$A$ musical instrument $P$ produces sound waves of frequency $n$ and amplitude $A_P$. Another musical instrument $Q$ produces sound waves of frequency $\frac{n}{4}$. The waves produced by $P$ and $Q$ have equal energies. If the amplitude of waves produced by $P$ is $A_P$,the amplitude of waves produced by $Q$ will be: (in $A_P$)

Consider the set of all triangles $OPQ$ where $O$ is the origin and $P$,$Q$ are distinct points in the plane with non-negative integral coordinates $(x, y)$ such that $5x + y = 99$. The number of such distinct triangles whose area is a positive integer is:

Plants follow ...$A$... pathways in response to environment or phases of life to form different kinds of structures. This ability is called ...$B$.... Complete the given statement with the correct combination of options.

$A$ car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. The speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is .... $Hz$.

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity $V$. If the wire $AB$ is replaced by a semicircular wire of the same chord length,the magnitude of the induced current will

The negation of the statement pattern $\sim p \vee (q \rightarrow \sim r)$ is