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Day 387: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 12 May 2024 S1 (same type asked 8 times) See all 8 of this type

    136
    The distance of the point P(−2,4,−5)P(-2,4,-5) from the line x+33=y−45=z+86\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6} is

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  2. Question 2

    Definite Integration. Asked once: 2 May 2023 S2 (same type asked 8 times) See all 8 of this type

    114
    The value of I=∫log⁡e2log⁡e3xsin⁡(x2)sin⁡(x2)+sin⁡(log⁡e6−x2) dxI = \displaystyle\int_{\sqrt{\log_e 2}}^{\sqrt{\log_e 3}} \frac{x\sin(x^2)}{\sin(x^2)+\sin(\log_e 6 - x^2)}\,dx is

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  3. Question 3

    Determinants and Matrices. Asked once: 13 Apr 2026 S1 (same type asked 8 times) See all 8 of this type

    67
    If A=[20−1510013]3×3A = \begin{bmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{bmatrix}_{3 \times 3}, and A−1=[γ−11α6−5β−22]3×3A^{-1} = \begin{bmatrix} \gamma & -1 & 1 \\ \alpha & 6 & -5 \\ \beta & -2 & 2 \end{bmatrix}_{3 \times 3}, then ∣α⋅β⋅γ∣=|\alpha \cdot \beta \cdot \gamma| = _____ (where ∣⋅∣|\cdot| denotes the absolute value)

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  4. Question 4

    Determinants and Matrices. Asked once: 2 May 2023 S2 (same type asked 8 times) See all 8 of this type

    102
    Let X=(abc)X = \begin{pmatrix}a\\b\\c\end{pmatrix}, A=(1−12201321)A = \begin{pmatrix}1&-1&2\\2&0&1\\3&2&1\end{pmatrix} and B=(314)B = \begin{pmatrix}3\\1\\4\end{pmatrix}. If AX=BAX = B, then the value of 2a−3b+4c2a - 3b + 4c will be

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  5. Question 5

    Applications of Derivative. Asked once: 3 May 2023 S2 (same type asked 8 times) See all 8 of this type

    142
    The value of cc for which Rolle's theorem for the function f(x)=x3−3x2+2xf(x)=x^{3}-3x^{2}+2x in the interval [0,2][0,2] are

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