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

The side of a square is increasing at the rate of $0.2\,cm/s$. The rate of increase of perimeter with respect to time is $...........\,cm/s$.

Which of the following relation$(s)$ is/are correct?
$(A)\ \sin (90^{\circ}+\theta)=\cos (-\theta)$
$(B)\ \sin (180^{\circ}-\theta)=\cos (90^{\circ}-\theta)$
$(C)\ \sin (360^{\circ}-\theta)=\cos (360^{\circ}-\theta)$
$(D)\ \sin (180^{\circ}+\theta)=\cos (90^{\circ}-\theta)$

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

$\frac{d}{dx}(\sin 30^\circ)$ is equal to

$\int\limits_0^{\frac{\pi }{4}} {\sin 2x} \,dx$ is equal to