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

Let $f$ be a positive function. Let $I_1 = \int_{1-k}^{k} x f\{x(1-x)\} dx$ and $I_2 = \int_{1-k}^{k} f\{x(1-x)\} dx$,where $2k-1 > 0$. Then $I_1/I_2$ is

What is the correct order of stability for the superoxides?

If $\int\limits_0^{\frac{\pi }{3}} {\frac{{\tan \theta }}{{\sqrt {2k \sec \theta } }}} \,d\theta = 1 - \frac{1}{\sqrt{2}}, (k > 0),$ then the value of $k$ is

Two circular coils $1$ and $2$ are made from the same wire,but the radius of the $1^{st}$ coil is twice that of the $2^{nd}$ coil. What is the ratio of potential difference in volts that should be applied across them so that the magnetic field at their centres is the same?

$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to the current,the temperature of the wire is raised by $\Delta T$ in time $t$. $N$ number of similar cells is now connected in series with a wire of the same material and cross section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is: