The value of $\cos\, 120^{\circ}$ is .....

If $log_{10} (xy) = 2$,then the value of $xy$ is

If $x^3+3xy+y^3=1$,then the correct option$(s)$ is/are:-
$(A) \left(\frac{dy}{dx}\right)_{(1,1)}=-1$
$(B) \left(\frac{dy}{dx}\right)_{(1,1)}=-2$
$(C) \left(\frac{dy}{dx}\right)_{(1,0)}=-1$
$(D) \left(\frac{dy}{dx}\right)_{(1,0)}=-3$

The value of $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\ldots$ up to $\infty$ is

If $y = x + \frac{1}{x}$,then

${d \over {dx}}({x^2}{e^x}\sin x) = $