1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of $$(\bar{z})^{2}+\frac{1}{z^{2}}$$ are integers, then which of the following is/are possible value(s) of $|z|$ ?
A
$\left(\frac{43+3 \sqrt{205}}{2}\right)^{\frac{1}{4}}$
B
$\left(\frac{7+\sqrt{33}}{4}\right)^{\frac{1}{4}}$
C
$\left(\frac{9+\sqrt{65}}{4}\right)^{\frac{1}{4}}$
D
$\left(\frac{7+\sqrt{13}}{6}\right)^{\frac{1}{4}}$
2
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Let $G$ be a circle of radius $R>0$. Let $G_{1}, G_{2}, \ldots, G_{n}$ be $n$ circles of equal radius $r>0$. Suppose each of the $n$ circles $G_{1}, G_{2}, \ldots, G_{n}$ touches the circle $G$ externally. Also, for $i=1,2, \ldots, n-1$, the circle $G_{i}$ touches $G_{i+1}$ externally, and $G_{n}$ touches $G_{1}$ externally. Then, which of the following statements is/are TRUE?
A
If $n=4$, then $(\sqrt{2}-1) r < R$
B
If $n=5$, then $r < R$
C
If $n=8$, then $(\sqrt{2}-1) r < R$
D
If $n=12$, then $\sqrt{2}(\sqrt{3}+1) r > R$
3
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Let $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let

\begin{aligned} & \vec{a}=3 \hat{\imath}+\hat{\jmath}-\hat{k} \text {, } \\ & \vec{b}=\hat{\imath}+b_{2} \hat{\jmath}+b_{3} \hat{k}, \quad b_{2}, b_{3} \in \mathbb{R} \text {, } \\ & \vec{c}=c_{1} \hat{\imath}+c_{2} \hat{\jmath}+c_{3} \hat{k}, \quad c_{1}, c_{2}, c_{3} \in \mathbb{R} \end{aligned}

be three vectors such that $b_{2} b_{3}>0, \vec{a} \cdot \vec{b}=0$ and

$$\left(\begin{array}{ccc} 0 & -c_{3} & c_{2} \\ c_{3} & 0 & -c_{1} \\ -c_{2} & c_{1} & 0 \end{array}\right)\left(\begin{array}{l} 1 \\ b_{2} \\ b_{3} \end{array}\right)=\left(\begin{array}{r} 3-c_{1} \\ 1-c_{2} \\ -1-c_{3} \end{array}\right) .$$

Then, which of the following is/are TRUE?
A
$\vec{a} \cdot \vec{c}=0$
B
$\vec{b} \cdot \vec{c}=0$
C
$|\vec{b}|>\sqrt{10}$
D
$|\vec{c}| \leq \sqrt{11}$
4
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
For $x \in \mathbb{R}$, let the function $y(x)$ be the solution of the differential equation

$$\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), \quad y(0)=0$$

Then, which of the following statements is/are TRUE ?
A
$y(x)$ is an increasing function
B
$y(x)$ is a decreasing function
C
There exists a real number $\beta$ such that the line $y=\beta \quad$ intersects the curve $y=y(x)$ at infinitely many points
D
$y(x)$ is a periodic function
2023
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
EXAM MAP
Joint Entrance Examination
Medical
NEET