If $cos^{2}\theta - sin\theta$ =$\frac{1}{4}$, then what is the value of $sin\theta$?
1). -1
2). $\frac{1}{2}$
3). 1
4). $\frac{3}{2}$
What is the simplified value of $\left(\frac{1}{cosecA + cotA}\right)^{2}$ ?
1). sec A tan A
2). $\frac{(1-cos A)}{(1 cos A)}$
3). $\frac{(1-cosec A)}{(1 cosec A)}$
4). sin A
What is the simplified value of $\frac{cotA + tanB}{cotB + tanA}$ ?
1). tan B cot A
2). tan A cot B
3). tan A tan B
4). cot A cot B
In $ \triangle PQR $, $\angle R$= $54^{0}$, the perpendicular bisector of PQ at S meets QR at T. If $\angle TPR$ = $46^{0}$, then what is the value (in degrees) of $\angle PQR$?
1). 25
2). 40
3). 50
4). 60
Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles?
1). 25
2). $25\sqrt{2}$
3). 50
4). $50\sqrt{2}$