BITSAT Mathematics Determinants MCQs

Question: If a > 0, b > 0, c > 0 are respectively the pth, qth, rth terms of G.P., then the value of the determinant  is

• a) 0
• b) 1
• c) -1
• d) None of these

Answer: 0

Question: The digits A, B and C are such that the three digit numbers A88, 6B8, 86C are divisible by 72 then the determinant is divisible by

• a) 72
• b) 144
• c) 288
• d) 216

Answer: 72

Question: If M (α) = M (β) =then [M(α) M (β)]^–1 is equal to -

• a) M(β) M (α)
• b) M (–α) M(–β)
• c) M(–β) M(–α)
• d) –M(β) M(α)

Answer: M(–β) M(–α)

Question: If a + b + c = 0 then determinant is equal to,

• a) 0
• b) 1
• c) 2
• d) 3

Answer: 0

Question: If the three linear equations x + 4ay + az = 0; x + 3by + bz = 0,  x + 2cy + cz = 0 have a non-trivial solution, where a ≠ 0, b ≠ 0, c ≠ 0, then ab + bc is equal to

• a) 2ac
• b) – ac
• c) ac
• d) – 2ac

Answer: 2ac

Question: The system of equations α x + y + z = α – 1, x + α y + z = α – 1, x + y + α z = α – 1 has no solution if α=

• a) –2
• b) α ≠ – 2
• c) Either – 2 or 1
• d) α = 1

Answer: –2

Question: If 1,ω,ω² are the cube roots of unity, the is equal to

• a) ω²
• b) 0
• c) 1
• d) ω

Answer: 0

Question: If A =, B =and M = AB, then find M^–1.

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Inverse matrix of

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The equations 2x + 3y + 4 = 0; 3x + 4y + 6 = 0 and 4x + 5y + 8 = 0 are

• a) Consistent with unique solution
• b) Inconsistent
• c) Consistent with infinitely many solutions
• d) None of the above

Answer: Consistent with unique solution

Question: If the matrix is singular, then λ =

• a) –2
• b) 4
• c) 2
• d) –4

Answer: 4

Question: If a system of equation – ax + y + z = 0 x – by + z = 0; x + y – cz = 0 (a, b, c ≠ –1) has a non-zero solution then

• a) 0
• b) 1
• c) 2
• d) 3

Answer: 1

Question: If  then the value of  is

• a) 0
• b) 1
• c) 2
• d) 4pqr

Answer: 2

Question: Let α₁, α₂ and β₁, β₂ be the roots of ax² + bx + c= 0 and px² + qx + r = 0 respectively. If the system of equations α₁y + α₂z = 0 and β₁y + β₂z = 0 has a non-trivial solution, then

• a) 

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: If [ ] denotes the greatest integer less than or equal to the real number under consideration and then the value of the determinant

is

• a) [z]
• b) [y]
• c) [x]
• d) None of these

Answer: [z]

Question: Let M be a 3 × 3 non-singular matrix with det (M) = α. If [M^–1 adj (adj (M)] = KI, then the value of K is

• a) 1
• b)  α
• c) α²
• d) α³

Answer:  α

Question: If the lines p₁x + q₁y = 1, p₂x + q₂y = 1 and p3x + q₃y = 1 be concurrent, then the points (p₁, q₁), (p₂, q₂) and (p₃, q₃)

• a) Are collinear
• b) Form an equilateral triangle
• c) Form a scalene triangle
• d) Form a right angled triangle

Answer: Are collinear

Question: One of the roots of  is

• a) abc
• b) a + b + c
• c) –(a + b + c)
• d) –abc

Answer: –(a + b + c)

Question: The value of λ , for which the lines 3x - 4y =13, 8x -11y = 33 and 2x - 3y + λ = 0 are concurrent is

• a) –1
• b) –7
• c)

  

• d) 9

Answer: –7 

Question: The determinant vanishes for

• a) 3 values of x
• b) 2 values of x
• c) 1 values of x
• d) No value of x

Answer: No value of x

Question: If the lines lx + my + n = 0, mx +ny + l = 0 and nx + ly + m = 0 are concurrent then

• a) l + m + n = 0
• b) l – m – n = 0
• c) l + m – n = 0
• d) m + n – l = 0

Answer: l + m + n = 0

Question: The equations 2x + 3y + 4 = 0; 3x + 4y + 6 = 0 and 4x + 5y + 8 = 0 are

• a) Consistent with unique solution
• b) Inconsistent
• c) Consistent with infinitely many solutions
• d) None of the above

Answer: Consistent with unique solution

Question: The value of the determinant

is

• a) 1000
• b) 779
• c) 679
• d) 0

Answer: 0

Question: If A =then adj ( adj A) is equal to -

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The value of is

• a) 213
• b) –231
• c) 231
• d) 39

Answer: 231