MCQ
$\int_0^{\pi /2} {} (\sin x - \cos x)\log (\sin x + \cos x)\,dx = $
- A$ - 1$
- B$1$
- ✓$0$
- DNone of these
Also as $x = 0$ to $\frac{\pi }{2},t = 1$ to $1$.
Since here limit is $'1$ to $1'$,
therefore the value of integral will be zero,
$\left\{ \because \int_{a}^{a}{f(x)dx=0} \right\}$ .
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$L_1: \frac{ x -1}{2}=\frac{ y -3}{1}=\frac{ z -2}{2}$
$L _2: \frac{ x -2}{1}=\frac{ y -2}{2}=\frac{ z -3}{3}$
A line $L _3$ having direction ratios $1,-1,-2$, intersects $L _1$ and $L _2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is
$1.$ The number of matrices in $\Omega$ is
$(A)$ $12$ $(B)$ $6$ $(C)$ $9$ $(D)$ $3$
$2.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique solution, is
$(A)$ less than $4$
$(B)$ at least $4$ but less than $7$
$(C)$ at least $7$ but less than $10$
$(D)$ at least $10$
$3.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is
$(A)$ $0$ $(B)$ more than $2$ $(C)$ $2$ $(D)$ $1$