Q225 / 225 · JEE Main 2003 · Physics

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $\overrightarrow{\mathrm{u}}$ and the other from rest with uniform acceleration $\overrightarrow{\mathrm{f}}$. Let $\alpha$ be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time.

  • Correct answer
    A
    $\frac{u \cos \alpha}{f}$
  • B
    $\frac{u \sin \alpha}{f}$
  • C
    $\frac{\mathrm{f} \cos \alpha}{\mathrm{u}}$
  • D
    u $\sin \alpha$.

Solution

Using ${ }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r={ }^n C_{r+1}+\underbrace{n} C_{r-1}+{ }^n C_r+{ }^n C_r={ }^n C_{r+1}+{ }^{n+1} C_r+{ }^n C_r$ ${ }^{n+1} C_{r+1}+{ }^{n+1} C_r \Rightarrow{ }^{n+2} C_{r+1}$

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

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