JEE Advanced 2017 Paper 1

Velocity of the wave depends upon the tension in the rope and mass per unit length of the rope.
⇒ Velocity is independent of frequency and wavelength
Option (B) is correctSince tension at the mid point is same, therefore speeds at that point will also be same. Option (A) is correct.Since the direction of motion of pulses is opposite, velocities will be equal and opposite. With this point of view A will be incorrect.
Since the velocities at position is dependent only on tension at every point (µ = constant) therefore time taken for the wave the reach A from O and O from A will be same.
TOA=TAO
Option (D) is correct
v=λv
Since v depends on source
⇒λ∝v⇒λ∝√T
Tension decreases as we move from O to A, therefore λ becomes shorter. Option (C) is incorrect.