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

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

Trival solution of homogeneous linear equation is

• (0, 0, 0) A
• (1, 2, 3) B
• (1, 3, 5) C
• a.b and c D

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 D

• 
  A
• 
  B
• 
  C
• 
  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

A non-homogeneous linear system AX = B has no solution if

• |A| = 0 A
• |A|≠ 0 B
• Rank (a) = no of variables C
• Rank > no of variables D

The transpose of a zero matrix is a ______

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

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None D

• A A
• -A B
• A^t C
• A^- D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

• 1 A
• 0 B
• 3 C
• -1 D

(ABC)' =

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

• 16 A
• 256 B
• 64 C
• 1024 D

The number of non zero rows in echelon form of a matrix is called

• Order of matrix A
• Rank of matrix B
• Row operation C
• None of these D

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

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 D

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix D

• -3 A
• -7 B
• 1 C
• 0 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

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

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 0 A
• abc B
• 1/abc C
• None of these D

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

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