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Day 278: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 14 May 2024 S1 (same type asked 7 times) See all 7 of this type

    106
    If ∫x3 dx1+x2=a(1+x2)1+x2+b1+x2+c\int\dfrac{x^3\,dx}{\sqrt{1+x^2}}=a(1+x^2)\sqrt{1+x^2}+b\sqrt{1+x^2}+c (Where c is a constant of integration), then the value of 3ab3ab is:

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  2. Question 2

    Limits. Asked once: 22 Apr 2025 S2 (same type asked 7 times) See all 7 of this type

    111
    lim⁡x→1(log⁡33x)log⁡x8=\lim_{x \rightarrow 1} \left( \log_{3}3x \right)^{\log_{x}8}=... .

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  3. Question 3

    Probability Distribution. Asked once: 16 May 2023 S1 (same type asked 7 times) See all 7 of this type

    135
    Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 34,12\frac{3}{4}, \frac{1}{2} and 58\frac{5}{8} respectively, then the probability that the target is hit by P or Q but not by R, is

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  4. Question 4

    Line and Plane. Asked once: 13 May 2026 S1 (same type asked 7 times) See all 7 of this type

    90
    The plane passing through the point (5,1,2)(5, 1, 2) and perpendicular to the line 2x−4=y−4=z−52x - 4 = y - 4 = z - 5 will meet the line at the point

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  5. Question 5

    Differential Equations. Asked once: 21 Apr 2025 S2 (same type asked 7 times) See all 7 of this type

    129
    The differential equation of all circles having their centres on the line y=5y= 5 and touching ( X -axis) is ____\_\_\_\_

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