} - \hat{k}, 3\hat{i} - \hat{j} - \hat{k}, \hat{j} + 3\hat{k} is

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  42. 42
    Given the following expressions A) (a⃗×b⃗)⋅c⃗(\vec{a} \times \vec{b})\cdot\vec{c} B) a⃗×(b⃗⋅c⃗)\vec{a} \times (\vec{b}\cdot\vec{c}) C) a⃗⋅(b⃗⋅c⃗)\vec{a}\cdot(\vec{b}\cdot\vec{c}) D) ∣a⃗∣(b⃗⋅c⃗)|\vec{a}|(\vec{b}\cdot\vec{c}) E) (a⃗⋅b⃗)×(b⃗⋅c⃗)(\vec{a}\cdot\vec{b}) \times (\vec{b}\cdot\vec{c}) Then which of the following is not correct

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  43. 43
    If the perpendicular distance of the plane passing through the point Q(1,0,−1)Q(1, 0, -1) and containing the line r⃗=(i^−3j^+k^)+λ(2i^−2j^+k^)\vec{r} = (\hat{i} - 3\hat{j} + \hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k}) from origin is p53\dfrac{p}{\sqrt{53}} then p=p = ...

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  44. 44
    If the line joining points (2,1,4)(2, 1, 4) and (a−1,4,−1)(a - 1, 4, -1) is parallel to the line joining points (0,2,b−1)(0, 2, b - 1) and (5,3,−2)(5, 3, -2) then the values of bb and aa are respectively

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  45. 45
    Lines r⃗=a⃗+λb⃗\vec{r} = \vec{a} + \lambda\vec{b} and r⃗=b⃗+μa⃗\vec{r} = \vec{b} + \mu\vec{a} intersect at point (2,4,−4)(2, 4, -4). If ∣a⃗−b⃗∣=4|\vec{a} - \vec{b}| = 4, then a⃗⋅b⃗=\vec{a}\cdot\vec{b} =

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  46. 46
    The Cartesian equations of the line passing through A(0,1,1)A(0, 1, 1) and parallel to the X-axis are ....

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  47. 47
    The LPP maximize z=2x+5yz = 2x + 5y subject to x+3y≤6,2x+6y≤18,x≥0,y≥0x + 3y \le 6, 2x + 6y \le 18, x \ge 0, y \ge 0 has

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  48. 48
    Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

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  49. 49
    For the following probability distribution of a random variable XX, the Expected value and Variance of XX are respectively
    X=xX = x123
    P(X=x)P(X = x)1/52/52/5

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  50. 50
    A fair die is rolled indefinitely. Player A wins if two consecutive rolls show 3 or 5, and player B wins if two consecutive rolls show 1 or 2 or 4 or 6. The probability that player A wins in the long run is

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