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:
  • $$\displaystyle \frac { 1 }{ 2 } $$
  • $$\displaystyle \frac { 3 }{ 2 } $$
  • $$\displaystyle \frac { -5 }{ 2 } $$
  • $$\displaystyle \frac { 5 }{ 2 } $$
The value of $$\displaystyle \begin{vmatrix}a - b - c & 2a & 2a\\ 2b & b - c- a & 2b\\ 2c & 2c & c- a -b\end{vmatrix}$$ will be
  • $$(a+b+c)^2$$
  • $$(a+b+c)^3$$
  • $$(a-b-c)^2$$
  • $$(a + b -c)^2$$
The points (-a, -b), (0, 0), (a, b) and ($$\displaystyle a^{2}$$, 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 
  • $$\displaystyle \frac{7}{9}$$
  • $$\displaystyle \frac{2}{3}$$
  • $$\displaystyle \frac{-2}{3}$$
  • $$\displaystyle \frac{-1}{3}$$
The points (-a, -b), (0, 0), (a, b) and (a$$^2$$, 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 $$\displaystyle \begin{vmatrix} 2 & -4   \\ 9 & d-3   \end{vmatrix}=4$$ 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?
  • $$-1$$
  • $$2$$
  • $$\displaystyle \frac{1}{2}$$
  • $$\displaystyle -\frac{1}{2}$$
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 $$\displaystyle \left[ \begin{matrix} \cos { \theta  }  \\ -\sin { \theta  }  \\ 0 \end{matrix}\begin{matrix} \sin { \theta  }  \\ \cos { \theta  }  \\ 0 \end{matrix}\begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right] $$ then the value of $$\displaystyle { a }_{ 11 }{ A }_{ 11 }+{ a }_{ 12 }{ A }_{ 12 }+{ a }_{ 13 }{ A }_{ 13 }=$$ where $$\displaystyle { A }_{ 11 },{ A }_{ 12 }{ A }_{ 13 }$$ are cofactors of $$\displaystyle { a }_{ 11 },{ a }_{ 12 },{ a }_{ 13 }$$ respectively
  • $$-1$$
  • $$1$$
  • $$0$$
  • $$\displaystyle \frac { 1 }{ 2 } $$
If $$z=\begin{vmatrix} 1 & 1+2i & -5i \\ 1-2i & -3 & 5+3i \\ 5i & 5-3i & 7 \end{vmatrix} $$, then $$i=\left( \sqrt { -1 }  \right) $$
  • $$z$$ is purely real
  • $$z$$ is purely imaginary
  • $$z+\overline { z } =0$$
  • $$\left( z-\overline { z } \right) i$$ is purely imaginery
If $$\Delta = \begin{vmatrix} -a & 2b & 0  \\ 0 & -a & 2 b \\ 2b & 0 &-a  \end{vmatrix}=0$$, then
  • $$\dfrac{1}{b}$$ is a cube root of unity
  • $$a$$ is one of the cube roots of unity
  • $$b$$ is one of the cube roots of $$8$$
  • $$\dfrac{a}{b}$$ 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 $$P = \begin{bmatrix} 1& 2 & 1\\ 1 & 3 & 1\end{bmatrix}, Q = PP^{T}$$, 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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