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Day 568: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 29 Jan 2023

    74
    A light ray emits from the origin making an angle 30∘30^{\circ} with the positive xx-axis. After getting reflected by the line x+y=1x + y = 1, if this ray intersects xx-axis at QQ, then the abscissa of QQ is

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  2. Question 2

    Three Dimensional Geometry. Asked once: 2021 Paper 18

    83
    Let the line LL be the projection of the line x−12=y−31=z−42\frac{x - 1}{2}=\frac{y - 3}{1}=\frac{z - 4}{2} in the plane x−2y−z=3x- 2y-z= 3. If dd is the distance of the point (0,0,6)(0,0,6) from LL, then d2d^{2} is equal to

  3. Question 3

    Vector Algebra. Asked once: 26 Jul 2022

    75
    Let a→=αi^+j^−k^\overrightarrow{a}= \alpha\widehat{i}+\widehat{j}-\widehat{k} and b→=2i^+j^−αk^,α>0\overrightarrow{b}= 2\widehat{i}+\widehat{j}- \alpha\widehat{k},\alpha > 0. If the projection of a→×b→\overrightarrow{a}\times\overrightarrow{b} on the vector −i^+2j^−2k^-\widehat{i}+ 2\widehat{j}- 2\widehat{k} is 30, then α\alpha is equal to

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  4. Question 4

    Application of Derivatives. Asked once: 27 Jul 2022

    160
    Consider a curve y=y(x)y = y(x) in the first quadrant as shown in the figure. Let the area A1A_{1} is twice the area A2A_{2}. Then the normal to the curve perpendicular to the line 2x−12y=152x - 12y = 15 does NOT pass through the point.

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  5. Question 5

    Application of Integrals. Asked once: 31 Jan 2023

    175
    Let the area of the region {(x,y):∣2x−1∣≤y≤∣x2−x∣,0≤x≤1}\left\{ (x,y):|2x - 1| \leq y \leq\left| x^{2}- x \right|,0 \leq x \leq 1 \right\} be A. Then (6 A+11)2(6\text{ }A + 11)^{2} is equal to