Arun Sharma Solutions for Exercise 3: XAT(2009-2017)

A square piece of paper is folded three times along its diagonal to get an isosceles triangle whose equal sides are $10 \mathrm{cm}$. What is the area of the unfolded original piece of paper?

The difference between the area of the circumscribed circle and the area of the inscribed circle of an equilateral triangle is $2156$sq. cm. What is the area of the equilateral triangle (in sq cm)?

Study the figure below and answer the question:

Four persons walk from point A to point D following different routes. The one following ABCD takes $70$ . minutes. Another person takes $45$minutes following ABD. The third person takes $30$minutes following route ACD. The last person takes 65 minutes following route ACBD. If all were to walk at the same speed, how long will it take to go from point B to point C?

In the figure below, two circular curves create $60°$ and $90°$ angles with their respective centers. If the length of the bottom curve Y is $10\mathrm{\pi }$, find the length of the other curve.

AB is a chord of a circle. The length of AB is $24 \mathrm{cm}$. P is (The midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If $\mathrm{PM}<\mathrm{PN}$ and $\mathrm{PM}=8 \mathrm{cm}$, then what will be the length of PN?

AB, CD and EF are three parallel lines, in that order. Let ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ be the distances from CD to AB and EF respectively. ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ are integers, where ${\mathrm{d}}_1:{\mathrm{d}}_2=2:1$, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is $30$square units, what is the value of QR when the value of SR is the least?

ABCD is a rectangle P, Q and R are the midpoint of BC, CD and DA. The point S lies on the line QR in such a way that $\mathrm{SR}:\mathrm{QS}=1:3$. The ratio of the triangle APS and rectangle ABCD is:

The volume of a pyramid with a square base is $200 {\mathrm{cm}}^3$. The height of the pyramid is $13 \mathrm{cm}$. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?