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Day 103: MHT-CET Maths

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

  1. Question 1

    Trigonometric Functions. Asked 2 times: 22 Apr 2025 S1, 20 Apr 2026 S2 See all 2 times it was asked

    66
    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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  2. Question 2

    Applications of Derivative. Asked 2 times: May 2022 S1, 20 Apr 2026 S1 See all 2 times it was asked

    74
    A spherical iron ball 1010 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min50\ \mathrm{cm^3/min}. When the thickness of ice is 55 cm, the rate at which the thickness of ice decreases is...

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  3. Question 3

    Definite Integration. Asked 2 times: 16 May 2023 S2*, 20 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    81
    If [x][x] denotes the greatest integer less than or equal to xx, then the value of the integral ∫02x2[x] dx\int_0^2 x^2[x]\,dx is equal to

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  4. Question 4

    Differentiation. Asked 2 times: 13 Apr 2026 S2, 20 Apr 2026 S1 See all 2 times it was asked

    71
    If y+x+y−x=c\sqrt{y + x} + \sqrt{y - x} = c and dydx=K−y2x2−1\dfrac{dy}{dx} = K - \sqrt{\dfrac{y^2}{x^2} - 1}, then the value of KK is

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  5. Question 5

    Sets, Relations and Functions. Asked 2 times: 11 Apr 2026 S1*, 20 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    68
    The domain of the function f(x)=x−1+6−xf(x) = \sqrt{x - 1} + \sqrt{6 - x} is...

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