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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 1 - MCQExams.com

The number of distinct real roots of the equation, |cosxsinxsinxsinxcosxsinxsinxsinxcosx|=0 
in the interval [π4,π4] is/are :
  • 3
  • 2
  • 1
  • 4
The points (0,83),(1,3) and (82,30) :
  • form an obtuse angled triangle.
  • form a right angled triangle.
  • lie on a straight line.
  • form an acute angled triangle.
If A=[2341], then adj (3A2+12A) is  equal to.
  • [72846351]
  • [51638472]
  • [51846372]
  • [72638451]
Let P = [a_{ij}] be a 3 \times 3 matrix and let Q = [b_{ij}], where b_{ij} = 2^{i + j} a_{ij} for 1 \leq i, j \leq 3. If the determinant of P is 2, then the determinant of the matrix Q is
  • 2^{10}
  • 2^{11}
  • 2^{12}
  • 2^{13}
Consider three points {P}=(-\sin(\beta-\alpha), -\cos\beta) , {Q}=(\cos(\beta-\alpha), \sin\beta) and {R}=(\cos(\beta-\alpha +\theta), \sin(\beta-\theta)) , where 0< \alpha,\ \beta,\ \theta <\displaystyle \frac{\pi}{4}. Then
  • P lies on the line segment RQ
  • Q lies on the line segment PR
  • R lies on the line segment QP
  • P, Q, R are non-collinear
The number of A in T_p such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p, is
  • (p - 1)^2
  • 2(p - 1)
  • (p - 1)^2 + 1
  • 2 p - 1
Let k be a positive real number and let A = \begin{bmatrix}2k-1 & 2\sqrt{k} & 2\sqrt{k}\\ 2\sqrt{k} & 1 & -2k\\ -2\sqrt{k} & 2k & -1\end{bmatrix} and B=\begin{bmatrix}0 & 2k-1 & \sqrt{k}\\ 1-2k & 0 & 2\sqrt{k}\\ -\sqrt{k} & -2\sqrt{k} & 0\end{bmatrix} . 
If det (adj A) + det (adj B) = 10^{6}, then [k] is equal to 

[Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k].
  • 3
  • 4
  • 5
  • 6
The value of |\mathrm{U}| is
  • 3
  • -3
  • 3/2
  • 2
A = \begin{bmatrix}1&2\\3&4\end{bmatrix}, B = \begin{bmatrix}2&1\\3&4\end{bmatrix} then \left|(B^TA^T)^{-1}\right| is equal to
  • 10
  • \dfrac{1}{10}
  • 1
  • - 1
If three points (k, 2k), (2k, 3k), (3, 1) are collinear, then k is equal to:
  • -2
  • 1
  • \displaystyle\frac{1}{2}
  • -\displaystyle\frac{1}{2}
\begin{vmatrix} 4\sin^{2}\theta  & \cos^{2}\theta \\ 3\sec^{2}\theta & \text{cosec}^{2}\theta \end{vmatrix}=
  • 8\sin^{2}\theta \cos^{2}\theta
  • 4\sin 2\theta \cos 2\theta
  • 1
  • 4\cos^{3}\theta -3\cos \theta
\left|\begin{array}{lllll} 0 & & \mathrm{c}\mathrm{o}\mathrm{s}\alpha & \mathrm{c}\mathrm{o}\mathrm{s} & \beta\\ \mathrm{c}\mathrm{o}\mathrm{s} & \alpha & 0 & \mathrm{c}\mathrm{o}\mathrm{s} & \gamma\\ \mathrm{c}\mathrm{o}\mathrm{s} & \beta & \mathrm{c}\mathrm{o}\mathrm{s}\gamma & 0 & \end{array}\right|=
  • \cos\alpha+\cos\beta+\cos\gamma
  • \cos\alpha\cos\beta\cos\gamma
  • 2\cos\alpha\cos\beta\cos\gamma
  • 2 \displaystyle \sum \cos\alpha\cos\beta
A=\left\{\begin{array}{ll} 8 & 9\\ 10 & 11 \end{array}\right\}, then cofactor of \mathrm{a}_{12} is:
  • 11
  • 10
  • -11
  • -10
If P =\begin{bmatrix} 1 & 4\\ 2 & 6 \end{bmatrix} ,then adj (P) 
  • \begin{bmatrix}1 & 4\\ 2 & 6\end{bmatrix}
  • \begin{bmatrix}6& -4\\ -2 & 1\end{bmatrix}
  • \begin{bmatrix}6& -2\\ -4 & 1\end{bmatrix}
  • \begin{bmatrix}2& 1\\ 6 & 4\end{bmatrix}
\begin{vmatrix} x^{2}+3 &x-1 &x+3 \\ x+3 & -2x &x-4 \\ x-3& x+4 & 3x \end{vmatrix} =px^{4}+qx^3+rx^{2}+sx+t,  then t =
  • 72
  • 0
  • 24
  • -48
Maximum value of a second order determinant whose every element is either 0,1 or 2 only is:
  • 0
  • 1
  • 2
  • 4
If \begin{vmatrix} cos(A+B) & -sin(A+B) &cos2B \\  sin A& cos A &sin B \\  -cos A& sin A & cos B \end{vmatrix} =0 then B=


