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Day 369: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 9 May 2024 S2 (same type asked 8 times) See all 8 of this type

    121
    The shortest distance between the lines x−12=y−23=z−34\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4} and x−23=y−44=z−55\dfrac{x-2}{3}=\dfrac{y-4}{4}=\dfrac{z-5}{5} is

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  2. Question 2

    Differentiation. Asked once: 4 May 2023 S2 (same type asked 8 times) See all 8 of this type

    105
    ddxcos⁡−1 ⁣(x−1xx+1x)=\frac{d}{dx}\cos^{-1}\!\left(\frac{x-\frac{1}{x}}{x+\frac{1}{x}}\right)=

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  3. Question 3

    Trigonometric Functions. Asked once: 16 May 2023 S2 (same type asked 8 times) See all 8 of this type

    136
    If tan⁡−1x+1x−1+tan⁡−1x−1x=tan⁡−1(−7)\tan^{-1}\frac{x+1}{x-1} + \tan^{-1}\frac{x-1}{x} = \tan^{-1}(-7), then xx is equal to

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  4. Question 4

    Linear Programming. Asked once: 14 May 2024 S1 (same type asked 8 times) See all 8 of this type

    107
    The solution set of the inequalities 4x+3y≤604x+3y\leq60, y≥2xy\geq2x, x≥3x\geq3, x,y≥0x,y\geq0 is represented by region

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  5. Question 5

    Differential Equations. Asked once: 9 May 2023 S1 (same type asked 8 times) See all 8 of this type

    116
    If y=y(x)y=y(x) is the solution of the differential equation xdydx+2y=x2x\frac{dy}{dx}+2y=x^2 satisfying y(1)=1y(1)=1, then the value of y ⁣(12)y\!\left(\frac{1}{2}\right) is

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