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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 3 - MCQExams.com

Adj [102112021][5a211022b] [ab]= 
  • [41]
  • [41]
  • [41]
  • [41]
A determinant of second order is made with the elements 0 and 1. The number of determinants with non-negative values is:
  • 3
  • 10
  • 11
  • 13
If A=\displaystyle \int_{1}^{sin\theta}\frac{t}{1+t^{2}}dt and
B=\displaystyle \int_{1}^{cosec\theta}\frac{1}{t(1+t^{2})}dt, then the value of determinant  \begin{vmatrix} A & A^{2}& B\\ e^{A+B}& B^{2} &-1 \\ 1& A^{2}+B^{2} & -1 \end{vmatrix} is 

  • \sin\theta
  • cosec \theta
  • 0
  • 1
I. If A,B,C are angles of angle and \begin{vmatrix} 1 & 1 & 1\\ 1+sinA& 1+sinB&1+sinC \\ sinA+sin^{2}A & sinB+sin^{2}B & sinC+sin^{2}C \end{vmatrix} =0  then triangle is isosceles
 II. lf a=1+2+4+--- upto \mathrm{n} terms b=1+3+9+--- up to \mathrm{n} terms c=1+5+25+----up to \mathrm{n} terms  then \Delta \begin{vmatrix} a &2b &4c \\ 2& 2& 2\\ 2^{n} & 3^{n} & 5^{n} \end{vmatrix} =0
  • I, II both are true
  • only I is true
  • only II is true
  • neither of them are true
1\mathrm{f}\mathrm{A}=\left[\begin{array}{lll} 1 & 5 & -6\\ -8 & 0 & 4\\ 3 & -7 & 2 \end{array}\right] then the cofactors of the elements 3,-7,2 are p,q,r respectively their ascending order is 
  • \mathrm{p},\ \mathrm{r}, \mathrm{q}
  • \mathrm{q},\mathrm{r},\ \mathrm{p}
  • \mathrm{p},\mathrm{q},\mathrm{r}
  • \mathrm{r},\mathrm{p},\ \mathrm{q}
If f(x)= \begin{vmatrix} \sin\, \, x &1 &0 \\ 1& 2\sin\, \, x& 1\\ 0& 1 & 2\sin\, \, x \end{vmatrix} then \displaystyle \int _{-\frac{\pi }{2}}^{\frac{\pi }{2}} f\left ( x \right ) equals 

  • 0
  • -1
  • 1
  • \dfrac{3\pi }{2}
\begin{vmatrix} 1 & cos\alpha & cos\beta \\ cos\alpha & 1 & cos\gamma \\ cos\beta &cos\gamma & 1 \end{vmatrix} = \begin{vmatrix} 0 & cos\alpha & cos\beta \\ cos\alpha & 0 & cos\gamma \\ cos\beta &cos\gamma & 0 \end{vmatrix} then 


  • cos\alpha +cos\beta +cos\gamma =0
  • cos\alpha .cos\beta .cos\gamma =0
  • cos^{2} \, \, \alpha +cos^{2}\, \, \beta + cos^{2}\gamma =1
  • \sum cos \: \: \alpha \, cos\, \, \beta \, \, =0
Match the following elements of \begin{vmatrix} 1 & -1 &0 \\ 0& 4 & 2\\ 3 & -4 & 6 \end{vmatrix} with their cofactors and choose the correct
answer 
Element                                                        Cofactor
I. -1                                                                   a) -2
II. 1                                                                   b) 32
III. 3                                                                  c) 4
IV. 6                                                                  d) 6
                                                                         e) -6
  • I-b,II-d,III-a,IV-c
  • I-b,II-d,III-c,IV-a
  • I-d,II-b,III-a,IV-c
  • I-d,II-a,III-b,IV-c
If {A}=\begin{bmatrix} cos\theta & sin\theta\\ -sin\theta & cos\theta \end{bmatrix} then \displaystyle \lim_{n\rightarrow\infty}\frac{1}{n}|A^{n}|=
  • 1
  • 0
  • A
  • \displaystyle \frac{1}{n}A
\mathrm{D}\mathrm{e}\mathrm{t} \left\{\begin{array}{lll} -2a & a+b & c+a\\ b+a & -2b & b+c\\ c+a & c+b & -2c \end{array}\right\}= 

