The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $\pi$)

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to

The product$(s)$ formed when $H_2O_2$ reacts with disodium hydrogen phosphate is

$A$ 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 .... $Hz$.

One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

The first compound of inert gases was prepared by scientist Neil Bartlett in $1962$. This compound is