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Day 518: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 31 Jan 2024

    86
    If α\alpha denotes the number of solutions of ∣1−i∣x=2x|1 - i|^{x}=2^{x} and β=(∣z∣arg(z))\beta =\left( \frac{|z|}{arg(z)} \right), where z=π4(1+i)4(1−πiπ+i+π−i1+πi),i=−1z =\frac{\pi}{4}(1 + i)^{4}\left( \frac{1 -\sqrt{\pi}i}{\sqrt{\pi}+ i}+\frac{\sqrt{\pi}- i}{1 +\sqrt{\pi}i} \right),i =\sqrt{- 1}, then the distance of the point (α,β)(\alpha,\beta) from the line 4x−3y=74x - 3y = 7 is

  2. Question 2

    Conic Sections. Asked once: 24 Jan 2026 S2

    72
    Let (h,k)(h,k) lie on the circle C:x2+y2=4C:x^{2} + y^{2} = 4 and the point ( 2 h+1,3k+22\text{ }h + 1,3k + 2 ) lie on an ellipse with eccentricity ee. Then the value of 5e2\frac{5}{e^{2}} is equal to ____\_\_\_\_ .

  3. Question 3

    Definite Integration. Asked once: 4 Apr 2025

    66
    The value of ∫−11(1+∣x∣−x)ex+(∣x∣−x)e−xex+e−xdx\int_{- 1}^{1} \frac{(1 +\sqrt{|x| -x})e^{x}+ (\sqrt{|x| -x})e^{-x}}{e^{x}+e^{-x}}dx is equal to.

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  4. Question 4

    Determinants. Asked once: 2021 Paper 21

    62
    Let A=[[x+1][x+2][x+3][x][x+3][x+3][x][x+2][x+4]]A =\begin{bmatrix} \lbrack x + 1\rbrack & \lbrack x + 2\rbrack & \lbrack x + 3\rbrack \\ \lbrack x\rbrack & \lbrack x + 3\rbrack & \lbrack x + 3\rbrack \\ \lbrack x\rbrack & \lbrack x + 2\rbrack & \lbrack x + 4\rbrack \end{bmatrix}, where [t]\lbrack t\rbrack denotes the greatest integer less than or equal to tt. If det(A)=192det(A) = 192, then the set of values of xx is the interval:

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  5. Question 5

    Differentiation. Asked once: 2021 Paper 25

    74
    Let ff be any function defined on R\mathbb{R} and let it satisfy the condition ∣f(x)−f(y)∣≤∣(x−y)2∣, ∀ (x,y)∈R|f(x)-f(y)|\le \left|(x-y)^{2}\right|,\ \forall\,(x,y)\in\mathbb{R}. If f(0)=1f(0)=1, then:

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