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Day 518: MHT-CET Maths

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

  1. Question 1

    Vectors. Asked once: 11 Apr 2026 S2

    89
    Let aˉ,bˉ,cˉ\bar{a}, \bar{b}, \bar{c} be the unit vectors such that aˉ\bar{a} is perpendicular to bˉ\bar{b} and the angle between bˉ\bar{b} and cˉ\bar{c} is 120∘120^\circ. If aˉ+cˉ\bar{a} + \bar{c} is perpendicular to bˉ+cˉ\bar{b} + \bar{c} then

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  2. Question 2

    Applications of Derivative. Asked once: 10 May 2024 S2

    134
    Let f(x)=ex−xf(x)=e^x-x and g(x)=x2−x,  ∀x∈Rg(x)=x^2-x,\;\forall x\in\mathbb{R}, then the set of all x∈Rx\in\mathbb{R}, where the function h(x)=(f∘g)(x)h(x)=(f\circ g)(x) is increasing, is

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  3. Question 3

    Differentiation. Asked once: 20 Apr 2025 S1

    143
    If y=log⁡ex3+3sin⁡−1x+kx2y=\log_{e}x^{3}+ 3\sin^{- 1}x+kx^{2} and y′(12)=23y^{'}\left( \frac{1}{2} \right)= 2\sqrt{3}, then k=k =

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  4. Question 4

    Indefinite Integration. Asked once: 26 Apr 2025 S1

    124
    If ∫(x4+1)x(x2+1)2 dx=Alog∣x∣+B1+x2+c\int\frac{\left( x^{4}+ 1 \right)}{x\left( x^{2}+ 1 \right)^{2}}\text{ }dx= Alog|x| +\frac{B}{1 +x^{2}}+ c, then A−BA - B is (where c is the constant of integration)

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  5. Question 5

    Line and Plane. Asked once: 21 Apr 2025 S2

    113
    The distance between the line rˉ=3i^−2j^+k^+λ(i^+j^+k^)\bar{r}= 3\widehat{i}- 2\widehat{j}+\widehat{k}+\lambda(\widehat{i}+\widehat{j}+\widehat{k}) and the plane rˉ⋅(2i^+j^+k^)=4\bar{r}\cdot (2\widehat{i}+\widehat{j}+\widehat{k}) = 4 is

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