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Day 328: MHT-CET Maths

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

  1. Question 1

    Differentiation. Asked once: 11 May 2024 S1 (same type asked 10 times) See all 10 of this type

    130
    Derivative of tan⁡−1 ⁣(1+x2−1−x21+x2+1−x2)\tan^{-1}\!\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right) w.r.t. cos⁡−1(x2)\cos^{-1}(x^2) is

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  2. Question 2

    Linear Programming. Asked once: 25 Apr 2025 S2 (same type asked 10 times) See all 10 of this type

    118
    In L.P.P., the maximum value of objective function Z=6x+3yZ = 6x+ 3y subject to constraints x+y≤5,x+2y≥4,4x+y≤12,x,y≥0x+y\leq 5,x+ 2y\geq 4,4x+y\leq 12,x,y\geq 0 is

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  3. Question 3

    Applications of Definite Integral. Asked once: 11 May 2024 S1 (same type asked 10 times) See all 10 of this type

    129
    The area of the region bounded by the parabola y=x2y = x^2 and the curve y=∣x∣y = |x| is

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  4. Question 4

    Limits. Asked once: 15 May 2023 S2 (same type asked 10 times) See all 10 of this type

    120
    If the function f(x)={−2sin⁡xx≤−π/2Asin⁡x+B−π/2<x<π/2cos⁡xx≥π/2f(x) = \begin{cases} -2\sin x & x \leq -\pi/2 \\ A\sin x+B & -\pi/2 < x < \pi/2 \\ \cos x & x \geq \pi/2 \end{cases} is continuous everywhere, then the values of AA and BB are respectively

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  5. Question 5

    Limits. Asked once: 13 Apr 2026 S2 (same type asked 10 times) See all 10 of this type

    70
    If f(x)f(x) is continuous at x=0x = 0, where f(x)=8x−2xkx−1f(x) = \dfrac{8^x - 2^x}{k^x - 1}, for x≠0x \neq 0 and f(0)=2f(0) = 2, then the value of kk is ...

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