The pulmonary trunk originates from which of the following?

The value of $k$ such that the lines $2x - 3y + k = 0$,$3x - 4y - 13 = 0$,and $8x - 11y - 33 = 0$ are concurrent,is

What is the percentage of lead in a lead pencil (in $\%$)?

$A$ motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times,the power of the motor is increased to $P_1$. The ratio of $P_1$ to $P_0$ is

If $y_k$ is the $k$-th derivative of $y$ with respect to $x$, and $y = \cos(\sin x)$, then $y_1 \sin x + y_2 \cos x$ is equal to

The upper half of an inclined plane with an angle of inclination $\phi$ is smooth, while the lower half is rough. $A$ body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is