Question : The average of 10 consecutive integers is $\frac{33}{2}$. What is the average of the first three integers?

Option 1: 12

Option 2: 13

Option 3: 15

Option 4: 11

Question : The average age of 30 students in a class is 12 years. The average age of a group of 5 of the students is 10 years and that of another group of 5 of them is 14 years. The average of the remaining students is:

Option 1: 14 years

Option 2: 12 years

Option 3: 11 years

Option 4: 13 years

Question : If $\cos \theta=\frac{9}{13}$, then what is the value of $\operatorname{cosec} \theta$?

Option 1: $\frac{13}{\sqrt{22}}$

Option 2: $\frac{13 \sqrt{22}}{44}$

Option 3: $\frac{2 \sqrt{22}}{13}$

Option 4: $\frac{\sqrt{22}}{13}$

Question : The radii of the two circles are 9 cm and 4 cm, the distance between their centres is 13 cm, then the length of the direct common tangent is:

Option 1: 8 cm

Option 2: 14 cm

Option 3: 12 cm

Option 4: 16 cm

Question : A is a point outside of a circle with centre O. AP and AQ are two tangents of the circle. If AP = a² + 14 and AQ = 239, then what is the value of a?

Option 1: 22

Option 2: 13

Option 3: 15

Option 4: 14