The centroid of the triangle formed by the pair of straight lines $12x^2 - 20xy + 7y^2 = 0$ and the line $2x - 3y + 4 = 0$ is:

Which of the following is a transparent tissue?

The distance between the lines represented by $4x^2 + 20xy + 25y^2 + 2x + 5y - 12 = 0$ is equal to

Two soap bubbles of radii $r_1 = 4 \, cm$ and $r_2 = 5 \, cm$ are touching each other over a common surface $S_1S_2$ (as shown in the figure). The radius of curvature of this common surface will be ....... $cm$.

The potential energy of a particle of mass $m$ is given by $U(x) = \begin{cases} E_0; & 0 \le x \le 1 \\ 0; & x > 1 \end{cases}$. $\lambda_1$ and $\lambda_2$ are the de-Broglie wavelengths for $0 \le x \le 1$ and $x > 1$ respectively. If the total energy of the particle is $2E_0$,the ratio $\frac{\lambda_1}{\lambda_2}$ will be

In $\triangle ABC$,the midpoints of the sides $AB, BC$,and $CA$ are respectively $(l, 0, 0), (0, m, 0)$,and $(0, 0, n)$. Then,$\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}$ is equal to