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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 4 - MCQExams.com

If the points (a,0),(0,b) and (1,1) are collinear, then 1a+1b equal to -
  • 1
  • 2
  • 3
  • 4
If A is a square matrix so that AadjA=diag(k,k,k) then |adjA|= 
  • k
  • k2
  • k3
  • k4
If A is a square matrix such that  |400040004|=
  • 4
  • 16
  • 64
  • 256
If  A=[1xx24y],B=[3110] and adj(A)+B=[1001], then the values of x and y are respectively
  • (1,1)
  • (1,1)
  • (1,0)
  • none of these
If A is a non-singular matrix of order 3×3, then adj (adjA) is equal to
  • |A|A
  • |A|2A
  • |A|1A
  • none of these
A=[100210321],U1,U2 and U3 are columns matrices satisfying AU1=[100],AU2=[230],AU3=[231] and U is 3×3 matrix whose columns are U1,U2,U3 then answer the following question
The value of |U| is
  • 3
  • 3
  • 32
  • 2
If ω is an imaginary cube root of unity,then the value of
|abω2aωbωcbω2cω2aωc|,is ?
  • a3+b3+c3
  • a2bb2c
  • 0
  • a3b+b3+3abc

If A=|abcxyzpqr| and B=|qbypaxrcz|, then 
  • A=2B
  • A=B
  • A=B
  • none of these
The value of the determinant |1ω3ω5ω31ω4ω5ω41| , where ω is an imaginary cube root of unity,is
  • (1ω)2
  • 3
  • -3
  • none of these
Let ω=12+i32,then the value of the determinant
|11111ω2ω21ω2ω4|,is
  • 3ω
  • 3ω(ω1)
  • 3ω2
  • 3(2ω1)
Let A=[100210321] and U1,U2,U3 be column
matrices satisfying AU1=[100],AU2=[230],AU3=[231]. If U is
3×3 matrix whose columns are  U1,U2,U3, then |U|=
  • 3
  • 3
  • 32
  • 2
The value of |111213121314131415|,is
  • 1
  • 0
  • -1
  • 67
If the lines L1:λ2xy1=0 L2:xλ2y+1=0 L3:x+yλ2=0 pass through the same point the value(s) of λ equals
  • 1
  • 2
  • 2
  • 0
When the determinant |cos2xsin2xcos4xsin2xcos2xcos2xcos4xcos2xcos2x| is expanded in powers of sinx, then the constant term in that expression is
  • 1
  • 0
  • -1
  • 2
If p+q+r=0=a+b+c, then the value of the determinant |paqbrcqcrapbrbpcqa| is

  • 0
  • pq+qb+ra
  • 1
  • none of these
If abc, are value of x which satisfies the equation |0xaxbx+a0xcx+bx+c0|=0 is given by
  • x=0
  • x=c
  • x=b
  • x=a
The value of |1213+222+2213222221| is equal to
  • zero
  • 162
  • 82
  • one of these
Number of values of a for which the lines 2x+y1=0,ax+3y3=0,3x+2y2=0 are concurrent is

  • 0
  • 1
  • 2
Let |x2xx2x6xx6|=Ax4+Bx3+Cx2+Dx+E. Then the value of 5A+4B+3C+2D+E is equal to
  • zero
  • -16
  • 16
  • -11
In triangle ABC, if |111cotA2cotB2cotC2tanB2+tanC2tanC2+tanA2tanA2+tanB2|=0, then the triangle must be

