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Day 639: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 8

    89
    Let In=∫1ex19(log⁡∣x∣)ndxI_{n}=\int_{1}^{e} x^{19}(\log|x|)^{n}dx, where n∈Nn \in N. If (20) I10=αI9+βI8I_{10}= \alpha I_{9}+ \beta I_{8}, for natural numbers α\alpha and β\beta, then α−β\alpha - \beta equal to

  2. Question 2

    Conic Sections. Asked once: 24 Jan 2023

    73
    Let a tangent to the curve y2=24xy^{2}= 24x meet the curve xy=2xy = 2 at the points AA and BB. Then the mid points of such line segments ABAB lie on a parabola with the

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  3. Question 3

    Definite Integration. Asked once: 2021 Paper 8

    61
    Let f:R→Rf:R \rightarrow R be defined as f(x)=e−xsin⁡xf(x) =e^{- x}\sin x. If F:[0,1]→RF:\lbrack 0,1\rbrack \rightarrow R is a differentiable function such that F(x)=∫0xf(t)dtF(x) =\int_{0}^{x} f(t)dt, then the value of ∫01(F′(x)+f(x))exdx\int_{0}^{1} \left( F^{'}(x) +f(x) \right)e^{x}dx lies in the interval

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  4. Question 4

    Conic Sections. Asked once: 29 Jul 2022

    68
    Let a line LL pass through the point of intersection of the lines bx+10y−8=0bx + 10y - 8 = 0 and 2x−3y=02x - 3y = 0, b∈R−{43}b \in R -\left\{ \frac{4}{3} \right\}. If the line LL also passes through the point (1,1)(1,1) and touches the circle 17(x2+y2)=1617\left( x^{2}+y^{2} \right)= 16, then the eccentricity of the ellipse x25+y2b2=1\frac{x^{2}}{5}+\frac{y^{2}}{b^{2}}= 1 is:

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  5. Question 5

    Definite Integration. Asked once: 2021 Paper 6

    77
    Let P(x)=x2+bx+cP(x) =x^{2}+ bx + c be a quadratic polynomial with real coefficients such that ∫01P(x)dx=1\int_{0}^{1} P(x)dx = 1 and P(x)P(x) leaves remainder 5 when it is divided by (x−2)(x- 2). Then the value of 9(b+c)9(b+c) is equal to:

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