The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

Product $(A)$ is

Two spheres made of the same substance have diameters in the ratio $1: 2$. Their thermal capacities are in the ratio of .............

$50 \Omega$ and $100 \Omega$ resistors are connected in series. This combination is connected to a battery of $2.4 \text{ V}$. When a voltmeter of $100 \Omega$ resistance is connected across the $100 \Omega$ resistor,the reading of the voltmeter will be .......... $\text{V}$.

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is . . . . . . .

$\left|\begin{array}{ccc}x+2 & x+3 & x+5 \\ x+4 & x+6 & x+9 \\ x+8 & x+11 & x+15\end{array}\right|$ is equal to