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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 9 - MCQExams.com

|abcc+ba+cbcaabb+ac| =
  • abc(a2+b2+c2)
  • abc(a+b+c)
  • a+b+c(a2+b2+c2)
  • abc(1+1a+1b+1c)
If A=[1221] then  adj(A)=?
  • [1221]
  • [2111]
  • [1221]
  • [1221]
To solve  x+y=3:3x2y4=0  by determinant method find  D.
  • 5
  • 1
  • 5
  • 1
The number of distinct real roots of the equation,\left| \begin{matrix} cosx & sinx & sinx \\ sinx & cosx & sinx \\ sinx & sinx & cosx \end{matrix} \right| =0In t interval \left[ -\dfrac { \pi  }{ 4 } \dfrac { \pi  }{ 4 }  \right] is/are:
  • 3
  • 2
  • 1
  • 4
If the point \left(\lambda+1,1\right),\left(2\lambda+1,3\right) and \left(2\lambda+2,2\lambda\right) are collinear then the possible value of \lambda is
  • 2
  • 1/2
  • 3
  • 1/3
Solve \begin{vmatrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{vmatrix}
  • 1
  • 0
  • x
  • xy
If (k,2-2k),(-k+1,2k),(-4-k,6-2k) are collinear, then k=
  • +1
  • -1
  • -2
  • 2
If { D }_{ P }=\left| \begin{matrix} P & 15 & 8 \\ { P }^{ 2 } & 35 & 9 \\ { P }^{ 3 } & 25 & 10 \end{matrix} \right| , then { D }_{ 1 }+{ D }_{ 2 }+{ D }_{ 3 }+{ D }_{ 4 }+{ D }_{ 5 } is equal to -
  • -29000
  • -25000
  • 25000
  • none of these
The value of determinant \left| \begin{matrix} { bc-a }^{ 2 } & { ac-b }^{ 2 } & ab-c^{ 2 } \\ { ac-b }^{ 2 } & { ab-c }^{ 2 } & { bc-a }^{ 2 } \\ { ab-c }^{ 2 } & { bc-a }^{ 2 } & ac-b^{ 2 } \end{matrix} \right|  is
  • always non-negative
  • always non-positive
  • always zero
  • can't say anything
If A=\begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}, then \text{adj} (3{ A }^{ 2 }+12A) is equal to 
  • \begin{bmatrix} 51 & 63 \\ 84 & 72 \end{bmatrix}
  • \begin{bmatrix} 51 & 84 \\ 63 & 72 \end{bmatrix}
  • \begin{bmatrix} 72 & -63 \\ -84 & 51 \end{bmatrix}
  • \begin{bmatrix} 72 & -84 \\ -63 & 51 \end{bmatrix}
If a,b,c are distinct and \left| \begin{matrix} a & { a }^{ 2 } & { a }^{ 3 }-1 \\ b & { b }^{ 2 } & { b }^{ 3 }-1 \\ c & { c }^{ 2 } & { c }^{ 3 }-1 \end{matrix} \right| =0 then
  • a+b+c=1
  • ab+bc+ca=0
  • a+b+c=0
  • abc=1
If \begin{bmatrix} 1 & \alpha  & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} is the adjoint of a 3\times 3 matrix A and |A|=4, then \alpha is equal to:
  • 4
  • 11
  • 5
  • 0
If f(x), g(x), h(x) are polynomials in x of degree 2 and F(x)=\left| \begin{matrix} f & g & h \\ { f' } & g' & h' \\ f" & g" & h" \end{matrix} \right| , , then F(x) is equal to
  • 1
  • 0
  • -1
  • f(x).g(x).h(x)
If  \left| \begin{array} { c c } { 1 } & { \sin x } & { \sin ^ { 2 } x } \\ { 1 } & { \cos x } & { \cos ^ { 2 } x } \\ { 1 } & { \tan x } & { \tan ^ { 2 } x } \end{array} \right| = 0 , x \in [ 0,2 \pi ] , then number of possible values of  x  is.
