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Day 623: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 28 Jun 2022

    87
    Let A={1,a1,a2……a18,77}A=\left\{ 1,a_{1},a_{2}\ldots\ldots a_{18},77 \right\} be a set of integers with 1<a1<a2<….<a18<771 <a_{1}<a_{2}< \ldots. <a_{18}< 77. Let the set A+A={x+y:x,y∈A} \mathbf{A + A = \{ x + y:x,y \in A\}\ } contain exactly 39 elements. Then, the value of a1+a2+…..+a18a_{1}+a_{2}+ \ldots.. +a_{18} is equal to

  2. Question 2

    Conic Sections. Asked once: 31 Jan 2024

    157
    Let PP be a parabola with vertex (2,3)(2,3) and directrix 2x+y=62x + y = 6. Let an ellipse E:x2a2+y2b2=1,a>bE:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1,a > b of eccentricity 12\frac{1}{\sqrt{2}} pass through the focus of the parabola PP. Then the square of the length of the latus rectum of EE, is

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  3. Question 3

    Definite Integration. Asked once: 28 Jul 2022

    80
    The minimum value of the twice differentiable function f(x)=∫0xex−tf′(t)dt−(x2−x+1)ex,x∈Rf(x) =\int_{0}^{x} e^{x - t}f^{'}(t)dt -\left( x^{2}- x + 1 \right)e^{x},x \in R, is:

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  4. Question 4

    Sequences and Series. Asked once: 27 Jun 2022

    156
    If a1,a2,a3…a_{1},a_{2},a_{3}\ldots and b1, b2, b3…b_{1},{\text{ }b}_{2},{\text{ }b}_{3}\ldots are A.P. and a1=2,a10=3,a1b1=1=a10b10a_{1}= 2,a_{10}= 3,a_{1}b_{1}= 1 =a_{10}b_{10} then a4b4a_{4}b_{4} is equal to

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  5. Question 5

    Conic Sections. Asked once: 30 Jan 2024

    153
    Let A(α,0)A(\alpha,0) and B(0,β)B(0,\beta) be the points on the line 5x+7y=505x + 7y = 50. Let the point PP divide the line segment ABAB internally in the ratio 7:37:3. Let 3x−3x - 25=025 = 0 be a directrix of the ellipse E:x2a2+y2b2=1E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 and the corresponding focus be S. If from SS, the perpendicular on the xx-axis passes through PP, then the length of the latus rectum of EE is equal to

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