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Day 300: JEE Mains Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 29 Jan 2024 (same type asked 7 times) See all 7 of this type

    90
    A line with direction ratios 2,1,22,1,2 meets the lines x=y+2=zx = y + 2 = z and x+2=2y=2zx + 2 = 2y = 2z respectively at the point PP and QQ. if the length of the perpendicular from the point (1,2,12)(1,2,12) to the line PQPQ is ll, then l2l^{2} is

  2. Question 2

    Limits and Continuity. Asked once: 6 Apr 2024 (same type asked 7 times) See all 7 of this type

    171
    Let [t]\lbrack t\rbrack denote the greatest integer less than or equal to tt. Let f:[0,∞)→Rf:\lbrack 0,\infty) \rightarrow R be a function defined by f(x)=[x2+3]−[x]f(x) =\left\lbrack \frac{x}{2}+ 3 \right\rbrack- \lbrack\sqrt{x}\rbrack. Let SS be the set of all points in the interval [0,8]\lbrack 0,8\rbrack at which ff is not continuous. Then ∑a∈Sa\sum_{a \in S} a is equal to

  3. Question 3

    Sequences and Series. Asked once: 27 Jan 2024 (same type asked 7 times) See all 7 of this type

    66
    The number of common terms in the progressions 4,9,14,19,….4,9,14,19,\ldots.. , up to 25th 25^{\text{th~}} term and 3,6,9,123,6,9,12, ......., up to 37th 37^{\text{th~}} term is :

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  4. Question 4

    Trigonometric Identities. Asked once: 8 Apr 2023 (same type asked 7 times) See all 7 of this type

    159
    The value of 36(4cos⁡29∘−1)(4cos⁡227∘−1)(4cos⁡281∘−1)(4cos⁡2243∘−1)36\left( 4\cos^{2}9^{\circ}- 1 \right)\left( 4\cos^{2}27^{\circ}- 1 \right)\left( 4\cos^{2}81^{\circ}- 1 \right)\left( 4\cos^{2}243^{\circ}- 1 \right) is

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  5. Question 5

    Differential Equations. Asked once: 31 Jan 2024 (same type asked 7 times) See all 7 of this type

    179
    Let y=y(x)y = y(x) be the solution of the differential equation
    sec⁡2xdx+(e2ytan⁡2x+tan⁡x)dy=00<x<π2,y(π4)=0. If y(π6)=α\begin{matrix} & \sec^{2}xdx +\left( e^{2y}\tan^{2}x + \tan x \right)dy = 0 \\ & 0 < x <\frac{\pi}{2},y\left( \frac{\pi}{4} \right)= 0.\text{~If~}y\left( \frac{\pi}{6} \right)= \alpha \end{matrix}
    Then e8αe^{8\alpha} is equal to