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Day 151: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 4 Apr 2024 (same type asked 5 times) See all 5 of this type

    177
    In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 13\frac{1}{3} and 23\frac{2}{3} respectively. Let xx be the number of matches that the team wins, and yy be the number of matches that team loses. If the probability P(∣x−y∣≤2)P(|x - y| \leq 2) is pp, then 39p3^{9}p equals

  2. Question 2

    Complex Numbers. Asked once: 24 Jan 2023 (same type asked 5 times) See all 5 of this type

    170
    The value of (1+sin⁡2π9+icos2π91+sin⁡2π9−icos2π9)3\left( \frac{1 + \sin\frac{2\pi}{9}+ icos\frac{2\pi}{9}}{1 + \sin\frac{2\pi}{9}- icos\frac{2\pi}{9}} \right)^{3} is

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  3. Question 3

    Differential Equations. Asked once: 26 Jun 2022 (same type asked 5 times) See all 5 of this type

    159
    If y=y(x)y = y(x) is the solution of the differential equation xdydx+2y=xx,y(1)=0x\frac{dy}{dx}+ 2y =x^{x},y(1) = 0 then the local maximum value of the function z(x)=x2y(x)−exz(x) =x^{2}y(x) -e^{x}, x∈Rx \in R is:

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  4. Question 4

    Sequences and Series. Asked once: 7 Apr 2025 (same type asked 5 times) See all 5 of this type

    63
    Let x1,x2,x3,x4x_{1},x_{2},x_{3},x_{4} be in a geometric progression. If 2,7,9,52,7,9,5 are subtracted respectively from x1,x2,x3x_{1},x_{2},x_{3}, x4x_{4} then the resulting numbers are in an arithmetic progression. Then the value of 124(x1x2x3x4)\frac{1}{24}\left( x_{1}x_{2}x_{3}x_{4} \right) is :

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  5. Question 5

    Complex Numbers. Asked once: 30 Jan 2024 (same type asked 5 times) See all 5 of this type

    166
    If zz is a complex number, then the number of common roots of the equation z1985+z100+1=0z^{1985}+z^{100}+ 1 = 0 and z3+2z2+2z+1=0z^{3}+ 2z^{2}+ 2z+ 1 = 0, is equal to :

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