# Consider a matrix, The trace of this matrix is equal to

$\inline&space;\mathbf{\begin{bmatrix}&space;1&&space;0&space;&&space;1\\&space;0&space;&&space;1&space;&&space;0\\&space;1&&space;0&space;&&space;1&space;\end{bmatrix}}$

1. 1
2. 3
3. 0
4. undefined

# If two matrices A and B can be diagonalized simultaneously

• Which of the following is true about A and B
1. A2B = B2A
2. A2B2 = B2A
3. AB = BA
4. AB2 AB = BA BA2

# The average value of the function f(x) = sinx in the interval (0, π) is

1. 1/2
2. 2/π
3. 1/π
4. 4/π
5. none of the above

# The eigenvalues of the matrix A = $\dpi{120}&space;\fn_jvn&space;\begin{bmatrix}&space;0&space;&&&space;\iota&space;\\&space;\iota&space;&&&space;0\end{bmatrix}$ are

1. real and distinct
2. complex and distinct
3. complex and coinciding
4. real and coinciding

# The eigenvalues of the given matrix are:

• $\dpi{100}&space;\fn_jvn&space;\mathbf{\begin{bmatrix}&space;2&space;&&&space;3&space;&&&space;0&space;\\&space;3&space;&&&space;2&space;&&&space;0&space;\\&space;0&space;&&&space;0&space;&&&space;1&space;\end{bmatrix}}$
1. 2, -2, 5
2. -5, -1, 1
3. 5, 1, -1
4. 1, 1, -5

# The eigenvalue of a matrix are ι, 2ι and 3ι. The matrix is:

1. Unitary
2. Anti-unitary
3. Hermitian
4. Anti-hermitian

# Find the curl of a given vector at the point (1, 2, 3)

• $\dpi{80}&space;\fn_jvn&space;V&space;=&space;(2x&space;-&space;y^{2})\hat{i}&space;+&space;(3z&space;+&space;x^{2})\hat{j}&space;+&space;(4y&space;-&space;z^{2})\hat{k}$
1. i + 6k
2. 6K
3. 0
4. i
5. i – 6k

# A force F = (5, 3, -6) is applied at a point r = (1, 0, -3) m. Calculate the torque due to this force:

1. 7i – 9j + 3k
2. -9i + 2j + 3k
3. 9i – 9j + 3k
4. 3i – 3j – k