The circumcentre of the triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is:

The angle between the lines $ab(x^2 - y^2) + (a^2 - b^2)xy = 0$ is

$\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x$ is equal to

In the figure below, what is the potential difference between the points $A$ and $B$ and between $B$ and $C$ respectively in steady state?

Read the following five statements $(1-5)$ carefully and answer the question that follows.
$(1)$ In $Equisetum$,the female gametophyte is retained on the parent sporophyte.
$(2)$ In $Ginkgo$,the male gametophyte is not independent.
$(3)$ The sporophyte of $Polytrichum$ is more developed than that of $Riccia$.
$(4)$ Sexual reproduction in $Volvox$ is isogamous.
$(5)$ Spores of slime molds lack a cell wall.
How many of the above statements are correct?

$A$ piece of metal weighs $45 \ g$ in air and $25 \ g$ in a liquid of density $1.5 \times 10^3 \ kg \ m^{-3}$ kept at $30^{\circ} C$. When the temperature of the liquid is raised to $40^{\circ} C$,the metal piece weighs $27 \ g$. The density of liquid at $40^{\circ} C$ is $1.25 \times 10^3 \ kg \ m^{-3}$. The coefficient of linear expansion of the metal is