Exercise

Can $2n^2-7$ be the ${\mathrm{n}}^{\mathrm{th}}$ term of an $\mathrm{A}.\mathrm{P}. ?$ Explain.
 

Semi-circles are described on the sides $AB \text{and} CD$ of a rectangle $ABCD$ as diameters, both inside the rectangle. If $AB=14 \mathrm{cm}$ and $BC=7 \mathrm{cm}$, find the area enclosed by the-semi circles.

$ABCD$ is a square of side $7 \mathrm{cm}$ and semi-circles are drawn with each side of the square as diameter, thereby forming four similar petals as shown in the adjoining figure. Find the cost of making design on the petals at the rate of $₹12$ per square centimetre. 

In the given figure, $O$ is the centre and $AOB$ is the diameter of the circle. Find the area of the shaded region. 

A circle has radius 5 cm. Three chords of lengths 6 cm, 8 cm and 10 cm are drawn.

Which chord subtends the largest angle on its minor arc?

Raghu was playing in his grandfather's old garage, where his grandfather kept many antique items. In a dark corner, he found a really old clock. He found that the clock was dead at $9:05 \mathrm{a}.\mathrm{m}$ . He pulled a lever on the clock and the minute hand shifted to $5$.

If the length of the minute hand of a clock is $3.5 \mathrm{cm}$, find the area swept on the face of the clock by it between $9:05 \mathrm{a}.\mathrm{m}.$ and $9:25 \mathrm{a}.\mathrm{m}.$ (Use the value $\mathrm{\pi }=\frac{22}{7}$)

In the figure, if $ABC$ is an equilateral triangle, then shaded area is equal to:

In a fair, a giant wheel was fixed. The giant wheel is in the shape of a circle divided into $12$ equal sectors as shown in the diagram below.

The highest point of the wheel is $150 \mathrm{m}$ above the ground level and the boarding platform of the wheel is $10 \mathrm{m}$ above the ground level. Based on the given information, answer the following question by choosing the correct option from the given four options in the question:

The perimeter of each sector of the circle is