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

The suspension of slaked lime in water is known as

$\int \frac{3^x dx}{\sqrt{9^x-1}}$ is equal to

Find the value of $V_{AB}$ in the given circuit.

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material,same area of cross-section,and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils,the ratio of magnetic induction at the centres of the two coils is

$\int_0^{\pi/6} \cos^4 3\theta \cdot \sin^2 6\theta \, d\theta$ is equal to