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Day 489: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 8 Apr 2023

    178
    Let P1P_{1} be the plane 3x−y−7z=113x-y-7z=11 and P2P_{2} be the plane passing through the points (2,−1,0),(2,0,−1)(2,-1,0),(2,0,-1) and (5,1,1)(5,1,1). If the foot of the perpendicular drawn from the point (7,4,−1)(7,4,-1) on the line of intersection of the planes P1P_{1} and P2P_{2} is (α,β,γ)(\alpha,\beta,\gamma), then α+β+γ\alpha+\beta+\gamma is equal to

  2. Question 2

    Trigonometric Equations. Asked once: 29 Jun 2022

    85
    The number of solutions of the equation 2θ−cos⁡2θ+2=02\theta-\cos^{2}\theta+\sqrt{2}= 0 in RR is equal to

  3. Question 3

    Trigonometric Identities. Asked once: 1 Feb 2024

    64
    If tan⁡A=1x(x2+x+1),tan⁡B=xx2+x+1\tan A =\frac{1}{\sqrt{x\left( x^{2}+ x + 1 \right)}},\tan B =\frac{\sqrt{x}}{\sqrt{x^{2}+ x + 1}} and tan⁡C=(x−3+x−2+x−1)12,0<A,B,C<π2\tan C =\left( x^{- 3}+x^{- 2}+x^{- 1} \right)^{\frac{1}{2}},0 < A,B,C <\frac{\pi}{2}, then A+BA + B is equal to:

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  4. Question 4

    Vector Algebra. Asked once: 22 Jan 2025

    75
    Let c→\overrightarrow{c} be the projection vector of b→=λi^+4k^, λ>0\overrightarrow{b}=\lambda\widehat{i}+4\widehat{k},\ \lambda>0, on the vector a→=i^+2j^+2k^\overrightarrow{a}=\widehat{i}+2\widehat{j}+2\widehat{k}. If ∣a→+c→∣=7|\overrightarrow{a}+\overrightarrow{c}|=7, then the area of the parallelogram formed by the vectors b→\overrightarrow{b} and c→\overrightarrow{c} is

  5. Question 5

    Application of Derivatives. Asked once: 8 Apr 2024

    77
    For the function f(x)=(cos⁡x)−x+1,x∈Rf(x) = (\cos x) - x + 1,x \in R, between the following two statements (S1) f(x)=0f(x) = 0 for only one value of xx is [0,π]\lbrack 0,\pi\rbrack. (S2) f(x)f(x) is decreasing in [0,π2]\left\lbrack 0,\frac{\pi}{2} \right\rbrack and increasing in [π2,π]\left\lbrack \frac{\pi}{2},\pi \right\rbrack.

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