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Day 523: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 2021 Paper 11

    58
    Let f:R→Rf:\mathbb{R}\to\mathbb{R} be defined as f(x)={sin⁡x−ex,x≤0a+[−x],0<x<12x−b,x≥1f(x)=\begin{cases} \sin x-e^{x}, & x\leq 0 \\ a+[-x], & 0<x<1 \\ 2x-b, & x\geq 1 \end{cases}, where [x][x] is the greatest integer ≤x\leq x. If ff is continuous on R\mathbb{R}, then (a+b)(a+b) is equal to:

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  2. Question 2

    Indefinite Integration. Asked once: 6 Apr 2023

    71
    Let I(x)=∫x2(xsec⁡2x+tan⁡x)(xtan⁡x+1)2dxI(x) = \int\frac{x^{2}\left( x\sec^{2}x + \tan x \right)}{(x\tan x + 1)^{2}}dx. If I(0)=0I(0) = 0, then I(π4)I\left( \frac{\pi}{4} \right) is equal to

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  3. Question 3

    Inverse Trigonometric Functions. Asked once: 2021 Paper 6

    73
    Given that the inverse trigonometric functions take principal values only. Then, the number of real values of xx which satisfy sin⁡−1(3x5)+sin⁡−1(4x5)=sin⁡−1x\sin^{- 1}\left( \frac{3x}{5} \right)+\sin^{- 1}\left( \frac{4x}{5} \right)=\sin^{- 1}x is equal to:

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  4. Question 4

    Limits and Continuity. Asked once: 30 Jan 2023

    156
    Let f,gf,g and hh be the real valued functions defined on RR as
    f(x)={x∣x∣,x≠01,x=0,g(x)={sin⁡(x+1)(x+1),x≠−11,x=−1 f(x) =\left\{ \begin{matrix} \frac{x}{|x|}, & x \neq 0 \\ 1, & x = 0 \end{matrix},g(x) =\left\{ \begin{matrix} \frac{\sin(x + 1)}{(x + 1)}, & x \neq - 1 \\ 1, & x = - 1 \end{matrix} \right.\ \right.
    and h(x)=2[x]−f(x)h(x) = 2\lbrack x\rbrack - f(x), where [x]\lbrack x\rbrack is the greatest integer ≤x\leq x. Then the value of lim⁡x→1 g( h(x−1))\lim_{x \rightarrow 1} \text{ }g(\text{ }h(x - 1)) is

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  5. Question 5

    Matrices. Asked once: 29 Jan 2024

    80
    Let A be a square matrix such that AAT=IAA^{T}= I. Then 12 A[( A+AT)2+(A−AT)2]\frac{1}{2}\text{ }A\left\lbrack \left( \text{ }A +A^{T} \right)^{2}+\left( A -A^{T} \right)^{2} \right\rbrack is equal to

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