The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60o. If the area of the quadrilateral is $$4\sqrt{3}$$, then the perimeter of the quadrilateral is :

A line drawn through the point P(4, 7) cuts the circle x2 + y2 = 9 at the points A and B. Then PA⋅PB is equal to :

If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles {\cos ^{ - 1}}\left( {{1 \over 7}} \right) and sec$$-$$1 (7) at the center respectivey, then the distance between these chords, is :

The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is :

The eccentricity of an ellipse whose centre is at the origin is {1 \over 2}. If one of its directrices is x = – 4, then the equation of the normal to it at \left( {1,{3 \over 2}} \right) is :

Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is {3 \over 5} and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is :

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is :

$$\underset{x\to 3}{\lim }$$ {{\sqrt {3x} - 3} \over {\sqrt {2x - 4} - \sqrt 2 }} is equal to :

The value of k for which the function f\left( x \right) = \left\{ {\matrix{ {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \cr {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \cr } } \right. is continuous at x = {\pi \over 2}, is :

\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\cot x - \cos x} \over {{{\left( {\pi - 2x} \right)}^3}}} equals

The value of tan-1 \left[ {{{\sqrt {1 + {x^2}} + \sqrt {1 - {x^2}} } \over {\sqrt {1 + {x^2}} - \sqrt {1 - {x^2}} }}} \right], \left| x \right| < {1 \over 2},x \ne 0, is equal to :

A value of x satisfying the equation sin[cot−1 (1+ x)] = cos [tan−1 x], is :

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is :

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:

If for a positive integer n, the quadratic equation $$x\left(x+1\right)+\left(x+1\right)\left(x+2\right)$$$$+....+\left(x+\overline{n-1}\right)\left(x+n\right)$$$$=10n$$ has two consecutive integral solutions, then n is equal to :

The sum of all the real values of x satisfying the equation 2(x$$-$$1)(x2 + 5x $$-$$ 50) = 1 is :

Let p(x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x$$-$$ 1 and it leaves remainder 6 when divided by x + 1; then :

A hyperbola passes through the point P$$\left(\sqrt{2},\sqrt{3}\right)$$ and has foci at $$\left(\pm 2,0\right)$$. Then the tangent to this hyperbola at P also passes through the point :

The locus of the point of intersection of the straight lines, tx $$-$$ 2y $$-$$ 3t = 0 x $$-$$ 2ty + 3 = 0 (t $$\in$$ R), is :