ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

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

A square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix 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

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

• At A
• -A B
• A C
• A-1 D

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

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| C
• None of these 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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

• 0 A
• 1 B
• 2 C
• 3 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 = [3] is a/an

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

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

The transport of a rectangular matrix is a

• Square matrix A
• Rectangular matrix B
• Row matrix C
• Column matrix D

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 D

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

• A² A
• A³ B
• A C
• None of above D

A diagonal matrix is always

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

If there are m rows and n columns in a matrix then its order is

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

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

System of linear equations is inconsistent if

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