GATE 2023 Engg. Mathematics Quiz 1

Find the value of integral  .

Find the value

Let f(z) = (x² + y²) + i 2xy and g(z) = 2xy + i(y² - x²) for z=x+ iy. where i= .Then in the complex plane C.

The general solution of the differential equation e^x tany dx + (1 – e^x) sec² y dy = 0 is

If A is 3 × 3 matrix and trace A = 9, |A| = 24 and one of the eigen value is 3, then sum of other eigen values is _______.

The smallest positive integers n for which

One of the eigen vector of matrix     is

If

Then sum of Eigen value of