ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

If the trace of matrix A is 5, then the trace of the matrix 3A is

• 3/5 A
• 5/3 B
• 8 C
• 15 D

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

• 0 A
• Independent of a B
• Independent of b C
• Independent of c D

• 
  A
• 
  B
• 
  C
• 
  D

A square matrix A for which A^t= A is called a

• Column matrix A
• Symmetric matrix B
• Skew-symmetric matrix C
• Row matrix D

• 0 A
• 1 B
• -2 C
• 10 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

• 0 A
• 1 B
• -A C
• -1 D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 2 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

A matrix with a single row is called a

• Column matrix A
• Row matrix B
• Null matrix C
• Identity matrix D

• Zero matrix A
• Diagonal matrix B
• Column matrix C
• Scalar matrix 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

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

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

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

• A² A
• A³ B
• A C
• None of above D

• 16 A
• 256 B
• 64 C
• 1024 D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all are correct 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

Matrices are represented by

• Natural numbers A
• Real numbers B
• Small letters C
• Capital letters D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these 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

• At A
• -A B
• A C
• A-1 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

• I A
• 14 I B
• 0 C
• None of these D