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Day 247: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 11 Apr 2023 (same type asked 5 times) See all 5 of this type

    159
    The domain of the function f(x)=1[x]2−3[x]−10f(x) =\frac{1}{\sqrt{\lbrack x\rbrack^{2}- 3\lbrack x\rbrack - 10}} is (where [x] denotes the greatest integer less than or equal to xx )

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  2. Question 2

    Sequences and Series. Asked once: 13 Apr 2023 (same type asked 5 times) See all 5 of this type

    85
    The sum to 20 terms of the series 2.22−32+2.42−52+2.62−2.2^{2}-3^{2}+2.4^{2}-5^{2}+2.6^{2}- is equal to

  3. Question 3

    Binomial Theorem. Asked once: 31 Jan 2024 (same type asked 5 times) See all 5 of this type

    174
    Let the coefficient of xrx^{r} in the expansion of
     (x+3)n−1+(x+3)n−2(x+2)+ (x+3)n−3(x+2)2+……..+(x+2)n−1\begin{matrix} & \ (x + 3)^{n - 1}+ (x + 3)^{n - 2}(x + 2) + \\ & \ (x + 3)^{n - 3}(x + 2)^{2}+ \ldots\ldots.. + (x + 2)^{n - 1} \end{matrix}
    be αr\alpha_{r}. If ∑r=0nαr=βn−γn,β,γ∈N\sum_{r = 0}^{n} \alpha_{r}=\beta^{n}-\gamma^{n},\beta,\gamma \in N, then the value of β2+γ2\beta^{2}+\gamma^{2} equals

  4. Question 4

    Conic Sections. Asked once: 9 Apr 2024 (same type asked 5 times) See all 5 of this type

    161
    Let the foci of a hyperbola HH coincide with the foci of the ellipse E:(x−1)2100+(y−1)275=1E:\frac{(x- 1)^{2}}{100}+\frac{(y- 1)^{2}}{75}= 1 and the eccentricity of the hyperbola HH be the reciprocal of the eccentricity of the ellipse E. If the length of the transverse axis of HH is α\alpha and the length of its conjugate axis is β\beta, then 3α2+2β23\alpha^{2}+ 2\beta^{2} is equal to:

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  5. Question 5

    Definite Integration. Asked once: 25 Jul 2022 (same type asked 5 times) See all 5 of this type

    159
    Let [t]\lbrack t\rbrack denote the greatest integer less than or equal to tt. Then the value of the integral ∫−3101([sin⁡(πx)]+e[cos⁡(2πx)])dx\int_{- 3}^{101} \left( \lbrack \sin(\pi x)\rbrack +e^{\lbrack \cos(2\pi x)\rbrack} \right)dx is equal to

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