Q116 / 225 · JEE Main 2003 · Mathematics

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

  • A
    ${ }^{n+1} C_{r+1}$
  • B
    ${ }^{n+2} C_r$
  • Correct answer
    C
    ${ }^{n+2} C_{r+1}$
  • D
    ${ }^{n+1} C_r$

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 $\mathrm{r}=33$.

Hence, the correct answer is option: 'C'.

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