List of practice Questions

A radioactive sample contains 5 × 10\(^7\) kg of each of two isotopes A and B with half-lives of 5 days and 8 days respectively. The fraction of A that decays in 3 days after a period of 3 days is:
A string of length 3 m and mass 0.035 kg is stretched with a tension of 50 N. The speed of the wave on the string is:
Two bodies of the same mass are projected with the same velocity at an angle \( 30^\circ \) and \( 60^\circ \) respectively. The ratio of their horizontal ranges will be:
Two point charges \( +3 \, \mu C \) and \( +8 \, \mu C \) repel each other with a force of 40 N. If a charge of \( -5 \, \mu C \) is added to each of them, then the force between them will become:
A sphere rolls down an inclined plane of inclination \( \theta \). What is the acceleration as the sphere reaches the bottom?
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and same material such that P, Q, and R are now combined as shown in figure. The ray will now suffer
The current in the 120 \( \Omega \) resistor shown in the circuit is
Identify the correct statement.
The distance travelled by a particle starting from rest and moving with an acceleration \(3 \, \text{m/s}^2\) in the third second is:
Photocathode work function is \( 1 \, \text{eV} \). Light of wavelength \( \lambda = 3000 \, \text{Å} \) falls on it. The photoelectron comes out with a maximum velocity of \( 1 \times 10^6 \, \text{m/s} \). What is the energy of the photon?
A steam engine operating between \( 100^\circ C \) and \( 40^\circ C \) has an efficiency of \( 25% \). The heat absorbed by the engine is:
Two point charges \( +q \) and \( -q \) are placed at a distance \( d \) apart. The electric potential at the midpoint will be
Two wires A and B are of the same material. Their lengths are in the ratio \( 1:2 \) and the diameter is in the ratio \( 2:1 \). If they are pulled by the same force, then increase in length will be in the ratio of
If \( x = at + bt^2 \), where \( x \) is the distance travelled by the body in kilometers while \( t \) is the time in seconds, then the unit of \( b \) is
A soap bubble of radius \( r_1 \) is placed on another soap bubble of radius \( r_2 \) (\( r_1<r_2 \)). The radius \( R \) of the soapy film separating the two bubbles is
A charge \( q \) is moving with a velocity \( v \) parallel to a magnetic field \( B \). Force on the charge due to magnetic field is
Two spheres A and B of masses \( m \) and \( 2m \) and radii \( R \) and \( 2R \) respectively are placed in contact as shown. The COM of the system lies
The distance of the centres of moon and earth is \( D \). The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero?
From which of the options, six pieces of shape S can be cut?
The image shows distribution of marks secured by 2500 students of a particular district in four subjects. Which of the statements must be TRUE?
The top view of four objects, resting on a planar ground, is shown in black colour in the given figure. When light falls on them at an angle of 45 degrees from the ground in the direction marked in the image, corresponding shadows are formed on the ground. Which option(s) depict(s) the correct arrangement of the objects?
P shows the way a T-shirt is folded. Q shows the image of ink spilled over such a folded T-shirt. If the T shirt is unfolded and viewed from behind, which image most accurately represents the ink stain?
Figure P shows a square tile with a 4×4 grid marked on it. One of the ways the tile can be cut along the grid lines into two similar and contiguous pieces is shown in figure Q. The different configurations of this cut, shown in figure R, are counted as the same cut. In how many ways, excluding the cut shown in Q, can the tile be cut into two similar and contiguous pieces along the grid lines?
The image is made by overlapping the first word rotated 90 degrees clockwise with the second word rotated 90 degrees counter-clockwise. Which are the words?
An animation is shown of a person speaking. Which option most accurately matches this animation?