  • 4
  • 5
  • 6
  • None of these
If  \begin{vmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{vmatrix} = (A+Bx)(x-A)^2,
then the ordered pair (A , B) is equal to:  
  • ( -4 , -5 )
  • ( -4 , 3 )
  • ( -4 , 5 )
  • ( 4 , 5 )
If A=\begin{vmatrix} 10 & 2 \\ 30 & 6 \end{vmatrix}\\ then \left|A\right|=
  • 0
  • 10
  • 12
  • 60
If \left|( {adj\,A}) \right| = 81, for 3 \times 3 matrix, then det A is equal to 
  • 1
  • 2
  • 4
  • 9
For what value of x, will the points (-1,x),(-3,2) and (-4,4) lie on a line?
  • -3
  • 3
  • -2
  • 2
\left| \begin{matrix} \frac { 1 }{ a }  & { a }^{ 2 } & bc \\ \frac { 1 }{ b }  & { b }^{ 2 } & ca \\ \frac { 1 }{ c }  & { c }^{ 2 } & ab \end{matrix} \right| =
  • abc
  • a+b+c
  • 0
  • 4abc
The point (x_{1}, y_{1}), (x_{2}, y_{2}), (x_{1}, y_{2}) & (x_{2}, y_{1}) are always
  • Collinear
  • Concyclic
  • Vertices of a square
  • Vertices of a rhombus.
Find the value of \begin{vmatrix} 5 & 3 \\ -7 & -4 \end{vmatrix}
  • -1
  • -41
  • 41
  • 1
If a,b,c are pth,qthand rth terms of a GP, then \begin{vmatrix} \log { a }  & p & 1 \\ \log { b }  & q & 1 \\ \log { c }  & r & 1 \end{vmatrix} is equal to
  • 0
  • 1
  • \log { abc }
  • none of these
|A|=6 and A is 3\times 3 matrix then det(2\ adj(2(A^{-1})^{T}))=
  • 162
  • 36
  • 216
  • 512
If \Delta{(x)} = \begin{vmatrix} e^x & \sin 2x & \tan x^2\\ ln(1 + x) & \cos x & \sin x\\ \cos x^2 & e^x - 1 & \sin x^2 \end{vmatrix} = A + Bx + Cx^2 + ..... then B is equal to
  • 0
  • 1
  • 2
  • 4
If A=\begin{bmatrix} 5 & 5x & x\\ 0 & x & 5x\\ 0 & 0 & 5\end{bmatrix} and |A^2|=25, then |x| is equal to?
  • \dfrac{1}{5}
  • 5
  • 5^2
  • 1
If a determinant of order 3\times 3 is formed by using the numbers 1 or -1, then the minimum value of the determinant is?
  • -2
  • -4
  • 0
  • -8
If \alpha, \beta are the roots of x^2+x+1=0 then \begin{vmatrix} y+1 & \beta & \alpha\\ \beta & y+\alpha & 1\\ \alpha & 1 & y+\beta\end{vmatrix}=?
  • y^2-1
  • y(y^2-1)
  • y^2-y
  • y^3
\begin{vmatrix} \sin ^{ 2 }{ \theta  }  & \cos ^{ 2 }{ \theta  }  \\ -\cos ^{ 2 }{ \theta  }  & \sin ^{ 2 }{ \theta  }  \end{vmatrix}=
  • \cos { 2\theta }
  • \cfrac { 1 }{ 2 } \left( 1+\cos ^{ 2 }{ 2\theta } \right)
  • \cfrac { 1 }{ 2 } \left( 1-\sin ^{ 2 }{ 2\theta } \right)
  • \cfrac { 1 }{ 2 } \sin ^{ 2 }{ 2\theta }
The sum of the real roots of the equation
\begin{vmatrix} x & -6 & -1 \\ 2 & -3x & x-3 \\ -3 & 2x & x+2 \end{vmatrix}=0 is equal to
  • 6
  • 1
  • 0
  • -4
\begin{vmatrix} a+ib & c+id \\ -c+id & a-ib \end{vmatrix}=?
