1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
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
$|\vec{c}| \leq \sqrt{11}$
2
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language
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
3
JEE Advanced 2022 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?
A
21816
B
85536
C
12096
D
156816
4
JEE Advanced 2022 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
If $M=\left(\begin{array}{rr}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right)$, then which of the

following matrices is equal to $M^{2022} ?$
A
$\left(\begin{array}{rr}3034 & 3033 \\ -3033 & -3032\end{array}\right)$
B
$\left(\begin{array}{ll}3034 & -3033 \\ 3033 & -3032\end{array}\right)$
C
$\left(\begin{array}{rr}3033 & 3032 \\ -3032 & -3031\end{array}\right)$
D
$\left(\begin{array}{rr}3032 & 3031 \\ -3031 & -3030\end{array}\right)$
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