MCQ
Which of the following represents collinear but not equal vectors:
- ✓$a, c$
- B$b, d$
- C$b, m$
- DBoth $(a)$ and $(b)$
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$(I)$ The curve $y=f(x)$ intersects the $x$-axis exactly at one point
$(II)$ The curve $y=f(x)$ intersects the $x$-axis at $\mathrm{x}=\cos \frac{\pi}{12}$
Then
The number of points in $[0, \pi]$ at which the function $f$ is continuous is
$\lim _{n \rightarrow 0^{+}} \int_n^{1-n} t^{-3}(1-t)^{a-1} d t$
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 $2.$