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Day 503: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 17 Apr 2026 S2

    88
    Let a⃗\vec{a} and b⃗\vec{b} be linearly independent vectors such that ∣a⃗∣=3,∣b⃗∣=3|\vec{a}| = \sqrt{3}, |\vec{b}| = 3 and ∣a⃗−b⃗∣=4|\vec{a} - \vec{b}| = 4. If a⃗×(2i^+2j^−k^)=(2i^+2j^−k^)×b⃗\vec{a} \times (2\hat{i} + 2\hat{j} - \hat{k}) = (2\hat{i} + 2\hat{j} - \hat{k}) \times \vec{b} and ∣(a⃗+b⃗)⋅(3i^+4j^+2k^)∣=λ|(\vec{a} + \vec{b})\cdot(3\hat{i} + 4\hat{j} + 2\hat{k})| = \sqrt{\lambda}, then λ=…\lambda = \ldots

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  2. Question 2

    Applications of Derivative. Asked once: 20 Apr 2025 S2

    133
    If the curve y=ax2−6x+by=ax^{2}- 6x+b passes through (0,4)(0,4) and has its tangent parallel to the X -axis at x=32x=\frac{3}{2}, then the values of aa and bb respectively are

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  3. Question 3

    Definite Integration. Asked once: 9 May 2024 S2

    117
    ∫12dx(x2−2x+4)3/2=kk+5\int_1^2 \dfrac{dx}{\left(x^2 - 2x + 4\right)^{3/2}} = \dfrac{k}{k+5}, then kk has the value

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  4. Question 4

    Differentiation. Asked once: 13 Apr 2026 S1

    68
    If y=tan⁡−1{1+x2−1−x21+x2+1−x2}y = \tan^{-1}\left\{\dfrac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}}\right\}, where ∣x∣<1|x| < 1, then dydx\dfrac{dy}{dx} is equal to

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  5. Question 5

    Indefinite Integration. Asked once: 16 Apr 2026 S2

    78
    ∫x4+1x6+1 dx=\displaystyle\int\dfrac{x^4 + 1}{x^6 + 1}\,dx =

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