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Day 492: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 20 Apr 2026 S2

    95
    Lines r⃗=a⃗+λb⃗\vec{r} = \vec{a} + \lambda\vec{b} and r⃗=b⃗+μa⃗\vec{r} = \vec{b} + \mu\vec{a} intersect at point (2,4,−4)(2, 4, -4). If ∣a⃗−b⃗∣=4|\vec{a} - \vec{b}| = 4, then a⃗⋅b⃗=\vec{a}\cdot\vec{b} =

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  2. Question 2

    Applications of Derivative. Asked once: 25 Apr 2025 S2

    139
    The length of the perpendicular drawn from the origin on the normal to the curve x2+2xy−3y2=0x^{2}+ 2xy- 3y^{2}= 0 at the point (2,2)(2,2) is

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  3. Question 3

    Conic Sections. Asked once: 21 Apr 2025 S2

    147
    Angle between the parabola y2=4(x−1)y^{2}= 4(x- 1) and x2+4(y−3)=0x^{2}+ 4(y- 3) = 0 at the common end of their latus rectum is

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  4. Question 4

    Definite Integration. Asked once: 22 Apr 2025 S1

    129
    ∫023x+1x2+4dx=\int_{0}^{2} \frac{3x+ 1}{x^{2}+ 4}dx=

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  5. Question 5

    Differentiation. Asked once: 16 Apr 2026 S1

    66
    If y=tan⁡−1[x−1−x2x+1−x2]y = \tan^{-1}\left[\dfrac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}}\right] , then dydx=\dfrac{dy}{dx} =

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