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Day 80: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked 2 times: 27 Jan 2024*, 3 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    128
    If the four distinct points (4,6),(−1,5),(0,0)(4,6),( - 1,5),(0,0) and ( k,3kk,3k ) lie on a circle of radius rr, then 10k+r210k+r^{2} is equal to.

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  2. Question 2

    Differential Equations. Asked 2 times: 2 Apr 2025*, 3 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    139
    Let y=y(x)y=y\left( x \right) be the solution of the differential equation dydx+3(tan⁡2x)y+3y=\frac{dy}{dx}+ 3\left( \tan^{2}x \right)y+ 3y= sec⁡2x\sec^{2}x, y(0)=13+e3y(0) =\frac{1}{3}+e^{3}. Then y(π4)y\left( \frac{\pi}{4} \right) is equal to.

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  3. Question 3

    Probability. Asked 2 times: 8 Apr 2023*, 3 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    138
    If the probability that the random variable XX takes the value x is given by P(X=x)=k(x+1)3−xP(X = x) = k(x + 1)3^{- x}, x=0,1,2,3……x = 0,1,2,3\ldots\ldots, where k is a constant, then P(X≥3)P(X \geq 3) is equal to

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  4. Question 4

    Application of Derivatives. Asked 2 times: 8 Apr 2024*, 2 Apr 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    59
    If the function f(x)=2x3−9ax2+12a2x+1f(x) = 2x^{3}- 9ax^{2}+ 12a^{2}x+ 1, where a >0> 0, attains its local maximum and local minimum values at pp and qq, respectively, such that p2=qp^{2}= q, then f(3)f(3) is equal to:

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  5. Question 5

    Binomial Theorem. Asked 2 times: 2021 Paper 10, 2 Apr 2025 See all 2 times it was asked

    56
    The term independent of xx in the expansion of ((x+1)(x23+1−x13)−(x−1)(x−x12))10,x>\left( \frac{\left( x+ 1 \right)}{\left( x^{\frac{2}{3}}+ 1 -x^{\frac{1}{3}} \right)}-\frac{\left( x- 1 \right)}{\left( x-x^{\frac{1}{2}} \right)} \right)^{10},x> 11 is:

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