Practice questions
88551 published questions with worked solutions.
- Let x and [x] denote the fractional part of x and the greatest integer x respectively of a real number x. If _0^n x dx, _0^n[x]dx...
- Let PQ be a diameter of the circle x^2+y^2=9. If and are the lengths of the perpendiculars from P and Q on the straight line, x +...
- If a =2 i + j +2 k , then the value of | i ( a i ) |^2+ | j ( a j ) |^2+ | k ( a k ) |^2 is equal to _________.
- A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of...
- In a resonance tube experiment when the tube is filled with water up to height of 17.0 cm from bottom, it resonates with a given...
- A helicopter reises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the...
- A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If...
- An electrical power line, having a total resistance of 2 , delivers 1 kW at 220 V. The efficiency of the transmission line is...
- Assume that the displacement(s) of air is proportional to the pressure difference ( p) created by a sound wave. Displacement(s)...
- A bullet of mass 5g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is...
- Number of molecules in a volume of 4 cm ^3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury...
- A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same...
- A physical quantity z depends on four observables a, b, c and d, as z= a^2b^ 2/3 c d^3 . The percentage of error in the...
- A galvanometer of resistance G is converted into a voltmeter of range 0 – 1V by connecting a resistance R_1 in series with it....
- A wheel is rotaing freely with an angular speed on a shaft. The moment of inertia of the wheel is I and the moment of inertia of...
- The value of the acceleration due to gravity is g_1 at a height h= R 2 (R = radius of the earth) from the surface of the earth....
- An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of...
- Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in...
- Two concentric circular coils, C_1 and C_2, are placed in the XY plane. C_1 has 500 turns, and a radius of 1 cm. C_2 has 200...
- A Force F =( i +2 j +3 k )N acts at a point (4 i +3 j - k )m. Then the magnitude of torque about the point ( i +2 j + k )m will...