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

Minor of an element a_ijis denoted by

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

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

• Null matrix A
• Triangular matrix B
• Unit matrix C
• Rectangular 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

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 D

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

• -a -b -c A
• 1 B
• 0 C
• -1 D

The transpose of a zero matrix is a ______

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

• 5 A
• 15 B
• 10 C
• 20 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

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

• BA A
• A² B
• AB C
• B² D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

• I3 A
• rI3 B
• r C
• none D

• K/6 A
• 2K B
• 3K C
• 6K D

A matrix in which the number of rows is equal to the number of columns is called a

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

• 
  A
• 
  B
• 
  C
• 
  D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

The transpose of a row matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None D

Every identity matrix is

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

• 9/4 A
• 4/9 B
• 1 C
• None of these D

(ABC)' =

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

The matrix A = [aij]mxn with m≠n is

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

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

For non-trival solution |A| is

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