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Day 532: MHT-CET Maths

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

  1. Question 1

    Line and Plane. Asked once: 10 May 2024 S1

    101
    ABC triangle: A(2,3,5), B(-1,3,2), C(λ\lambda,5,μ\mu). Median through A equally inclined to co-ordinate axes. Value of λ+μ\lambda+\mu is

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  2. Question 2

    Trigonometric Functions. Asked once: 14 May 2024 S1

    133
    If f′(x)=tan⁡−1(sec⁡x+tan⁡x)f'(x)=\tan^{-1}(\sec x+\tan x), −π2<x<π2-\dfrac{\pi}{2}<x<\dfrac{\pi}{2} and f(0)=0f(0)=0, then f(1)f(1) is:

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  3. Question 3

    Vectors. Asked once: 20 Apr 2025 S1

    114
    If aˉ,bˉ,cˉ,dˉ\bar{a},\bar{b},\bar{c},\bar{d} are unit vectors such that aˉ⋅bˉ=12,cˉ⋅dˉ=12\bar{a}\cdot\bar{b}=\frac{1}{2},\bar{c}\cdot\bar{d}=\frac{1}{2} and the angle between aˉ×bˉ\bar{a}\times\bar{b} and cˉ×dˉ\bar{c}\times\bar{d} is π6\frac{\pi}{6}, then the value of ∣[a‾b‾d‾]c‾−[a‾b‾c‾]d‾∣=|\lbrack\overline{a}\overline{b}\overline{d}\rbrack\overline{c}- \lbrack\overline{a}\overline{b}\overline{c}\rbrack\overline{d}| =

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  4. Question 4

    Applications of Derivative. Asked once: 4 May 2023 S1

    121
    The approximate value of log⁡101002\log_{10}1002 is (Given log⁡10e=0.4343\log_{10}e=0.4343)

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  5. Question 5

    Differentiation. Asked once: 4 May 2023 S2

    139
    If y=Acos⁡(nx)+Bsin⁡(nx)y=A\cos(nx)+B\sin(nx), then d2ydx2=\frac{d^2y}{dx^2}=

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