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Day 498: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 21 Jan 2026 S1

    72
    Let a1=1a_{1} = 1 and for n≥1,an+1n \geq 1,a_{n + 1} =12an+n2−2n−1n2(n+1)2= \frac{1}{2}a_{n} + \frac{n^{2} - 2n - 1}{n^{2}(n + 1)^{2}}. Then ∣∑n=1∞(an−2n2)∣\left| \sum_{n = 1}^{\infty} \left( a_{n} - \frac{2}{n^{2}} \right) \right| is equal to ............. .

  2. Question 2

    Statistics. Asked once: 2021 Paper 2

    84
    If the variance of 10 natural numbers 1,1,1,…,1,k1,1,1,\ldots,1,k is less than 10 , then the maximum possible value of kk is

  3. Question 3

    Straight Lines. Asked once: 29 Jan 2025

    133
    Let the line x+y=1x + y = 1 meet the axes of xx and yy at AA and BB, respectively. A right angled triangle AMN is inscribed in the triangle OABOAB, where OO is the origin and the points M and N lie on the lines OB and ABAB, respectively. If the area of the triangle AMN is 49\frac{4}{9} of the area of the triangle OABOAB and AN:NB=λ:1AN:NB = \lambda:1, then the sum of all possible value(s) of λ\lambda is :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 6 Apr 2023

    162
    Let the line LL pass through the point (0,1,2)(0,1,2), intersect the line x−12=y−23=z−34\frac{x - 1}{2}=\frac{y - 2}{3}=\frac{z - 3}{4} and be parallel to the plane 2x+y−3z=42x + y - 3z = 4. Then the distance of the point P(1,−9,2)P(1, - 9,2) from the line LL is

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  5. Question 5

    Trigonometric Equations. Asked once: 2021 Paper 24

    68
    If nn is the number of solutions of the equation 2cos⁡x(4sin⁡(π4+x)sin⁡(π4−x)−1)=1,x∈[0,π]2\cos x\left( 4\sin\left( \frac{\pi}{4}+ x \right)\sin\left( \frac{\pi}{4}- x \right)- 1 \right)= 1,x \in \lbrack 0,\pi\rbrack and SS is the sum of all these solutions, then the ordered pair (n,S)(n,S) is:

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