For the following questions answer them individually
TWO pipes A and B can fill an empty tank in 10 hours and 16 hours respectively. They are opened alternately for 1 hour each, starting with pipe A first. In how many hours, the empty tank will be filled?
If $$\sin (A+ B) = \frac{\sqrt3}{2}$$ and $$\tan (A— B) = \frac{1}{\sqrt3}$$, then $$(2A + 3B)$$ is equal to:
A sum of ₹ 12,000 is invested for 15 months at 10% per annum compounded half yearly. What is the percentage gain, at the end of 15 months. correct to one decimal place?
What is the ratio of mean proportional between 1.8 and 3.2 and the third proportional of 5 and 3?
In $$\triangle ABC, \angle A = 40^\circ$$. If the bisectors ofthe $$\angle B$$ and $$\angle C$$, meet at a point $$O$$. then $$\angle BOC$$ is equal to:
Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours. All three pipes are opened together, but after 4 hours pipe A is closed. In how many hours from the beginning the tank be filled?
8 cubes, each of edge 5 cm, are joined end to end. What is the total surface area of the resulting cuboid?
A shopkeeper sold two articles for ₹ 9639 each. On one, he gained 19% and on the other, he lost 19%. What is the overall percentage gain or loss?