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Day 607: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 2021 Paper 7

    71
    In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

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  2. Question 2

    Sequences and Series. Asked once: 30 Jan 2023

    152
    Let a,b,c>1,a3,b3a,b,c > 1,a^{3},b^{3} and c3c^{3} be in A.P., and log⁡ab,log⁡ca\log_{a}b,\log_{c}a and log⁡bc\log_{b}c be in G.P. If the sum of first 20 terms of an A.P., whose first term is a+4b+c3\frac{a + 4b + c}{3} and the common difference is a−8b+c10\frac{a - 8b + c}{10} is -444 , then abc is equal to:

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  3. Question 3

    Straight Lines. Asked once: 2021 Paper 17

    72
    Two sides of a parallelogram are along the lines 4x+5y=04x+ 5y= 0 and 7x+2y=07x+ 2y= 0. If the equation of one of the diagonals of the parallelogram is 11x+7y=911x+ 7y= 9, then other diagonal passes through the point:

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  4. Question 4

    Application of Derivatives. Asked once: 2021 Paper 24

    69
    The function f(x)=x3−6x2+ax+bf(x) =x^{3}- 6x^{2}+ ax + b is such that f(2)=f(4)=0f(2) = f(4) = 0. Consider two statements. (S1) there exists x1,x2∈(2,4),x1<x2x_{1},x_{2}\in (2,4),x_{1}<x_{2}, such that f′(x1)=−1f^{'}\left( x_{1} \right)= - 1 and f′(x2)=0f^{'}\left( x_{2} \right)= 0. (S2) there exists x3,x4∈(2,4),x3<x4x_{3},x_{4}\in (2,4),x_{3}<x_{4}, such that ff is decreasing in (2,x4)\left( 2,x_{4} \right), increasing in (x4,4)\left( x_{4},4 \right) and 2f′(x3)=3f(x4)2f^{'}\left( x_{3} \right)=\sqrt{3}f\left( x_{4} \right). Then

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  5. Question 5

    Complex Numbers. Asked once: 2021 Paper 11

    48
    If zz and ω\omega are two complex numbers such that ∣zω∣=1|z\omega| = 1 and arg(z)−arg(ω)=3π2arg(z) - arg(\omega) =\frac{3\pi}{2}, then arg(1−2zˉω1+3zˉω)arg\left( \frac{1 - 2\bar{z}\omega}{1 + 3\bar{z}\omega} \right) is : (Here arg(z)arg(z) denotes the principal argument of complex number z)

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