PYQ Vault

Day 138: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked 2 times: 11 May 2023 S2*, 9 May 2024 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    123
    If A=[2−1−13]A = \begin{bmatrix} 2 & -1 \\ -1 & 3 \end{bmatrix}, then the inverse of (2A2+5A)\left(2A^2 + 5A\right) is

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  2. Question 2

    Differential Equations. Asked 2 times: 10 May 2023 S2, 9 May 2024 S1 See all 2 times it was asked

    145
    A spherical raindrop evaporates at a rate proportional to its surface area. If originally its radius is 3 mm and 1 hour later it reduces to 2 mm, then the expression for the radius R of the raindrop at any time tt is

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  3. Question 3

    Differentiation. Asked 2 times: 11 May 2023 S1, 9 May 2024 S1 See all 2 times it was asked

    102
    If x2+y2=t+1tx^2+y^2=t+\frac{1}{t} and x4+y4=t2+1t2x^4+y^4=t^2+\frac{1}{t^2}, then dydx\frac{dy}{dx} is equal to

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  4. Question 4

    Probability Distribution. Asked 2 times: 10 May 2023 S1*, 9 May 2024 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    132
    A, B, C are three events, one of which must and only one can happen. The odds in favor of A are 4:64:6, the odds against B are 7:37:3. Thus, odds against C are

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  5. Question 5

    Vectors. Asked 2 times: 10 May 2023 S2, 9 May 2024 S1 See all 2 times it was asked

    150
    Let two non-collinear unit vectors a^\hat{a} and b^\hat{b} form an acute angle. A point P moves, so that at any time tt the position vector OP→\overrightarrow{OP}, where O is origin, is given by a^sin⁡t+b^cos⁡t\hat{a}\sin t+\hat{b}\cos t. When P is farthest from origin O, let M be the length of OP and u^\hat{u} be the unit vector along OP, then

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