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

• 
  A
• 
  B
• 
  C
• 
  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

• 2 A
• 4 B
• 6 C
• 8 D

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

For non-trival solution |A| is

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

• 1 A
• 0 B
• -1 C
• 2 D

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

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

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

A diagonal matrix is always

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

• K/6 A
• 2K B
• 3K C
• 6K D

A diagonal matrix in which the diagonal elements are equal is called a

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

In order of A is m x n and order of B is n x p then order of AB is

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

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

• -a -b -c A
• 1 B
• 0 C
• -1 D

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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D 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

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A = [aij]1xn is a

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

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix 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 matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 
  A
• 
  B
• 
  C
• 
  D

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