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

$$\left| \begin{matrix} a & b-c & c+b \\ a+c & b & c-a \\ a-b & b+a & c \end{matrix} \right| $$ =
  • $$abc({ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 })$$
  • $$abc({ a }+{ b }+{ c })$$
  • $$a+b+c({ a }^{ 2 }+{ b^{ 2 } }+{ c^{ 2 } })$$
  • $$abc\left( 1+\frac { 1 }{ a } +\dfrac { 1 }{ b } +\frac { 1 }{ c } \right) $$
If $$A = \left[ \begin{array} { l l } { 1 } & { 2 } \\ { 2 } & { 1 } \end{array} \right]$$ then  $$adj (A) =?$$
  • $$\left[ \begin{array} { c c } { 1 } & { - 2 } \\ { - 2 } & { 1 } \end{array} \right]$$
  • $$\left[ \begin{array} { l l } { 2 } & { 1 } \\ { 1 } & { 1 } \end{array} \right]$$
  • $$\left[ \begin{array} { c c } { 1 } & { - 2 } \\ { - 2 } & { - 1 } \end{array} \right]$$
  • $$\left[ \begin{array} { c c } { - 1 } & { 2 } \\ { 2 } & { - 1 } \end{array} \right]$$
To solve  $$x + y = 3 : 3 x - 2 y - 4 = 0$$  by determinant method find  $$D.$$
  • $$5$$
  • $$1$$
  • $$-5$$
  • $$-1$$
The number of distinct real roots of the equation,$$\left| \begin{matrix} cosx & sinx & sinx \\ sinx & cosx & sinx \\ sinx & sinx & cosx \end{matrix} \right| =0$$In 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 $$pth$$,$$qth$$and $$rth$$ 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


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers