List of practice Questions

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:

If \(\frac{1}{6}\)sinθ.cosθ.tanθ are in G.P, then the solution set θ is

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

The number of ways in which the letter of the word 'VERTICAL' can be arranged without changing the order of the vowels is

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

A missile is fired from the ground level rises x meters vertically upwards in t sec, where \(x=100t-\frac{25}{2}t^2\). the maximum height reached is

The dimensions of four wires if the same material are given below. The increase in length is maximum in the wire of :

Let f(x)=\(\begin{Bmatrix} x+1&\,\,\,-1\leq x\leq 0\\ -x&\,\,\,\,\,0<x\leq1 \end{Bmatrix}\)

A man weighing 75 kg is standing in a lift. The weight of the man standing on a weighing machine kept in the lift when the lift is moving downwards freely under gravity is:

If a hyperbola passes through the point P(\(\sqrt{2},\sqrt{3}\)) and has foci at (±2,0), then the tangent to this hyperbola at P is

The displacement of a particle executing simple harmonic motion is given by x = 2cos(t) where t is the time in seconds then the time period of the particle is: