Q6. 
\(\triangle ABC\) is an equilateral triangle of side 14 cm. A semi circle on \(BC\) as diameter is drawn to meet \(AB\) at \(D\), and \(AC\) at \(E\). Find the area of the shaded region. 
A.  \(49\left(\dfrac{\pi}{3}\sqrt{3}\right)\text{ cm}^2\) 

B.  \(49\left(\dfrac{\pi}{3}\dfrac{\sqrt{3}}{2}\right)\text{ cm}^2\) 

C.  \(49\text{ cm}^2\) 

D.  None 
Q7. 
Through \(T\), the midpoint of the side \(QR\) of a \(\triangle PQR \) , a straight line is drawn to meet \(PQ\) produced to \(S\) and \(PR\) at \(U\), so that \(PU = PS\). If length of \(UR = 2\) units then the length of \(QS\) is 
A.  \(2\sqrt{2}\) units 

B.  \(\sqrt{2}\) units 

C.  \(2\)units 

D.  cannot be determined 
Q8. 
A sphere of radius $r$ is cut by a plane at a distance of $h$ from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere. What is the value of $h$? 
A.  $\dfrac{r}{\sqrt{2}}$ 

B.  $\dfrac{r}{\sqrt{5}}$ 

C.  $\dfrac{r}{\sqrt{7}}$ 

D.  $\dfrac{r}{\sqrt{11}}$ 
Q9. 
Two mutually perpendicular chords $AB$ and $CD$ meet at a point $P$ inside the circle such that $AP = 6$ cms, $PB = 4$ units and $DP = 3$ units. What is the area of the circle? 
A.  $\dfrac{125\pi}{4}$ sq cms 

B.  $\dfrac{100\pi}{7}$ sq cms 

C.  $\dfrac{125\pi}{8}$ sq cms 

D.  $\dfrac{52\pi}{3}$ sq cms 
Q10. 
The figure below shows two concentric circle with centre O. PQRS a square, inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD? 
A.  $\pi / 4$ 

B.  $3 \pi / 2$ 

C.  $\pi / 2$ 

D.  $\pi$ 