List of practice Questions

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

n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one of them will not get any object is

If 1,\(log_9\)(\(3^{1-x}+2\)).\(log_3\)(\(4.3^x-1\)) are in A.P. then \(x\) equals

If the vertices of a square z₁,z₂,z₃ and z₄ taken in the anti-clockwise order, then z₃=

Reflection of the line \(\bar{a}z\)+\(a\bar{z}\)=0 in the real axis is given by

The average length of all vertical chords of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), \(a \leq x\leq 2a\), is

A cylinder of mass m and material density ρ hanging from a string is lowered into a vessel of cross - sectional area A containing a liquid of density σ (< ρ) until it is fully immersed. The increase in pressure at the bottom of the vessel is:

A cylindrical vessel, open at the top, contains 15 liters of water. Water drains out through a small opening at the bottom. 5 liters of water comes out in time t1, the next 5 litre in further time t₂, and the last 5 litre in further time t₃. then:

A, B are fixed points with coordinates (0,a) and (0,b) (a>0,b>0). P is a variable point (x,0) referred to as the rectangular axis. If the angle \(\angle\)APB is maximum, then