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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 6 - MCQExams.com

Value of p for which the points (-5, 1), (1, p) and (4, -2) are collinear is
  • 0
  • 2
  • -1
  • None of these
If the points (-2, -5), (2, -2) and (8, a) are collinear then value of a will be:
  • 12
  • 32
  • 52
  • 52
The value of |abc2a2a2bbca2b2c2ccab| will be
  • (a+b+c)2
  • (a+b+c)3
  • (abc)2
  • (a+bc)2
The points (-a, -b), (0, 0), (a, b) and (a2, ab) are
  • Collinear
  • Vertices of a parallelogram
  • Vertices of a rectangle
  • None of these
The points (0, 8/3), (1, 3) and (82, 30) are the vertices of :
  • obtuse angled triangle
  • right angled triangle
  • isosceles triangle
  • None of these
Find the value of K if A(8, 1), B(K, -4), C(2, -5) are collinear :
  • 2
  • 3
  • 4
  • 5
If the points (k,2k), (3k,3k) and (3,1) are collinear then the value of k is 
  • 79
  • 23
  • 23
  • 13
The points (-a, -b), (0, 0), (a, b) and (a2, ab) are
  • collinear
  • vertices of a rectangle
  • vertices of a parallelogram
  • None of these
Find the value of P for which the points A(-1, 3), B(2, P) and C(5, -1) are collinear :
  • 3
  • 1
  • 2
  • 4
Find the value of K if (2, 3), (4, K) and (6, -3) are collinear :
  • 0
  • 1
  • 2
  • 3
If |249d3|=4 then d=
  • 10
  • 11
  • 12
  • 13
If the coordinates of the vertices of a triangle are (0,0) , (0,2) and(3,1) , then area of the triangle is 
  • 3 sq.units
  • -3 sq. units
  • 2 sq. units
  • 1 sq.units
What is the value of y if (y,3),(5,6) and (8,8) are collinear?
  • 1
  • 2
  • 12
  • 12
Which of the following points are collinear?
  • (2a,0), (3a,0), (a,2a)
  • (3a,0), (0,3b), (a,2b)
  • (3a,b), (a,2b), (-a,b)
  • (a,-6), (-a,3b), (-2a,-2b)
If [cosθsinθ0sinθcosθ0001] then the value of a11A11+a12A12+a13A13= where A11,A12A13 are cofactors of a11,a12,a13 respectively
  • 1
  • 1
  • 0
  • 12
If z=|11+2i5i12i35+3i5i53i7|, then i=(1)
  • z is purely real
  • z is purely imaginary
  • z+¯z=0
  • (z¯z)i is purely imaginery
If Δ=|a2b00a2b2b0a|=0, then
  • 1b is a cube root of unity
  • a is one of the cube roots of unity
  • b is one of the cube roots of 8
  • ab is a cube root of 8
Find the correct option regarding given points (1,2),(2,4) and (3,6) 
  • Non-colllinear
  • Exists on parallel lines
  • Collinear
  • Exists on perpendicular lines
Find the value of k for which the points (2,3),(3,k) and (3,7) are collinear.
  • 5
  • 6
  • 8
  • 7
If the points (a,b),(3,5) and (5,2) are collinear. Then find the value of 3a+8b
  • 20
  • 31
  • 10
  • None
If P=[121131],Q=PPT, then the value of the determinant of Q is
  • 2
  • 2
  • 1
  • 0
Find the correct option regarding the given points (2,1),(0,2) and (3,2).
  • Collinear
  • Non-collinear
  • Exists on parallel lines
  • Exists on perpendicular lines
Find the correct option regarding given points (2,2),(1,2) and (3,1).
  • Collinear
  • Non-collinear
  • Exists on parallel lines
  • Exists on perpendicular lines
Consider the three collinear points (3,p),(4,4) and (5,6). Find the value of p.
  • 1
  • 2
  • 3
  • 4
The graph of f(x) is shown above in the xy-plane. The points (0,3),(5b,b) and (10b,b) are on the line described by f(x). If b is a positive constant, find the coordinates of point C.
