Two identical piano wires have a fundamental frequency of $600 \text{ Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of $6 \text{ beats per second}$ when both wires vibrate simultaneously?

$A$ student measures the distance traversed in free fall of a body,initially at rest in a given time. He uses this data to estimate $g$,the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively,the percentage error in the estimation of $g$ is

$A$ galvanometer,having a resistance of $50 \,\Omega$,gives a full-scale deflection for a current of $0.05 \,A$. The length in meters of a resistance wire of cross-sectional area $2.97 \times 10^{-2} \,cm^2$ that can be used to convert the galvanometer into an ammeter which can read a maximum of $5 \,A$ current is (Specific resistance of the wire = $5 \times 10^{-7} \,\Omega \cdot m$)

The diameters of a circle are along $2x+y-7=0$ and $x+3y-11=0$. Then,the equation of this circle,which also passes through $(5,7)$,is

In which of the following plants can hybrid embryos be obtained?

The solution of the differential equation $(3xy + y^2)dx + (x^2 + xy)dy = 0$ is