MCQ
$\int_0^\pi {x\sin x\,dx = } $
- ✓$\pi $
- B$0$
- C$1$
- D${\pi ^2}$
==> $2I = \pi \int_0^\pi {\sin xdx = \pi [ - \cos x]_0^\pi \Rightarrow I = \pi } $.
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$E_1$ : Six fair dice are rolled and at least one die shows six.
$E_2$ : Twelve fair dice are rolled and at least two dice show six.
Let $p_1$ be the probability of $E_1$ and $p_2$ be the probability of $E_2$. Which of the following is true?
$\begin{bmatrix}1&-5\\0&4\end{bmatrix}=\begin{bmatrix}1&-1\\-2&2\end{bmatrix}\begin{bmatrix}3&-5\\2&0\end{bmatrix}$
$\begin{bmatrix}1&-5\\0&4\end{bmatrix}=\begin{bmatrix}1&-1\\0&1\end{bmatrix}\begin{bmatrix}3&-5\\-0&2\end{bmatrix}$
$\begin{bmatrix}1&-5\\2&0\end{bmatrix}=\begin{bmatrix}1&-3\\0&1\end{bmatrix}\begin{bmatrix}3&1\\-2&4\end{bmatrix}$
$\begin{bmatrix}1&-5\\2&0\end{bmatrix}=\begin{bmatrix}1&-1\\0&1\end{bmatrix}\begin{bmatrix}3&-5\\2&0\end{bmatrix}$
$\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\geq1\}$
$\{(\text{x},\text{y}):\text{y}^2\geq\text{x}\}$
$\{(\text{x},\text{y}):3\text{x}^2+4\text{y}^2\geq5\}$
$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$