Question : The radius of a circle is 1.75 cm. What is the circumference of the circle?
(Take $\pi=\frac{22}{7}$)

Option 1: 5.5 cm

Option 2: 11 cm

Option 3: 9.63 cm

Option 4: 22 cm

Question : Three equal circles of unit radius touch one another. Then the area of the circle circumscribing the three circles is:

Option 1: $6 \pi (2+ \sqrt3)^2$

Option 2: $\frac{\pi}{6} (2+ \sqrt3)^2$

Option 3: $\frac{\pi}{3} (2+ \sqrt3)^2$

Option 4: $3\pi (2+ \sqrt3)^2$

Question : If $x^2 = y+z$, $y^2=z+x$, $z^2=x+y$, then the value of $\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}$ is:

Option 1: –1

Option 2: 1

Option 3: 2

Option 4: 4

Question : What is the value of $\frac{x^2-x-6}{x^2+x-12}÷\frac{x^2+5x+6}{x^2+7x+12}$?

Option 1: $1$

Option 2: $\frac{(x-3)}{(x+3)}$

Option 3: $\frac{(x+4)}{(x-3)}$

Option 4: $\frac{(x-3)}{(x+4)}$

Question : Two identical circles each of radius $2\;\mathrm{cm}$ intersect each other such that the circumference of each one passes through the centre of the other. What is the area (in $\mathrm{cm^2}$) of the intersecting region?

Option 1: $\frac{8\pi }{3}-2\sqrt{3}$

Option 2: $\frac{8\pi }{3}-\sqrt{3}$

Option 3: $\frac{4\pi }{3}-\sqrt{3}$

Option 4: $\frac{4\pi }{3}-2\sqrt{3}$