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Day 603: JEE Mains Maths

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

  1. Question 1

    Complex Numbers. Asked once: 2021 Paper 19

    90
    The least positive integer nn such that (2i)n(1−i)n−2,i=−1\frac{(2i)^{n}}{(1 - i)^{n - 2}},i =\sqrt{- 1} is a positive integer, is

  2. Question 2

    Conic Sections. Asked once: 22 Jan 2025

    63
    Let the parabola y=x2+px−3y=x^{2}+px-3 meet the coordinate axes at the points P,QP,Q and RR. If the circle CC with centre at (−1,−1)(-1,-1) passes through the points P,QP,Q and RR, then the area of △PQR\triangle PQR is:

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  3. Question 3

    Definite Integration. Asked once: 1 Feb 2023

    88
    If ∫01(x21+x14+x7)(2x14+3x7+6)1/7dx=1l(11)m/n\int_{0}^{1} \left( x^{21}+x^{14}+x^{7} \right)\left( 2x^{14}+ 3x^{7}+ 6 \right)^{1/7}dx =\frac{1}{l}(11)^{m/n} where l,m,n∈N,ml,m,n \in N,m and nn are coprime then l+m+nl + m + n is equal to

  4. Question 4

    Matrices. Asked once: 2021 Paper 11

    47
    Let A=[23a0],a∈RA =\begin{bmatrix} 2 & 3 \\ a & 0 \end{bmatrix},a \in R be written as P+QP + Q where PP is a symmetric matrix and QQ is skew symmetric matrix. If det(Q)=9det(Q) = 9, then the modulus of the sum of all possible values of determinant of PP is equal to:

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  5. Question 5

    Relations and Functions. Asked once: 2021 Paper 9

    76
    If the functions are defined as f(x)=xf(x) =\sqrt{x} and g(x)=1−xg(x) =\sqrt{1 - x}, then what is the common domain of the following functions: f+g,f−g,f/g,g/f, g−ff + g,f - g,f/g,g/f,\text{ }g - f where (f±g)(x)=(f \pm g)(x) = f(x)±g(x),(f/g)(x)=f(x)g(x)f(x) \pm g(x),(f/g)(x) =\frac{f(x)}{g(x)}

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