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Day 441: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 8 Apr 2026 S2

    65
    Let the foot of perpendicular from the point (λ,2,3)(\lambda,2,3) on the line x−41=y−92=z−51\frac{x- 4}{1}=\frac{y- 9}{2}=\frac{z- 5}{1} be the point ( 1,μ,21,\mu,2 ). Then the distance between the lines x−12=y−23=z+46\frac{x- 1}{2}=\frac{y- 2}{3}=\frac{z+ 4}{6} and x−λ2=y−μ3=z+56\frac{x-\lambda}{2}=\frac{y-\mu}{3}=\frac{z+ 5}{6} is equal to

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  2. Question 2

    Trigonometric Equations. Asked once: 2 Apr 2026 S1

    62
    Let S={x∈[−π,π]:sin⁡x(sin⁡x+cos⁡x)=aS = \{x\in \lbrack -\pi,\pi\rbrack:\sin x(\sin x+ \cos x) =a, a∈Z}a \in Z\}. Then n(S)n(S) is equal to :

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  3. Question 3

    Trigonometric Identities. Asked once: 5 Apr 2026 S1

    56
    Let tan⁡A,tan⁡B\tan A,\tan B, where A,B∈(−π2,π2)A,B \in\left( -\frac{\pi}{2},\frac{\pi}{2} \right), be the roots of the quadratic equation x2−2x−5=0x^{2}- 2x - 5 = 0. Then 20sin⁡2(A+B2)20\sin^{2}\left( \frac{A+B}{2} \right) is equal to :

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  4. Question 4

    Vector Algebra. Asked once: 5 Apr 2026 S2

    66
    Let O be the origin, OP→=a→\overrightarrow{OP}=\overrightarrow{a} and OQ→=b→\overrightarrow{OQ}=\overrightarrow{b}. If RR is the point on OP→\overrightarrow{OP} such that OP→=5OR→\overrightarrow{OP}= 5\overrightarrow{OR}, and M is the point such that OQ→=5RM→\overrightarrow{OQ}= 5\overrightarrow{RM}, then PM→\overrightarrow{PM} is equal to :

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  5. Question 5

    Application of Derivatives. Asked once: 2 Apr 2026 S1

    68
    The number of critical points of the function f(x)={∣sin⁡xx∣,x≠01,x=0f(x) =\left\{ \begin{matrix} \left| \frac{\sin x}{x} \right|, & x\neq 0 \\ 1, & x= 0 \end{matrix} \right. in the interval (−2π,2π)( - 2\pi,2\pi) is equal to:

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