The motion of a particle in the XY plane is given by \( x(t) = 25 + 6t^2 \, \text{m} \); \( y(t) = -50 - 20t + 8t^2 \, \text{m} \). The magnitude of the initial velocity of the particle, \( v_0 \), is given by:
Consider a rope fixed at both ends under tension so that it is horizontal (i.e. assume the rope is along x-axis, with gravity acting along z-axis). Now the right end is continually oscillated at high frequency n (say n=100 Hz) horizontally and in a direction along the rope; amplitude of oscillation is negligible. The oscillation travells along the rope and is reflected at the left end.
Let the total length of rope be l, total mass be m and the acceleration due to gravity be g.
After initial phase (say a mintue or so), the rope has __(BLANK-1)__ wave, which is __(BLANK-2)__ in nature. It results from superposition of left travelling and right travelling __(BLANK-3)__ waves. This resulting wave has a frequency __ (BLANK-4)_ that of oscillation frequency nu. Simple dimensional analysis indicates that the frequency of can be of the form: ___(BLANK-5)__ .
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A) : 02 is liberated in the non-cyclic photophosphorylation.
Reason (R) : Liberation of oxygen is due to photolysis of water.
In the light of the above statements, choose the correct answer from the options given below
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A) : The Cro-Magnon man was the direct ancestor of the living modern man.
Reason (R) : Cro-Magnon man had slightly prognathous face.
In the light of the above statements, choose the correct answer from the options given below