ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 3 x 1 A
• 1 x 3 B
• 3 x 3 C
• 1 x 1 D

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries 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

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 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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  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

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

• k3 A
• 0 B
• 3k C
• k6 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

For a square matrix A, if A = At, then A is called

• Matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

The matrix A = [aij]1xn is a

• Vector A
• Rectangular matrix B
• Column vector C
• Square matrix D

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

• 
  A
• 
  B
• 
  C
• 
  D

A = [3] is a/an

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

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

If order of A is m x n, then order of A^tis

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

The order of the matrix [1 2 3] is

• 1 x 1 A
• 3 x 3 B
• 3 x 1 C
• 1 x 3 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

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

• 
  A
• 
  B
• 
  C
• 
  D