List of practice Questions

If x=sinθ and y=sin kθ, then (1-x2)y2-xy1-αy=0, for α=
\(\int_{0}^{2\pi}\theta sin^6\theta cos\theta\,d\theta\) is equal to
In the interval (-2\(\pi\),0), the function f(x)=sin(\(\frac{1}{x^3}\)).
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=easin 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: 

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)

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 Mr is given by Mr=\(\begin{pmatrix}r &r-1 \\ r-1&r \end{pmatrix}\) 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, 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
Let f(x)=\(\begin{Bmatrix}  x+1&\,\,\,-1\leq x\leq 0\\   -x&\,\,\,\,\,0<x\leq1    \end{Bmatrix}\)
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