Arun Sharma Solutions for Exercise 2: IIFT(2008-2017)

A ladder of $7.6 \mathrm{m}$ long is standing against a wall and the difference between the wall and the base of the ladder is $6.4 \mathrm{m}.$ If the top of the ladder now slips by $1.2 \mathrm{m},$ then the foot of the ladder shifts by approximately:

Let $\mathrm{PQRSTU}$ be a regular hexagon. The ratio of the area of the triangle$\mathrm{PRT}$ to that of the hexagon $\mathrm{PQRSTU}$PQRSTU is

A right circular cylinder has a height of $15$ and a radius of $7.$ A rectangular solid with a height of $12$ and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. The volume of the liquid is

A rectangular plank $\sqrt{10}$ metre wide, is placed symmetrically along the diagonal of a square of side $10$ metres as shown in the figure. The area of the plank is:

A flag pole on the top of a mall building is $75 \mathrm{m}$ high. The height of the mall building is $325 \mathrm{m}.$ To an observer at a height of $400 \mathrm{m},$ the mall building and the pole subtend equal angle$\mathrm{\theta }$. If the horizontal distance of the observer from the pole is $\text{'}\mathrm{x}\text{'}\mathrm{m}$ then what is the value of $\mathrm{x}?$

A chord $\mathrm{AB}$ of length $24 \mathrm{cm}$ is drawn in a circle of radius $13 \mathrm{cm}.$ Find the area of the shaped portion $\mathrm{APB}$.

Two tangents are drawn from a point P on the circle with centre at $\mathrm{O},$ touching the circle at point $\mathrm{Q}$ and $\mathrm{T}$ respectively. Another tangent $\mathrm{AB}$ touches the circle at point $\mathrm{S}.$ If angle $\mathrm{QPT}=55°$, find the angle $\mathrm{AOB} ?$

The coordinates of a triangle $\mathrm{ABC}$ are $\mathrm{A}(1,5)$, $\mathrm{B}(-2,3)$, and $\mathrm{C}(0,-4);$ find the equation of the median $\mathrm{AD}?$