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Day 225: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 5 Apr 2026 S2 (same type asked 41 times) See all 41 of this type

    75
    Let y=y(x)y = y(x) be the solution of the differential equation (tan⁡x)1/2dy=(sec⁡3x−(tan⁡x)3/2y)dx(\tan x)^{1/2}dy = \left( \sec^{3}x - (\tan x)^{3/2}y \right)dx, 0<x<π2,y(π4)=6250 < x < \frac{\pi}{2},y\left( \frac{\pi}{4} \right) = \frac{6\sqrt{2}}{5}. If y(π3)=45αy\left( \frac{\pi}{3} \right) = \frac{4}{5}\alpha, then α4\alpha^{4} equals ____\_\_\_\_

  2. Question 2

    Three Dimensional Geometry. Asked once: 24 Jan 2026 S2 (same type asked 33 times) See all 33 of this type

    61
    The sum of all values of α\alpha, for which the shortest distance between the lines  x+1α=y−2−1=z−4−α\ \ \frac{x + 1}{\alpha}=\frac{y - 2}{- 1}=\frac{z - 4}{- \alpha} and xα=y−12=z−12α\frac{x}{\alpha}=\frac{y - 1}{2}=\frac{z - 1}{2\alpha} is 2\sqrt{2}, is

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  3. Question 3

    Determinants. Asked once: 2 Apr 2026 S2 (same type asked 26 times) See all 26 of this type

    53
    If the system of equations
    x+5y+6z=4x+ 5y+ 6z= 4
    2x+3y+4z=72x+ 3y+ 4z= 7
    x+6y+az=bx+ 6y+az=b
    has infinitely many solutions, then the point (a,b)(a,b) lies on the line

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  4. Question 4

    Three Dimensional Geometry. Asked once: 28 Jan 2026 S2 (same type asked 19 times) See all 19 of this type

    66
    Let Q(a,b,c)Q(a,b,c) be the image of the point P(3,2,1)P(3,2,1) in the line x−11=y2=z−11\frac{x- 1}{1}=\frac{y}{2}=\frac{z- 1}{1}. Then the distance of QQ from the line x−93=y−92=z−5−2\frac{x- 9}{3}=\frac{y- 9}{2}=\frac{z- 5}{- 2} is

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  5. Question 5

    Differential Equations. Asked once: 9 Apr 2024 (same type asked 19 times) See all 19 of this type

    77
    The solution of the differential equation (x2+y2)dx−5xydy=0,y(1)=0\left( x^{2}+y^{2} \right)dx - 5xydy = 0,y(1) = 0, is :

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