List of practice Questions

The initial pressure and volume of an ideal gas are P0 and V0. The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{V_0}{4}\) will be(Given γ = ratio of specific heats at constant pressure and at constant volume)
In the network shown below, the charge accumulated in the capacitor in steady state will be
the charge accumulated in the capacitor
Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. 
Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of above statements, choose the correct answer from the options given below :
In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is
Given below are two statements:
Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.
In the light of above statements, choose the correct answer from the options given below :
The output from a NAND gate having inputs A and B given below will be.
The output from a NAND gate having inputs A and B
A car accelerates from rest to \( u \, \text{m/s} \). The energy spent in this process is \( E \, \text{J} \). The energy required to accelerate the car from \( u \, \text{m/s} \) to \( 2u \, \text{m/s} \) is \( nE \, \text{J} \). The value of \( n \) is.
A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be rad s-2
Two plates A and B have thermal conductivities 84 \(Wm^{-1}K^{-1}\) and 126 \(Wm^{-1}K^{-1}\) respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at 100 °C and 0 ºC respectively, then the temperature of the surface of contact in steady state is ________°C.
In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is ______g.
Three point charges q, –2q and 2q are placed on x-axis at a distance x = 0, x = \(\frac{3}{ 4}\) R and x = R respectively from origin as shown. If q = 2 × 10-6 C and R = 2 cm, the magnitude of net force experienced by the charge –2q is ________ N.
Three point charges q, –2q and 2q are placed on x-axis
A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.40 T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is (Take g = 10 ms-2).
A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads
An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross- sectional area 24 cm2. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 129. If an externally applied uniform magnetic field in the core along its axis changes from 1.5 T in one direction to 1.5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ________mC.
An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm. The net energy absorbed by the atom in this process is n × 10-4 eV. The value of n is____.[Assume the atom to be stationary during the absorption and emission process](Take h = 6.6 x 10-34 js and c = 3 x 108 m/s)
If the system of equations
2x + y - z = 5
2x -5y + λz = μ
x + 2y - 5z = 7
has infinitely many solutions, then (λ + μ)2 +  (λ - μ)2 is equal to
Let for A = \(\begin{bmatrix} 1 & 2 & 3 \\ \alpha & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix}\), |A| = 2. If |2adj (2adj (2A))| = 32n , then 3n + α is equal to
The coefficient of x5 in the expansion of \((2x^3 - \frac{1}{3x^2})^5\) is
Let a1, a2, a3, …. be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a2 + a4) (a4 + a6) is equal to
The value of \(\frac{e^{-\frac{\pi}{4}}+\int^{\frac{\pi}{4}}_{0}e^{-x}\tan^{50}x\ dx}{\int^{\frac{\pi}{4}}_{0}e^{-x}(\tan^{49}x+\tan^{51}x)dx}\) is
The area of the region \(\left\{(x,y):x^2≤y≤|x^2-4|,y≥1\right\}\) is 
Let the centre of a circle C be (α, β) and its radius r < 8. Let 3x + 4y = 24 and 3x – 4y = 32 be two tangents and 4x + 3y =1 be a normal to C. Then (α – β + r) is equal to
The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parellel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point
The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\) is
Let for a triangle ABC,
\(\vec{AB}=-2\hat{i}+\hat{j}+3\hat{k} \)
\(\vec{CB}=α\hat{i}+β\hat{j}+γ\hat{k} \)
\(\vec{CA}=4\hat{i}+3\hat{j}+δ\hat{k} \)
If \(δ>0\) and the area of the triangle ABC is \(5\sqrt6\), then \(\vec{CB}.\vec{CA}\) is equal to
Let A= {–4, –3, –2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A : b = |a| or b2 = a + 1} be a relation on A. Then the minimum number of elements, that must be added to the relation R so that it becomes reflexive and symmetric, is_____.