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Day 180: MHT-CET Maths

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

  1. Question 1

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

    92
    The length of the perpendicular from the point (3,2,1)(3, 2, 1) to the line x−7−2=y−72=z−63\dfrac{x - 7}{-2} = \dfrac{y - 7}{2} = \dfrac{z - 6}{3} is kk units. then the value of kk....

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  2. Question 2

    Definite Integration. Asked once: 26 Apr 2025 S2 (same type asked 8 times) See all 8 of this type

    110
    ∫0π2300sin⁡x+100cos⁡xsin⁡x+cos⁡x dx=…\int_{0}^{\frac{\pi}{2}} \frac{300\sin x+ 100\cos x}{\sin x+ \cos x}\text{ }dx= \ldots

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  3. Question 3

    Determinants and Matrices. Asked once: 14 May 2026 S2 (same type asked 8 times) See all 8 of this type

    71
    If the matrix A=[123115247]A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7 \end{bmatrix} and its inverse is A−1=[ac−7b−1c−201]A^{-1} = \begin{bmatrix} a & c & -7 \\ b & -1 & c \\ -2 & 0 & 1 \end{bmatrix}, then ....

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  4. Question 4

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

    69
    Let AT=[1121−1112−1]A^T = \begin{bmatrix} 1 & 1 & 2 \\ 1 & -1 & 1 \\ 1 & 2 & -1 \end{bmatrix}, BT=[651]B^T = \begin{bmatrix} 6 & 5 & 1 \end{bmatrix} and X=[xyz]X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}. If AX=BAX = B, then the values of x,y,zx, y, z are..........

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  5. Question 5

    Vectors. Asked once: 20 Apr 2026 S1 (same type asked 8 times) See all 8 of this type

    88
    Let aˉ=i^+j^+k^,bˉ=i^−3j^+2k^\bar{a} = \hat{i} + \hat{j} + \hat{k}, \bar{b} = \hat{i} - 3\hat{j} + 2\hat{k} and cˉ=3i^−2k^\bar{c} = 3\hat{i} - 2\hat{k}. If a vector pˉ\bar{p} satisfies the conditions pˉ⋅cˉ=0\bar{p}\cdot\bar{c} = 0 and pˉ×aˉ=bˉ×aˉ\bar{p} \times \bar{a} = \bar{b} \times \bar{a}, then the value of ∣pˉ∣=|\bar{p}| =...

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