What will be the acute angle between hands of a clock at 2 : 30?

In 16 minutes, the minute had gains over the hour hand by

Find the value of $$ {1\over{2×5}}+{1\over {5×8}}+{1\over {8 × 11}}+......{1\over {23 × 26}}=?$$

Find the value of $$ \sqrt{20+\sqrt{29-\sqrt{12+\sqrt{19-\sqrt{9}}}}}$$.

If $$ {x+{1\over {x}}=1}$$, then find the value of $$ {x^{208}+{x^{205}+x^{204}+x^{201}}}$$.

Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hour and 40 km/hour respectively. By the time they met the first train had travelled 100 km more than the second. Find the distance between P and Q?

The ratio of the present ages of Sunita and Vinita is 4 : 5. Six years hence the ratio of their ages will be 14 : 17. What will be the ratio of their ages 12 years hence?

A man has 60 pens. He sells some of these at a profit of 12 % and the rest at 8 % loss. On the whole, he gets a profit 11 %. How many pens were sold at 12 % profit.