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 Bihar Board 12th Maths Objective Answers Chapter 4 Determinants

Bihar Board 12th Maths Objective Answers Chapter 4 Determinants

Question 1.
Evaluate the determinant Δ=log3512log38log43log49
(a) 152
(b) 12
(c) 143
(d) 6
Answer:
(a) 152

Direction (2 – 3): Evaluate the following determinants.

Question 2.
xx75x+1
(a) 3x2 + 4
(b) x(5x + 8)
(c) 3x + 4x2
(d) x(3x + 4)
Answer:
(b) x(5x + 8)

Question 3.
cos15sin75sin15cos75
(a) 0
(b) 5
(c) 3
(d) 7
Answer:
(a) 0

Question 4.

Answer:
(b) 1

Question 5.

Answer:
(c) -1

Question 6.
2xyx2y2x2y22xyy22xyx2=
(a) (x3 + y3)2
(b) (x2 + y2)3
(c) -(x2 + y2)3
(d) -(x3 + y3)2
Answer:
(d) -(x3 + y3)2

Question 7.
The value of cos(α+β)sinαcosαsin(α+β)cosαsinαcos2βsinβcosβ is independent of
(a) α
(b) β
(c) α, β
(d) none of these
Answer:
(a) α

Question 8.
Let Δ=xx2x3yy2y3zz2z3, then the value of ∆ is
(a) (x – y) (y – z) (z – x)
(b) xyz
(c) (x2 + y2 + z2)2
(d) xyz (x – y) (y – z) (z – x)
Answer:
(d) xyz (x – y) (y – z) (z – x)

Question 9.
The value of the determinant αα2β+γββ2γ+αγγ2α+β=
(a) (α + β)(β + γ)(γ + α)
(b) (α – β)(β – γ)(γ – α)(α + β + γ)
(c) (α + β + γ)2 (α – β – γ)2
(d) αβγ (α + β + γ)
Answer:
(b) (α – β)(β – γ)(γ – α)(α + β + γ)

Question 10.
Using properties of determinants, 111abca2bcb2cac2ab=
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0

Question 11.
If a, b, c are the roots of the equation x3 – 3x2 + 3x + 7 = 0, then the value of 2bca2c2b2c22acb2a2b2a22abc2 is
(a) 9
(b) 27
(c) 81
(d) 0
Answer:
(d) 0

Question 12.
If 1+a2x(1+a2)x(1+a2)x(1+b2)x1+b2x(1+B2)x(1+c2)x(1+c2)x1+c2x, then f(x) is apolynomial of degree
(a) 2
(b) 3
(c) 0
(d) 1
Answer:
(a) 2

Question 13.
a2b22ab2aba2b2b22aba2 is equal to
(a) a3 – b3
(b) a3 + b3
(c) (a3 – b3)2
(d) (a3 + b3)2
Answer:
(d) (a3 + b3)2

Question 14.
If α, β, γ are in A.P., then x3x2x1x4x3x2xαxβxγ=
(a) 0
(b) (x – 2)(x – 3)(x – 4)
(c) (x – α)(x – β)(x – γ)
(d) αβγ (α – β)(β – γ)2
Answer:
(a) 0

Direction (15 – 19): Find the value of the following determinants.

Question 15.
111a2+bcb2+cac2+aba3b3c3
(a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)
(b) (a – b)(b – c)(c – a)
(c) (a2 + b2 + c2)
(d) (a – b)(b – c)(c – a)(a2 + b2 + c2)
Answer:
(a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)

Question 16.
(b+c)2(c+a)2(a+b)2a2b2c2bccaab=
(a) (a – b)(b – c)(c – a)(a2 + b2 + c2)
(b) -(a – b)(b – c)(c – a)
(c) (a – b)(b – c)(c – a)(a + b + c)(a2 + b2 + c2)
(d) 0
Answer:
(c) (a – b)(b – c)(c – a)(a + b + c)(a2 + b2 + c2)

Question 17.
Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).
(a) 21 sq. units
(b) 35 sq. units
(c) 30 sq. units
(d) 40 sq. units
Answer:
(b) 35 sq. units

Question 18.
If the points (a1, b1), (a2, b2) and(a1 + a2, b1 + b2) are collinear, then
(a) a1b2 = a2b1
(b) a1 + a2 = b1 + b2
(c) a2b2 = a1b1
(d) a1 + b1 = a2 + b2
Answer:
(a) a1b2 = a2b1

Question 19.
If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.
(a) 4
(b) 7/140
(c) 47
(d) 40/7
Answer:
(d) 40/7

Question 20.
Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).
(a) 30 sq. units
(b) 35 sq. units
(c) 40 sq. units
(d) 15.5 sq. units
Answer:
(d) 15.5 sq. units

Question 21.
If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(d) 5

Question 22.
Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).
(a) y = 2x
(b) x = 3y
(c) y = x
(d) 4x – y = 5
Answer:
(a) y = 2x

Question 23.
Find the minor of the element of second row and third column in the following determinant 261305547
(a) 13
(b) 4
(c) 5
(d) 0
Answer:
(a) 13

Question 24.
If Δ=521302813, then write the minor of the element a23.
(a) 7
(b) -7
(c) 4
(d) 8
Answer:
(a) 7

Direction (25 – 27): Write the cofactors of each element of the first column of the following matrices.

