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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

(ABC)' =

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

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

• Scalar matrix A
• Identity matrix B
• Null matrix C
• Symmetric matrix D

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

• At A
• -A B
• A C
• A-1 D

• 1 A
• 0 B
• -1 C
• 2 D

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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

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

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

• 2 AB A
• 2 BA B
• A + B C
• AB D

• 3K A
• K2 B
• K3 C
• K D

A = [3] is a/an

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

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

• 
  A
• 
  B
• 
  C
• 
  D

A matrix in which the number of rows is not equal to the number of columns is called a

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

• 
  A
• 
  B
• 
  C
• all are correct D

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) 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

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

• 6, -12, -18 A
• -6, 4, 9 B
• -6, -4, -9 C
• -6, 12, 18 D

A diagonal matrix is always

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

• 
  A
• 
  B
• 
  C
• 
  D