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Day 245: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 30 Jan 2023 (same type asked 6 times) See all 6 of this type

    179
    50th 50^{\text{th~}} root of a number xx is 12 and 50th 50^{\text{th~}} root of another number yy is 18 . Then the remainder obtained on dividing (x+y)(x + y) by 25 is

  2. Question 2

    Conic Sections. Asked once: 26 Jun 2022 (same type asked 6 times) See all 6 of this type

    83
    Let the common tangents to the curves 4(x2+y2)=4\left( x^{2}+y^{2} \right)= 9 and y2=4xy^{2}= 4x intersect at the point QQ. Let an ellipse, centered at the origin OO, has lengths of semi-minor and semi-major axes equal to OQOQ and 6 , respectively. If e and ll respectively denote the eccentricity and the length of the latus rectum of this ellipse, then le2\frac{l}{e^{2}} is equal to

  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 20 (same type asked 6 times) See all 6 of this type

    70
    If Un=(1+1n2)(1+22n2)2….(1+n2n2)nU_{n}=\left( 1 +\frac{1}{n^{2}} \right)\left( 1 +\frac{2^{2}}{n^{2}} \right)^{2}\ldots.\left( 1 +\frac{n^{2}}{n^{2}} \right)^{n}, then lim⁡n→∞(Un)−4n2\lim_{n\rightarrow \infty} \left( U_{n} \right)^{\frac{- 4}{n^{2}}} is equal to :

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  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 26 (same type asked 6 times) See all 6 of this type

    61
    Let LL be the line of intersection of the two planes x+2y+z=6x+ 2y+z= 6 and y+2z=4y+ 2z= 4. If point P(α,β,γ)P(\alpha,\beta,\gamma) is the foot of perpendicular from (3,2,1)(3,2,1) on LL, then the value of 21(α+β+γ)21(\alpha+\beta+\gamma) equals:

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  5. Question 5

    Definite Integration. Asked once: 2021 Paper 13 (same type asked 6 times) See all 6 of this type

    59
    ∫0100πsin⁡2xe(xπ−[xπ])dx=απ31+4π2,α∈R\int_{0}^{100\pi} \frac{\sin^{2}x}{e^{\left( \frac{x}{\pi}-\left\lbrack \frac{x}{\pi} \right\rbrack \right)}}dx=\frac{\alpha\pi^{3}}{1 + 4\pi^{2}},\alpha\in R, where [x]\lbrack x\rbrack is the greatest integer function, then α\alpha is

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