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Day 378: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 2 May 2023 S1 (same type asked 5 times) See all 5 of this type

    147
    ∫dx3−2cos⁡2x=tan⁡−1(f(x))5+c\displaystyle\int \dfrac{dx}{3 - 2\cos 2x} = \dfrac{\tan^{-1}(f(x))}{\sqrt{5}} + c, (where cc is constant of integration), then f(π/4)f(\pi/4) has the value

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  2. Question 2

    Limits. Asked once: 9 May 2023 S2 (same type asked 5 times) See all 5 of this type

    147
    Let f(x)=[x[x2]]f(x) = \left[x\left[\frac{x}{2}\right]\right], for −10<x<10-10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to

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  3. Question 3

    Line and Plane. Asked once: 21 Apr 2025 S1 (same type asked 5 times) See all 5 of this type

    141
    The equation of the plane containing the line x−23=y+12=z−4−2\frac{x- 2}{3}=\frac{y+ 1}{2}=\frac{z- 4}{- 2} and the point (0,5,0)(0,5,0) is

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  4. Question 4

    Linear Programming. Asked once: 22 Apr 2025 S1 (same type asked 5 times) See all 5 of this type

    148
    If the difference between the maximum and minimum values of the objective function z=7x−8yz = 7x- 8y subject to the constraints x+y⩽20,y⩾5,x,y⩾0x+y\leqslant 20,y\geqslant 5,x,y\geqslant 0 is 5k+2005k + 200, then the value of k is

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  5. Question 5

    Trigonometric Functions. Asked once: May 2021 S1 (same type asked 5 times) See all 5 of this type

    101
    With usual notations, in any △ABC\triangle ABC, if acos⁡B=bcos⁡Aa\cos B = b\cos A, then the triangle is

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