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Day 234: MHT-CET Maths

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

  1. Question 1

    Definite Integration. Asked once: May 2022 S1 (same type asked 3 times) See all 3 of this type

    101
    ∫π/43π/4dx1+cos⁡x\int_{\pi/4}^{3\pi/4} \frac{dx}{1+\cos x} is equal to

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  2. Question 2

    Differential Equations. Asked once: 17 Apr 2026 S1 (same type asked 3 times) See all 3 of this type

    87
    If y=e−mxy = e^{-mx} is a solution of the differential equation d2ydx2+4dydx+3y=0\dfrac{d^2y}{dx^2} + 4\dfrac{dy}{dx} + 3y = 0, then the values of mm are

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  3. Question 3

    Sets, Relations and Functions. Asked once: 11 May 2024 S2 (same type asked 3 times) See all 3 of this type

    128
    If f(x)=3x+45x−7f(x)=\frac{3x+4}{5x-7} and g(x)=7x+45x−3g(x)=\frac{7x+4}{5x-3}, then f(g(x))=f(g(x))=

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  4. Question 4

    Probability Distribution. Asked once: 20 Apr 2025 S1 (same type asked 3 times) See all 3 of this type

    119
    Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X is the random variable of getting queens, then the value of 2E(X)+3E(X2)2E(X) + 3E\left( X^{2} \right) for the number of queens is

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  5. Question 5

    Vectors. Asked once: 21 Apr 2025 S1 (same type asked 3 times) See all 3 of this type

    114
    Let a‾,b‾\overline{a},\overline{b}, and c‾\overline{c} be unit vectors. Suppose that aˉ⋅bˉ=aˉ⋅cˉ=0\bar{a}\cdot\bar{b}=\bar{a}\cdot\bar{c}= 0 and if the angle between bˉ\bar{b} and cˉ\bar{c} is π6\frac{\pi}{6}, then aˉ\bar{a} is

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