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

• a = -1/2, b = -1 A
• a = 1, b = 2 B
• a = 2, b = 3 C
• None of above D

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

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

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

A matrix with a single column is called

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

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 16 C
• None of these D

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

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 D

The matrix A = [aij]mxn with m≠n is

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

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

• At Bt A
• AB B
• -AB C
• BA D

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

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

A diagonal matrix is always

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

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

(ABC)' =

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

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 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

• k3 A
• 0 B
• 3k C
• k6 D

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

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

• I A
• |A| B
• |A| I C
• None of these D