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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 A^2 = I, then the value of det(A - I) is (where A has order 3)
  • 1
  • -1
  • 0
  • cannot say anything
If A=\begin{vmatrix} 1 & 2 \\ 2 & 1 \end{vmatrix}and f(x) = \displaystyle \frac{1 + x}{1- x}, then f(|A|) is
  • \dfrac{-1}{2}
  • \dfrac{1}{2}
  • \dfrac{-1}{3}
  • none of these
If A is a square matrix of order n\times n and k is a scalar, then adj(kA) is equal to _____________.
  • k^{n-1}adj\space A
  • k^{n}adj\space A
  • k^{n+1}adj\space A
  • kadj\space A
Find the adjoint of the matrix A = \begin{bmatrix}1 & 2 & 3 \\ 1 & 3 & 5 \\ 1 & 5 & 12\end{bmatrix}.
If \mbox{Adjoint A: } \begin{bmatrix}a & -9 & 1 \\ b & 9 & -2 \\ 2 & c & 1\end{bmatrix} \\, find the value of abc.
  • 231
  • 213
  • 321
  • 312
If matrix A is given by A = \begin{bmatrix}6 & 11\\ 2 & 4\end{bmatrix}, then the determinant of A^{2005} - 6A^{2004} is
  • 2^{2006}
  • (-11) 2^{2005}
  • -2^{2005}
  • (-9)2^{2004}
\displaystyle \left | \begin{matrix}0 &p-q  &p-r \\ q-p &0  &q-r \\ r-p &r-q  &0 \end{matrix} \right | is equal to
  • \displaystyle p+q+r
  • 0
  • \displaystyle p-q-r
  • \displaystyle -p+q+r
If \displaystyle \left | \begin{matrix}6i &-3i  &1 \\ 4 &3i  &-1 \\ 20 &3  &i \end{matrix} \right |=x+iy then
  • \displaystyle x=3, y=1
  • \displaystyle x=1, y=3
  • \displaystyle x=0, y=3
  • \displaystyle x=0, y=0
If A = \begin{bmatrix}3& -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{bmatrix} then find Adj(Adj\space A).
  • \quad \begin{bmatrix}3& -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{bmatrix}
  • \quad \begin{bmatrix}3& 3 & 4 \\ 2 & -3 & -4 \\ 0 & -1 & 1\end{bmatrix}
  • \quad \begin{bmatrix}3& 3 & 4 \\ 2 & -3 & 4 \\ 0 & 1 & 1\end{bmatrix}
  • \quad \begin{bmatrix}3& -3 & 4 \\ 2 & -3 & -4 \\ 0 & 1 & 1\end{bmatrix}
The matrix \begin{bmatrix}1 & 0 & 1 \\ 2 & 1 & 0 \\ 3 & 1 & 1 \end{bmatrix} is
  • non-singular
  • singular
  • skew-symmetric
  • symmetric
The value of the \displaystyle m^{th} order determinant of a matrix \displaystyle A is \displaystyle 15 then the value of determinant formed by the cofactors of \displaystyle A will be
  • \displaystyle \left ( 15 \right )^{m}
  • \displaystyle 15^{2m}
  • \displaystyle \left ( 15 \right )^{m-1}
  • \displaystyle \left ( 15 \right )^{2m-1}
The points \displaystyle(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 a_{ij} denotes the element in the ith row and the jth column If a_{ij} = \left\{\begin{matrix}0, & i = j\\ 1, & i > j\\ -1,  & i < j\end{matrix}\right. then the value of the determinant
  • 0
  • 1
  • -1
  • none of these
The value of the determinant \begin{vmatrix} \sqrt { 6 }  & 2i & 3+\sqrt { 6 }  \\ \sqrt { 12 }  & \sqrt { 3 } +\sqrt { 8 } i & 3\sqrt { 2 } +\sqrt { 6 } i \\ \sqrt { 18 }  & \sqrt { 2 } +\sqrt { 12 } i & \sqrt { 27 } +2i \end{vmatrix} is
  • complex
  • real
  • irrational
  • rational
If \displaystyle \left | \begin{matrix}a+x &a  &x \\ a-x &a  &x \\ a-x &a  &-x \end{matrix} \right |=0 then \displaystyle x is
  • 0
  • \displaystyle a
  • 3
  • \displaystyle 2a
If \Delta =\begin{vmatrix} \cos \theta /2 & 1 & 1\\ 1 & \cos \theta /2 & -\cos \theta /2\\ -\cos \theta /2 & 1 & -1 \end{vmatrix}, If the minimun of \Delta is m_{1} and maximum of \Delta is m_{2}, then \left [ m_{1}, m_{2} \right ] are related
  • [-4, -2]
  • [2, 4]
  • [-4, 0]
  • [0, 2]
If \displaystyle A= \begin{bmatrix}2 &14  &17 \\0  &\sin 2x  &\cos 2x \\0  &\cos 2x  &\sin 2x \end{bmatrix} then \displaystyle \left | A \right | equals
  • \displaystyle \cos 2x
  • -2
  • \displaystyle -2 \cos 4x
  • \displaystyle \sin 4x
If x is a non-real cube root of -2, then the value of
\begin{vmatrix} 1 & 2x & 1\\ x^{2} & 1 & 3x^{2}\\ 2 & 2x & 1 \end{vmatrix} equals to
  • -7
  • -13
  • 0
  • -12
If \begin{vmatrix}x^{2}+3x &x+1  &x-2 \\ x-1 &1-2x  &x+4 \\ x+3 &x-4  &3x \end{vmatrix}= Ax^{4}+Bx^{3}+Cx^{2}+Dx+\varrho  
Then value of \varrho equals to,
  • -10
  • 10
  • 0
  • None of these
If A=\begin{pmatrix} 1 & 2 & 1\\ -1 & 0 & 3\\ 2 & -1 & 1 \end{pmatrix} then characteristic equation is given by
  • -\lambda ^{3}+2\lambda ^{2}-4\lambda +18=0
  • \lambda ^{3}+2\lambda ^{2}+4\lambda +18=0
  • 2\lambda ^{3}-\lambda ^{2}+6\lambda -2=0
  • None of these
If the determinant \begin{vmatrix}a & b & at-b\\ b & c & bt-c\\ 2 & 1 & 0\end{vmatrix}=0, if a, b, c are in
  • A.P.
  • G.P.
  • H.P.
  • k=1/2
If A=\begin{bmatrix} -1 & -3 & -3\\ 3 & 1 & -3\\ 3 & -3 & 1 \end{bmatrix} then adj (A) is
  • =4\begin{bmatrix} -2 & 3 & 3 \\ -3 & 2 & -3 \\ -3 & 3 & 2 \end{bmatrix}
  • =4\begin{bmatrix} -2 & 3 & 3 \\ 3 & 2 & -3 \\ -3 & -3 & 2 \end{bmatrix}
  • =4\begin{bmatrix} -2 & -3 & 3 \\ -3 & 2 & -3 \\ -3 & -3 & 2 \end{bmatrix}
  • =4\begin{bmatrix} -2 & 3 & 3 \\ -3 & 2 & -3 \\ -3 & -3 & 2 \end{bmatrix}
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