The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?

The incentre of the triangle with vertices $(1, \sqrt{3})$,$(0, 0)$ and $(2, 0)$ is

$A$ ball is projected from the ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path,it makes an elastic collision with a vertical wall and returns to the ground. The total time of flight of the ball is:

Read the following five statements and answer the question.
$(a)$ In $Equisetum$ the female gametophyte is retained on the parent sporophyte.
$(b)$ In $Ginkgo$ male gametophyte is not independent.
$(c)$ The sporophyte in $Riccia$ is more developed than that in $Polytrichum$.
$(d)$ Sexual reproduction in $Volvox$ is isogamous.
$(e)$ The spores of slime molds lack cell walls.
How many of the above statements are correct?

The equation of the straight line perpendicular to $5x - 2y = 7$ and passing through the point of intersection of the lines $2x + 3y = 1$ and $3x + 4y = 6$ is

On which of the following lines does the point of intersection of the line $\frac{x - 4}{2} = \frac{y - 5}{2} = \frac{z - 3}{1}$ and the plane $x + y + z = 2$ lie?