  • (a^2+b^2-c^2-d^2)
  • (a^2-b^2+c^2-d^2)
  • (a^2+b^2+c^2+d^2)
  • none\ of\ these
For square matrices A and B of the same order, we have adj (AB) = ?
  • (adj\ A)(adj\ B)
  • (adj\ B)(adj\ A)
  • |AB|
  • None of these
\begin{vmatrix} \cos { { 70 }^{ o } }  & \sin { { 20 }^{ o } }  \\ \sin { { 70 }^{ o } }  & \cos { { 20 }^{ o } }  \end{vmatrix}=?
  • 1
  • 0
  • \cos 50^o
  • \sin 50^o
Evaluate : \begin{vmatrix} \sin { { 23 }^{ o } }  & -\sin { { 7 }^{ o } }  \\ \cos { { 23 }^{ o } }  & \cos { { 7 }^{ o } }  \end{vmatrix}
  • \dfrac {\sqrt 3}{2}
  • \dfrac {1}{2}
  • \sin 16^o
  • \cos 16^o
If A = \begin{bmatrix} a& b\\c  & d\end{bmatrix} then adj\ A = ?
  • \begin{bmatrix} d& -c\\ -b & a\end{bmatrix}
  • \begin{bmatrix} -d& b\\ c & -a\end{bmatrix}
  • \begin{bmatrix} d& -b\\ -c & a\end{bmatrix}
  • \begin{bmatrix} -d& -b\\ c & a\end{bmatrix}
If A is a 3-rowed square matrix and |A| = 5 then |adj\ A| = ?
  • 5
  • 25
  • 125
  • None of these
\begin{vmatrix} \cos { { 15 }^{ o } }  & \sin { { 15 }^{ o } }  \\ \sin { { 15 }^{ o } }  & \cos { { 15 }^{ o } }  \end{vmatrix}=?
  • 1
  • \dfrac {1}{2}
  • \dfrac {\sqrt 3}{2}
  • none\ of\ these
The roots of the equation
\begin{vmatrix} 3{ x }^{ 2 } & { x }^{ 2 }+x\cos { \theta  } +\cos ^{ 2 }{ \theta  }  & { x }^{ 2 }+x\sin { \theta  } +\sin ^{ 2 }{ \theta  }  \\ { x }^{ 2 }+x\cos { \theta  } +\cos ^{ 2 }{ \theta  }  & 3\cos ^{ 2 }{ \theta  }  & 1+\dfrac { \sin { 2\theta  }  }{ 2 }  \\ { x }^{ 2 }+x\sin { \theta  } +\sin ^{ 2 }{ \theta  }  & 1+\dfrac { \cos { 2\theta  }  }{ 2 }  & 3\sin ^{ 2 }{ \theta  }  \end{vmatrix}=0 are
  • \sin {\theta},\ \cos {\theta}
  • \sin^2 {\theta},\ \cos^2 {\theta}
  • \sin {\theta},\ \cos^2 {\theta}
  • \sin^2 {\theta},\ \cos {\theta}
When the determinant \begin{vmatrix} \cos { 2x }  & \sin ^{ 2 }{ x }  & \cos { 4x }  \\ \sin ^{ 2 }{ x }  & \cos { 2x }  & \cos ^{ 2 }{ x }  \\ \cos { 4x }  & \cos ^{ 2 }{ x }  & \cos { 2x }  \end{vmatrix} is expanded in powers of \sin x, then the constant term in that expression is
  • 1
  • 0
  • -1
  • 2
If the determinant \begin{vmatrix} \cos  2x & \sin ^{ 2 } x & \cos  4x \\ \sin ^{ 2 } x & \cos  2x & \cos ^{ 2 } x \\ \cos  4x & \cos ^{ 2 } x & \cos  2x \end{vmatrix} is expanded in powers of \sin x then the constant term in the expansion is 
  • 1
  • 2
  • -1
  • -2
If |A| = 3 and A^{-1} = \begin{bmatrix}3 & -1\\ \dfrac {-5}{3} & \dfrac {2}{3}\end{bmatrix} then adj\ A = ?
