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Day 78: MHT-CET Maths

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

  1. Question 1

    Vectors. This type asked 3 times: 11 Apr 2026 S2, 15 Apr 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 3 of this type

    91
    A parallelopiped is determined by vectors a⃗=i^+2k^,b⃗=i^+j^−k^\vec{a} = \hat{i} + 2\hat{k}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and c⃗=2i^+2j^+3k^\vec{c} = 2\hat{i} + 2\hat{j} + 3\hat{k}. The length (in units) of its altitude drawn to the base determined by vectors b⃗\vec{b} and c⃗\vec{c} is

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  2. Question 2

    Vectors. This type asked 3 times: 19 Apr 2025 S2, 26 Apr 2025 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 3 of this type

    89
    In a triangle PQR, L and M are the points on QR and PR respectively such that QL=2LRQL = 2LR and PM=3MRPM = 3MR. Let S be the point of intersection of PL and QM; then S divides segment QM internally in the ratio ...

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  3. Question 3

    Applications of Derivative. This type asked 3 times: 4 May 2023 S1, 13 Apr 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 3 of this type

    76
    The tangent to the curve y=e2xy = e^{2x} is drawn at the point P(0,1)P(0, 1). If this tangent intersects the xx-axis at point AA and the yy-axis at point BB, then the area of △OAB\triangle OAB (where OO is the origin) in square units is:

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  4. Question 4

    Determinants and Matrices. This type asked 3 times: 15 Apr 2026 S1, 15 May 2026 S1, 19 May 2026 S1. This one: 19 May 2026 S1 See all 3 of this type

    68
    If A=[−12−3232−12]A = \begin{bmatrix} -\dfrac{1}{2} & -\dfrac{\sqrt{3}}{2} \\ \dfrac{\sqrt{3}}{2} & -\dfrac{1}{2} \end{bmatrix}, the value of ∣Adj(A2026)∣|\mathrm{Adj}(A^{2026})| is equal to:

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  5. Question 5

    Differential Equations. This type asked 3 times: 11 May 2023 S1, 22 Apr 2025 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 3 of this type

    88
    If the general solution of the differential equation dydx=cos⁡(2x−3y)−cos⁡(2x+3y)\dfrac{dy}{dx} = \cos(2x - 3y) - \cos(2x + 3y) is cos⁡2x=g(y)+c\cos 2x = g(y) + c, then g(y)=…g(y) = \ldots

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