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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 7 - MCQExams.com

If A=|a1b1c1a2b2c2a3b3c3| and B=|c1c2c3a1a2a3b1b2b3| then.
  • A=B
  • A=B
  • B=0
  • B=A2
If |1sinθ1sinθ1sinθ1sinθ1| then,
  • Δ=0
  • Δ(0,)
  • Δ[1,2]
  • Δ[2,4]
If A=\begin{bmatrix} x & 1 & -x \\ 0 & 1 & -1 \\ x & 0 & 7 \end{bmatrix} and det(A)=\begin{vmatrix} 3 & 0 & 1 \\ 2 & -1 & 0 \\ 0 & 6 & 7 \end{vmatrix} then the value of x is
  • -3
  • 3
  • 2
  • -8
  • -2
If A=\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{vmatrix}, then the value of \left| A \right| \left| adj\left( A \right)  \right| is
  • { a }^{ 3 }
  • { a }^{ 6 }
  • { a }^{ 9 }
  • { a }^{ 27 }
If A=\begin{bmatrix} 1 & 2 & -1 \\ -1& 1 & 2 \\ 2 & -1 & 1\end{bmatrix}, then \text{det} (\text{adj}(\text{adj} A)) is equal to.
  • 14^4
  • 14^3
  • 14^2
  • 14
If \begin{vmatrix} x & 2 & 8 \\ 2 & 8 & x \\ 8 & x & 2 \end{vmatrix}=\begin{vmatrix} 3 & x & 7 \\ x & 7 & 3 \\ 7 & 3 & x \end{vmatrix}=\begin{vmatrix} 5 & 5 & x \\ 5 & x & 5 \\ x & 5 & 5 \end{vmatrix}=0 then x is equal to
  • 0
  • -10
  • 3
  • None of these
If A = \begin{bmatrix} \dfrac {-1 + i\sqrt {3}}{2i}& \dfrac {-1 - i\sqrt {3}}{2i}\\ \dfrac {1 + i\sqrt {3}}{2i} & \dfrac {1 - i\sqrt {3}}{2i}\end{bmatrix}, i = \sqrt {-i} and f(x) = x^{2} + 2, then f(A) is equal to
  • \left (\dfrac {5 - i\sqrt {3}}{2}\right ) \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}
  • \left (\dfrac {3 - i\sqrt {3}}{2}\right ) \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}
  • \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}
  • (2 + i\sqrt {3})\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}
If 3x+2y=I and 2x-y=O, where I and O are unit and null matrices of order 3 respectively, then
  • x=\dfrac { 1 }{ 7 } , y=\dfrac { 2 }{ 7 }
  • x=\dfrac { 2 }{ 7 } , y=\dfrac { 1 }{ 7 }
  • x=\left( \dfrac { 1 }{ 7 } \right) I, y=\left( \dfrac { 2 }{ 7 } \right) I
  • x=\left( \dfrac { 2 }{ 7 } \right) I, y=\left( \dfrac { 1 }{ 7 } \right) I
\begin{vmatrix} { \left( { a }^{ x }+{ a }^{ -x } \right)  }^{ 2 } & { \left( { a }^{ x }-{ a }^{ -x } \right)  }^{ 2 } & 1 \\ { \left( b^{ x }+{ b }^{ -x } \right)  }^{ 2 } & { \left( { b }^{ x }-{ b }^{ -x } \right)  }^{ 2 } & 1 \\ { \left( { c }^{ x }+{ c }^{ -x } \right)  }^{ 2 } & { \left( { c }^{ x }-{ c }^{ -x } \right)  }^{ 2 } & 1 \end{vmatrix} is equal to
  • 0
  • 2abc
  • { a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 }
  • None of these
If the determinant \Delta =\begin{vmatrix} 3 & -2 & \sin { 3\theta  }  \\ -7 & 8 & \cos { 2\theta  }  \\ -11 & 14 & 2 \end{vmatrix}=0, then the value of \sin { \theta  } is
  • \dfrac { 1 }{ 3 } or 1
  • \dfrac { 1 }{ \sqrt { 2 } } or \dfrac { \sqrt { 3 } }{ 2 }
  • 0 or \dfrac { 1 }{ 2 }
  • None of these
If A, B, C are collinear points such that A(3, 4), C(11, 10) and AB = 2.5 then point B is
  • \left(5,\dfrac{11}{2}\right)
  • \left(\dfrac{5}{2},11\right)
  • (5, 5)
  • (5, 6)
If A = \begin{bmatrix} 2& -3\\ 4 & 1\end{bmatrix}, then adjoint of matrix A is _______.