479301_205f8c81dc934e7da45b65c8b3ea8304.png
  • (5,1)
  • (10,1)
  • (15,0.5)
  • (20,2)
If C = 2 \cos \theta, then the value of the determinant to \Delta = \left |\begin{matrix} c & 1 & 0 \\ 1 & c & 1 \\ 6 & 1 & c \end{matrix}\right | is
  • \dfrac{2\,\sin^22\theta}{\sin\,\theta}
  • 8\, \cos^3\theta-4\,cos\theta+6
  • \dfrac{2\,\sin\,2\theta}{\sin\, \theta}
  • 8\,\cos^3\theta+4\,\cos\theta+6
If A = \begin{bmatrix}-8 & 5\\ 2 & 4\end{bmatrix} satisfies the equation x^2\, +\, 4x\, -\, p\, =\, 0, then p = 
  • 64
  • 42
  • 36
  • 24
Evaluate \begin{vmatrix} \cos 15^o& \sin 15^o\\ \sin 75^o & \cos 75^o\end{vmatrix}
  • 1
  • 0
  • 2
  • 3
Let A be a 3 \times 3 matrix and B be its adjoint matrix. If |B| = 64, then |A| =
  • \pm 2
  • \pm 4
  • \pm 8
  • \pm 12
The points (-a, -b), (a, b), (0, 0) and (a^2, ab), a\ne 0, b\ne 0 are 
  • Collinear
  • Vertices of a parallelogram
  • Vertices of rectangle
  • Lie on a circle
If A(x)=\begin{vmatrix} x+1 & 2x+1 & 3x+1 \\ 2x+1 & 3x+1 & x+1 \\ 3x+1 & x+1 & 2x+1 \end{vmatrix} 
then \displaystyle \int _{ 0 }^{ 1 }{ A(x) } dx=
  • -15
  • \cfrac { -15 }{ 2 }
  • -30
  • -5
If a, b and c are in A, P., then the value of \begin{vmatrix} x+2 & x+3 &x+a \\  x+4& x+5 &x+b \\ x+6 & x+7 & x+c \end{vmatrix} is.
  • x-(a+b+c)
  • 9x^2+a+b+c
  • 0
  • a+b+c
If the points (2,5),(4,6) and (a,a) are collinear, then the value of a is equal to
  • -8
  • 4
  • -4
  • 8
If \Delta_r = \begin{vmatrix}2r - 1 & ^mC_r & 1\\ m^2 - 1 & 2^m & m+1\\ sin^2(m^2) & sin^2(m) & sin^2(m+1)\end{vmatrix}, then the value of \displaystyle \sum_{r = 0}^m \Delta_r, is
  • 1
  • 0
  • 2
  • None of these
The centre of a circle is (-6,4). If one end of the diameter of the circle is at (-12,8), then the other end is at
  • (-18,12)
  • (-9,6)
  • (-3,2)
  • (0,0)
If a, b and c are in AP, then determinant \begin{vmatrix}x + 2 & x + 3 & x + 2a\\ x + 3 & x + 4 & x + 2b\\ x + 4 & x + 5 & x + 2c\end{vmatrix} is
  • 0
  • 1
  • x
  • 2x
The value of the determinant \begin{vmatrix}1 & \cos (\alpha - \beta) & \cos \alpha\\ \cos(\alpha - \beta) & 1 & \cos \beta\\ \cos \alpha & \cos \beta & 1\end{vmatrix} is
  • \alpha^{2} + \beta^{2}
  • \alpha^{2} - \beta^{2}
  • 1
  • 0
The value of the determinant \begin{vmatrix}cos\, \alpha  & -sin \,\alpha   &1 \\ sin \, \alpha  & cos \, \alpha  & 1\\ cos (\alpha +\beta)  & -sin (\alpha +\beta ) & 1\end{vmatrix} is
  • Independent of \alpha
  • Independent of \beta
  • Independent of \alpha and \beta
  • None of the above
If \triangle (r) = \begin{vmatrix}r & r^{3}\\ 1 & n(n + 1)\end{vmatrix}, then \displaystyle \sum_{r = 1}^{n} \triangle (r) is equal to
  • \displaystyle \sum_{r = 1}^{n} r^{2}
  • \displaystyle \sum_{r = 1}^{n} r^{3}
  • \displaystyle \sum_{r = 1}^{n} r
  • \displaystyle \sum_{r = 1}^{n} r^{4}
If \begin{vmatrix} a & b & 0 \\ 0 & a & b \\ b & 0 & a\end{vmatrix}=0, then which one of the following is correct?
