If ${ }^n C_r$ denotes the number of combination of $n$ things taken $r$ at a time, then the expression ${…
If ${ }^n C_r$ denotes the number of combination of $n$ things taken $r$ at a time, then the expression ${ }^n C_{r+1}+{ }^n C_{r-1}+2 x^n C_r$ equals
${ }^{n+1} C_{r+1}$
${ }^{n+2} C_r$
${ }^{n+2} C_{r+1}$
${ }^{n+1} C_r$
Solution
After t; velocity $=\mathrm{f} \times \mathrm{t}$
$V_{B A}=\vec{f} t+(-\vec{u})=\sqrt{f^2 t^2+u^2-2 f u t \cos \alpha}$
For max. and min.
$\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{V}_{\mathrm{BA}}^2\right)=2 \mathrm{f}^2 \mathrm{t}-2 \mathrm{fu} \cos \alpha=0 \quad$ or $\quad \mathrm{t}=\frac{\mathrm{u} \cos \alpha}{\mathrm{f}}$
Therefore, total no. of values of $\mathrm{r}=33$.