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Day 130: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked 2 times: 16 May 2023 S1, 13 May 2024 S2 See all 2 times it was asked

    129
    If ∫log⁡(t+1+t2)1+t2 dt=12[g(t)]2+c\int\frac{\log(t+\sqrt{1+t^2})}{\sqrt{1+t^2}}\,dt=\frac{1}{2}[g(t)]^2+c, (Where cc is a constant of integration) then g(2)g(2) is:

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  2. Question 2

    Pair of Straight Lines. Asked 2 times: 12 May 2024 S1, 13 May 2024 S2 See all 2 times it was asked

    120
    Let PQR be a right angled isosceles triangle, right angled at Q(2,1)Q(2,1). If the equation of the line PR is 2x+y=32x+y=3, then the combined equation representing the pair of lines PQ and QR is

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  3. Question 3

    Vectors. Asked 2 times: 4 May 2023 S2, 13 May 2024 S2 See all 2 times it was asked

    136
    The incentre of the triangle ABC, whose vertices are A(0,2,1),B(−2,0,0)A(0,2,1), B(-2,0,0) and C(−2,0,2)C(-2,0,2), is

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  4. Question 4

    Differential Equations. Asked 2 times: 10 May 2023 S2, 12 May 2024 S2 See all 2 times it was asked

    143
    The solution of ey−xdydx=y(sin⁡x+cos⁡x)1+ylog⁡ye^{y-x}\dfrac{dy}{dx} = \dfrac{y(\sin x + \cos x)}{1+y\log y} is

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  5. Question 5

    Differentiation. Asked 2 times: 10 May 2024 S1, 12 May 2024 S2 See all 2 times it was asked

    128
    For x>1x > 1, if (2x)2y=4e2x−2y(2x)^{2y} = 4e^{2x-2y}, then (1+log⁡e2x)2dydx\left(1+\log_e 2x\right)^2 \frac{dy}{dx} is equal to

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