Question : In the given figure, PAB is a secant and PT is a tangent to the circle from P. If PT = 5 cm, PA = 4 cm and AB = x cm, then x is: 

Option 1: $\frac{4}9$ cm

Option 2: $\frac{9}4$ cm

Option 3: 5 cm

Option 4: $\frac{2}{3}$ cm

Question : In the following figure, if PT = 12 cm and PB = 24 cm, then find AB.

Option 1: 24 cm

Option 2: 18 cm

Option 3: 16 cm

Option 4: 12 cm

Question : P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the circle is:

Option 1: 10 cm

Option 2: 13 cm

Option 3: 11 cm

Option 4: 12 cm

Question : In the given figure, the circle with centre O has a radius of 10 cm. The radius of the circle with centre P is $x$. STR is a common tangent to the two circles at points R and S as shown in the figure. RT =16 cm and TS = 24 cm. What is the value of $x$(in cm)?

Option 1: 15

Option 2: 16

Option 3: 12

Option 4: 18

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

Option 1: $\frac{3\sqrt{3}}{5}$

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$

Question : Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm, and PD = 5 cm, then the length of PB is:

Option 1: 5 cm

Option 2: 7.35 cm

Option 3: 6 cm

Option 4: 4 cm