  • (\mathrm{a}+\mathrm{b})(\mathrm{b}+\mathrm{c})(\mathrm{c}+\mathrm{a})
  • (a-b) (b-c) (c-a)
  • 4(\mathrm{a}+\mathrm{b})(\mathrm{b}+\mathrm{c})(\mathrm{c}+\mathrm{a})
  • 4(a-b) (b-c) (c-a)
The sum of infinite series \begin{vmatrix} 1 &2 \\ 6 & 4 \end{vmatrix}+\begin{vmatrix} \frac{1}{2} &2 \\ 2& 4 \end{vmatrix}+\begin{vmatrix} \frac{1}{4} & 2\\ \frac{2}{3}& 4 \end{vmatrix}+ ....... is 
  • -10
  • 0
  • 10
  • \infty
lf f(x)=\left| \begin{matrix} \sec { x }  & \cos { x }  \\ \cos ^{ 2 }{ x }  & \cos ^{ 2 }{ x }  \end{matrix} \right| , then \displaystyle \int_{0}^{\pi/2}f(x)dx=
  • 1/2
  • 1/3
  • 0
  • 1
lf a\neq b\neq c Then one value of \mathrm{x} which satisfies the equation \begin{vmatrix} 0 & x-a &x-b \\ x+a & 0 & x-c\\ x+b& x+c& 0 \end{vmatrix} = 0 is given by 

  • x = a
  • x = b
  • x = c
  • x = 0
.Let \begin{vmatrix} x&2 & x\\ x^{2}&x & 6\\ x & x& 6 \end{vmatrix} =ax^{4}+bx^{3}+cx^{2}+dx+e ,then the value of 5a + 4b + 3c + 2d + e is
equal to 

  • 0
  • 16
  • -16
  • -11
\begin{vmatrix} 1+i &1-i &1 \\ 1-i& i&1+i \\ i & 1+i & 1-i \end{vmatrix} is a 
  • real number
  • irrational number
  • complex member
  • Purely imaginary
{A}=\begin{bmatrix} -1 & -2 & -2\\ 2 & 1 & -2\\ 2 & -2 & 1 \end{bmatrix} then Adj(A)= 

  • \mathrm{A}^{\mathrm{T}}
  • 3\mathrm{A}^{\mathrm{T}}
  • \mathrm{A}^{-1}
  • -\mathrm{A}^{\mathrm{T}}
If \Delta = \begin{vmatrix} cos\frac{\theta }{2} &1  &1 \\   1&cos\frac{\theta }{2}  &-cos\frac{\theta }{2} \\ -cos\frac{\theta }{2} &1  & -1 \end{vmatrix} the minimum of \Delta is m_{1} and maximum of \Delta is m_{2} then [m_{1} , m_{2}] is
  • [ 4, 2]
  • [2,4]
  • [4,0]
  • [0,2]
f(x)= \begin{vmatrix} \cos x &x &1 \\ 2 \sin x & x^{2} &2x \\ \tan x& x & 1 \end{vmatrix} then \displaystyle \lim _{ x\rightarrow 0 }{ f(x) } =
  • 0
  • -1
  • -2
  • 2
The value of \begin{vmatrix} 1+x&2 & 3\\ 1& 2+x&3\\ 1 & 2 & 3+x \end{vmatrix} is 
  • (x-6)x^{2}
  • (x-6)x
  • x^{2}(x+6)
  • (x-6)
If [\mathrm{x}] stands greatest integer \leq \mathrm{x} then the value of \begin{vmatrix} \left [ e \right ]& \left [ \pi \right ] &\left [ \pi ^{2}-6 \right ]\\ \left [ \pi \right ] & \pi ^{2}-6 & \left [ e \right ]\\ \left [ \pi ^{2}-6 \right ]&\left [ e \right ] & \left [ \pi \right ] \end{vmatrix} equals 
  • -8
  • 8
  • -1
  • 1
lf adjA=\left\{\begin{array}{lll} 1 & -1 & 0\\ 2 & 3 & 1\\ 2 & 1 & -1 \end{array}\right\} then adj 2 \mathrm{A}= 