  • \displaystyle\frac{a}{b} is one of the cube roots of unity
  • \displaystyle\frac{a}{b} is one of the cube roots of -1.
  • a is one of the cube roots of unity
  • b is one of the cube roots of unity.
If A is an invertible matrix, then what is det (A^{-1}) equal to?
  • det A
  • \displaystyle\frac{1}{det A}
  • 1
  • None of the above
\begin{vmatrix}1 & 1 & 1\\ a & b & c\\ a^2 - bc & b^2 - ca & c^2 - ab\end{vmatrix} =
  • 0
  • 1
  • abc
  • (a -b), \,(b-c),\, (c-a)
If A = \begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix} and B = \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix} then what is determinant of AB ?
  • 0
  • 1
  • 10
  • 20
If \begin{vmatrix} 8 & -5 & 1 \\ 5 & x & 3\\ 6 & 3 & 1 \end{vmatrix} = 2  then what is the value of x ?
  • 44
  • 55
  • 61
  • 84
The cofactor of the element 4 in the determinant
                    \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 5 & 8 & 9 \end{vmatrix}
is
  • 2
  • 4
  • 6
  • -6
Consider the following statements in respect of the determinant \begin{vmatrix}{\cos}^2\dfrac{\alpha}{2}&{\sin}^2\dfrac{\alpha}{2}\\{\sin}^2\dfrac{\beta}{2}&{\cos}^2\dfrac{\beta}{2}\end{vmatrix} where \alpha , \beta are complementary angles
The value of the determinant is \dfrac{1}{\sqrt{2}}\cos \begin{pmatrix}\dfrac{\alpha - \beta}{2}\end{pmatrix}.
The maximum value of the determinant is \dfrac{1}{\sqrt{2}}.
Which of the above statements is/are correct?
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
Let A = \begin{pmatrix}x + 2 & 3x\\ 3 & x + 2\end{pmatrix}, B = \begin{pmatrix}x & 0\\ 5 & x + 2\end{pmatrix}. Then all solutions of the equation det (AB) = 0 is
  • 1, -1, 0, 2
  • 1, 4, 0, -2
  • 1, -1, 4, 3
  • -1, 4, 0, 3
If C = 2 \cos \theta , then the value of the determinant \triangle = \begin{vmatrix} C & 1 & 0 \\ 1 & C & 1 \\ 6 & 1 & C  \end{vmatrix} is :
  • \dfrac { \sin 4 \theta } { \sin \theta}
  • \dfrac { 2 \sin^2 \theta } { \sin \theta}
  • 4 \cos^2 \theta (2 \cos \theta - 1)
  • None of these above
If A = \begin{bmatrix} 1& 2\\ 3 & 4\end{bmatrix}, then A^{-1} =
  • \dfrac {-1}{2}\begin{bmatrix} 4& -2\\ -3 & 1\end{bmatrix}
  • \dfrac {1}{2}\begin{bmatrix} 4& -2\\ -3 & 1\end{bmatrix}
  • \begin{bmatrix} -2& 4\\ 1 & 3\end{bmatrix}
  • \begin{bmatrix} 2& 4\\ 1 & 3\end{bmatrix}
If \alpha, \beta, \gamma are the roots of the equation x^{3} + px + q = 0 then the value of the determinant \begin{vmatrix} \alpha& \beta & \gamma\\ \beta & \gamma & \alpha\\ \gamma & \alpha & \beta\end{vmatrix} is
  • q
  • 0
  • p
  • p^{2} - 2q
0:0:1


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