  • (2n+1)\frac{\pi }{2}
  • n\pi
  • (2n+1)\pi
  • 2n\pi
If A  =\begin{bmatrix} 0 & c &-b \\ -c& 0& a\\ b & -a & 0 \end{bmatrix} then \left ( a^{2}+b^{2}-c^{2} \right )\left | A \right |= 
  • abc
  • a + b + c
  • \left ( a^{3}+b^{3}+c^{3} \right )
  • 0
Find x if it is given that:
\det \left[\begin{array}{lll} 2 & 0 & 0\\ 4 & 3 & 0\\ 4 & 6 & x \end{array}\right]=42
  • 8
  • 7
  • 6
  • 21/4
\mathrm{If} \left|\begin{array}{lll} 1 & 0 & 0\\ 2 & 3 & 4\\ 5 & -6 & x \end{array}\right| = 45 \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n} \mathrm{x}=

  • 4
  • 7
  • - 5
  • -7
If A is a singular matrix, then A (adj A) is a 
  • scalar matrix
  • zero matrix
  • identity matrix
  • orthogonal matrix
If A is a singular matrix, then adj A is
  • \displaystyle non-singular
  • singular
  • symmetric
  • not defined
If the value of the determinant \begin{vmatrix}m & 2\\ -5 & 7\end{vmatrix} is 31, find m.
  • 3
  • 8
  • 6
  • 2
If A is a 3\times 3 matrix and \text{det}  (3A)=k(\text{det}  A), then k=
  • 9
  • 6
  • 1
  • 27
If A and B are similar matrices such that det  (AB)=0, then 
  • det (A)=0 and det (B)=0
  • det (A)=0 and det (B) \neq 0
  • A=0 and B=0
  • A=0 or B=0
Let a, b, c be three complex numbers, and let
z=\begin{vmatrix} 0 & -b & -c\\ b & 0 & -a\\ c & a & 0 \end{vmatrix}
then z equal
  • 0
  • purely imaginary
  • abc
  • none of these
Two n\times n square matrices A and B are said to be similar if there exists a non-singular matrix P such that P^{-1}A  P=B.
If A and B are similar matrices such that det  (A)=1, then
  • det (B)=1
  • det (A)=-det (B)
  • det (B)=-1
  • none of these
If A is a square matrix of order n then adj \left ( adj A \right ) is equal to
  • \displaystyle \left | A \right |^{n}A
  • \displaystyle \left | A \right |^{n-1}A
  • \displaystyle \left | A \right |^{n-2}A
  • \displaystyle \left | A \right |^{n-3}A
If\displaystyle \left | \begin{matrix}-12 &0   &\lambda  \\  0&  2& -1\\  2& 1 &15 \end{matrix} \right |=-360, then the value of \lambda,is
  • -1
  • -2
  • -3
  • 4
If A is any skew-symmetric matrix of odd order then \left| A \right| equals
  • -1
  • 0
  • 1
  • none of these
If \begin{vmatrix} x & y\\ 4 & 2 \end{vmatrix}=7 and \begin{vmatrix} 2 & 3\\ y & x \end{vmatrix}=4 then
  • x=-3, y=-\dfrac {5}{2}
  • x=-\dfrac {5}{2}, y=-3
  • x=-3, y=\dfrac {5}{2}
  • x=-\dfrac {5}{2}, y=3
If \begin{vmatrix}a & -b & -c\\-a & b & -c \\ -a & -b & -c\end{vmatrix}+\lambda abc=0, then \lambda is equal to
  • 2
  • 4
  • -2
  • -4
The cofactors of elements in second row of the determinant \begin{vmatrix} 2 & -1 & 4 \\ 4 & 2 & -3 \\1 & 1 & 2 \end{vmatrix} are
  • 5, 6, 4
  • 6, 0, -3
  • 5, 1, 8
  • 6, 0, 3
A set of points which do not lie on the same line are called as
  • collinear
  • non-collinear
  • concurrent
  • square