  • \begin{bmatrix} 1& 3\\ -4 & 2\end{bmatrix}
  • \begin{bmatrix} 1& -3\\ -4 & 2\end{bmatrix}
  • \begin{bmatrix} 1& 3\\ 4 & -2\end{bmatrix}
  • \begin{bmatrix} -1& -3\\ -4 & 2\end{bmatrix}
If maximum and minimum values of D = \begin{vmatrix}1 & -\cos \theta & 1\\ \cos \theta & 1 & -\cos \theta\\ 1 & \cos \theta & 1\end{vmatrix} are p and q respectively, then the value of 2p + 3q is _________.
  • 16
  • 6
  • 14
  • 8
The value of the determinant \begin{vmatrix}b^2-ab & b-c & bc-ac\\ ab-a^2 & a-b & b^2-ab\\ bc-ac & c-a & ab-a^2\end{vmatrix}= ____________.
  • abc
  • a+b+c
  • 0
  • ab+bc+ca
If the vectors \vec {a}, \vec {b}, \vec {c} are coplanar, then the value of \begin{vmatrix}\vec {a}& \vec {b} & \vec {c}\\ \vec {a}.\vec {a} & \vec {a}.\vec {b} & \vec {a}.\vec {c}\\ \vec {b}.\vec {a} & \vec {b}.\vec {b} & \vec {b} . \vec {c}\end{vmatrix} =
  • 1
  • 0
  • -1
  • \vec {a} + \vec {b} + \vec {c}
Let A^{-1}\begin{bmatrix} 1 & 2017 & 2\\ 1 & 2017 & 4 \\ 1 & 2018 & 8\end {bmatrix}. Then |2A|-|2A^{-1}| is equal to.
  • 3
  • -3
  • 12
  • -12
The value of the determinant 
\begin{vmatrix} \cos^2 \dfrac{\theta}{2}&\sin^2\dfrac{\theta}{2}\\ \sin^2\dfrac{\theta}{2} &\cos^2\dfrac{\theta}{2}  \end{vmatrix} 
for all values of \theta , is
  • 1
  • \cos\theta
  • \sin\theta
  • \cos2\theta
Let z = \begin{vmatrix} 1& 1 + 2i & -5i\\ 1 - 2i & -3 & 5 + 3i\\ 5i & 5 - 3i & 7\end{vmatrix}, then
  • z is purely real
  • z is purely imaginary
  • (z - \overline {z})i = 0
  • (z + \overline {z})i = 0
The adjoint of the matric A = \begin{bmatrix}1 & 0 & 2\\ 2 & 1 & 0\\ 0 & 3 & 1\end{bmatrix} is
  • \begin{bmatrix}-1 & 6 & 2\\ -2 & 1 & -4\\ 6 & 3 & 1\end{bmatrix}
  • \begin{bmatrix}1 & 6 & -2\\ -2 & 1 & 4\\ 6 & -3 & 1\end{bmatrix}
  • \begin{bmatrix}6 & 1 & 2\\ 4 & -1 & 2\\ 6 & 3 & -1\end{bmatrix}
  • \begin{bmatrix}-6 & 2 & 1\\ 4 & -2 & 1\\ 3 & 1 & -6\end{bmatrix}
Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (-1, 0) is equal to \displaystyle \frac{1}{3}. Then the circumcentre of the triangle ABC is at the point:
  • \displaystyle \left( \frac{5}{2}, 0 \right)
  • \displaystyle \left( \frac{5}{3}, 0 \right)
  • \displaystyle \left( 0, 0 \right)
  • \displaystyle \left( \frac{5}{8}, 0 \right)
If A + B + C = \pi, then \begin{vmatrix} \sin (A + B + C)& \sin B & \cos C\\ -\sin B & 0 & \tan A\\ \cos (A + B) & -\tan A & 0\end{vmatrix} is equal to
  • 0
  • 2\sin B \tan A \cos C
  • 1
  • None of these
If A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} satisfies the equation x^2 - (a + d) x + k = 0, then ?
  • k = bc
  • k = ad
  • k = a^2 + b^2 + c^2 + d^2
  • ad - bc
For a positive numbers x, y and z the numerical value of the determinant \begin{bmatrix}1 & \log_{x} y & \log_{x} z \\ \log_{y} x & 1 & \log_{y} z\\ \log_{z} x & \log_{z} y & 1\end{bmatrix} is:
  • 0
  • 1
  • \log_{e} xyz
  • -\log_{e} xyz

The value of the determinant \begin{vmatrix}b^{2}-ab\,\,  b-c\,\, bc-ac &  & \\ ab-a^{2}\,\, a-b\,\, b^{2}-ab&  & \\  bc-ac\,\, c-a\,\, ab-a^{2}&  & \end{vmatrix} =
  • abc
  • a+b+c
  • 0
  • ab+bc+ca
If the points A(-2,1),B(a,b) and C(4,-1) are collinear and a-b=1, find the values of a and b.
