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Day 455: MHT-CET Maths

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

  1. Question 1

    Conic Sections. Asked once: 18 Apr 2026 S2

    57
    A parabola has its focus on the positive X-axis and the Y-axis as its directrix. If P(α,4)P(\alpha, 4) is a point on this parabola such that the tangent to the parabola at point P passes through the origin, then the distance of P from origin is

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  2. Question 2

    Definite Integration. Asked once: 14 May 2026 S1

    70
    If f(x)=∣sin⁡x+sin⁡2x+sin⁡3xsin⁡2xsin⁡3x3+4sin⁡x34sin⁡x1+sin⁡xsin⁡x1∣f(x) = \begin{vmatrix} \sin x + \sin 2x + \sin 3x & \sin 2x & \sin 3x \\ 3 + 4\sin x & 3 & 4\sin x \\ 1 + \sin x & \sin x & 1 \end{vmatrix}, then ∫0π2f(x) dx=\int_0^{\frac{\pi}{2}}f(x)\,dx =

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  3. Question 3

    Determinants and Matrices. Asked once: 13 Apr 2026 S1

    66
    Let A=[−5−321]A = \begin{bmatrix} -5 & -3 \\ 2 & 1 \end{bmatrix}. The Row transformation R1→R1+3R2R_1 \to R_1 + 3R_2 will transform matrix A into

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  4. Question 4

    Differential Equations. Asked once: 13 May 2024 S2

    146
    The solution of (1+xy)y dx+(1−xy)x dy=0(1+xy)y\,dx+(1-xy)x\,dy=0 is

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  5. Question 5

    Differentiation. Asked once: 13 May 2026 S2

    75
    If f(x)f(x) is a differentiable function of xx, then lim⁡h→0[f(x+h)]2−[f(x)]22h=\lim_{h \to 0}\dfrac{[f(x + h)]^2 - [f(x)]^2}{2h} =

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