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Day 491: JEE Mains Maths

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

  1. Question 1

    Determinants. Asked once: 31 Jan 2023

    163
    If a point P(α,β,γ)P(\alpha,\beta,\gamma) satisfying
    (α β γ)(2108938848)=(0 0 0)(\alpha\ \beta\ \gamma)\begin{pmatrix} 2 & 10 & 8 \\ 9 & 3 & 8 \\ 8 & 4 & 8 \end{pmatrix}= (0\ 0\ 0)
    lies on the plane 2x+4y+3z=52x + 4y + 3z = 5, then 6α+9β+7γ6\alpha + 9\beta + 7\gamma is equal to:

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  2. Question 2

    Differential Equations. Asked once: 28 Jun 2022

    160
    Let x=x(y)x = x(y) be the solution of the differential equation 2yex/y2dx+(y2−4xex/y2)dy=02ye^{x/y^{2}}dx +\left( y^{2}- 4xe^{x/y^{2}} \right)dy = 0 such that x(1)=0x(1) = 0. Then, x(e)x(e) is equal to

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  3. Question 3

    Differentiation. Asked once: 13 Apr 2023

    173
    Let f(x)=∑k=110kxk,x∈Rf(x) =\sum_{k = 1}^{10} kx^{k},x \in R. If 2f(2)+f′(2)=119(2)n+12f(2) +f^{'}(2) = 119(2)^{n}+1 then nn is equal to

  4. Question 4

    Indefinite Integration. Asked once: 4 Apr 2024

    172
    If ∫csc⁡5xdx=αcot⁡xcsc⁡x(csc⁡2x+32)+βlog⁡e∣tan⁡x2∣+C\int \csc^{5}xdx = \alpha \cot x\csc x\left( \csc^{2}x +\frac{3}{2} \right)+ \beta\log_{e}\left| \tan\frac{x}{2} \right|+ C where α,β∈R\alpha,\beta \in R and CC is constant of integration, then the value of 8(α+β)8(\alpha + \beta) equals ............

  5. Question 5

    Inverse Trigonometric Functions. Asked once: 24 Jan 2023

    77
    tan⁡−1(1+33+3)+sec⁡−1(8+436+33)\tan^{- 1}\left( \frac{1 +\sqrt{3}}{3 +\sqrt{3}} \right)+\sec^{- 1}\left( \sqrt{\frac{8 + 4\sqrt{3}}{6 + 3\sqrt{3}}} \right) is equal to:

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