List of top Questions asked in CPET

The value \( \Gamma\!\left(\dfrac{5}{2}\right) \) is:

Find the value of the integral
\[\int_{-1}^{1} x\,P_n(x)\,P_{n-1}(x)\,dx\]

The residue of \(\dfrac{z}{(z-a)(z-b)}\) at infinity is:

A long wire carrying a current \(i\) is bent to form a plane angle \(\alpha\). The magnetic field \(B\) at a point on the bisector of this angle situated at a distance \(x\) from the vertex is:

Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current be placed to experience no magnetic force?

A paramagnetic material is kept in a magnetic field. The field is increased till the magnetization becomes constant. If the temperature is now decreased, the magnetization:

The value of the integral
\[ I = \int_{0}^{2\pi} \frac{\cos 2\theta \, d\theta}{5 + 4\cos\theta} \]
is:

A non-conducting sheet of large surface area and thickness \(d\) contains uniform charge distribution of density \(\rho\). What is the electric field at a point \(P\) inside the plate, at a distance \(x\) from the central plane?

Two thin metallic spherical shells of radii \(r_1\) and \(r_2\) \((r_1 < r_2)\) are placed with their centres coinciding. A thermal conductivity material, \(K\), fills the space between the shells. The inner shell is maintained at a temperature \(\theta_1\) and the outer shell at temperature \(\theta_2\) \((\theta_1 < \theta_2)\). The rate at which heat flows radially through the material \(\dfrac{dQ}{dt}\), is:

A capacitor of capacitance \(C\) is given a charge \(Q\). At \(t = 0\), it is connected to an uncharged capacitor of equal capacitance through a resistance \(R\). The charge on the second capacitor as a function of time is:

The magnetic field that exists in a region is given by \(\vec{B} = B_0\left[1 + \dfrac{x}{l}\right]\hat{k}\). A square loop of edge \(l\) carrying a current \(i\) is placed with its edges parallel to the X and Y axes. The magnitude of the net magnetic force experienced by the loop is:

An ideal gas is taken through a process in which the pressure and volume change according to the equation \(P = kV\). The molar heat capacity of the gas for the process is given by:

A Young's double slit apparatus has slits separated by \(0.28\,\text{mm}\) and a screen \(48\,\text{cm}\) away from the slits. The whole apparatus is immersed in water, and the slits are illuminated by red light \(\lambda=700\,\text{nm}\) in vacuum. The fringe width of the pattern formed on the screen is:

A source emitting a sound of frequency \(v\) is placed at a large distance from an observer. The source starts moving towards the observer with uniform acceleration \(a\). The speed of sound in the medium is \(v\). The frequency the observer hears, corresponding to the wave emitted just after the source starts, is:

What is the terminal velocity of a raindrop of radius \(0.01\,\text{mm}\), where the coefficient of viscosity is \(1.8\times10^{-5}\,\text{N-s/m}^2\) and its density is \(1.2\,\text{kg/m}^3\), density of water \(=1000\,\text{kg/m}^3\)? (Take \(g=10\,\text{m/s}^2\))

A guitar string is \(90\,\text{cm}\) long and has a fundamental frequency of \(124\,\text{Hz}\). Where should it be pressed to produce a fundamental frequency of \(186\,\text{Hz}\)?

If the sound level in a room is increased from \(50\,\text{dB}\) to \(60\,\text{dB}\), by what factor is the pressure amplitude increased?

Two mercury drops each of radius \(r\) merge to form a bigger drop. If the surface tension of mercury is \(S\), the surface energy released is:

A U-tube containing liquid is accelerated horizontally with a constant acceleration \(a_0\). If the separation between the vertical limbs is \(l\), then the difference in the heights of the liquid in the two arms is:

Water and mercury are filled in two cylindrical vessels up to the same height. Both the vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are \(V_1\) and \(V_2\) respectively, then the relation between \(V_1\) and \(V_2\) is:

A uniform heavy rod of weight \(W\), cross-sectional area \(A\), and length \(L\) is hanging from a fixed support. Young's modulus of the material of the rod is \(Y\). Neglect the lateral contraction. The elongation of the rod is:

Three simple harmonic motions of equal amplitudes \(A\) and equal time periods in the same direction combine. The phase of the second motion is \(60^\circ\) ahead of the first and the phase of the third motion is \(60^\circ\) ahead of the second. The amplitude of the resultant motion will be:

A spherical ball of mass \(m\) and radius \(r\) rolls without slipping on a rough concave surface of large radius \(R\). It makes small oscillations about the lowest point. The time period is:

The gravitational field in a region is given by \(\vec{E} = (2\hat{i} + 3\hat{j})\ \text{N/kg}\). The amount of work done by the gravitational field when a particle is moved on the line \(3y + 2x = 5\) is:

A solid sphere rolling on a rough horizontal surface with linear speed \(v\) collides elastically with a fixed, smooth vertical wall. The speed of the sphere after it has started pure rolling in the backward direction is: