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

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

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

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

• 
  A
• 
  B
• 
  C
• 
  D

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

• A2 A
• A3 B
• A C
• None of above D

If the matrices A and B are conformable for multiplication then (AB)^t= ______

• AB A
• A^tB^t B
• B^tA^t C
• A^tB 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

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B 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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• k3 A
• 0 B
• 3k C
• k6 D

• 
  A
• 
  B
• 
  C
• all are correct 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

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

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

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

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

(ABC)' =

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

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

• 1 A
• -1 B
• 0 C
• I D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

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

The square matrix A is skew Hermitian when (A)'=

• A A
• A' B
• -A C
• A D

• 
  A
• 
  B
• 
  C
• 
  D

• A^- A
• A^t B
• -A C
• A D

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

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

• 0 A
• 1 B
• -A C
• -1 D