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Day 569: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 2021 Paper 14

    53
    If the coefficient of the middle term of (1+x)20(1 +x)^{20} is A and the coefficient of middle terms of (1+x)19(1 +x)^{19} are BB and CC then find AB+C\frac{A}{B+C}

  2. Question 2

    Complex Numbers. Asked once: 25 Jan 2023

    65
    Let z1=2+3iz_{1}= 2 + 3i and z2=3+4iz_{2}= 3 + 4i. The set S={z∈C:∣z−z1∣2−∣z−z2∣2=∣z1−z2∣2}S =\left\{ z \in C:\left| z -z_{1} \right|^{2}-\left| z -z_{2} \right|^{2}=\left| z_{1}-z_{2} \right|^{2} \right\} represents a

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  3. Question 3

    Conic Sections. Asked once: 2 Apr 2025

    75
    The absolute difference between the squares of the radii of the two circles passing through the point (−9,4)(-9,4) and touching the lines x+y=3x+y=3 and x−y=3x-y=3, is equal to

  4. Question 4

    Definite Integration. Asked once: 31 Jan 2024

    81
    If the integral 525∫0π2sin⁡2xcos⁡112x(1+cos⁡52x)12dx525\int_{0}^{\frac{\pi}{2}} \sin2x\cos^{\frac{11}{2}}x\left( 1 +\cos^{\frac{5}{2}}x \right)^{\frac{1}{2}}dx is equal to (n2−64)(n\sqrt{2}- 64), then nn is equal to

  5. Question 5

    Limits and Continuity. Asked once: 2021 Paper 25

    76
    The value of lim⁡h→02{3sin⁡(π6+h)−cos⁡(π6+h)3h(3cos⁡h−sin⁡h)}\lim_{h\rightarrow 0} 2\left\{ \frac{\sqrt{3}\sin\left( \frac{\pi}{6}+h \right)- \cos\left( \frac{\pi}{6}+h \right)}{\sqrt{3}h(\sqrt{3}\cos h - \sin h)} \right\} is:

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