Two massless springs with spring constants 2k and 9k carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then the ratio of their respective amplitude will be
The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assume that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:
The bulk modulus of a liquid is 3 × 1010 Nm-2. The pressure required to reduce the volume of liquid by 2% is
One mole of ideal gas goes through process then change in temperature of the gas when volume changes from V = 1 m3 to 2 m3 is:
A piece of copper having a rectangular cross-section of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain? Take Young's modulus of copper as 42 × 109Pa
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 nuclei. The time taken for the ratio of the number of nuclei to become (1/e)2 will be:
A planet of mass M is revolving around sun in an elliptical orbit. If dA is the area swept in a time dt, angular momentum can be expressed as
Four equal masses m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be:
An insulator plate is passed through the plates of a capacitor as shown. The current
Two cars are moving in same direction with speed of 30 kmph. They are separated by a distance of 5 km. What is the speed of a car moving in opposite direction if it meets the two cars at an interval of 4 min?
A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104 N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to
In an LCR circuit as shown below, both switches are open initially. Later, switch S1 is closed and S2 is kept open. (q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statements is correct?
As shown in the given figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest, the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be
When dilute H2SO4 is electrolysed at room temperature between Pt electrodes. The substance liberated at anode is
Consider the reaction:
P + 2Q → R
When concentration of Q alone was tripled, the half-life did not change. When the concentration of P alone was made four times, the rate increased two times. The unit of rate constant for this reaction would be
For a hypothetical reaction A → B, the activation energy for forward and backward reactions are 19 kJ/mol and 9 kJ/mol respectively. The heat of reaction is
A and B are square matrices of the same order. Which is correct?
If A and B are two matrices such that AB=B and BA=A, then A2+B2=
The curve represented by Im (z2) = K where K is a non-zero real number is
The system of equations
2x + 2y - 3z - 1 = 0
4x + 4y + z -2 = 0
6x + 6y - z -3 = 0
has-
If a,b,c are position vectors of vertices ABC, then the position vector of a centroid of ∆ABC is
10 tests
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