ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 5

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

• 1 x 1 A
• 1 x 10 B
• 10 x 10 C
• 10 x 1 D

The order of the matrix A is 3 x 2 and that of B is 2 x 3. The order of the matrix BA is

• 3 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

(ABC)' =

• CBA' A
• CBA B
• C' B' A' C
• None of these D

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

• BA A
• A² B
• AB C
• B² D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

A diagonal matrix is always

• Identity A
• Triangular B
• Scalar C
• Non-singular D

• 2 A
• 4 B
• 6 C
• 8 D

If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P' AP is

• Skew-symmetric A
• Symmetric B
• Null C
• Diagonal D

• Hermitian matrix A
• Skew-hermitian matrix B
• Symmetric matrix C
• Identity matrix D

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

• A2 A
• A5 B
• A3 C
• A7 D

• 
  A
• 
  B
• 
  C
• all are correct D

• 0 A
• 1 B
• 2 C
• 3 D

• -3 A
• -7 B
• 1 C
• 0 D

A square matrix A for which A^t= -A is called a

• Column matrix A
• Symmetric matrix B
• Skew-symmetric matrix C
• Row matrix D

• k3 A
• 0 B
• 3k C
• k6 D

• 2 x 2 A
• 2 x 3 B
• 3 x 2 C
• 3 x 3 D

An equation of the form ax + by = k is homogeneous linear equation when:

• 
  A
• 
  B
• 
  C
• 
  D

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

• 
  A
• 
  B
• 16 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

If for the matrix A, A⁵= I, then A^-1=

• A² A
• A³ B
• A C
• None of above D

• 3K A
• K2 B
• K3 C
• K D

A square matrix A = [aij] is lower triangular matrix when:

• aij = 0 for all i < j A
• bij = 0 B
• cij = 0 C
• dij =0 D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

• 0 A
• 1 B
• -A C
• -1 D