The driver of a car travelling with speed $30 \,m/s$ towards a hill sounds a horn of frequency $600 \,Hz$. If the velocity of sound in air is $330 \,m/s$,the frequency of reflected sound as heard by the driver is ........ $Hz$.

The resistance of a wire is $R$. If the length of the wire is doubled by stretching,then the new resistance will be

If $\lim _{x \rightarrow 0}\left(\frac{\cos 4 x+a \cos 2 x+b}{x^4}\right)$ is finite,then the values of $a, b$ are respectively :

The centre of mass of a system of particles does not depend on:

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why?
${3, 4} \subset A$

Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K,$ and $4K$ and equal cross-sectional areas and lengths $2l, l,$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\ ^oC, 50\ ^oC,$ and $0\ ^oC$ respectively,then the temperature $\theta$ of the junction is