The value of `(A^(-1))^(T` is

The value of (A^(T))^(-1) is

The value of int_(e^(-1))^(e) (dt)/(t(t+1)) is equal to

If A is matrix of order 3 such that |A|=5 and B= adj A, then the value of ||A^(-1)|(AB)^(T)| is equal to (where |A| denotes determinant of matrix A. A^(T) denotes transpose of matrix A, A^(-1) denotes inverse of matrix A. adj A denotes adjoint of matrix A)

If A= [{:( 1,-tanx ),( tanx ,1):}] then the value of [A^(T) A^(-1) ] is

If f(t)=(1-t)/(1+t) then the value of f'(1/t) is

The value of (T_(3))/(T_(1)) is

The normal to the rectangular hyperbola xy=4 at the point t_(1), meets the curve again at the point t_(2) Then the value of t_(1)^(2)t_(2) is

A simple pendulam has time period T_(1) when on the earth's surface and T_(2) when taken to a height R above the earth's surface where R is the radius of the earth. The value of (T_(2))/(T_(1)) is-