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Day 270: MHT-CET Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 9 May 2023 S1 (same type asked 10 times) See all 10 of this type

    107
    If ∫dx3sin⁡11xcos⁡x=−38f(x)+32g(x)+c\int\frac{dx}{3\sin^{11}x\cos x} = -\frac{3}{8}f(x) + \frac{3}{2}g(x) + c then

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  2. Question 2

    Line and Plane. Asked once: 19 Apr 2025 S2 (same type asked 9 times) See all 9 of this type

    130
    The equation of the plane passing through the line of intersection of the planes x+y+z=1x+y+z= 1 and 3x+4y+5z=23x+ 4y+ 5z= 2 and perpendicular to the XY - plane is

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  3. Question 3

    Mathematical Logic. Asked once: 12 May 2024 S2 (same type asked 9 times) See all 9 of this type

    150
    Let Statement 1: If a quadrilateral is a square, then all of its sides are equal. Statement 2: All the sides of a quadrilateral are equal, then it is a square.

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  4. Question 4

    Probability Distribution. Asked once: 26 Apr 2025 S2 (same type asked 9 times) See all 9 of this type

    133
    A random variable X has the following probability distribution :
    X=xX = x1234
    P(X=x)P(X = x)0.10.20.30.4
    The mean and standard deviation of XX are respectively

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  5. Question 5

    Limits. Asked once: 20 Apr 2025 S1 (same type asked 9 times) See all 9 of this type

    122
    If f(x)={mx+1,x⩽π2sin⁡x+n,x>π2f(x) =\left\{ \begin{matrix} mx+ 1, & x\leqslant \frac{\pi}{2} \\ \sin x+ n, & x>\frac{\pi}{2} \end{matrix} \right., is continuous at x=π2,( m,n∈Z)x=\frac{\pi}{2},(\text{ }m,n \in\mathbb{Z}) then

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