Maths MCQs for Class 12 with Answers Chapter 4 Determinants

  

Determinants Class 12 Maths MCQs Pdf

Determinants Class 12 MCQ Questions Question 1.
    
Answer:
(b) [4−3−21]

Determinants MCQs With Answers Question 2.
    
Answer:
(b) ⎡⎣⎢150−106−30−1505⎤⎦⎥

MCQ Of Determinants Class 12 Question 3.
Find x, if ⎡⎣⎢112211x1−1⎤⎦⎥ is singular
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Determinants Class 12 MCQ Question 4.
Find the value of x for which the matrix A=⎡⎣⎢3−x2−224−x−421−1−x⎤⎦⎥ is singular.
(a) 0, 1
(b) 1, 3
(c) 0, 3
(d) 3, 2
Answer:
(c) 0, 3

Class 12 Maths Chapter 4 MCQ Question 5.
    
Answer:
(b) −2513

Determinants MCQs Class 12 Question 6.
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

Class 12 Determinants MCQ Question 7.
The number of distinct real roots of ∣∣∣∣sinxcosxcosxcosxsinxcosxcosxcosxsinx∣∣∣∣=0 in the interval −π4≤x≤π4 is
(a) 0
(b) 2
(c) 1
(d) 3
Answer:
(c) 1

MCQ On Determinants Class 12 Pdf Download Question 8.
    
(a) 0
(b) -1
(c) 2
(d) 3
Answer:
(a) 0

MCQ Of Chapter 4 Maths Class 12 Question 9.
    
Answer:
(a) 12

Determinants MCQs With Answers Pdf Question 10.
The value of the determinant ∣∣∣∣xx+2yx+yx+yxx+2yx+2yx+yx∣∣∣∣ is
(a) 9x2 (x + y)
(b) 9y2 (x + y)
(c) 3y2 (x + y)
(d) 7x2 (x + y)
Answer:
(b) 9y2 (x + y)

Matrices And Determinants Class 12 MCQ Question 11.
For what value of x, matrix [6−x3−x41] is a singularmatrix?
(a) 1
(b) 2
(c) -1
(d) -2
Answer:
(b) 2

MCQ Determinants Class 12 Question 12.
Compute (AB)-1, If
    
Answer:
(a) 119⎡⎣⎢1621101211−21−73⎤⎦⎥

MCQ Questions On Determinants Class 12 Question 13.
    
Answer:
(a) A-1

Determinants MCQs Question 14.
    
Answer:
(a) 111[14551]

MCQs Of Determinants Class 12 Question 15.
    
Answer:
(b) 117[4−332]

MCQs On Determinants Class 12 Question 16.
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

MCQs On Matrices And Determinants Question 17.
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

MCQ On Determinants Class 12 With Solutions Question 18.
Find the minor of the element of second row and third column in the following determinant ⎡⎣⎢261−30554−7⎤⎦⎥
(a) 13
(b) 4
(c) 5
(d) 0
Answer:
(a) 13

Determinants MCQ Class 12 Question 19.
If Δ=∣∣∣∣521302813∣∣∣∣, then write the minor of the element a23.
(a) 7
(b) -7
(c) 4
(d) 8
Answer:
(a) 7

Matrices And Determinants MCQs Question 20.
If a, b, c are the roots of the equation x3 – 3x2 + 3x + 7 = 0, then the value of ∣∣∣∣∣2bc−a2c2b2c22ac−b2a2b2a22ab−c2∣∣∣∣∣ is
(a) 9
(b) 27
(c) 81
(d) 0
Answer:
(d) 0

Question 21.
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 22.
∣∣∣∣∣a2b22ab2aba2b2b22aba2∣∣∣∣∣ is equal to
(a) a3 – b3
(b) a3 + b3
(c) (a3 – b3)2
(d) (a3 + b3)2
Answer:
(d) (a3 + b3)2

Question 23.
If α, β, γ are in A.P., then ∣∣∣∣x−3x−2x−1x−4x−3x−2x−αx−βx−γ∣∣∣∣=
(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

Question 24.
∣∣∣∣∣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 25.
Evaluate the determinant Δ=∣∣∣log3512log38log43log49∣∣∣
(a) 152
(b) 12
(c) 143
(d) 6
Answer:
(a) 152

Question 26.
∣∣∣xx−75x+1∣∣∣
(a) 3x2 + 4
(b) x(5x + 8)
(c) 3x + 4x2
(d) x(3x + 4)
Answer:
(b) x(5x + 8)

Question 27.
∣∣∣cos15∘sin75∘sin15∘cos75∘∣∣∣
(a) 0
(b) 5
(c) 3
(d) 7
Answer:
(a) 0

Question 28.
    
Answer:
(b) 1

Question 29.
    
Answer:
(c) -1

Question 30.
    
Answer:
(a) [4−121]

Question 31.
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 32.
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 33.
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 34.
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 35.
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 36.
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 37.
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 38.
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 39.
If ∣∣∣2x85x∣∣∣=∣∣∣67−23∣∣∣, then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6
Answer:
(c) ±6

Question 40.
∣∣∣∣∣(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 41.
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 42.
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 43.
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 44.
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 45.
∣∣∣∣∣2xyx2y2x2y22xyy22xyx2∣∣∣∣∣=
(a) (x3 + y3)2
(b) (x2 + y2)3
(c) -(x2 + y2)3
(d) -(x3 + y3)2
Answer:
(d) -(x3 + y3)2

Question 46.
The value of ∣∣∣∣cos(α+β)sinα−cosα−sin(α+β)cosαsinαcos2βsinβcosβ∣∣∣∣ is independent of
(a) α
(b) β
(c) α, β
(d) none of these
Answer:
(a) α

Question 47.
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 48.
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 49.
Using properties of determinants, ∣∣∣∣∣111abca2−bcb2−cac2−ab∣∣∣∣∣=
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0

Question 50.
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