In ΔABC, AB=c cm, AC= b cm and CB=a cm, If  ∠A=2 ∠B, then which of the following is true?

A right circular cone of largest volume is cut out from a solid wooden hemisphere. The remaining material is what percentage of the volume of the original hemisphere?

If 2sinθ+ 15 cos²θ=7, 0°˂θ˂90°, then what is the value of $$ {3-tanθ\over 2+tanθ}$$?

If $$ {x^{4}+x^{2}y^{2}+y^{4}={21\over256}}$$ and $$ {x^{2}+xy+y^{2}={3\over16}}$$ then $$ {2(x^{2}+y^{2})}=?$$

The profit on selling an article for Rs.1,100 is equal to three times the amount of loss on selling it for Rs.700. To gain 12.5%, the article must be sold for:

A certain sum (in Rs.) is invested at simple interest at x% p.a. for 5 years. Had it been invested at (x+5)% p.a, the simple interest would have been Rs.9,200 more than the earlier one. What is the sum?

Pipes A and B together can fill a tank in 16 hours, whereas pipe C alone can empty the full tank in 24 hours. A and B were opened together for 10 hours and then closed. Pipe C was then opened. The tank will now be emptied by C in:

When 3738, 5659 and 9501 are divided by the greatest possible number x, the remainder in each case is y. What is the sum of x and y?