Practice questions
88551 published questions with worked solutions.
- If the line, x-1 2 = y+1 3 = z-2 4 meets the plane, x + 2y + 3z = 15 at a point P, then the distance of P from the origin is:
- A plane passing through the points (0, −1, 0) and (0, 0, 1) and making an angle 4 with the plane y − z + 5 = 0, also passes...
- If the tangent to the curve, y = x^3 + ax - b at the point (1, −5) is perpendicular to the line, −x + y + 4 = 0, then which one...
- If the fourth term in the Binomial expansion of ( 2x + x^ _8x )^6 (x > 0) is 20 8^7, then a value of x is:
- The area (in sq. units) of the region A = (x, y) : x^2 y x + 2 is:
- In the formula X = 5YZ^2, X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y...
- In free space, a particle A of charge 1 μC is held fixed at a point P. Another particle B of the same charge and mass 4 μg is...
- A bullet of mass 20 g has an initial speed of 1 ms^ -1 , just before it starts penetrating a mud wall of thickness 20 cm. If the...
- A coil of self inductance 10 mH and resistance 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω....
- Water from a tap emerges vertically downwards with an initial speed of 1.0 ms^ -1 . The cross-sectional area of the tap is 10^ -4...
- A submarine experiences a pressure of 5.05 10^ 6 Pa at a depth of d_1 in a sea. When it goes further to a depth of d_2, it...
- Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0, a sample has the same number of the two...
- A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet...
- A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the...
- A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of 7M 8 and is converted into...
- Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm^ -2 . If the surface has an area of...
- The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10...
- The time dependence of the position of a particle of mass m = 2 is given by r(t) = 2t , i - 3t^2 , j. Its angular momentum, with...
- A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on...
- A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is: [Given Planck's constant...