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MHT-CET 2026 (19 May 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 domain of the function f(x)=1∣x∣−xf(x) = \dfrac{1}{\sqrt{|x| - x}} is

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  2. 2
    If ∣z−5i∣=∣z+3∣|z - 5i| = |z + 3|, where zz is a complex number, then the equation of the locus of zz in Cartesian coordinates is ...

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  3. 3
    The equation of the line 3x−y+4=0\sqrt{3}x - y + 4 = 0 in the normal form is _____

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  4. 4
    If the slopes of the lines given by ax2+2hxy+by2=0ax^2 + 2hxy + by^2 = 0 are in the ratio 2:32 : 3, then h2=h^2 =

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  5. 5
    The maximum number of points of intersection between 44 circles and 44 straight lines is:

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  6. 6
    The equation of the common tangent to the parabolas y2=4xy^2 = 4x and x2=32yx^2 = 32y is ...

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  7. 7
    The point on the ellipse x225+y29=1\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1 which is equidistant from its foci can be

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  8. 8
    The value of lim⁡x→π4[4−(cos⁡x+sin⁡x)41−sin⁡2x]\lim_{x \to \frac{\pi}{4}}\left[\dfrac{4 - (\cos x + \sin x)^4}{1 - \sin 2x}\right] is equal to

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  9. 9
    The statement pattern [p∧(q∨r)]∨[∼r∧∼q∧p][p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p] is equivalent to _____

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  10. 10
    Consider the following statements - (i) If a person is social, then he is happy. (ii) If a person is not social, then he is not happy. (iii) If a person is not happy, then he is not social. (iv) If a person is happy, then he is social. Which of the above statements are equivalent?

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  11. 11
    The negation of the statement (p∧∼q)→(∼p∨r)(p \wedge \sim q) \to (\sim p \vee r) is equivalent to:

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  12. 12
    If sin⁡−1x+sin⁡−1y+sin⁡−1z=π\sin^{-1}x + \sin^{-1}y + \sin^{-1}z = \pi, then x4+y4+z4+4x2y2z2=x^4 + y^4 + z^4 + 4x^2y^2z^2 =

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  13. 13
    If tan⁡−1(13)+tan⁡−1(15)+tan⁡−1(17)=π4−tan⁡−1(1k)\tan^{-1}\left(\dfrac{1}{3}\right) + \tan^{-1}\left(\dfrac{1}{5}\right) + \tan^{-1}\left(\dfrac{1}{7}\right) = \dfrac{\pi}{4} - \tan^{-1}\left(\dfrac{1}{k}\right) then the value of kk is

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  14. 14
    The value of cot⁡(csc⁡−153+tan⁡−123)\cot\left(\mathrm{\csc}^{-1}\dfrac{5}{3} + \tan^{-1}\dfrac{2}{3}\right) is ...

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  15. 15
    If aa and bb are respectively the minimum and maximum values of the expression f(x)=(sin⁡−1x+2cos⁡−1x)f(x) = (\sin^{-1}x + 2\cos^{-1}x), then a+ba + b is equal to...

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  16. 16
    sin⁡−1(cos⁡(sin⁡−1x))+cos⁡−1(sin⁡(cos⁡−1x))=…\sin^{-1}(\cos(\sin^{-1}x)) + \cos^{-1}(\sin(\cos^{-1}x)) = \ldots

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  17. 17
    If A+I=(3−21−1)A + I = \begin{pmatrix} 3 & -2 \\ 1 & -1 \end{pmatrix}, then the inverse of the matrix (A−I)(A - I) is:

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  18. 18
    The sum of the matrix [2−35−7]\begin{bmatrix} 2 & -3 \\ 5 & -7 \end{bmatrix} and its multiplicative inverse is

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  19. 19
    If f(x)={x−ex+cos⁡2xx2,if x≠0k,if x=0f(x) = \begin{cases} \dfrac{x - e^x + \cos 2x}{x^2}, & \text{if } x \ne 0 \\ k, & \text{if } x = 0 \end{cases} is continuous at x=0x = 0, then the value of kk is...

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  20. 20
    If 1−x6+1−y6=a3(x3−y3)\sqrt{1 - x^6} + \sqrt{1 - y^6} = a^3(x^3 - y^3), then dydx=…\dfrac{dy}{dx} = \ldots

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  21. 21
    If f(x)=1+cos⁡2(x2)f(x) = \sqrt{1 + \cos^2(x^2)}, then f′(π2)=…f'\left(\dfrac{\sqrt{\pi}}{2}\right) = \ldots

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  22. 22
    If f(x)=log⁡(1+x1−x)f(x) = \log\left(\dfrac{1 + x}{1 - x}\right) and g(x)=(3x+x31+3x2)g(x) = \left(\dfrac{3x + x^3}{1 + 3x^2}\right), then ddx(f(g(x)))=\dfrac{d}{dx}(f(g(x))) =

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  23. 23
    If x=1−y1+yx = \dfrac{1 - \sqrt{y}}{1 + \sqrt{y}}, then dydx=\dfrac{dy}{dx} =

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  24. 24
    The maximum volume (in cubic units) of a right circular cylinder for which the sum of the square of its height and the square of its radius of base 4848, is

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  25. 25
    If the slope of the tangent to the curve 2y2=ax2+b2y^2 = ax^2 + b at (1,−1)(1, -1) is −1-1, then ...

