23MA1001 MCQ Test

Calculate the sum of the squares of the eigenvalues of the matrix A = [1 3 5; 0 2 1; 0 0 5].

• 8

• 30

• 25

• 64

What is the nature of the quadratic form if its eigenvalues are -1, 1 and 7?

• Positive Semi-definite

• Indefinite

• Negative Semi-definite

• Negative definite

What is the type of the function y = 3x²-2x+9?

• non-linear function

• linear function

• Trigonometric function

• Algebraic function

Evaluate

• 0

• infinity

• 6

• -6

Find ∇φ given φ =4x³-3y²+3z³.

• 12x²I-6yJ+9z²K

• x²I+yJ+z²K

• 12x²-6y+9z²

• 12xI+6yJ+9zK

Determine the curl of F = x²I+y²J+z²K.

• xyz

• 2x+2y+2z

• 0

• 2

Integrate sin(4x+2).

• -cos(4x+2)/4

• cos(4x+2)/4

• -cos(4x+2)

• cos(4x)

Integrate x² with respect to x within the limits 1 to 3.

• 27/3

• 1/3

• 1

• 26/3

Determine the value of f(x,y) = x²y in double integration within the limits of x = 0 to 2 and y = 0 to 1.

• 8/3

• 1/3

• 4/3

• 2/3

• 2

• 1

• 0

• -3