The number of pairs of natural numbers the difference of whose squares is 45 will be –

If $$ {x^2-12x+33=0}$$, then what is the value of $${(x-4)^2+[{1\over({x-4})^2}}]$$.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm. and the total height of the toy is 10.2 cm., find the volume of the wooden toy (nearly).

Find the value of $$ {5^{1\over2}-[3^{1\over4}+6-4÷2]}$$

Three numbers are in the ratio of 5: 6: 7. If the product of those numbers is 5670 then the largest number is-

ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to 

What is the area (in cm²) of the circumcircle of a triangle whose sides are 6 cm, 8 cm and 10 cm respectively?

By selling 25 m of cloth a man gains the selling price of 5 m of cloth. Find the gain percent?