The radius of the circle with the polar equation $r^2-8r(\sqrt{3}\cos\theta+\sin\theta)+15=0$ is

Which of the following is correctly matched?

Evaluate $\int_{-2}^1 f(x) dx$,where $f(x)= \begin{cases} 1-2x, & x \leq 0 \\ 1+2x, & x > 0 \end{cases}$

For better survival of the human population,which of the following steps is most important?

$A$ vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75\, cm$ inside a tube closed at one end. The string also generates $4\, beats$ per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased,the number of beats reduces to $2\, per second$. Assuming the velocity of sound in air to be $340\, m/s$,the frequency $n$ of the tuning fork in $Hz$ is

$A$ current of $5 ~A$ is flowing at $220 ~V$ in the primary coil of a transformer. If the voltage produced in the secondary coil is $2200 ~V$ and $50 \%$ of power is lost,then the current in the secondary coil will be: (in $~A$)