The domain of {\sin ^{ - 1}}\left[ {{{\log }_3}\left( {{x \over 3}} \right)} \right] is

The period of $${\sin }^2\theta$$ is

Two common tangents to the circle $$x^2+y^2=2a^2$$ and parabola $$y^2=8ax$$ are :

\mathop {\lim }\limits_{n \to \infty } {{{1^p} + {2^p} + {3^p} + ..... + {n^p}} \over {{n^{p + 1}}}} is

$$I_n=\underset{0}{\overset{\pi /4}{\int }}{\tan }^{n}xdx$$ then $$\underset{n\to \infty }{\lim }n\left[I_n+I_{n+2}\right]$$ equals

$$\underset{0}{\overset{10\pi }{\int }}\left|\sin x\right|dx$$ is

$$\underset{0}{\overset{2}{\int }}\left[x^2\right]dx$$ is

\int_{ - \pi }^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} dx is

If $$y=f(x)$$ makes +$$ve$$ intercept of $$2$$ and $$0$$ unit on $$x$$ and $$y$$ axes and encloses an area of $$3/4$$ square unit with the axes then $$\underset{0}{\overset{2}{\int }}x{f}^{\prime }\left(x\right)dx$$ is

If $$\left|z-4\right|<\left|z-2\right|$$, its solution is given by :

z and w are two nonzero complex numbers such that $$\left|z\right|=\left|w\right|$$ and Arg z + Arg w =$$\pi$$ then z equals

The locus of the centre of a circle which touches the circle $$\left|z-z_1\right|=a$$ and$$\left|z-z_2\right|=b$$ externally ($$z,z_1\&z_2$$ are complex numbers) will be :

If the chord y = mx + 1 of the circle $$x^2+y^2=1$$ subtends an angle of measure $$45^{\circ }$$ at the major segment of the circle then value of m is :

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $$x^2+y^2=9$$ is :

The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $$3$$$$a$$ is :

The centres of a set of circles, each of radius 3, lie on the circle $$x^2+y^2=25$$. The locus of any point in the set is :

\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}} is

Let $$f(2)=4$$ and $$f^{\prime }(x)=4.$$ Then \mathop {\lim }\limits_{x \to 2} {{xf\left( 2 \right) - 2f\left( x \right)} \over {x - 2}} is given by

\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}, $$n\in N$$, ( [x] denotes the greatest integer less than or equal to x )