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Day 274: MHT-CET Maths

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

  1. Question 1

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

    122
    ∫35x dx8−x+x=\int_{3}^{5} \frac{\sqrt{x}\text{ }dx}{\sqrt{8 -x}+\sqrt{x}}=

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  2. Question 2

    Determinants and Matrices. Asked once: 12 May 2026 S2 (same type asked 8 times) See all 8 of this type

    68
    If the matrix A=[3−54−7]A = \begin{bmatrix} 3 & -5 \\ 4 & -7 \end{bmatrix} and A−1=[7−54a]A^{-1} = \begin{bmatrix} 7 & -5 \\ 4 & a \end{bmatrix}, then the value of aa is...

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  3. Question 3

    Determinants and Matrices. Asked once: 11 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    66
    If [21−1−1211−12][abc]=[40−2]\begin{bmatrix} 2 & 1 & -1 \\ -1 & 2 & 1 \\ 1 & -1 & 2 \end{bmatrix}\begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} 4 \\ 0 \\ -2 \end{bmatrix} then the distance of point P(a,b,c)P(a, b, c) from the plane 2x+y+2z=102x + y + 2z = 10 is

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  4. Question 4

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

    103
    The vectors a\mathbf{a} and b\mathbf{b} are not perpendicular and c\mathbf{c} and d\mathbf{d} are two vectors satisfying b×c=b×d\mathbf{b}\times\mathbf{c}=\mathbf{b}\times\mathbf{d} and a⋅d=0\mathbf{a}\cdot\mathbf{d}=0, then the vector d\mathbf{d} is equal to

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  5. Question 5

    Applications of Derivative. Asked once: 13 Apr 2026 S2 (same type asked 8 times) See all 8 of this type

    74
    If Rolle's theorem is applicable for the function f(x)=log⁡(x2+ax)f(x) = \log\left(\dfrac{x^2 + a}{x}\right) on [3,4][3, 4] with c∈(3,4)c \in (3, 4) such that f′(c)=0f'(c) = 0, then the value of f′′(c)f''(c) is

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