The $P-V$ diagram of an ideal gas is as shown in the figure. The work done by the gas in the process $ABCD$ is:

The value of $\lambda$ with $|\lambda| < 16$ such that $2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0$ represents a pair of straight lines,is

If $f_n(x) = \log \log \log \ldots \log x$ (where $\log$ is repeated $n$ times),then $\int (x f_1(x) f_2(x) \ldots f_n(x))^{-1} dx$ is equal to

$A$ body weighs $700 \, gm \, wt$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth?

Carbon,silicon,and germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(Eg)_C$,$(Eg)_{Si}$,and $(Eg)_{Ge}$ respectively. Which one of the following relationships is true in their case?

$A$ wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum,then: