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Day 403: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 4 Apr 2024 (same type asked 19 times) See all 19 of this type

    179
    Consider a line LL passing through the points P(1,2,1)P(1,2,1) and Q(2,1,−1)Q(2,1, - 1). If the mirror image of the point A(2,2,2)A(2,2,2) in the line LL is (α,β,γ)(\alpha,\beta,\gamma), then α+β+6γ\alpha+\beta+ 6\gamma is equal to ....

  2. Question 2

    Differential Equations. Asked once: 25 Jul 2022 (same type asked 19 times) See all 19 of this type

    175
    Let y=y(x)y = y(x) be the solution of the differential equation dydx=4y3+2yx23xy2+x3,y(1)=1\frac{dy}{dx}=\frac{4y^{3}+ 2yx^{2}}{3xy^{2}+x^{3}},y(1) = 1. If for some n∈N,y(2)∈[n−1,n)n \in N,y(2) \in \lbrack n - 1,n), then nn is equal to

  3. Question 3

    Determinants. Asked once: 13 Apr 2023 (same type asked 19 times) See all 19 of this type

    165
    Let for A=[123a31112],∣A∣=2A =\begin{bmatrix} 1 & 2 & 3 \\ a & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix},|A| = 2. If ∣2adj(2adj(2A))∣|2adj(2adj(2A))| =32n=32^{n}, then 3n+a3n + a is equal to

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  4. Question 4

    Vector Algebra. Asked once: 5 Apr 2024 (same type asked 18 times) See all 18 of this type

    156
    Let a→=2i^+5j^−k^,b→=2i^−2j^+2k^\overrightarrow{a}= 2\widehat{i}+ 5\widehat{j}-\widehat{k},\overrightarrow{b}= 2\widehat{i}- 2\widehat{j}+ 2\widehat{k} and c→\overrightarrow{c} be three vectors such that
    (c→+i^)×(a→+b→+i^)=a→×(c→+i^)(\overrightarrow{c}+\widehat{i}) \times (\overrightarrow{a}+\overrightarrow{b}+\widehat{i}) =\overrightarrow{a}\times (\overrightarrow{c}+\widehat{i})
    and a→⋅c→=−29\overrightarrow{a}\cdot\overrightarrow{c}= - 29, then c→⋅(−2i^+j^+k^)\overrightarrow{c}\cdot ( - 2\widehat{i}+\widehat{j}+\widehat{k}) is equal to:

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  5. Question 5

    Limits and Continuity. Asked once: 29 Jul 2022 (same type asked 16 times) See all 16 of this type

    154
    Let the function
    f(x)={log⁡e(1+5x)−log⁡e(1+αx)x;if x≠010 if x=0f(x) =\left\{ \begin{matrix} \frac{\log_{e}(1 + 5x) -\log_{e}(1 + \alpha x)}{x} & \text{;if~}x \neq 0 \\ 10 & \text{~if~}x = 0 \end{matrix} \right.
    be continuous at x=0x = 0. The α\alpha is equal to:

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