Find the value of $$ {\sqrt{(cos^{2}20°+cos^{2}70°)}}$$

The volume of the largest right circular cone that can be cut out of a cube of edge 14 cm.

The average marks of 42 students in an examination, were 64. Later it was found that the marks of three students were misread as 72, 58 and 44 instead of the actual marks 64, 42 and 26 respectively. What are the correct average marks?

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The teachers' colony has 2800 members, out of which 650 members read only English newspaper. 550 members read only Hindi newspaper and 450 members read only Marathi newspaper. The number of members reading all the 3 newspapers is 100. Members reading Hindi as well as English newspapers are 200. 400 members read Hindi as well as Marathi newspaper and 300 members read English as well as Marathi newspaper.

How many members read only one newspaper?

D and E are midpoints of side AB and AC respectively of the ΔABC. A line drawn from A meets BC at H and DE at K. AK : KH = ?

A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60 ° with the ground. When a man starts climbing on it, it slips and now ladder makes an angle of 30° with ground. How much did the ladder slip? 

If 40% of a number is equal to 3 / 5th of another number, what will be the ratio of the first number and the second number?

Balls of marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm?