The approximate value of $y=(1.01)^3+2(1.01)^{\frac{3}{2}}+5$ is

The approximate value of $\cos 31^{\circ}$ is (Take $1^{\circ} = 0.0174 \text{ rad}$)

$A$ point on the hypotenuse of a triangle is at distances $a$ and $b$ from the sides of the triangle. Show that the minimum length of the hypotenuse is $(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}$.

The approximate value of $\sin(60^{\circ} 0^{\prime} 10^{\prime \prime})$ is (given that $\sqrt{3}=1.732, 1^{\circ}=0.0175^{c}$):

The approximate value of the function $f(x) = x^{3} - 3x + 5$ at $x = 1.99$ is

The diameter of a sphere is measured as $42 \text{ cm}$. If there is an error of $1/77 \text{ cm}$ in measuring it, then the error involved in the volume of that sphere (in cubic centimeters) is