Kinematics

JEE Main level, single correct, medium

150 of 308

Question 150 of 308

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u→\overrightarrow{\mathrm{u}} and the other from rest with uniform acceleration f→\overrightarrow{\mathrm{f}}. Let α\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.

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Answer: (A) ucos⁡αf\frac{u \cos \alpha}{f}

Using nCr+nCr−1=n+1Cr=nCr+1+n⏟Cr−1+nCr+nCr=nCr+1+n+1Cr+nCr{ }^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+1Cr+1+n+1Cr⇒n+2Cr+1{ }^{n+1} C_{r+1}+{ }^{n+1} C_r \Rightarrow{ }^{n+2} C_{r+1}

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