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Day 463: MHT-CET Maths

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

  1. Question 1

    Conic Sections. Asked once: 15 Apr 2026 S2

    61
    The equation of the common tangent touching the circle (x−3)2+y2=9(x - 3)^2 + y^2 = 9 and the parabola y2=4xy^2 = 4x above the X-axis is

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  2. Question 2

    Definite Integration. Asked once: 13 May 2026 S1

    82
    The values of aa for which ∫0a(3x2+4x−5) dx<a3−2\int_0^a(3x^2 + 4x - 5)\,dx < a^3 - 2 are...

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  3. Question 3

    Determinants and Matrices. Asked once: 19 Apr 2025 S1

    149
    If A=[cos⁡θsin⁡θ0−sin⁡θcos⁡θ0001]A=\begin{bmatrix} \cos\theta & \sin\theta & 0 \\ - \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}, where A21,A22,A23A_{21},A_{22},A_{23} are cofactors of a21,a22,a23a_{21},a_{22},a_{23} respectively, then the value of a21A21+a22A22+a23A23=a_{21}A_{21}+a_{22}A_{22}+a_{23}A_{23}=

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  4. Question 4

    Differentiation. Asked once: 12 May 2026 S2

    72
    If ddx(1+x4+x81+x2+x4)=ax3+bx\dfrac{d}{dx}\left(\dfrac{1 + x^4 + x^8}{1 + x^2 + x^4}\right) = ax^3 + bx, then the values of aa and bb are respectively...

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  5. Question 5

    Indefinite Integration. Asked once: 20 Apr 2026 S2

    78
    If ∫f(x) dx=g(x)+c\displaystyle\int f(x)\,dx = g(x) + c then ∫f−1(x) dx=\displaystyle\int f^{-1}(x)\,dx =

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