ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

Cofactor of an element a_ijis defined by

• (-1)^i+j|A| A
• (-1)^i+jM_ij B
• (-1)^i+jM^-1 C
• None of these D

A and B be two square matrices and if their inverse exist, the (AB)^-1=

• A^-1B^-1 A
• AB^-1 B
• A^-1B C
• B^-1A^-1 D

• -a -b -c A
• 1 B
• 0 C
• -1 D

System of linear equation is inconsistent if

• System has no solution A
• System has one solution B
• System has two solution C
• None of above D

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 D

• k3 A
• 0 B
• 3k C
• k6 D

• Diagonal matrix A
• Scalar matrix B
• Triangular matrix C
• Identity matrix D

A = [3] is a/an

• Square matrix A
• Scalar matrix B
• Diagonal matrix C
• Identity matrix D

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None D

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

• m x m A
• m x n B
• n x n C
• n x m D

• 2 A
• 4 B
• 6 C
• 8 D

If A = |aij| is (m x n) matrix then transpose of A is of the order

• m x m A
• m x n B
• n x n C
• n x m D

• 
  A
• 
  B
• 
  C
• 
  D

• 16 A
• 256 B
• 64 C
• 1024 D

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 D

• Square matrix A
• Row matrix B
• Symmetric matrix C
• Null matrix 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

• 
  A
• 
  B
• 
  C
• 
  D

• I3 A
• rI3 B
• r C
• none D

If A = [aij]mxpand B =[aij]pxnthen order of BA is

• m x n A
• p x n B
• n x m C
• None of these D

• Singular A
• Non-singular B
• Adjoint C
• None of above D

• 
  A
• 
  B
• 
  C
• 
  D

We solve the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a,b and c D

For trival solution |A| is

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

The transpose of a zero matrix is a ______

• Column matrix A
• Zero matrix B
• Row matrix C
• Scalar matrix D

A square matrix A = [aij] is upper triangular when

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

A and B be two square matrices and if their inverse exist the (AB)-1 =

• A-1 B-1 A
• AB-1 B
• A-1B C
• B-1A-1 D

• 
  A
• 
  B
• 
  C
• 
  D