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Day 530: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 10 Apr 2023

    174
    Let quadratic curve passing through the point (−1,0)( - 1,0) and touching the line y=xy = x at (1,1)(1,1) be == f(x)f(x). Then the xx-intercept of the normal to the curve at the point (α,α+1)(\alpha,\alpha + 1) in the first quadrant is

  2. Question 2

    Application of Integrals. Asked once: 4 Apr 2024

    66
    One of the points of intersection of the curves y=1+3x−2x2y = 1 + 3x - 2x^{2} and y=1xy =\frac{1}{x} is (12,2)\left( \frac{1}{2},2 \right). Let the area of the region enclosed by these curves be 124(l5+m)−nlog⁡e(1+5)\frac{1}{24}(l\sqrt{5}+ m) -n\log_{e}(1 +\sqrt{5}), where l,m,n∈Nl,m,n \in N. Then l+m+nl +m + n is equal to

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  3. Question 3

    Binomial Theorem. Asked once: 29 Jan 2023

    170
    Let KK be the sum of the coefficients of the odd powers of xx in the expansion of (1+x)99(1 + x)^{99}. Let aa be the middle term in the expansion of (2+12)200\left( 2 +\frac{1}{\sqrt{2}} \right)^{200}. If  200C99Ka=2lmn\frac{\ ^{200}C_{99}K}{a}=\frac{2^{l}m}{n}, where mm and nn are odd numbers, then the ordered pair (l,n)(l,n) is equal to

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  4. Question 4

    Complex Numbers. Asked once: 27 Jan 2024

    71
    If S={z∈C:∣z−i∣=∣z+i∣=∣z−1∣}\mathbf{S = \{ z \in C:|z - i| = |z + i| = |z - 1|\}}, then, n(S)n(S) is:

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  5. Question 5

    Conic Sections. Asked once: 22 Jan 2026 S2

    67
    Let the locus of the mid-point of the chord through the origin O of the parabola y2=4xy^{2}= 4x be the curve S. Let P be any point on S. Then the locus of the point, which internally divides OP in the ratio 3:13:1, is :

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