Three waves of equal frequency having amplitudes $10\, \mu m, 4\, \mu m$ and $7\, \mu m$ arrive at a given point with successive phase difference of $\pi/2$. The amplitude of the resulting wave in $\mu m$ is given by

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \, years$ and $810 \, years$. The time (in years) after which one-fourth of the material remains is

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $3\pi/4$ with the positive $x$-axis, then $f'(3)$ is

Two soap bubbles combine to form a single bubble. In this process, the change in volume and surface area are respectively $V$ and $A$. If $P$ is the atmospheric pressure, and $T$ is the surface tension of the soap solution, the following relation is true :

$A$ car is moving with a speed of $72 ~km/h$ towards a hill. The car blows its horn at a distance of $1800 ~m$ from the hill. If the echo is heard after $10 ~s$,what is the speed of sound in $m/s$?

Consider the following statements:
$(I)$ The radius of an anion is larger than that of the parent atom.
$(II)$ The ionization energy generally increases with increasing atomic number in a period.
$(III)$ The electronegativity of an element is the tendency of an isolated atom to attract an electron.
Which of the above statements is/are correct?