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Day 299: MHT-CET Maths

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

  1. Question 1

    Determinants and Matrices. Asked once: 20 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    67
    Let A=[a11b]A = \begin{bmatrix} a & 1 \\ 1 & b \end{bmatrix}, where aa and bb are the roots of the equation x2−4x+2=0x^2 - 4x + 2 = 0. If A+A−1=kI2A + A^{-1} = kI_2, then the value of kk is ____

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  2. Question 2

    Line and Plane. Asked once: 9 May 2024 S1 (same type asked 4 times) See all 4 of this type

    116
    The foot of the perpendicular drawn from the origin to the plane is (4,−2,5)(4,-2,5), then the Cartesian equation of the plane is

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  3. Question 3

    Limits. Asked once: 9 May 2023 S2 (same type asked 4 times) See all 4 of this type

    131
    lim⁡x→π/2(1−sin⁡x)(8x3−π3)cos⁡x(π−2x)4\lim_{x\to\pi/2}\dfrac{(1-\sin x)(8x^3-\pi^3)\cos x}{(\pi-2x)^4} is equal to

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  4. Question 4

    Linear Programming. Asked once: 13 May 2026 S2 (same type asked 4 times) See all 4 of this type

    97
    The minimum value of z=4x+2yz = 4x + 2y subject to the constraints 3x+y≥27,x+y≥21,x+2y≥30,x≥0,y≥03x + y \ge 27, x + y \ge 21, x + 2y \ge 30, x \ge 0, y \ge 0 is

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  5. Question 5

    Straight Line. Asked once: 3 May 2023 S2 (same type asked 4 times) See all 4 of this type

    101
    The equation of the line passing through the point of intersection of the lines 3x−y=53x-y=5 and x+3y=1x+3y=1 and making equal intercepts on the axes is

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