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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 1 - MCQExams.com

The number of distinct real roots of the equation, |cosxsinxsinxsinxcosxsinxsinxsinxcosx|=0 
in the interval [π4,π4] is/are :
  • 3
  • 2
  • 1
  • 4
The points (0,83),(1,3) and (82,30) :
  • form an obtuse angled triangle.
  • form a right angled triangle.
  • lie on a straight line.
  • form an acute angled triangle.
If A=[2341], then adj (3A2+12A) is  equal to.
  • [72846351]
  • [51638472]
  • [51846372]
  • [72638451]
Let P=[aij] be a 3 × 3 matrix and let Q=[bij], where bij=2i+jaij for 1i,j3. If the determinant of P is 2, then the determinant of the matrix Q is
  • 210
  • 211
  • 212
  • 213
Consider three points P=(sin(βα),cosβ),Q=(cos(βα),sinβ) and R=(cos(βα+θ),sin(βθ)) , where 0<α, β, θ<π4. Then
  • P lies on the line segment RQ
  • Q lies on the line segment PR
  • R lies on the line segment QP
  • P,Q,R are non-collinear
The number of A in Tp such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p, is
  • (p1)2
  • 2(p1)
  • (p1)2+1
  • 2p1
Let k be a positive real number and let A=[2k12k2k2k12k2k2k1] and B=[02k1k12k02kk2k0] . 
If det (adjA)+det(adjB)=106,then[k] is equal to 

[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k].
  • 3
  • 4
  • 5
  • 6
The value of |U| is
  • 3
  • 3
  • 3/2
  • 2
A=[1234],B=[2134] then |(BTAT)1| is equal to
  • 10
  • 110
  • 1
  • 1
If three points (k,2k),(2k,3k),(3,1) are collinear, then k is equal to:
  • 2
  • 1
  • 12
  • 12
|4sin2θcos2θ3sec2θcosec2θ|=
  • 8sin2θcos2θ
  • 4sin2θcos2θ
  • 1
  • 4cos3θ3cosθ
|0cosαcosβcosα0cosγcosβcosγ0|=
  • cosα+cosβ+cosγ
  • cosαcosβcosγ
  • 2cosαcosβcosγ
  • 2cosαcosβ
A={891011}, then cofactor of a12 is:
  • 11
  • 10
  • -11
  • -10
If P =[1426] ,then adj (P) 
  • [1426]
  • [6421]
  • [6241]
  • [2164]
|x2+3x1x+3x+32xx4x3x+43x| =px4+qx3+rx2+sx+t,  then t=
  • 72
  • 0
  • 24
  • 48
Maximum value of a second order determinant whose every element is either 0,1 or 2 only is:
  • 0
  • 1
  • 2
  • 4
If |cos(A+B)sin(A+B)cos2BsinAcosAsinBcosAsinAcosB| =0 then B=


  • (2n+1)π2
  • nπ
  • (2n+1)π
  • 2nπ
If A =[0cbc0aba0] then (a2+b2c2)|A|= 
  • abc
  • a+b+c
  • (a3+b3+c3)
  • 0
Find x if it is given that:
det[20043046x]=42
  • 8
  • 7
  • 6
  • 21/4
If |10023456x| =45 then x=

  • 4
  • 7
  • 5
  • 7
If A is a singular matrix, then A (adj A) is a 
  • scalar matrix
  • zero matrix
  • identity matrix
  • orthogonal matrix
If A is a singular matrix, then adj A is
  • nonsingular
  • singular
  • symmetric
  • not defined
If the value of the determinant |m257| is 31, find m.
  • 3
  • 8
  • 6
  • 2
If A is a 3×3 matrix and det(3A)=k(detA), then k=
  • 9
  • 6
  • 1
  • 27
If A and B are similar matrices such that det(AB)=0, then 
  • det(A)=0 and det(B)=0
  • det(A)=0 and det(B)0
  • A=0 and B=0
  • A=0 or B=0
Let a, b, c be three complex numbers, and let
z=|0bcb0aca0|
then z equal
  • 0
  • purely imaginary
  • abc
  • none of these
Two n×n square matrices A and B are said to be similar if there exists a non-singular matrix P such that P1AP=B.
If A and B are similar matrices such that det(A)=1, then
  • det(B)=1
  • det(A)=det(B)
  • det(B)=1
  • none of these
If A is a square matrix of order n then adj (adjA) is equal to
  • |A|nA
  • |A|n1A
  • |A|n2A
  • |A|n3A
If|120λ0212115|=360, then the value of λ,is
  • 1
  • 2
  • 3
  • 4
If A is any skew-symmetric matrix of odd order then |A| equals
  • 1
  • 0
  • 1
  • none of these
If |xy42|=7 and |23yx|=4 then
  • x=3,y=52
  • x=52,y=3
  • x=3,y=52
  • x=52,y=3
If |abcabcabc|+λabc=0, then λ is equal to
  • 2
  • 4
  • 2
  • 4
The cofactors of elements in second row of the determinant |214423112| are
  • 5,6,4
  • 6,0,3
  • 5,1,8
  • 6,0,3
A set of points which do not lie on the same line are called as
  • collinear
  • non-collinear
  • concurrent
  • square
A and B are two points and C is any point collinear with A and B. IF AB=10, BC=5, then AC is equal to:
  • either 15 or 5
  • necessarily 5
  • necessarily 16
  • none of these
If A=[3510], then adj. A is equal to
  • [3510]
  • [0513]
  • [0513]
  • [0153]
The value of the determinant |ab00abb0a| is equal to
  • a3b3
  • a3+b3
  • 0
  • none of these
The value of the determinant |12335781420| is equal to
  • 20
  • 10
  • 0
  • 45
If |6i3i143i1203i|=x+iy, then
  • x=3,y=1
  • x=1,y=3
  • x=0,y=3
  • x=0,y=0
The points which are not collinear are:
  • (0,1), (8,3) and (6,7)
  • (4,3), (5,1) and (1,9)
  • (2,5), (1,2) and (4,7)
  • (3,2)(1,2) and (9,10)
If A=[abba], then |A+AT| equals
  • 4(a2b2)
  • 2(a2b2
  • a2b2)
  • 4ab
If Δ1=|10ab| and Δ2=|10cd| then Δ2Δ1 is equal to
  • ac
  • bd
  • (ba)(dc)
  • none of these
If A and B are two matrices of same order 3×3, where
A=[123234568] and B=[325238729]
The value of Adj(AdjA) is equal to
  • A
  • A
  • 8A
  • 16A
If ω is a cube root of unity and Δ=|12ωωω2|, then Δ2 is equal to
  • ω
  • ω
  • 1
  • ω2
If |x218x|=|623x6|, then x is equal to
  • 6
  • ±6
  • 6
  • 0
Which of the following is correct?
  • Determinant is a square matrix
  • Determinant is a number associated to a matrix
  • Determinant is a number associated to a square matrix
  • None of these
If |A|0, then A is
  • zero matrix
  • singular matrix
  • non - singular matrix
  • diagonal matrix
A=[1234] and A(adjA)=KI, then the value of K is:
  • 2
  • 2
  • 10
  • 10
What is the determinant of the matrix [3612]?
  • 0
  • 12
  • |0|
  • |6|
If A=[1logbalogab1] then |A| is equal to
  • 0
  • logab
  • 1
  • logba
0:0:1


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