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Day 298: JEE Mains Maths

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

  1. Question 1

    Statistics. Asked once: 1 Feb 2023 (same type asked 8 times) See all 8 of this type

    169
    Let 9=x1<x2<…<x79 =x_{1}<x_{2}< \ldots <x_{7} be in an A.P. with common difference dd. If the standard deviation of x1,x2,…,x7x_{1},x_{2},\ldots,x_{7} is 4 and mean is x‾\overline{x}, then x‾+x6\overline{x}+x_{6} is equal to:

    Tap an option to check your answer.

  2. Question 2

    Conic Sections. Asked once: 24 Jan 2025 (same type asked 8 times) See all 8 of this type

    126
    The equation of the chord, of the ellipse x225+y216=1\frac{x^{2}}{25}+\frac{y^{2}}{16}= 1, whose mid-point is (3,1)(3,1) is :

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  3. Question 3

    Limits and Continuity. Asked once: 29 Jan 2025 (same type asked 8 times) See all 8 of this type

    147
    If lim⁡t→0(∫01(3x+5)tdx)1t=α5e(85)23\lim_{t \rightarrow 0} \left( \int_{0}^{1} (3x + 5)^{t}dx \right)^{\frac{1}{t}}=\frac{\alpha}{5e}\left( \frac{8}{5} \right)^{\frac{2}{3}}, then α\alpha is equal to ____\_\_\_\_ .

  4. Question 4

    Binomial Theorem. Asked once: 2021 Paper 25 (same type asked 8 times) See all 8 of this type

    83
    Let m,n∈Nm,n\in N and gcd(2,n)=1gcd(2,n) = 1. If 30(300)+29(301)+…+2(3028)+1(3029)=n⋅2m30\begin{pmatrix} 30 \\ 0 \end{pmatrix}+ 29\begin{pmatrix} 30 \\ 1 \end{pmatrix}+ \ldots + 2\begin{pmatrix} 30 \\ 28 \end{pmatrix}+ 1\begin{pmatrix} 30 \\ 29 \end{pmatrix}=n\cdot2^{m}, then n+mn+m is equal to

  5. Question 5

    Quadratic Equations. Asked once: 6 Apr 2024 (same type asked 8 times) See all 8 of this type

    178
    Let α,β\alpha,\beta be roots of x2+2x−8=0x^{2}+\sqrt{2}x - 8 = 0. If Un=αn+βnU_{n}=\alpha^{n}+\beta^{n}, then U10+2U92U8\frac{U_{10}+\sqrt{2}U_{9}}{2U_{8}} is equal to