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Day 77: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked 2 times: 21 Jan 2026 S2*, 4 Apr 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    70
    The integral ∫01cot⁡−1(1+x+x2)dx\int_{0}^{1} \cot^{- 1}\left( 1 + x +x^{2} \right)dx is equal to :

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  2. Question 2

    Conic Sections. Asked 2 times: 27 Jun 2022*, 2 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    60
    Let an ellipse x2a2+y2 b2=1,a<b\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,a < b, pass through the point (4,3)(4,3) and have eccentricity 53\frac{\sqrt{5}}{3}. Then the length of its latus rectum is :

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  3. Question 3

    Quadratic Equations. Asked 2 times: 21 Jan 2026 S2*, 2 Apr 2026 S1 (* = numbers or wording changed that year) See all 2 times it was asked

    51
    Let α,α+2,α∈Z\alpha,\alpha+ 2,\alpha\in Z, be the roots of the quadratic equation x(x+2)+(x+1)(x+3)+(x+2)(x+4)+...+(x+n−1)(x+n+1)=4nx(x+ 2) + (x+ 1)(x+ 3) + (x+ 2)(x+ 4) + ... + (x+n- 1)(x+n+ 1) = 4n for some n∈Nn\in N. Then ( n+αn +\alpha ) is equal to :

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  4. Question 4

    Conic Sections. Asked 2 times: 8 Apr 2023*, 28 Jan 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    53
    Let A be the focus of the parabola y2=8xy^{2}= 8x. Let the line y=mx+cy = mx + c intersect the parabola at two distinct points B and C . If the centroid of the triangle ABCABC is (73,43)\left( \frac{7}{3},\frac{4}{3} \right), then (BC)2(BC)^{2} is equal to :

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  5. Question 5

    Limits and Continuity. Asked 2 times: 28 Jul 2022*, 28 Jan 2026 S2 (* = numbers or wording changed that year) See all 2 times it was asked

    55
    Let f(x)=lim⁡θ→0(cos⁡πx−x(2θ)sin⁡(x−1)1+x(2θ)(x−1)),x∈Rf(x) =\lim_{\theta\rightarrow 0} \left( \frac{\cos\pi x-x^{\left( \frac{2}{\theta} \right)}\sin(x- 1)}{1 +x^{\left( \frac{2}{\theta} \right)}(x- 1)} \right),x\in R. Consider the following two statements : (I) f(x)f(x) is discontinous at x=1x = 1. (II) f(x)f(x) is continous at x=−1x = - 1. Then,

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