Find the value of $$\left({1\over {sin 60°}} \right)^{2} + (cos 30°)^{2} \over(tan 45°)^{2}$$.

AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is 

Directions: The bar chart given below shows the percentage distribution of the production of various models of a mobile manufacturing company in 2007 and 2008. The total production in 2007 was 35 lakh mobile phones and in 2008 the production was 44 lakh. Study the chart and answer the following questions.
Percentage of six different types of mobiles manufactured by a company over two year

If the percentage production of A type mobiles in 2008 as same as that in 2007, then the number of A type mobiles produced in 2008 would have been 

A corner of a cube of side length 8 m. When cut by a plane which bisects the sides of the cube, we get a pyramid whose volume is : 

What is the value of a when $$ {x^{2(3a+1)}}={x^{3}}$$ ?

The area of a triangle is 456 sq.cm and its height is 24 cm. The length of its base is

A woman invests Rs. 2000 at the start of each year at 5% compound interest per annum. How much will her investment be at the end of the 2^nd year?

If (a+b)=16 and a³+b³=1456, then what is the value of ab?