The equation of a curve is given as $y = x^2 - 3x + 2$. The curve intersects the $x$-axis at

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

If $F = \frac{2}{\sin \theta + \sqrt{3} \cos \theta}$,then the minimum value of $F$ is

The graph of an exponential function $y = 2 + ae^{-x}$ is shown in the figure. What is the value of $a$?

The slope of the tangent to the curve $y = \ln(\cos x)$ at $x = \frac{3\pi}{4}$ is

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