${\left( -\frac{1}{2} + \frac{\sqrt{3}}{2}i \right)^{1000}} = .....$

$A$ magnet makes $40$ oscillations per minute at a place having a magnetic field of $0.1 \times 10^{-5} \, T$. At another place, it takes $2.5 \, s$ to complete one vibration. The value of the Earth's horizontal magnetic field at that place is:

If $f(x)=2 x^4-13 x^2+a x+b$ is divisible by $x^2-3 x+2$,then $(a, b)$ is equal to

In $DNA$,the two polynucleotide chains are ...

If $y = (\sin x)^{\tan x}$,then $\frac{dy}{dx}$ is equal to

$A$ block of mass $2 \ kg$ slides down an inclined plane of inclination $30^{\circ}$. The coefficient of friction between the block and the plane is $0.5$. The contact force between the block and the plane is: