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Day 395: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 9 (same type asked 8 times) See all 8 of this type

    75
    132−1+152−1+172−1+…+1(201)2−1\frac{1}{3^{2}- 1}+\frac{1}{5^{2}- 1}+\frac{1}{7^{2}- 1}+ \ldots +\frac{1}{(201)^{2}- 1} is equal to

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  2. Question 2

    Application of Integrals. Asked once: 2021 Paper 1 (same type asked 8 times) See all 8 of this type

    73
    The area (in sq. units) of the part of the circle x2+y2=36x^{2}+y^{2}= 36, which is outside the parabola y2=9xy^{2}= 9x, is:

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  3. Question 3

    Trigonometric Equations. Asked once: 14 Jun 2022 (same type asked 7 times) See all 7 of this type

    163
    The number of solutions of the equation cos⁡(x+π3)cos⁡(π3−x)=14cos⁡22x,x∈[−3π\cos\left( x +\frac{\pi}{3} \right)\cos\left( \frac{\pi}{3}- x \right)=\frac{1}{4}\cos^{2}2x,x \in \lbrack - 3\pi, 3π]3\pi\rbrack is:

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  4. Question 4

    Differential Equations. Asked once: 7 Apr 2025 (same type asked 41 times) See all 41 of this type

    56
    Let y=y(x)y=y(x) be the solution curve of the differential equation
    x(x2+ex)dy+(ex(x−2)y−x3)dx=0,x>0x\left( x^{2}+e^{x} \right)dy+\left( e^{x}(x- 2)y-x^{3} \right)dx= 0,x> 0
    passing through the point (1,0)(1,0). Then y(2)y(2) is equal to :

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  5. Question 5

    Three Dimensional Geometry. Asked once: 23 Jan 2025 (same type asked 33 times) See all 33 of this type

    143
    If the square of the shortest distance between the lines x−21=y−12=z+3−3\frac{x - 2}{1}=\frac{y - 1}{2}=\frac{z + 3}{- 3} and x+12=y+34=z+5−5\frac{x + 1}{2}=\frac{y + 3}{4}=\frac{z + 5}{- 5} is mn\frac{m}{n}, where m,nm,n are coprime numbers, then m+nm + n is equal to:

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