Question : A person has three iron bars whose lengths are 20, 30 and 40 metres, respectively. He wants to cut pieces of the same length from each of the three bars. What is the least number of total pieces if he cuts without any wastage?

Option 1: 8

Option 2: 10

Option 3: 9

Option 4: 11

Question : A person observes that the angle of elevation at the top of a pole of height 5 metres is 30°. Then the distance of the person from the pole is:

Option 1: $5\sqrt3$ metres

Option 2: $\frac{5}{\sqrt3}$ metres

Option 3: $\sqrt3$ metres

Option 4: $10\sqrt3$ metres

Question : A person observes that the angle of elevation of the top of a pole of height 15 metres is 30°. What is the distance (in metres) of the person from the pole?

Option 1: $15$

Option 2: $15\sqrt3$

Option 3: $\frac{15}{\sqrt3}$

Option 4: $30$

Question : A person bought 50 pens for Rs 50 each. He sold 40 of them at a loss of 5%. He wants to gain 10% on the whole. Then his gain percentage on the remaining pens should be:

Option 1: 15%

Option 2: 40%

Option 3: 50%

Option 4: 70%

Question : The shadow of a tower standing on a level plane is 40 metres longer when the sun's altitude is 45°, than when it is 60°. The height of the tower is:

Option 1: $30(3+\sqrt{3})$ metres

Option 2: $40(3+\sqrt{3})$ metres

Option 3: $20(3+\sqrt{3})$ metres

Option 4: $10(3+\sqrt{3})$ metres

Question : The angle of elevation of a ladder leaning against a house is 60°, and the foot of the ladder is 6.5 metres from the house. The length of the ladder is:

Option 1: $\frac{13}{\sqrt{3}}$ metres

Option 2: $13$ metres

Option 3: $15$ metres

Option 4: $3.25$ metres