  • a=1,b=5
  • a=1,b=0
  • a=2,b=0
  • None of these
State true or false.
The determinants \left | \begin{array}{111} 1 & a & bc \\ 1 & b & cd \\ 1 & c & ab \\ \end {array} \right | and \left | \begin{array}{111} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \\ \end {array} \right | are not identically equal.
  • True
  • False
If \triangle = \left | \begin{array}{111} x_1+y_1\omega  & x_1\omega^2+y_1 & x_1+y_1\omega+z_1\omega^2 \\ x_2+y_2\omega & x_2\omega^2+y_2 & x_2+y_2\omega+z_2\omega^2 \\ x_3+y_3\omega & x_3\omega^2+y_3 & x_3+y_3\omega+z_3\omega^2 \\ \end {array} \right |
where 1,\omega,\omega^2 are cube roots of unity then \triangle is equal to
  • 0
  • 1
  • -1
  • None of these
\left| \begin{matrix} 1+a & 1 & 1 & 1 \\ 1 & 1+b & 1 & 1 \\ 1 & 1 & 1+c & 1 \\ 1 & 1 & 1 & 1+d \end{matrix} \right|
=abcd\left( 1+\dfrac { 1 }{ a } +\dfrac { 1 }{ b } +\dfrac { 1 }{ c } +\dfrac { 1 }{ d }  \right)\\ =s-r
if a,b,c,d are the roots of { x }^{ 4 }+p{ x }^{ 3 }+q{ x }^{ 2 }+rx+s=0.
  • True
  • False
If \left |\begin{array}{111}6i & -3i & 1 \\4 & 3i & -1 \\20 & 3 & i \\\end {array}\right | =x+iy, then
  • x=3, y=1
  • x = 1, y=3
  • x=0, y=3
  • x=0, y=0
The value of determinant \begin{vmatrix} x+1 & x+2 & x+4\\ x+3 & x+5 & x+8\\ x+7 & x+10 & x+14\end{vmatrix} is?
  • -2
  • x^2+2
  • 2
  • None of these
If \Delta_1=\begin{vmatrix} x & b & b\\ a & x & b\\ a & a & x\end{vmatrix} and \Delta_2=\begin{vmatrix} x & b\\ a & x\end{vmatrix} are the given determinants, then.
  • \Delta_1=3(\Delta_2)^2
  • (d/dx)\Delta_1=3\Delta_2
  • (d/dx)\Delta_1=3(\Delta_2)^2
  • \Delta_1=3\Delta_2^{3/2}
If A = \begin{bmatrix}               a & 0 & 0 \\[0.3em]               0 & a & 0 \\[0.3em]               0 & 0 & a               \end{bmatrix}, then the value of |A| |Adj. A|
  • a^3
  • a^6
  • a^9
  • a^{27}
If f(x) = \left | \begin{array}{111} 1 & x & x+1 \\ 2x & x(x-1) & (x+1)x \\ 3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1) \\ \end {array} \right |
then f(100) is equal to
  • 0
  • 1
  • 100
  • -100
If A =  \begin{bmatrix} \alpha & 2 \\ 2 & \alpha\end{bmatrix} and | A^3 | = 125 then \alpha is 
  • \pm1
  • =2
  • \pm3
  • \pm5
If a, b, c are three non-zero distinct numbers in A.P., then 
\triangle = \left | \begin{array}{111} (b-c)(c-a) & (a-b)(c-a) & (a-b)(b-c) \\ (c-a)(a-b) & (b-c)(a-b) & (b-c)(c-a) \\ (a-b)(b-c) & (c-a)(b-c) & (c-a)(a-b) \\ \end {array} \right | is always +ve.
  • True
  • False
If the points (-2, -5), (2, -2), (8, a) are collinear, then the value of a is ________.
  • \dfrac 52
  • \dfrac 32
  • \dfrac 72
  • None of these
State true or false
Following points are collinear. 
(-2, 1) , (0, 5) , (-1, 2).
