MCQ
If $A$ and $B$ are two sets then $(A -B) \cup (B -A) \cup (A \cap B)$ is equal to
- ✓$A \cup B$
- B$A \cap B$
- C$A$
- D$B'$
$\therefore (A - B)\, \cup (B - A) \cup (A \cap B) = A \cup B$.
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$x+y+z=2$
$x+2 y+3 z=5$
$x+3 y+\lambda z=\mu$
has infinitely many solutions are, respectively
$\lim _{n \rightarrow 0^{+}} \int_n^{1-n} t^{-3}(1-t)^{a-1} d t$
exists. Let this limit be $g(a)$. In addition, it is given that the function $g(a)$ is differentiable on $(0,1)$.
$1.$ The value of $g\left(\frac{1}{2}\right)$ is
$(A)$ $\pi$ $(B)$ $2 \pi$ $(C)$ $\frac{\pi}{2}$ $(D)$ $\frac{\pi}{4}$
$2.$ The value of $g ^{\prime}\left(\frac{1}{2}\right)$ is
$(A)$ $\frac{\pi}{2}$ $(B)$ $\pi$ $(C)$ $-\frac{\pi}{2}$ $(D)$ $0$
Give the answer question $1$ and $2.$