Application of ...

If there is an error of $$0.01 cm$$ in the diameter of a sphere then percentage error in surface area when the radius $$= 5 cm$$, is

If errors of $$1\%$$ each are made in the base radius and height of a cylinder, then the percentage error in its volume is

If $$y = 4x - 5$$ is a tangent to the curve $$\displaystyle y^2 = px^3 + q$$ at $$(2, 3)$$, then

The point(s) at each of which the tangents to the curve $$\displaystyle y = x^3 - 3x^2 - 7x + 6$$ cut off on the positive semi axis $$OX$$ a line segment half that on the negative semi axis $$OY$$, then the co-ordinates of the point(s) is/are give by:

If the tangent to the curve $$xy + ax + by = 0$$ at (1, 1) makes an angle $$\displaystyle \tan ^{-1}(2)$$ with x-axis, then $$\displaystyle a + 2b$$ is equal to

If the tangent at each point of the curve $$\displaystyle y=\frac { 2 }{ 3 } { x }^{ 3 }-2a{ x }^{ 2 }+2x+5$$ makes an acute angle with the positive direction of x-axis, then 

The set of values of $$a$$ for which the function $$\displaystyle f(x) = (4a - 3) (x + \ln5) + 2(a - 7) \cot \frac {x}{2} \sin^2 \frac {x}{2}$$ does not posses critical points in its domain is

Let $$f\left( x \right) =\left\{ \begin{matrix} { x }^{ { 3 }/{ 5 } }\quad \quad \quad  x\le 1 \\ -{ \left( x-2 \right)  }^{ 3 }\quad x>1 \end{matrix} \right. $$
then the number of critical points on the graph of the function is

Let $$f$$ be a decreasing function in $$(a,b]$$, then which of the following must be true?

$$\displaystyle f:(0, \infty) \rightarrow (-\frac {\pi}{2}, \frac {\pi}{2})$$ be defined as, $$\displaystyle f(x) = arc \: \tan( \: x)$$