If the gravitational acceleration at the surface of the Earth is $g$,then the increase in potential energy in lifting an object of mass $m$ to a height equal to half of the radius of the Earth from the surface will be:

If the curves $x^2+p y^2=1$ and $q x^2+y^2=1$ are orthogonal to each other,then

$\lim _{x \rightarrow \infty}\left(\frac{x+6}{x+1}\right)^{x+4}$ is equal to

If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ $(a>b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

$A$ working transistor with its three legs marked $P, Q$ and $R$ is tested using a multimeter. No conduction is found between $P$ and $Q$. By connecting the common (negative) terminal of the multimeter to $R$ and the other (positive) terminal to $P$ or $Q$,some resistance is seen on the multimeter. Which of the following is true for the transistor?

Find the missing numbers in the following factorization tree: