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Day 144: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked 2 times: 4 May 2023 S2, 9 May 2023 S2 See all 2 times it was asked

    132
    The integral ∫π/6π/4dxsin⁡2x(tan⁡5x+cot⁡5x)\int_{\pi/6}^{\pi/4} \frac{dx}{\sin 2x(\tan^5 x + \cot^5 x)} is equal to

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  2. Question 2

    Trigonometric Functions. Asked 2 times: 3 May 2023 S1, 9 May 2023 S2 See all 2 times it was asked

    107
    Let 2sin⁡2x+3sin⁡x−2>02\sin^2 x + 3\sin x - 2 > 0 and x2−x−2<0x^2 - x - 2 < 0 (x is measured in radians). Then x lies in the interval

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  3. Question 3

    Line and Plane. Asked 2 times: 3 May 2023 S2*, 9 May 2023 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    111
    The equation of the plane, passing through the point (1,1,1)(1,1,1) and perpendicular to the planes 2x+y−2z=52x+y-2z=5 and 3x−6y−2z=73x-6y-2z=7, is

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  4. Question 4

    Linear Programming. Asked 2 times: 3 May 2023 S2, 9 May 2023 S1 See all 2 times it was asked

    126
    The maximum value of z=x+yz=x+y, subjected to x+y≤10x+y\leq10, 5x+3y≥155x+3y\geq15, x≤6x\leq6, x,y≥0x,y\geq0

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  5. Question 5

    Differential Equations. Asked 2 times: 3 May 2023 S1*, 4 May 2023 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    127
    The decay rate of radium is proportional to the amount present at any time t. If initially 60 gms was present and half life period of radium is 1600 years, then the amount of radium present after 3200 years is

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