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Day 562: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 29 Jul 2022

    80
    Let f(x)=3(x2−2)3+4,x∈Rf(x) =3^{\left( x^{2}- 2 \right)^{3}+ 4},x \in R. Then which of the following statements are true? P:x=0P:x = 0 is a point of local minima of ff Q:x=2Q:x =\sqrt{2} is a point of inflection of ff R:f′R:f^{'} is increasing for x>2x >\sqrt{2}

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  2. Question 2

    Application of Integrals. Asked once: 6 Apr 2023

    84
    If the area of the region S={(x,y):2y−y2≤x2≤2y,x≥y}S =\left\{ (x,y):2y -y^{2}\leq x^{2}\leq 2y,x \geq y \right\} is equal to n+2n+1−πn−1\frac{n + 2}{n + 1}-\frac{\pi}{n - 1}, then the natural number nn is equal to

  3. Question 3

    Binomial Theorem. Asked once: 25 Jun 2022

    81
    Let CrC_{r} denote the binomial coefficient of xrx^{r} in the expansion of (1+x)10(1 + x)^{10}. If α,β∈R\alpha,\beta\in R. C1+3⋅2C2+5⋅3C3+…C_{1}+ 3 \cdot 2C_{2}+ 5 \cdot 3C_{3}+ \ldots upto 10 terms =α×2112β−1(C0+C12+C23+….=\frac{\alpha\times2^{11}}{2^{\beta}- 1}\left( C_{0}+\frac{C_{1}}{2}+\frac{C_{2}}{3}+ \ldots. \right.. upto 10 terms )) then the value of α+β\alpha+\beta is equal to

  4. Question 4

    Complex Numbers. Asked once: 29 Jan 2023

    69
    For two non-zero complex numbers z1z_{1} and z2z_{2}, if Re(z1z2)=0Re\left( z_{1}z_{2} \right)= 0 and Re(z1+z2)=0Re\left( z_{1}+z_{2} \right)= 0, then which of the following are possible? A. Im(z1)>0Im\left( z_{1} \right)> 0 and Im(z2)>0Im\left( z_{2} \right)> 0 B. Im(z1)<0Im\left( z_{1} \right)< 0 and Im(z2)>0Im\left( z_{2} \right)> 0 C. Im(z1)>0Im\left( z_{1} \right)> 0 and Im(z2)<0Im\left( z_{2} \right)< 0 D. Im(z1)<0Im\left( z_{1} \right)< 0 and Im(z2)<0Im\left( z_{2} \right)< 0 Choose the correct answer from the options given below:

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  5. Question 5

    Conic Sections. Asked once: 3 Apr 2025

    56
    A line passing through the point P(5,5)P(\sqrt{5},\sqrt{5}) intersects the ellipse x236+y225=1\frac{x^{2}}{36}+\frac{y^{2}}{25}= 1 at AA and BB such that (PA).(PB)(PA).(PB) is maximum. Then 5(PA2+PB2)5\left( PA^{2}+PB^{2} \right) is equal to:

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