A and B are two points and C is any point collinear with A and B. IF AB=10, BC=5, then AC is equal to:
  • either 15 or 5
  • necessarily 5
  • necessarily 16
  • none of these
If A=\begin{bmatrix} 3 & -5 \\ -1 & 0 \end{bmatrix}, then adj. A is equal to
  • \begin{bmatrix} 3 & 5 \\ 1 & 0 \end{bmatrix}
  • \begin{bmatrix} 0 & -5 \\ -1 & 3 \end{bmatrix}
  • \begin{bmatrix} 0 & 5 \\ 1 & 3 \end{bmatrix}
  • \begin{bmatrix} 0 & -1 \\ -5 & 3 \end{bmatrix}
The value of the determinant \begin{vmatrix}a & b & 0\\ 0 & a & b\\ b & 0 &a \end{vmatrix} is equal to
  • a^3-b^3
  • a^3+b^3
  • 0
  • none of these
The value of the determinant \begin{vmatrix} 1 & 2 & 3\\ 3 & 5 & 7\\ 8 & 14 & 20\end{vmatrix} is equal to
  • 20
  • 10
  • 0
  • 45
If \begin{vmatrix} 6i & -3i & 1\\ 4 & 3i & -1 \\ 20 & 3 & i\end{vmatrix}=x+iy, then
  • x = 3, y = 1
  • x = 1, y = 3
  • x = 0, y = 3
  • x = 0, y = 0
The points which are not collinear are:
  • (0, 1),\  (8, 3)\ and\ (6, 7)
  • (4, 3),\ (5, 1)\ and\ (1, 9)
  • (2, 5),\ (-1, 2)\ and\ (4, 7)
  • (-3, 2)\, (1, -2)\ and\ (9, -10)
If A=\begin{bmatrix} a & b \\ b & a \end{bmatrix}, then \left| A+{ A }^{ T } \right| equals
  • 4({a}^{2}-{b}^{2})
  • 2({a}^{2}-{b}^{2}
  • {a}^{2}-{b}^{2})
  • 4ab
If \Delta_1=\begin{vmatrix} 1 & 0\\ a & b\end{vmatrix} and \Delta_2=\begin{vmatrix} 1 & 0\\ c & d\end{vmatrix} then \Delta_2 \Delta_1 is equal to
  • ac
  • bd
  • (b-a)(d-c)
  • none of these
If A and B are two matrices of same order 3\times 3, where
A=\begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 5 & 6 & 8 \end{bmatrix} and B=\begin{bmatrix} 3 & 2 & 5 \\ 2 & 3 & 8 \\ 7 & 2 & 9 \end{bmatrix}
The value of \text{Adj} (\text{Adj}\, A) is equal to
  • -A
  • A
  • 8A
  • 16A
If \omega is a cube root of unity and \Delta=\begin{vmatrix}1 & 2\omega \\ \omega & \omega^2\end{vmatrix}, then \Delta^2 is equal to
  • -\omega
  • \omega
  • 1
  • \omega^2
If \begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix}=\begin{vmatrix} 6 & 2 \\ 3x & 6 \end{vmatrix}, then x is equal to
  • 6
  • \pm 6
  • -6
  • 0
Which of the following is correct?
  • Determinant is a square matrix
  • Determinant is a number associated to a matrix
  • Determinant is a number associated to a square matrix
  • None of these
If |A|  \displaystyle \neq    0, then A is
  • zero matrix
  • singular matrix
  • non - singular matrix
  • diagonal matrix
A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} and A(\text{adj}\,A)=KI, then the value of K is:
  • 2
  • -2
  • 10
  • -10
What is the determinant of the matrix \left [\begin{matrix} 3& 6\\ -1 & 2\end {matrix} \right]?
  • 0
  • 12
  • |0|
  • |6|
If A = \begin{bmatrix} 1& \log_{b}a\\ \log_{a}b & 1\end{bmatrix} then |A| is equal to
  • 0
  • \log_{a}b
  • -1
  • \log_{b}a
0:0:1


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