Question 25.
A=111bccaababc
(a) a(c2 – b2), b(a2 – c2), c(b2 – a2)
(b) a(c2 – b2), b(c2 – a2), c(b2 – a2)
(c) bc, ab, 2b
(d) None of these
Answer:
(a) a(c2 – b2), b(a2 – c2), c(b2 – a2)

Question 26.
A=017253601
(a) 5, 16, 30
(b) 5, -16, -30
(c) 5, 16, -30
(d) -5, -16, -30
Answer:
(c) 5, 16, -30

Question 27.
A=231501111
(a) -1, 4, 5
(b) -4, 5, -1
(c) 4, 5, 1
(d) -4, -5, 1
Answer:
(a) -1, 4, 5

Question 28.
Find cofactors of a21 and a31 of the matrix A = [aij] = 143355262
(a) -16, 8
(b) -16, -8
(c) 16, 8
(d) 16, -8
Answer:
(a) -16, 8

Question 29.
Find the minor of 6 and cofactor of 4 respectively in the determinant Δ=147258369
(a) 6, 6
(b) 6, -6
(c) -6, -6
(d) -6, 6
Answer:
(d) -6, 6

Question 30.
Find the cofactors of the element of third row and second column of the following determinant 111xyzy+zz+xx+y
(a) x – y
(b) y – x
(c) x – z
(d) z – x
Answer:
(b) y – x

Question 31.

Answer:
(b) [4321]

Question 32.

Answer:
(b) 150106301505

Question 33.
Find x, if 112211x11 is singular
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 34.
Find the value of x for which the matrix A=3x2224x4211x is singular.
(a) 0, 1
(b) 1, 3
(c) 0, 3
(d) 3, 2
Answer:
(c) 0, 3

Question 35.

Answer:
(b) 2513

Question 36.
For what value of x, matrix [6x3x41] is a singularmatrix?
(a) 1
(b) 2
(c) -1
(d) -2
Answer:
(b) 2

Question 37.
Compute (AB)-1, If

Answer:
(a) 11916211012112173

Question 38.

Answer:
(a) A-1

Question 39.

Answer:
(a) 111[14551]

Question 40.

Answer:
(b) 117[4332]

Question 41.

Answer:
(a) [4121]

Question 42.
If for the non-singular matrix A, A2 = I, then find A-1.
(a) A
(b) I
(c) O
(d) None of these
Answer:
(a) A

Question 43.
If the equation a(y + z) = x, b(z + x) = y, c(x + y) = z have non-trivial solutions then the value of 11+a+11+b+11+c is
(a) 1
(b) 2
(c) -1
(d) -2
Answer:
(b) 2

Question 44.
A non-trivial solution of the system of equations x + λy + 2z = 0, 2x + λz = 0, 2λx – 2y + 3z = 0 is given by x : y : z =
(a) 1 : 2 : -2
(b) 1: -2 : 2
(c) 2 : 1 : 2
(d) 2 : 1 : -2
Answer:
(d) 2 : 1 : -2

Question 45.
If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = ________
(a) 1
(b) 3
(c) -2
(d) 2
Answer:
(d) 2

Question 46.
If the equations 2x + 3y + z = 0, 3x + y – 2z = 0 and ax + 2y – bz = 0 has non-trivial solution, then
(a) a – b = 2
(b) a + b + 1 = 0
(c) a + b = 3
(d) a – b – 8 = 0
Answer:
(a) a – b = 2

Question 47.
Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and 2x + y + 3z = 1.
(a) x = -4, y = -3, z = 2
(b) x = -1, y = -3, z = 2
(c) x = 2, y = 4, z = 6
(d) x = 3, y = 6, z = 9
Answer:
(b) x = -1, y = -3, z = 2

Question 48.
If the system of equations x + ky – z = 0, 3x – ky – z = 0 & x – 3y + z = 0 has non-zero solution, then k is equal to
(a) -1
(b) 0
(c) 1
(d) 2
Answer:
(c) 1

Question 49.
If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 has non-trivial solution, then the value of k is
(a) -2, 125
(b) -1, 15
(c) -6, 175
(d) 6, 125
Answer:
(c) -6, 175

Question 50.
If 2x85x=6723, then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6
Answer:
(c) ±6

Question 51.
The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be
(a) 9
(b) 3
(c) -9
(d) 6
Answer:
(b) 3

Question 52.
The number of distinct real roots of sinxcosxcosxcosxsinxcosxcosxcosxsinx=0 in the interval π4xπ4 is
(a) 0
(b) 2
(c) 1
(d) 3
Answer:
(c) 1

Question 53.
Bihar Board 12th Maths Objective Answers Chapter 4 Determinants Q53
(a) 0
(b) -1
(c) 2
(d) 3
Answer:
(a) 0

Question 54.

Answer:
(a) 12

Question 55.
The value of the determinant xx+2yx+yx+yxx+2yx+2yx+yx is
(a) 9x(x + y)
(b) 9y(x + y)
(c) 3y(x + y)
(d) 7x(x + y)
Answer:
(b) 9y(x + y)

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