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  26. 26
    If f(x)f(x) satisfy the condition of Rolle's Theorm in [1,2][1, 2] and f(x)f(x) is continuous in [1,2][1, 2] then ∫12f′(x) dx\int_1^2 f'(x)\,dx is equal to _____

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  27. 27
    ∫dx(x+2)(x2+1)\int \dfrac{dx}{(x + 2)(x^2 + 1)} is equal to

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  28. 28
    ∫sin⁡3xcos⁡3x dx=…\int \sin^3 x\cos^3 x\,dx = \ldots

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  29. 29
    ∫5x12+6x11(x6+x+1)3 dx=\int \dfrac{5x^{12} + 6x^{11}}{(x^6 + x + 1)^3}\,dx =

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  30. 30
    If ∫1f(x) dx=log⁡∣f(x)∣2+c\int \dfrac{1}{f(x)}\,dx = \log|f(x)|^2 + c, then f(x)=…f(x) = \ldots

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  31. 31
    If ∫0πlog⁡(sin⁡x) dx=k\int_0^\pi \log(\sin x)\,dx = k, then the value of ∫0π4log⁡(1+tan⁡x) dx\int_0^{\frac{\pi}{4}}\log(1 + \tan x)\,dx in terms of kk is...

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  32. 32
    The value of ∫121x(1+log⁡x)2 dx\int_1^2 \dfrac{1}{x(1 + \log x)^2}\,dx is.......

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  33. 33
    ∫0π2(1+sin⁡x)3 dx=\int_0^{\frac{\pi}{2}}(1 + \sin x)^3\,dx =

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  34. 34
    The area bounded by the curve y=x2+4,x=y,x=3,y = x^2 + 4, x = y, x = 3, and Y-axis is

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  35. 35
    The differential equation dydx=1−y2y\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y} determines a family of circles with

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  36. 36
    If y=c1sin⁡2x+c2y = c_1\sin^2 x + c_2, then its differential equation is:

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  37. 37
    The general solution of edydx=xe^{\frac{dy}{dx}} = x is

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  38. 38
    Which of the following is not a correct pair of a linear differential equation and its integrating factor?

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  39. 39
    In a triangle PQR, L and M are the points on QR and PR respectively such that QL=2LRQL = 2LR and PM=3MRPM = 3MR. Let S be the point of intersection of PL and QM; then S divides segment QM internally in the ratio ...

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  40. 40
    If a⃗=i^+2j^+3k^,b⃗=3i^+4j^+4k^,c⃗=3i^+2j^+3k^\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}, \vec{b} = 3\hat{i} + 4\hat{j} + 4\hat{k}, \vec{c} = 3\hat{i} + 2\hat{j} + 3\hat{k} are the position vectors of the vertices A,BA, B and CC respectively of △ABC\triangle ABC and the bisector of ∠A\angle A meets side BCBC at DD where B−D−CB - D - C, then ∣AD⃗∣|\vec{AD}| is...

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  41. 41
    A parallelopiped is determined by vectors a⃗=i^+2k^,b⃗=i^+j^−k^\vec{a} = \hat{i} + 2\hat{k}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and c⃗=2i^+2j^+3k^\vec{c} = 2\hat{i} + 2\hat{j} + 3\hat{k}. The length (in units) of its altitude drawn to the base determined by vectors b⃗\vec{b} and c⃗\vec{c} is

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  42. 42
    If three coterminous edges of a parallelopiped are represented by a⃗−b⃗,b⃗−c⃗\vec{a} - \vec{b}, \vec{b} - \vec{c} and c⃗−a⃗\vec{c} - \vec{a} then its volume is

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  43. 43
    If 8AB⃗−3AC⃗−5AD⃗=0⃗8\vec{AB} - 3\vec{AC} - 5\vec{AD} = \vec{0}, then the point CC divides BDBD in the ratio ...

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  44. 44
    If the lines x−11=y−12=z−13\dfrac{x - 1}{1} = \dfrac{y - 1}{2} = \dfrac{z - 1}{3} and x−31=y−k2=z−51\dfrac{x - 3}{1} = \dfrac{y - k}{2} = \dfrac{z - 5}{1} are intersect at the point PP, then the distance (in units) of the point PP from the origin O(0,0,0)O(0, 0, 0) is ...

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  45. 45
    The foot of the perpendicular from the origin to the plane is N=(4,5,a),a>0N = (4, 5, a), a > 0 and l(ON)=7l(ON) = 7, then vector equation of the plane is ...

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  46. 46
    The equation of a plane passing through the intersection of two planes r⃗⋅(i^−2j^+3k^)=4\vec{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 4 and r⃗⋅(2i^+j^−3k^)=7\vec{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = 7 and parallel to Y-axis is

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  47. 47
    The planes 5x−2y+3z=95x - 2y + 3z = 9 and 15x−6y+9z=−515x - 6y + 9z = -5 are

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  48. 48
    If XX follows a Binomial distribution with parameters n=8n = 8 and p=12p = \dfrac{1}{2} then P(∣X−4∣≤2)P(|X - 4| \le 2)

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  49. 49
    The variance of randam variable XX, for the following probability mass function (p. m. f.) is ...
    X=xX = x112233
    P(X=x)P(X = x)15\dfrac{1}{5}25\dfrac{2}{5}25\dfrac{2}{5}

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  50. 50
    Two fair dice are thrown. The probability that the sum of the scores is 77 such that the number on the second die is greater than that on the first die is ...

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