  • True
  • False
The points (-a, -b), (0, 0), (a, b) (a^2,ab)  are 
  • collinear
  • vertices of rectangle
  • vertices of parallelgram
  • none of these
2x - 3y + z = 0 
x + 2y - 3z =0
4x - y - 2z = 0
The system of equations have a non trivial solution
  • True
  • False
If the lines p_{ 1 }x+q_{ 1 }y=1, p_{ 2 }x+q_{ 2 }y=1 and p_{3}x+q_{3}y=1 be concurrent, show that the points (p_{1},q_{1}), (p_{2}, q_{2}) and  (p_{3}, q_{3}) are collinear.
  • vertices of right angle triangle
  • vertices of an equilateral triangle
  • vertices of an isosceles triangle
  • Collinear
If A = \begin{bmatrix}               a & 0 & 0 \\[0.3em]               0 & a & 0 \\[0.3em]               0 & 0 & a               \end{bmatrix}, then the value of  |Adj. A| is equal to
  • a^3
  • a^6
  • a^9
  • a^{27}
If \begin{vmatrix}a & a & x \\ m & m & m \\b & x & b\end{vmatrix}=0  then x is:
  • a
  • b
  • a or b
  • 0
\begin{vmatrix} 2^{ 3 } & 3^{ 3 } & 3.2^{ 2 }+3.2+1 \\ 3^{ 3 } & 4^{ 3 } & 3.3^{ 2 }+3.3+1 \\ 4^{ 3 } & 5^{ 3 } & 3.4^{ 2 }+3.4+1 \end{vmatrix} is equal to
  • 0
  • 1
  • 2
  • 3
Find \begin{vmatrix}\log e & \log e^{2} & \log e^{3} \\ \log e^{2} & \log e^{3} & \log e^{4} \\ \log e^{3} & \log e^{4} & \log e^{5}\end{vmatrix}.
  • 0
  • 1
  • 4 \log e
  • 5 \log e
If \left| {\begin{array}{*{20}{c}}1&3&2\\1&{x - 1}&{2x + 2}\\2&5&9\end{array}} \right| = 0, then x is equal to :-
  • 2
  • 1
  • 4
  • 0
If \Delta = \begin{vmatrix} x-3 & 2x+1 & 2 \\ 3x+2 & x+2 & 1 \\ 5x+1 & 5x+4 & 5 \end{vmatrix} , then \Delta is
  • multiple of x^2
  • 15
  • a multiple of x
  • -15
Find the determinant of given matrix \left[ \begin{matrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{matrix} \right]
  • 2(a+b+c)^{3}
  • (a-b-c)^{3}
  • 2(a-b-c)^{3}
  • (a+b+c)^{3}
If \triangle =\begin{bmatrix} { a }_{ 1 } & { b }_{ 1 } & { c }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } & { c }_{ 2 } \\ { a }_{ 3 } & { b }_{ 3 } & { c }_{ 3 } \end{bmatrix} and {A}_{2},{B}_{2},{C}_{2} are respectively cofactors of {a}_{2},{b}_{2},{c}_{2} then {a}_{1}{A}_{2}+{b}_{1}{B}_{2}+{c}_{1}{C}_{2} is equal to ?
  • -\triangle
  • 0
  • \triangle
  • none\ of\ these
the below matrix  relation is 
\begin{vmatrix} 1 & { a }^{ 2 } & { a }^{ 3 } \\ 1 & { b }^{ 2 } & { b }^{ 3 } \\ 1 & { c }^{ 2 } & { c }^{ 3 } \end{vmatrix}=\begin{vmatrix} 0 & { a }^{ 2 }-{ c }^{ 2 } & { a }^{ 3 }-{ c }^{ 3 } \\ 0 & { b }^{ 2 }-{ c }^{ 2 } & { b }^{ 3 }-{ c }^{ 3 } \\ 1 & { c }^{ 2 } & { c }^{ 3 } \end{vmatrix}=\left( a-b \right) \left( b-c \right) \begin{vmatrix} 0 & { a }-{ c } & { a }^{ 2 }+ac{ +c }^{ 2 } \\ 0 & { b }-{ c } & { b }^{ 2 }+bc+{ c }^{ 2 } \\ 1 & { c }^{ 2 } & { c }^{ 3 } \end{vmatrix}
  • True
  • False
Let the matrix A and B be defined as A = \left( {\matrix{    3 & 2  \cr    2 & 1  \cr  } } \right) and B = \left( {\matrix{    3 & 1  \cr    7 & 3  \cr  } } \right) then the value of Det.\left( {2{A^9}{b^{ - 1}}} \right), is

  • 2
  • 1
  • -1
  • -2
0:0:1


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