JEE Mathematics Matrices MCQs Set B

Question:

• a) symmetric matrix
• b) skew-symmetric matrix
• c) a diagonal matrix
• d) None of the above

Answer: symmetric matrix

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 4I
• b) None of these
• c) 3I
• d) 5I

Answer: 4I

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

(1) x = 0 (2) x + y + z = 3
(3) y = 0 (4) none of these

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question:

(1) A³ = 27A    (2) A³ = 9A
(3) A + A = A² (4) A^–1 does not exist

• a) 2 and 4 are correct
• b) 1, 2 and 3 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 2 and 4 are correct

Question:

(1) a + d = 0 (2) k = – |A|
(3) k = |A|     (4) none of these

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

More Questions..............................

Question: Let A and B are two matrices of same order 3 × 3, where

If A is singular matrix, then transpose of (A + B) is equal to

• a) 24
• b) 6
• c) 12
• d) 17

Answer: 24

Question: Let A and B are two matrices of same order 3 × 3, where

• a) 17
• b) 13
• c) 11
• d) 15

Answer: 17

Question: Let A and B are two matrices of same order 3 × 3, where

• a) 34
• b) 84
• c) 42
• d) 63

Answer: 34

Question:

Statement -1 : If a matrix of order 2 × 2, commutes with every matrix of order 2 × 2, then it is scalar matrix.
Statement-2 : A scalar matrix of order 2 × 2 commutes with every 2 × 2 matrix.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• b) Statement -1 is False, Statement-2 is True
• c) Statement -1 is True, Statement-2 is False.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement 1 : If A and B are two matrices such that AB = B, BA = A then A² + B² = A + B
Statement 2 : A and B are idempotent matrices.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question: If a square matrix A is such that AA^T = I = A^T A, then | A | is equal to :

• a) ± 1
• b) 0
• c) ± 2
• d) none

Answer: ± 1

Question: The rank of the matrix

• a) 2
• b) 4
• c) 3
• d) 1

Answer: 2

Question: If A is a skew symmetric matrix of order n and C is a column matrix of order n × 1, then C^T AC is:

• a) a zero matrix of order 1
• b) none of these
• c) an identity matrix of order 1
• d) an identity matrix of order n

Answer: a zero matrix of order 1

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The matrix A satisfying the equation

• a)

  

• b)

  

• c)

  

• d) none

Answer:

Question: If A is a matrix of the order 3 and | A | = 8, then | adj A | is equal to

• a) 8²
• b) 8³
• c) 8
• d) 1

Answer: 8²

Question:

(1) a = cos 2Θ (2) a = 1
(3) b = sin 2Θ  (4) b = 1

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question:

(1) x = 1 (2) y = 2
(3) z = 3 (4) n = 3

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

(1) adj (adj A) = A (2) | adj (adj A) | = 1
(3) | adj A | = 1     (4) | adj A | = 2

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement 1 : (a₁₁, a₂₂, .........a_nn) is a diagonal matrix then A^–1 = dia (a₁₁^–1, a₂₂^–1, a_nn^–1)

Statement 2 : If A = dia (2, 1, –3) and B = dia (1, 1, 2) then det (AB^–1) = 3

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False.

Question:

Statement 2: If | A | = 0 then A^–1 does not exist.

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.