List of practice Questions

A copper disc of radius 0.1 m rotates about an axis passing through its center and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of 0.1 T. The emf induced across the radius of the disc is:

Metal detector works on the principle of

If x=sinθ and y=sin kθ, then (1-x²)y₂-xy₁-αy=0, for α=

If γ is the susceptibility and μr is the relative permeability of a ferromagnetic substance, then

\(\int_{0}^{2\pi}\theta sin^6\theta cos\theta\,d\theta\) is equal to

In the interval (-2\(\pi\),0), the function f(x)=sin(\(\frac{1}{x^3}\)).

It is found that a non-zero current is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is:

A wire of resistance 2R is stretched such that its length is doubled. Then the increase in its resistance is:

The value of \(\lim_{n\rightarrow\infty}[(\frac{1}{2.3}+\frac{1}{2^2.3})+(\frac{1}{2^2.3^2}+\frac{1}{2^3.3^2})+.....+(\frac{1}{2^n.3^n}+\frac{1}{2^{n+1}.3^n})]\)

The family of curves y=e^{asin x}, where a is an arbitrary constant, is represented by the differential equation

The effective capacitance between points A and B shown in the circuit is:

If the electrical potential at a point on the surface of a hollow conducting sphere of radius R is V, then the electric potential at a point which is at a distance R/3 from the centre of the sphere is:

A point source of light is placed at the focus of a concave mirror. Consider only paraxial rays. The shapes of the wavefronts of incident and reflected lights respectively are:

Two convex lenses of focal lengths 20 cm and 30 cm are placed in contact with each other co-axially. The focal length of the combination is:

A source and an observer move away from each other with same velocity of 10 m^-1 with respect to the ground. If the observer finds the frequency of sound coming from the source as 1980 Hz, then the actual frequency of the source is (speed of sound in air = 340 ms^-1)

Among the following statements, the correct statement for a wave is:

N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in a vessel which is maintained at a temperature T. The mean square velocity of the molecules of gas B is denoted by V₂² and the mean square of the x-component velocity of the molecules of gas B is denoted by V₁², then V₁\V₂ is:

If the ratio of densities of two substances is 5:6 and the ratio of their specific heat capacities is 3:5, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is:

The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of:

Let x be a nonvoid set.If ρ1 and ρ2 be the transitive relations of x, then-(° denotes the compositions of relations )

Let A and B be two independent events. The probability that both A and B happens is \(\frac{1}{12}\) and the probability that neither A nor B happens is \(\frac{1}{2}\). Then

If the matrix M_r is given by M_r=\(\begin{pmatrix}r &r-1 \\ r-1&r \end{pmatrix}\) for r=1,2,3....then det(M₁)+det(M₂)+.......+det(M₂₀₀₈)=

Let \(A=\begin{pmatrix}2&0&3\\4&7&11\\5&4&8\end{pmatrix}\). Then

Let \(P(n)=3^{2n+1}+2^{n+2}\) where n∈N. Then

If one root of \(x^2+px-q^2=0\), p and q are real, be less than 2, and other be greater than 2. Then