The centres of those circles which touch the circle, $$x^2+y^2-8x-8y-4=0$$, externally and also touch the $$x$$-axis, lie on :

If one of the diameters of the circle, given by the equation, $$x^2+y^2-4x+6y-12=0,$$ is a chord of a circle $$S$$, whose centre is at $$(-3,2)$$, then the radius of $$S$$ is :

Equation of the tangent to the circle, at the point (1, −1), whose centre is the point of intersection of the straight lines x − y = 1 and 2x + y = 3 is :

A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?

If the tangent at a point on the ellipse {{{x^2}} \over {27}} + {{{y^2}} \over 3} = 1 meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :

Let P = {$$\theta$$ : sin$$\theta$$ $$-$$ cos$$\theta$$ = $$\sqrt{2}\cos \theta$$} and Q = {$$\theta$$ : sin$$\theta$$ + cos$$\theta$$ = $$\sqrt{2}\sin \theta$$} be two sets. Then

Let a, b $$\in$$ R, (a $$\ne$$ 0). If the function f defined as f\left( x \right) = \left\{ {\matrix{ {{{2{x^2}} \over a}\,\,,} & {0 \le x < 1} \cr {a\,\,\,,} & {1 \le x < \sqrt 2 } \cr {{{2{b^2} - 4b} \over {{x^3}}},} & {\sqrt 2 \le x < \infty } \cr } } \right. is continuous in the interval [0, $$\infty$$), then an ordered pair ( a, b) is :

\mathop {\lim }\limits_{x \to 0} \,{{{{\left( {1 - \cos 2x} \right)}^2}} \over {2x\,\tan x\, - x\tan 2x}} is :

For $$x\in R,f\left(x\right)=\left|\log 2-\sin x\right|$$ and $$g\left(x\right)=f\left(f\left(x\right)\right),$$ then :

Let p = \mathop {\lim }\limits_{x \to {0^ + }} {\left( {1 + {{\tan }^2}\sqrt x } \right)^{{1 \over {2x}}}} then $$log$$ $$p$$ is equal to :

If the function f(x) = \left\{ {\matrix{ { - x} & {x < 1} \cr {a + {{\cos }^{ - 1}}\left( {x + b} \right),} & {1 \le x \le 2} \cr } } \right. is differentiable at x = 1, then {a \over b} is equal to :

If \mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} - {4 \over {{x^2}}}} \right)^{2x}} = {e^3}, then 'a' is equal to :

The number of x $$\in$$ [0, 2$$\pi$$ ] for which $$\left|\sqrt{2{\sin }^{4}x+18{\cos }^{2}x}-\sqrt{2{\cos }^{4}x+18{\sin }^{2}x}\right|=1$$ is :

If $$0\le x<2\pi$$, then the number of real values of $$x$$, which satisfy the equation $$\cos x+\cos 2x+\cos 3x+\cos 4x=0$$ is:

If the four letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is R and the fourth letter is E, then the total number of all such words is :

The sum $$\sum _{r=1}^{10}\left(r^2+1\right)\times \left(r!\right)$$ is equal to :

If {{{}^{n + 2}C{}_6} \over {{}^{n - 2}{P_2}}} = 11, then n satisfies the equation :

The value of \sum\limits_{r = 1}^{15} {{r^2}} \left( {{{{}^{15}{C_r}} \over {{}^{15}{C_{r - 1}}}}} \right) is equal to :

If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :

If x is a solution of the equation, $$\sqrt{2x+1}$$ $$-\sqrt{2x-1}=1,$$ \,\,\left( {x \ge {1 \over 2}} \right), then $$\sqrt{4x^2-1}$$ is equal to :