JEE Mathematics Determinants MCQs

Question:

If a^–1 + b^–1 + c^–1 = 0 such that

then the value of λ is :

• a) abc
• b) none
• c) – abc
• d) 0

Answer: abc

Question:

• a) 0
• b) 12 cos² x – 10 sin² x
• c) 12 cos² x – 10 sin² x – 2
• d) 10 sin 2x

Answer: 0

Question: If a, b, c are in A. P., then the value of

• a) 0
• b) 3
• c) – 3
• d) none

Answer: 0

Question: The system of simultaneous equations kx + 2y – z = 1, (k – 1) y – 2z = 2 and (k + 2) z = 3 have a unique solution if k equals:

• a) – 1
• b) – 2
• c) 0
• d) 1

Answer: – 1

Question:

• a)

  

• b)

  

• c)

  

• d) 0

Answer:

Question: The value of the determinant is

• a) – 2
• b) 2
• c) x² + 2
• d) 3

Answer: – 2

Question:

• a) 0
• b) 1
• c) – 1
• d) x + y + z

Answer: 0

Question:

• a) (x – 2) (x – 7)
• b) (x + 9) (x – a)
• c) (x – 2) (x – a)
• d) (x + 2) (x + a)

Answer: (x – 2) (x – 7)

Question:

• a) {2, – 1}
• b) {1, 2}
• c) {0, 1}
• d) {1, 5}

Answer: {2, – 1}

Question: If A and B are square matrix of the same order such that AB = A and BA = B, then A and B are both :

• a) non-singular
• b) involutory
• c) idempotent
• d) singular

Answer: non-singular

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

Question: If p + q + r = 0 = a + b + c, then the value of the determinant

• a) 0
• b) 1
• c) pa + qb + rc
• d) none of these

Answer: 0

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 0
• b) – 39
• c) 57
• d) 96

Answer: 0

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) 0
• b) a + b + c
• c) 1
• d) 3

Answer: 0

Question: x + ky – z = 0, 3x – ky – z = 0 and x – 3y + z = 0 has non-zero solution for k is equal to :

• a) 1
• b) – 1
• c) 0
• d) 2

Answer: 1

Question: The value of determinant

is independent of :

• a) n
• b) x
• c) a
• d) none

Answer: n

Question: The value of a for which the system of equations x + y + z = 0, x + ay + az = 0, x – ay + z = 0, possesses nonzero solutions, are given by :

• a) 1, – 1
• b) none
• c) 1, 2
• d) 1, 0

Answer: 1, – 1

Question: If x, y, z are all distinct and

then the value of xyz is

• a) –1
• b) None
• c) –2
• d) –3

Answer: –1

Question:

• a) ax (2a + 3x)
• b) None of these
• c) ax
• d) ax (2 + 3x)

Answer: ax (2a + 3x)

Question: The value of x obtained from the equation

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: System of equation : x + 3y + 2z = 6 ; x + λy + 2z = 7 ; x + 3y + 2z = μ has

(1) infinitely many solution if λ= 4, μ = 6
(2) no solution if λ= 5, μ = 7
(3) no solution if λ = 3, μ = 5
(4) unique solution if λ= 2, μ ≠6

• 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: The value of x for which

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

Answer: 2 and 4 are correct

Question: The value of determinant

(1) complex number (2) real number
(3) rational number (4) irrational number

• 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: Consider the determinant

M_ij = Minor of the element if i^th row and j^th column
C_ij = Cofactor of the element if i^th row and j^th column

Value of b₁.C₃₁ + b₂.C₃₂ + b₃.C₃₃ is

• a) 0
• b)

  

• c)

  

• d)

  

Answer: 0

Question: Consider the determinant

M_ij = Minor of the element if i^th row and j^th column
C_ij = Cofactor of the element if i^th row and j^th column

If all the elements of the determinants are multiplied by 2, then the value of new determinant is –

• a)

  

• b)

  

• c)

  

• d) 0

Answer:

Question: Consider the determinant

M_ij = Minor of the element if i^th row and j^th column
C_ij = Cofactor of the element if i^th row and j^th column

a₃M₁₃ – b₃.M₂₃ + d₃M₃₃ is equal to –

• a)

  

• b)

  

• c) 0
• d) None of these

Answer:

Question: 

Statement-1 : If a, b, c are even natural numbers, then

is an even natural number.

Statement-2 : Sum and product of two even natural numbers is also even natural number.

• 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.

Question: Let x, y, z are three integers lying between 1 and 9 such that x 51, y 41, z 31 are three digit numbers.

Statement 1 : The value of determinant

Statement 2 : The value of determinant is zero, if the entries any two rows (or columns) of the determinants are correspondingly proportional.

• 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.

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.