Find the value of `.^20C_0`

Find the value of .^10C_0

Find the value of .^5C_1

Find the value of .^100C_99

Find the value of .^(n-1)C_(n-1)

Area of the triangle with vertices (k,0),(1,1) and (0,3) is 5 sq. units. Find the values of k.

If sec 4A=cosec(A-20^@) ,where 4A is an acute angle,find the value of A.

If the function f(x)={{:((sin x)/(x) + cos x", if " x ne 0 ), (k", if " x =0 ):} is continuous at x=0, then find the value of k.

Find the value of sin 20^@ sin 40^@sin 80^@

Find the value of cos 20^@ cos 40^@ cos 80^@

If alpha and beta are the zeros of the polynomial ax^2+bx+c . Find the value of alpha^2 + beta^2