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Day 520: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 12 Apr 2023

    79
    Two dice A and B are rolled, Let the numbers obtained on A and B be α\alpha and β\beta respectively. If the variance of α−β\alpha - \beta is pq\frac{p}{q}, where pp and qq are coprime, then the sum of the positive divisors of pp is equal to

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  2. Question 2

    Quadratic Equations. Asked once: 31 Jan 2024

    62
    Let aa be the sum of all coefficients in the expansion of (1−2x+2x2)2023(3−4x2+2x3)2024\left( 1 - 2x+ 2x^{2} \right)^{2023}\left( 3 - 4x^{2}+ 2x^{3} \right)^{2024} and b=lim⁡x→0(∫0xlog⁡(1+t)t2024+1dtx2)b=\lim_{x\rightarrow 0} \left( \frac{\int_{0}^{x} \frac{\log(1 +t)}{t^{2024}+ 1}dt}{x^{2}} \right). If the equations cx2+dx+e=0cx^{2}+ dx + e = 0 and 2bx2+ax+4=02bx^{2}+ ax + 4 = 0 have a common root, where c,d,e∈Rc,d,e \in R, then d:c:ed:c:e equals

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  3. Question 3

    Relations and Functions. Asked once: 31 Jan 2024

    163
    If the function f:(−∞,−1]→(a,b]f:( - \infty, - 1\rbrack \rightarrow (a,b\rbrack defined by f(x)=ex3−3x+1f(x) =e^{x^{3}- 3x+ 1} is one-one and onto, then the distance of the point P(2 b+4P(2\text{ }b + 4, a+2)a + 2) from the line x+e−3y=4x+e^{- 3}y= 4 is :

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  4. Question 4

    Sequences and Series. Asked once: 29 Jan 2025

    132
    Let S=N∪{0}\mathbf{S = N \cup \{ 0\}}. Define a relation RR from S to RR by :
    R={(x,y):log⁡ey=xlog⁡e(25),x∈ S,y∈R}.R =\left\{ (x,y):\log_{e}y = x\log_{e}\left( \frac{2}{5} \right),x \in\text{ }S,y \in R \right\}.
    Then, the sum of all the elements in the range of RR is equal to

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  5. Question 5

    Straight Lines. Asked once: 5 Apr 2024

    63
    Let two straight lines drawn from the origin OO intersect the line 3x+4y=123x + 4y = 12 at the points PP and QQ such that △OPQ\bigtriangleup OPQ is an isosceles triangle and ∠POQ=90∘\angle POQ =90^{\circ}. If l=OP2+PQ2+QO2l =OP^{2}+PQ^{2}+QO^{2}, then the greatest integer less than or equal to ll is:

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