If $y=2x^3-2x^2+3x-5$,then for $x=2$ and $\Delta x=0.1$,the value of $\Delta y$ is:

The approximate value of $\log _{10} 99$ is (Given $\log _{10} e = 0.4343$)

An equilateral triangle has a side of $10$ units. If an error of $0.05$ units is made in measuring the side,then the percentage error in the area of the triangle is:

The radius and the height of a right circular solid cone are measured as $7 \text{ ft}$ each. If there is an error of $0.002 \text{ ft}$ for every foot in measuring them,then the error in the total surface area of the cone (in $\text{sq. ft}$) is:

The approximate value of $(1.0002)^{3000}$ is

Find the approximate value of $(0.999)^{\frac{1}{10}}$.