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Day 399: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked once: 22 Apr 2025 S2 (same type asked 8 times) See all 8 of this type

    109
    If matrix A=111[−17−242a42−315]A =\frac{1}{11}\begin{bmatrix} - 1 & 7 & - 24 \\ 2 & a & 4 \\ 2 & - 3 & 15 \end{bmatrix} and A−1=[3342−34b−1c]A^{- 1}=\begin{bmatrix} 3 & 3 & 4 \\ 2 & - 3 & 4 \\ b & - 1 & c \end{bmatrix}, then the values of a,b,ca,b,c respectively are ____\_\_\_\_

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  2. Question 2

    Definite Integration. Asked once: 19 Apr 2025 S1 (same type asked 8 times) See all 8 of this type

    113
    The value of ∫14log⁡[x]dx\int_{1}^{4} \log\lbrack x\rbrack dx, where [x]\lbrack x\rbrack is the greatest integer function less than or equal to xx is equal to

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  3. Question 3

    Differentiation. Asked once: 15 May 2023 S1 (same type asked 8 times) See all 8 of this type

    133
    If x=2cos⁡θ−cos⁡2θx=2\cos\theta-\cos 2\theta and y=2sin⁡θ−sin⁡2θy=2\sin\theta-\sin 2\theta, then d2ydx2\frac{d^{2}y}{dx^{2}} is equal to

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  4. Question 4

    Mathematical Logic. Asked once: 10 May 2023 S1 (same type asked 8 times) See all 8 of this type

    146
    The inverse of p→(q→r)p\to(q\to r) is logically equivalent to

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  5. Question 5

    Probability Distribution. Asked once: 23 Apr 2025 S1 (same type asked 8 times) See all 8 of this type

    147
    Bag I contain 3 red and 2 green balls and Bag II contains 5 red and 3 green balls. A ball is drawn from one of the bag at random and it is found to be green. Then the probability that it is drawn from Bag I is

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