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Day 572: JEE Mains Maths

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

  1. Question 1

    Application of Integrals. Asked once: 31 Jan 2023

    82
    Let for x∈Rx \in R,
    f(x)=x+∣x∣2 and g(x)={x,x<0x2,x≥0.f(x) =\frac{x + |x|}{2}\text{~and~}g(x) =\left\{ \begin{matrix} x, & x < 0 \\ x^{2}, & x \geq 0 \end{matrix}. \right.
    Then area bounded by the curve y=(f∘g)(x)y = (f \circ g)(x) and the lines y=0,2y−x=15y = 0,2y - x = 15 is equal to

  2. Question 2

    Binomial Theorem. Asked once: 2021 Paper 6

    88
    Let nn be a positive integer. Let
    A=∑k=0n(−1)k nCk[(12)k+(34)k+(78)k+(1516)k+(3132)k]A =\sum_{k = 0}^{n} ( - 1)^{k}\ ^{n}C_{k}\left\lbrack \left( \frac{1}{2} \right)^{k}+\left( \frac{3}{4} \right)^{k}+\left( \frac{7}{8} \right)^{k}+\left( \frac{15}{16} \right)^{k}+\left( \frac{31}{32} \right)^{k} \right\rbrack
    If 63 A=1−123063\text{ }A = 1 -\frac{1}{2^{30}}, then nn is equal to

  3. Question 3

    Complex Numbers. Asked once: 29 Jul 2022

    151
    If z≠0z \neq 0 be a complex number such that ∣z−1z∣=2\left| z -\frac{1}{z} \right|= 2, then the maximum value of ∣z∣|z| is:

    Tap an option to check your answer.

  4. Question 4

    Conic Sections. Asked once: 2 Apr 2025

    70
    Let the focal chord PQPQ of the parabola y2=4xy^{2}= 4x make an angle of 60∘60^{\circ} with the positive xx-axis, where PP lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y -axis at the point (0,α)(0,\alpha), then 5α25\alpha^{2} is equal to :

    Tap an option to check your answer.

  5. Question 5

    Definite Integration. Asked once: 30 Jan 2024

    85
    The value 9∫09[10xx+1]dx9\int_{0}^{9} \left\lbrack \sqrt{\frac{10x}{x+ 1}} \right\rbrack dx, where [t]\lbrack t\rbrack denotes the greatest integer less than or equal to tt, is