  • \begin{bmatrix} 9 & 3\\ -5 & -2 \end{bmatrix}
  • \begin{bmatrix} 9 & -3\\ -5 & 2 \end{bmatrix}
  • \begin{bmatrix} -9 & 3\\ 5 & -2 \end{bmatrix}
  • \begin{bmatrix} 9 & -3\\ 5 & -2 \end{bmatrix}
If \begin{vmatrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & a+b & c \end{vmatrix}=0, then the line ax+by+c=0 passes through the fixed point whcih is
  • (1,2)
  • (1,1)
  • (-2,1)
  • (1,0)
If A = \begin{bmatrix}2 & 5\\ 1 & 3\end{bmatrix} then adj\ A = ?
  • \begin{bmatrix}3 & -5\\ -1 & 2\end{bmatrix}
  • \begin{bmatrix}3 & -1\\ -5 & 2\end{bmatrix}
  • \begin{bmatrix}-1 & 2\\ 3 & -5\end{bmatrix}
  • None of these
If A is singular matrix , then adj A is 
  • singular
  • non-singular
  • symmetric
  • not defined
If A = \left[ \begin{matrix} 1 & -1 & 2 \\ 0 & 3 & 1 \\ 0 & 0 & -1/3 \end{matrix} \right]   , then 
  • | A | = -1
  • adj A = \left[ \begin{matrix} -1 & 1 & -2 \\ 0 & -3 & -1 \\ 0 & 0 & -1/3 \end{matrix} \right]
  • A = \left[ \begin{matrix} 1 & 1/3 & 7 \\ 0 & 1/3 & 1 \\ 0 & 0 & -3 \end{matrix} \right]
  • A= \left[ \begin{matrix} 1 & -1/3 & -7 \\ 0 & -3 & 0 \\ 0 & 0 & 1 \end{matrix} \right]
There are two values of a which makes determinant \Delta =\left| \begin{matrix} 1\quad  & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{matrix} \right| =86 then sum of these number is
  • 4
  • 5
  • - 4
  • 9
If \begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix}=\begin{vmatrix} 6 & -2 \\ 7 & 3 \end{vmatrix} then value of x is
  • 3
  • \pm 3
  • \pm 6
  • 6
Choose the correct answer from the given alternatives in the following question:
If A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} , {\text{adj}} A = \begin{bmatrix} 4 & a \\ -3 & b \end{bmatrix} , then the values of a and b are 
  • a = -2 , b = 1
  • a = 2 , b = 4
  • a = 2 , b = -1
  • a = 1 , b = -2
Choose the correct answer from the given alternatives in the following question:
If A = \begin{bmatrix} 2 & -4 \\ 3 & 1  \end{bmatrix} , then the adjoint of matrix A is 
  • \begin{bmatrix} -1 & 3 \\ -4 & 1 \end{bmatrix}
  • \begin{bmatrix} 1 & 4 \\ -3 & 2 \end{bmatrix}
  • \begin{bmatrix} 1 & 3 \\ 4 & -2 \end{bmatrix}
  • \begin{bmatrix} -1 & -3 \\ -4 & 2 \end{bmatrix}
State whether true or false:
If the value of a third order determinant is 12 , then the value of determinant formed by replacing each element by its co-factor will be 144
  • True
  • False
Choose the correct answer from the given alternatives in the following question:
If A = \begin{bmatrix} 1 & 2 \\ 2 & 1  \end{bmatrix} and A ({\text{adj}} A) = KI , then the value of k is 
  • 1
  • -1
  • 0
  • -3
0:0:1


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Practice Class 12 Commerce Maths Quiz Questions and Answers