Application of ...

If $$x+ 4y=14$$ is a normal to the curve $$y^2=\alpha x ^3-\beta $$ at $$(2,3)$$, then the value of $$\alpha+\beta$$ is

The slope of the tangent to the curve $$y= \sqrt {4-x^2}$$ at the point where the ordinate and the abscissa are equal is

The curve given by $$x+y=e^{xy}$$ has a tangent parallel to the y-axis at the point

The pressure P and volume V of a gas are connected by the relation $$PV^{1/4}=constant$$. The percentage increase in the pressure corresponding to a deminition of $$\dfrac12 \%$$ in the volume is

If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is

If there is an error of $$a \%$$ in measuring the edge of a cube, then the percentage error in its surface area is

While measuring the side of an equilateral triangle an error of $$k \%$$ is marked, the percentage error in its area is

If $$y=x^n$$, then the ratio of relative errors in $$y$$ and $$x$$ is

The circumference of a circle is measured as $$28 cm$$ with an error of $$0.01 cm$$. The percentage error in the area is

The height of a cylinder is equal to the radius. If an error of $$\alpha$$ % is made in the height, then percentage error in its volume is