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Day 503: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 28 Jan 2025

    142
    Two equal sides of an isosceles triangle are along −x+2y=4-x+ 2y= 4 and x+y=4x+y= 4. If mm is the slope of its third side, then the sum of all possible distinct values of mm, is :

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  2. Question 2

    Three Dimensional Geometry. Asked once: 31 Jan 2023

    157
    The foot of perpendicular from the origin OO to a plane PP which meets the co-ordinate axes at the points A,B,CA,B,C is (2,a,4),a∈N(2,a,4),a \in N. If the volume of the tetrahedron OABC is 144 unit  3\ ^{3}, then which of the following points is NOT on PP ?

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  3. Question 3

    Trigonometric Equations. Asked once: 2021 Paper 21

    81
    Let SS be the sum of all solutions (in radians) of the equation sin⁡4θ+cos⁡4θ−sin⁡θcos⁡θ=0\sin^{4}\theta+\cos^{4}\theta- \sin\theta \cos\theta= 0 in [0,4π]\lbrack 0,4\pi\rbrack. Then 8 Sπ\frac{8\text{ }S}{\pi} is equal to

  4. Question 4

    Trigonometric Identities. Asked once: 29 Jan 2024

    74
    Consider the function f:[12,1]→Rf:\left\lbrack \frac{1}{2},1 \right\rbrack\rightarrow R defined by f(x)=42x3−32x−1f(x) = 4\sqrt{2}x^{3}- 3\sqrt{2}x - 1. Consider the statements (I) The curve y=f(x)y = f(x) intersects the xx-axis exactly at one point (II) The curve y=f(x)y = f(x) intersects the xx-axis at x=cos⁡π12x = \cos\frac{\pi}{12} Then

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  5. Question 5

    Vector Algebra. Asked once: 29 Jan 2024

    68
    Let a→,b→\overrightarrow{a},\overrightarrow{b} and c→\overrightarrow{c} be three non-zero vectors such that b→\overrightarrow{b} and c→\overrightarrow{c} are non-collinear if a→+5b→\overrightarrow{a}+ 5\overrightarrow{b} is collinear with c→,b→+6c→\overrightarrow{c},\overrightarrow{b}+ 6\overrightarrow{c} is collinear with a→\overrightarrow{a} and a→+αb→+βc→=0→\overrightarrow{a}+ \alpha\overrightarrow{b}+ \beta\overrightarrow{c}=\overrightarrow{0}, then α+β\alpha + \beta is equal to

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