GATE 2020: Engineering Mathematics Rapid Mini Mock (App update required to attempt this test)

The rank of the matrix is?

Which of the following is True for this matrix A?

Find the determinant of ?

If A is 5x5 order skew symmetric matrix then maximum possible rank is

Consider the homogeneous ordinary differential equation with y(x) as a general solution. Given that y(1) = 1 and y(2) = 14 the value of y(1.5), rounded off to two decimal places, is _______________.

Consider the system of linear equations, for what value of the constant k, the system will have only trivial solutions
X – ky + z = 0

Kx + 3y – kz = 0

3x + y – z = 0

Evaluate the complex integration  , where C is the right half of a circle having radius 2 traversed in anticlockwise direction .(Z = complex variable )

The directional directive of 4x²y + z³ at (1, 2, 1) in the direction of is

The maximum slope of the curve

y = –x³ + 3x² + 2x – 27 is

Let  where z is a complex number not equal to zero. Then z is solution of