If tan (11 θ)=cot (7θ), then what is the value of sin²(6 θ) + Sec² (9 θ) + cosec²(12 θ)?

If a cube whose side is 7.5 cm, what will be its volume?

A cistern can be filled by two pipes A and B in 4 hours and 6 hours respectively. When full, the tank can be emptied by a third pipe C in 8 hours. If all the taps be turned on at the same time, the cistern will be full in 

 A 450 meter long train crosses a bridge 650 meters long in 36 seconds. What is speed (in km/hr) of the train? 

Pipes P and Q can fill a tank in 18 and 27 minutes, respectively, whereas Pipe R can empty the full tank in 54 minutes.  P and Q were opened together for 6 minutes and then   closed and R was opened. The tank was emptied by R alone in :

8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed? 

Alex sold his goods after announcing two successive discounts of 30% each. The effective discount altogether is-

If efficiency of B increased by $$ {33{1\over 3}{\%}}$$ and A and B start work together, while at the same time C starts destroying the work. Find in how many days work will be completed?