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Day 408: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 28 Jun 2022 (same type asked 19 times) See all 19 of this type

    70
    Let the solution curve y=y(x)y = y(x) of the differential equation,
    [xx2−y2+eyx]xdydx=x+[xx2−y2+eyx]y\left\lbrack \frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}} \right\rbrack x\frac{dy}{dx}= x +\left\lbrack \frac{x}{\sqrt{x^{2}-y^{2}}}+e^{\frac{y}{x}} \right\rbrack y
    pass through the points (1,0)(1,0) and (2α,α),α>0(2\alpha,\alpha),\alpha > 0. Then α\alpha is equal to

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  2. Question 2

    Determinants. Asked once: 10 Apr 2023 (same type asked 19 times) See all 19 of this type

    69
    If AA is a 3×33 \times 3 matrix and ∣A∣=2|A| = 2, then ∣3adj(∣3A∣A2)∣\left| 3adj\left( |3A|A^{2} \right) \right| is equal to

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  3. Question 3

    Vector Algebra. Asked once: 1 Feb 2024 (same type asked 18 times) See all 18 of this type

    175
    Let  a→=i^+j^+k^, b→=−i^−8j^+2k^\ \overrightarrow{a}=\widehat{i}+\widehat{j}+\widehat{k},\ \overrightarrow{b}= -\widehat{i}- 8\widehat{j}+ 2\widehat{k} and c→=4i^+c2j^+c3k^\overrightarrow{c}= 4\widehat{i}+c_{2}\widehat{j}+c_{3}\widehat{k} be three vectors such that b→×a→=c→×a→\overrightarrow{b}\times\overrightarrow{a}=\overrightarrow{c}\times\overrightarrow{a}. If the angle between the vector c→\overrightarrow{c} and the vector 3i^+4j^+k^3\widehat{i}+ 4\widehat{j}+\widehat{k} is θ\theta, then the greatest integer less than or equal to tan⁡2θ\tan^{2}\theta is:

  4. Question 4

    Limits and Continuity. Asked once: 26 Jul 2022 (same type asked 16 times) See all 16 of this type

    67
    If the function f(x)={log⁡e(1−x+x2)+log⁡e(1+x+x2)secx−cos⁡x,x∈(−π2,π2)−{0}kf(x) =\left\{ \begin{matrix} \frac{\log_{e}\left( 1 - x +x^{2} \right)+\log_{e}\left( 1 + x +x^{2} \right)}{secx - \cos x},x \in\left( \frac{- \pi}{2},\frac{\pi}{2} \right)\mathbf{- \{ 0\}} \\ k \end{matrix} \right. is continuous at x=0x = 0, then kk is equal to :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 21 (same type asked 15 times) See all 15 of this type

    67
    The equation of the plane through the line of intersection of the planes r→⋅(i^+j^+k^)=1\overrightarrow{r}\cdot (\widehat{i}+\widehat{j}+\widehat{k}) = 1 and r→⋅(2i^+3j^−k^)+4=0\overrightarrow{r}\cdot (2\widehat{i}+ 3\widehat{j}-\widehat{k}) + 4 = 0 and parallel to the xx-axis is:

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