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Day 102: MHT-CET Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Differentiation. Asked 2 times: 19 Apr 2025 S2*, 12 May 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    73
    If y=(x−1)(x−2)(x−3)⋯(x−100)y = (x - 1)(x - 2)(x - 3)\cdots(x - 100) and the value of dydx\dfrac{dy}{dx} at x=5x = 5 is equal to λ(100!100C5)\lambda\left(\dfrac{100!}{^{100}C_5}\right), then λ=\lambda = ...

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  2. Question 2

    Applications of Derivative. Asked 2 times: 21 Apr 2025 S1, 20 Apr 2026 S2 See all 2 times it was asked

    77
    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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  3. Question 3

    Definite Integration. Asked 2 times: 14 May 2024 S2*, 20 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    84
    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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  4. Question 4

    Differential Equations. Asked 2 times: 18 Apr 2026 S2, 20 Apr 2026 S2 See all 2 times it was asked

    87
    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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  5. Question 5

    Pair of Straight Lines. Asked 2 times: 19 Apr 2026 S2*, 20 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    56
    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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