Application of ...

If $$f(x)=x^{3/2}(3x-10), x\ge-0)$$, then $$f(x)$$ is decreasing in

The numbers of tangent to the curve $$y - 2 = {x^5}$$  which are drawn
from point $$\left( {2,2} \right)$$ is/are 

If the curves $$\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{4}=1$$ and $$y^{2}=16x$$ intersect at right angles then value of $$a^{2}$$ is

Tangents are drawn from a point on the circle $$x^2+y^2=25$$ to the ellipse $$9x^2+16y^2-144=0$$ then the angle between the tangents is 

Slope of the line $$ \sqrt { { x }^{ 2 }+{ 4y }^{ 2 }-4xy+4 } +x-2y=1$$ equals to

The radius of the sphere is measured as $$ \left( {10 \pm 0.02} \right)cm$$. The error in the measurement of its volume is 

If the normal to the curve $$y=f\left( x \right)$$ at $${(3,4)}$$ makes angle $$\dfrac {3\pi}{4}$$ with $$\bar {OX}$$ then $$f^{ 1 }\left( 3 \right)=$$

Area of the triangle formed by the tangent, normal to the curve $$x^{2}/a^{2}+y^{2}/b^{2}=1$$ at the point $$(a/\sqrt{2} , b/\sqrt{2})$$ and the $$x-$$axis is

The inclination of the tangent at $$\theta = \dfrac {\pi}{3}$$ on the curve $$x = a(\theta + \sin \theta), y = a(1 + \cos \theta)$$ is

The greatest slope among the lines represented by the equation $$4x^2 - y^2 + 2y - 1 = 0 $$ is -