When a string is divided into three segments of length l₁, l₂, and l₃ the fundamental frequencies of these three segments are v₁, v₂, and v₃ respectively. The original fundamental frequency (v) of the string is

• 

• v = v₁ +v₂ +v₃

• 
• 

A 200 W sodium street lamp emits yellow light of wavelength 0.6 um. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

• 1.5 x 10²⁰

• 6 x 10¹⁸

• 62 x 10²⁰

• 62 x 10²⁰

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

• a line perpendicular to the plane of rotation

• the line making an angle of 45^o to the plane of rotation

• the radius

• the radius

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

Two persons of masses 55 kg and 65 kg respectively. are at the opposite ends of the boat. The length of the boat is 3.0 m and weigh 100 kg. The 55 kg man walks to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by

• 3.0 m

• 2.3 m

• zero

• zero

6.

The height at which the weight of a body becomes 1/16th, its weight on the surface of earth (radius R), is

• 5R

• 15 R

• 3R

• 3R

A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is 45^o, the speed of the car is 

• 20 ms^-1

• 30ms^-1

• 5 ms^-1

• 5 ms^-1

The motion of a particle along a straight line is described by equation
 x=8+12 t -t³

where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is

• 24 ms^-2

• zero

• 6 ms^-2

• 6 ms^-2

ABC is an equilateral triangle with O as its centre F₁, F₂ and F₃ represent three forces acting on the sides AB, BC and AC respectively. If the total torque about O zero then the magnitude of F₃ is

• F₁ +F₂

• F₁ - F₂

• F₁ +F₂/2

• F₁ +F₂/2

A particle has initial velocity (2i+3j) and acceleration (0.31i +0.2j). The magnitude of velocity after 10 s will be

•  units
•  units

• 5 units

• 5 units