MCQ
$\int_{}^{} {\frac{{dx}}{{2\sqrt x (1 + x)}} = } $
- A$\frac{1}{2}{\tan ^{ - 1}}(\sqrt x ) + c$
- ✓${\tan ^{ - 1}}(\sqrt x ) + c$
- C$2{\tan ^{ - 1}}(\sqrt x ) + c$
- Dએકપણ નહિ.
Put $\sqrt x \, = t$==> $\frac{1}{{2\sqrt x }}dx = dt$
$\therefore I = \int {\frac{{dt}}{{1 + {t^2}}}} = {\tan ^{ - 1}}t + c$$ = {\tan ^{ - 1}}(\sqrt x ) + c$.
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$1.$ If $1$ ball is drawn from each of the boxes $B_1, B_2$ and $B_3$, the probability that all $3$ drawn balls are of the same colour is
$(A)$ $\frac{82}{648}$ $(B)$ $\frac{90}{648}$ $(C)$ $\frac{558}{648}$ $(D)$ $\frac{566}{648}$
$2.$ If $2$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these $2$ balls are drawn from bo $B _2$ is
$(A)$ $\frac{116}{181}$ $(B)$ $\frac{126}{181}$ $(C)$ $\frac{65}{181}$ $(D)$ $\frac{55}{181}$
Give the answer question $1$ and $2.$