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Day 575: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 26 Jul 2022

    69
    Let f(x)={x3−x2+10x−7,x≤1−2x+log⁡2(b2−4),x>1f(x) =\left\{ \begin{matrix} x^{3}-x^{2}+ 10x - 7,x \leq 1 \\ - 2x +\log_{2}\left( b^{2}- 4 \right),x > 1 \end{matrix} \right. Then the set of all values of bb, for which f(x)f(x) has maximum value at x=1x = 1, is:

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  2. Question 2

    Application of Integrals. Asked once: 30 Jan 2023

    174
    Let AA be the area of the region {(x,y):y≥x2,y≥(1−x)2,y≤2x(1−x)}\left\{ (x,y):y \geq x^{2},y \geq (1 - x)^{2},y \leq 2x(1 - x) \right\}. Then 540 A540\text{ }A is equal to

  3. Question 3

    Binomial Theorem. Asked once: 2021 Paper 1

    76
    The value of − 15C1+2⋅ 15C2−3. 15C3+….−15. 15C15+ 14C1+ 14C3+ 14C5+….+ 14C11-\ ^{15}C_{1}+ 2 \cdot\ ^{15}C_{2}- 3.\ ^{15}C_{3}+ \ldots. - 15.\ ^{15}C_{15}+\ ^{14}C_{1}+\ ^{14}C_{3}+\ ^{14}C_{5}+ \ldots. +\ ^{14}C_{11} is:

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  4. Question 4

    Complex Numbers. Asked once: 29 Jul 2022

    167
    Let S={z=x+iy:∣z−1+i∣≥∣z∣,∣z∣<2,∣z+i∣=\mathbf{S = \{ z = x + iy:|z - 1 + i| \geq |z|,|z| < 2,|z + i| =} ∣z−1∣}|z - 1|\}. Then the set of all values of xx, for which w=2x+iy∈Sw = 2x + iy \in S for some y∈Ry \in R, is

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  5. Question 5

    Conic Sections. Asked once: 29 Jan 2025

    51
    Let the line x+y=1x + y = 1 meet the circle x2+y2=4x^{2}+y^{2}= 4 at the points AA and BB. If the line perpendicular to ABAB and passing through the mid point of the chord ABAB intersects the circle at C and D , then the area of the quadrilateral ADBC is equal to

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