Question : Three sets of 40, 50, and 60 students appeared for an examination and the pass percentages were 100, 90, and 80, respectively. The pass percentage of the whole set is:

Option 1: $88\frac{2}{3}\%$

Option 2: $84\frac{2}{3}\%$

Option 3: $88\frac{1}{3}\%$

Option 4: $84\frac{1}{3}\%$

Question : From the top of a cliff 100 metres high, the angles of depression of the top and bottom of a tower are 45° and 60°, respectively. The height of the tower is:

Option 1: $\frac{100}{3}(3-\sqrt{3})$ m

Option 2: $\frac{100}{3}(\sqrt3-1)$ m

Option 3: $\frac{100}{3}(2\sqrt3-1)$ m

Option 4: $\frac{100}{3}(\sqrt3-\sqrt{2})$ m

Question : In $\triangle P Q R, \angle P=90^{\circ}. {S}$ and ${T}$ are the mid points of sides ${PR}$ and ${PQ}$, respectively. What is the value of $\frac{\text{RQ}^2}{(\text{QS}^2 + \text{RT}^2)}$?

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{5}$

Option 3: $\frac{1}{2}$

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

Question : The reciprocal of the sum of the reciprocals of $\frac{2}{9}$ and $\frac{7}{10}$ is:

Option 1:  $\frac{14}{83}$

Option 2: $\frac{83}{14}$

Option 3: $\frac{90}{83}$

Option 4: $\frac{83}{90}$

Question : What is the value of $\frac{\frac{1}{3}+\frac{1}{3}\times\frac{1}{3}}{\frac{1}{3}\times\frac{1}{3}+\frac{1}{3}}$?

Option 1: 1

Option 2: 3

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

Option 4: $\frac{1}{2}$

Question : The probabilities of solving a problem by three students A, B, and C are $\frac{3}{7}, \frac{5}{9}$ and $\frac{1}{5}$, respectively. The probability that the problem will be solved is:

Option 1: $\frac{155}{315}$

Option 2: $\frac{64}{315}$

Option 3: $\frac{251}{315}$

Option 4: $\frac{32}{315}$