If $$0<x<\pi$$ and \cos x + \sin x = {1 \over 2}, then $$\tan x$$ is :

If $$A$$ and $$B$$ are square matrices of size $$n\times n$$ such that $$A^2-B^2=\left(A-B\right)\left(A+B\right),$$ then which of the following will be always true?

Let A = \left( {\matrix{ 1 & 2 \cr 3 & 4 \cr } } \right) and B = \left( {\matrix{ a & 0 \cr 0 & b \cr } } \right),a,b \in N. Then

At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of $$5$$ phone calls during $$10$$ minute time intervals. The probability that there is at the most one phone call during a $$10$$-minute time period is :

If $$x^m.y^n={\left(x+y\right)}^{m+n},$$ then {{{dy} \over {dx}}} is

The differential equation whose solution is $$A{x}^2+B{y}^2=1$$ where $$A$$ and $$B$$ are arbitrary constants is of

If $$\left(a,a^2\right)$$ falls inside the angle made by the lines y = {x \over 2}, $$x>0$$ and $$y=3x,$$ $$x>0,$$ then a belong to :

A straight line through the point $$A(3,4)$$ is such that its intercept between the axes is bisected at $$A$$. Its equation is :

If the expansion in powers of $$x$$ of the function {1 \over {\left( {1 - ax} \right)\left( {1 - bx} \right)}} is $$a_0+a_{1}x+a_2{x}^2+a_3{x}^3.....$$ then $$a_n$$ is

For natural numbers $$m$$ , $$n$$, if $${\left(1-y\right)}^m{\left(1+y\right)}^n=1+a_{1}y+a_2{y}^2+..........$$ and $$a_1=a_2=10,$$ then $$\left(m,n\right)$$ is

The locus of the vertices of the family of parabolas y = {{{a^3}{x^2}} \over 3} + {{{a^2}x} \over 2} - 2a is :

The value of $$\underset{1}{\overset{a}{\int }}\left[x\right]f^{\prime }\left(x\right)dx,a>1$$ where $$\left[x\right]$$ denotes the greatest integer not exceeding $$x$$ is

\int\limits_{ - {{3\pi } \over 2}}^{ - {\pi \over 2}} {\left[ {{{\left( {x + \pi } \right)}^3} + {{\cos }^2}\left( {x + 3\pi } \right)} \right]} dx is equal to

$$\underset{0}{\overset{\pi }{\int }}xf\left(\sin x\right)dx$$ is equal to

The value of \sum\limits_{k = 1}^{10} {\left( {\sin {{2k\pi } \over {11}} + i\,\,\cos {{2k\pi } \over {11}}} \right)} is :

If $$z^2+z+1=0$$, where z is complex number, then value of {\left( {z + {1 \over z}} \right)^2} + {\left( {{z^2} + {1 \over {{z^2}}}} \right)^2} + {\left( {{z^3} + {1 \over {{z^3}}}} \right)^2} + .......... + {\left( {{z^6} + {1 \over {{z^6}}}} \right)^2} is :

If the lines $$3x-4y-7=0$$ and $$2x-3y-5=0$$ are two diameters of a circle of area $$49\pi$$ square units, the equation of the circle is :

Let $$C$$ be the circle with centre $$(0,0)$$ and radius $$3$$ units. The equation of the locus of the mid points of the chords of the circle $$C$$ that subtend an angle of {{2\pi } \over 3} at its center is :

In the ellipse, the distance between its foci is $$6$$ and minor axis is $$8$$. Then its eccentricity is :

Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R=\{(x,y)\in W\times W\mid$ the words $x$ and $y$ have at least one letter in common}. Then, $R$ is