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Day 310: MHT-CET Maths

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

  1. Question 1

    Applications of Derivative. Asked once: 4 May 2023 S1 (same type asked 3 times) See all 3 of this type

    122
    The sum of intercepts on coordinate axes made by tangent to the curve x+y=a\sqrt{x}+\sqrt{y}=\sqrt{a} is

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  2. Question 2

    Determinants and Matrices. Asked once: 15 Apr 2026 S1 (same type asked 3 times) See all 3 of this type

    65
    Let A=[2k−11102k−11002k−1]A = \begin{bmatrix} 2k-1 & 1 & 1 \\ 0 & 2k-1 & 1 \\ 0 & 0 & 2k-1 \end{bmatrix} and B=[02k−111−2k0k−1−k0]B = \begin{bmatrix} 0 & 2k-1 & 1 \\ 1-2k & 0 & k \\ -1 & -k & 0 \end{bmatrix} where k is a real number. If det⁡(adjA)+det⁡(adjB)=116\det(\mathrm{adj}A) + \det(\mathrm{adj}B) = 11^6, then the value of k−5k - 5 is equal to...

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  3. Question 3

    Indefinite Integration. Asked once: 9 May 2023 S1 (same type asked 3 times) See all 3 of this type

    131
    ∫x4+x2+1x2−x+1 dx\int\frac{x^4+x^2+1}{x^2-x+1}\,dx is equal to

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  4. Question 4

    Line and Plane. Asked once: 2 May 2023 S2 (same type asked 3 times) See all 3 of this type

    122
    The equation of the plane passing through the midpoint of the line segment joining P(1,2,5)P(1,2,5) and Q(3,4,3)Q(3,4,3) and perpendicular to it, is

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  5. Question 5

    Pair of Straight Lines. Asked once: 15 May 2023 S2 (same type asked 3 times) See all 3 of this type

    113
    If one of the lines represented by ax2+2hxy+by2=0ax^2+2hxy+by^2=0 is perpendicular to mx+ny=18mx+ny=18, then

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