A boy instead of writing `.^nP_r` writes `.^nC_r` By what number should he multiply his result to get the correct answer?

By what number should sin45^@cos45^@tan60^@ be multiplied to get the value of tan^2 45^@-cos^2 60^@ ?

Write the relation between ^nP_r and ^nC_r

A swimmer can swim with Velocity of 10 km/h. w.r.t, the water flowing in a river with velocity of 5 km/h. In what direction should he swim to reach the point on the other bank just opposite to his starting point?

If you subtract frac(1)(2) from a number and multiply the result by frac(1)(2) , you get frac(1)(8) . What is the number?

Write the relation R={(x,x^3)} :x is a prime number less than 10}in roaster form.