  • equilateral
  • isosceles
  • obtuse angled
  • none of these
The value of the determinant |111mC1m+1C1m+2C1mC2m+1C2m+2C2| is equal to
  • 1
  • 1
  • 0
  • none of these
If a,b,c are different, then the value of x satisfying |0x2ax3bx2+a0x2+cx4+bxc0|=0 is
  • a
  • c
  • b
  • 0
Δ=|aa2012a+b(a+b)012a+3b| is divisible by
  • a+b
  • a+2b
  • 2a+3b
  • a2
If Δ=|sinθcosϕsinθsinϕcosθcosθcosϕcosθsinϕsinθsinθsinϕsinθcosϕ0|, then
  • Δ is independent of θ
  • Δ is independent of ϕ
  • Δ is a constant
  • dΔdθ|θ=π/2=0
If α is a characteristic root of a nonsingular matrix, then the corresponding characteristic root of adj A is
  • |A|α
  • |Aα|
  • |adjA|α
  • |adjAα|
If A is a square matrix of order m×n, then adj(adj A) is equal to
  • |A|nA
  • |A|n1A
  • |A|n2A
  • |A|n3A
If A=[122212221], Then adj(A) equals
  • A
  • AT
  • 3A
  • 3AT
Find the determinants of minors and cofactors of the determinant |234725813|
  • |16123132626233817| and |16123132626233817|
  • |16123132626233817| and |16123132626233817|
  • |16123132626233817| and |16123132626233817|
  • None of these.
The adjoint of the matrix A=[111213123] is
  • 111[914345531]
  • [914345531]
  • [935143451]
  • [914345531]
If A2=I, then the value of det(AI) is (where A has order 3)
  • 1
  • 1
  • 0
  • cannot say anything
If A=|1221|and f(x)=1+x1x, then f(|A|) is
  • 12
  • 12
  • 13
  • none of these
If A is a square matrix of order n×n and k is a scalar, then adj(kA) is equal to _____________.
  • kn1adj A
  • knadj A
  • kn+1adj A
  • kadj A
Find the adjoint of the matrix A=[1231351512].
If Adjoint A: [a91b922c1], find the value of abc.
  • 231
  • 213
  • 321
  • 312
If matrix A is given by A=[61124], then the determinant of A20056A2004 is
  • 22006
  • (11)22005
  • 22005
  • (9)22004
|0pqprqp0qrrprq0| is equal to
  • p+q+r
  • 0
  • pqr
  • p+q+r
If |6i3i143i1203i|=x+iy then
  • x=3,y=1
  • x=1,y=3
  • x=0,y=3
  • x=0,y=0
If A=[334234011] then find Adj(Adj A).
  • [334234011]
  • [334234011]
  • [334234011]
  • [334234011]
The matrix [101210311] is
  • non-singular
  • singular
  • skew-symmetric
  • symmetric
The value of the mth order determinant of a matrix A is 15 then the value of determinant formed by the cofactors of A will be
  • (15)m
  • 152m
  • (15)m1
  • (15)2m1
The points (a,b+c),(b,c+a),(c,a+b) are 
  • vertices of an equilateral triangle
  • collinear
  • concyclic
  • none of these
In a third order determinant aij denotes the element in the ith row and the jth column If aij={0,i=j1,i>j1,i<j then the value of the determinant
  • 0
  • 1
  • -1
  • none of these
The value of the determinant |62i3+6123+8i32+6i182+12i27+2i| is
  • complex
  • real
  • irrational
  • rational
If |a+xaxaxaxaxax|=0 then x is
  • 0
  • a
  • 3
  • 2a
If Δ=|cosθ/2111cosθ/2cosθ/2cosθ/211|, If the minimun of Δ is m1 and maximum of Δ is m2, then [m1,m2] are related
  • [-4, -2]
  • [2, 4]
  • [-4, 0]
  • [0, 2]
If A=[214170sin2xcos2x0cos2xsin2x] then |A| equals
  • cos2x
  • 2
  • 2cos4x
  • sin4x
If x is a non-real cube root of 2, then the value of
|12x1x213x222x1| equals to
  • 7
  • 13
  • 0
  • 12
If |x2+3xx+1x2x112xx+4x+3x43x|=Ax4+Bx3+Cx2+Dx+ϱ
Then value of ϱ equals to,
  • -10
  • 10
  • 0
  • None of these
If A=(121103211) then characteristic equation is given by
  • λ3+2λ24λ+18=0
  • λ3+2λ2+4λ+18=0
  • 2λ3λ2+6λ2=0
  • None of these
If the determinant |abatbbcbtc210|=0, if a,b,c are in
  • A.P.
  • G.P.
  • H.P.
  • k=1/2
If A=[133313331] then adj (A) is
  • =4[233323332]
  • =4[233323332]
  • =4[233323332]
  • =4[233323332]
0:0:3


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