Which of the following does not exist?

If $y=y(x)$ is the solution of the differential equation $\left(\frac{2+\sin x}{y+1}\right) \frac{d y}{d x}+\cos x=0$ with $y(0)=1$,then $y\left(\frac{\pi}{2}\right)$ is equal to

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency is doubled. The temperature of the source is ....... $^{\circ}C$.

The more commonly used baking powder contains about $30 \% NaHCO_3$,$20 \% NaAl(SO_4)_2$,$10 \% Ca(H_2PO_4)_2$ and $40 \% \text{starch}$. Which of the following statements is/are correct?

The length of the perpendicular from the point $P(2, -1, 4)$ to the straight line $\frac{x+3}{10} = \frac{y-2}{-7} = \frac{z}{1}$ is:

The points of intersection of the perpendicular tangents drawn to the ellipse $4x^2 + 9y^2 = 36$ lie on the curve: