If the pair of straight lines given by $Ax^2+2Hxy+By^2=0$ $(H^2 > AB)$ forms an equilateral triangle with the line $ax+by+c=0$,then $(A+3B)(3A+B)$ is equal to:

$A$ magnet of length $10 \text{ cm}$ and magnetic moment $1 \text{ Am}^2$ is placed along side $AB$ of an equilateral triangle $ABC$. If the length of the side $AB$ is $10 \text{ cm}$,find the magnetic induction at the point $C$. (Given $\mu_0 = 4\pi \times 10^{-7} \text{ Hm}^{-1}$)

If $\frac{3+2i \sin \theta}{1-2i \sin \theta}$ is a real number and $0 < \theta < 2\pi$,then $\theta$ is equal to

The complete hydrolysis of $ICl , ClF _3$ and $BrF _5$, respectively, gives

In which of the following does the central atom $NOT$ use $sp^3$ hybrid orbitals in its bonding?

$A$ sonometer wire is stretched by hanging a metal bob. The fundamental frequency of vibration of the wire is '$n_1$'. When the bob is completely immersed in water,the frequency of vibration of the wire becomes '$n_2$'. The relative density of the metal of the bob is