List of top Mathematics Questions

\(\int_{0}^{2\pi}\theta sin^6\theta cos\theta\,d\theta\) 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=e^{asin x}, where a is an arbitrary constant, is represented by the differential equation

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, 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

Given \(\frac{d^2y}{dx^2}=cot\,x\frac{dy}{dx}+4y\,cosec^2x=0\). Changing the independent variable x to z by the substitution z=log tan \(\frac{x}{2}\), the equation is changed to 

If y=\(\frac{x}{log_e|cx|}\) is the solution of the differential equation \(\frac{dy}{dx}=\frac{y}{x}+\phi(\frac{x}{y})\), then \(\phi (\frac{x}{y})\) is given by 

If \(\int \frac{dx}{(x+1)(x-2)(x-3)}=\frac{1}{k}log_e\left \{ \frac{|x-3|^3|x+1|}{(x-2)^4}\right \}+c\), then the value of k is 

The expression \(\frac{\int_{0}^{n}[x]dx}{\int_{0}^{n}\left \{ x\right \}dx}\), where [x] and {x} are respectively integral and fractional part of x and n∈N, is equal to

Let f:[1,3]\(\rightarrow\)R be continuous and be derivable in (1,3) and f'(x)=[f(x)]²+4∀x∈(1,3). Then

Let \(cos^{-1}\frac{y}{b}\)=\(log_e (\frac{x}{n})^n\), then Ay₂+By₁+Cy=0 is possible :  (where y₂=\(\frac{d^2y}{dx^2}\), y₁=\(\frac{dy}{dx}\))