  • \left\{\begin{array}{lll} 2 & -2 & 0\\ 4 & 6 & 2\\ 4 & 2 & -2 \end{array}\right\}
  • \left\{\begin{array}{ll} 4&-4 & 0\\ 8&12 & 4\\ 8&4 & -4 \end{array}\right\}
  • \left\{\begin{array}{lll} 8 & -8 & 0\\ 16 & 24 & 8\\ 16 & 8 & -8 \end{array}\right\}
  • \left\{\begin{array}{lll} 1 & -1 & 0\\ 2 & 3 & 1\\ 2 & 1 & -1 \end{array}\right\}
A=\begin{bmatrix}4 &-2&5\end{bmatrix},  B= \begin{bmatrix} 2\\ 0\\ 3\end{bmatrix}, then Adj(BA)= 
  • \left\{\begin{array}{lll} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{array}\right\}
  • \left\{\begin{array}{lll} 8 & -4 & 10\\ 0 & 0 & 0\\ 12 & -6 & 15 \end{array}\right\}
  • \left\{\begin{array}{lll} 8 & 0 & 12\\ -4 & 0 & -6\\ 10 & 0 & 5 \end{array}\right\}
  • None of the above
.Let \Delta (x)=\begin{vmatrix} x+a & x+b &x+a-c \\ x+b & x+c &x-1 \\ x+c & x+d &x-b+d \end{vmatrix} and \displaystyle \int_{0}^{2}\Delta(x) dx =-16, where \mathrm{a}, b,c,d are in A.\mathrm{P}. then the common difference of the A.\mathrm{P}. is 

  • \pm 1
  • \pm 2
  • \pm 3
  • \pm 4
A= \begin{bmatrix}  b^{2}c^{2}& bc & b+c\\  c^{2}a^{2}& ca &c+a \\  a^{2}b^{2}& ab & a+b \end{bmatrix} then \left | A \right | =?
  • abc
  • abc-1
  • abc+1
  • 0
The straight lines \mathrm{x}+2\mathrm{y}-9=0,3\mathrm{x}+5\mathrm{y}-5=0 and \mathrm{a}\mathrm{x}+\mathrm{b}\mathrm{y}-1=0 are concurrent if the straight line 22\mathrm{x}-35\mathrm{y}-1=0 passes through the point 

  • (a, b)
  • (b,a)
  • (-a,b)
  • (-a, -b)
If maximum and minimum values of the determinant \begin{vmatrix} 1+\sin ^{ 2 }{ x }  & \cos ^{ 2 }{ x }  & \sin { 2x }  \\ \sin ^{ 2 }{ x }  & 1+\cos ^{ 2 }{ x }  & \sin { 2x }  \\ \sin ^{ 2 }{ x }  & \cos ^{ 2 }{ x }  & 1+\sin { 2x }  \end{vmatrix} are \alpha and \beta, then 
  • \alpha +{ \beta  }^{ 99 }=4
  • { \alpha  }^{ 3 }-{ \beta  }^{ 17 }=26
  • \left( { \alpha  }^{ 2n }-{ \beta  }^{ 2n } \right) is always an even integer for n\in N
  • a triangle can be constructed having its sides as \alpha -\beta ,\alpha +\beta and \alpha+3\beta

\mathrm{y}=\sin \mathrm{x},\ y_{n}=\displaystyle \frac{d^{n}(\sin x)}{dx^{n}}
then \begin{vmatrix} y& y_{1} & y_{2}\\  y_{3}& y_{4} &y_{5} \\  y_{6}& y_{7} & y_{8} \end{vmatrix} =?



  • -sin x
  • 0
  • sin x
  • cos x
If f (x) = tan x and A, B, C are the angles of \Delta ABC, then \begin{vmatrix} f(A) & f(\pi /4) & f(\pi /4)\\ f(\pi /4) &f(B) & f(\pi /4)\\ f(\pi /4) &f(\pi /4) & f(C) \end{vmatrix} 

  • 0
  • -2
  • 2
  • 1
If the lines 2\mathrm{x}-\mathrm{a}\mathrm{y}+1 =0,\ 3\mathrm{x}-\mathrm{b}\mathrm{y}+1 =0,\ 4\mathrm{x}-\mathrm{c}\mathrm{y}+1 =0 are concurrent then a,b,c are in ?

.
  • G.P.
  • A.P.
  • H.P.
  • A.G.P.
If \mathrm{a}\neq b\neq \mathrm{c} and if ax+by+\mathrm{c}=0\  bx+cy+\mathrm{a}=0 and cx+ay+b=0 are concurrent, 
then find the value of 
 2^{\mathrm{a}^{2}b^{-1}\mathrm{c}^{-1}}2^{b^{2}\mathrm{c}^{-1}\mathrm{a}^{-1}}2^{\mathrm{c}^{2}\mathrm{a}^{-1}b^{-1}}
  • 1
  • 4
  • 8
  • 16
lf the lines 3\mathrm{x}+2\mathrm{y}-5=0,\ 2\mathrm{x}-5\mathrm{y}+3=0,\ 5\mathrm{x}+\mathrm{b}\mathrm{y}+\mathrm{c}=0 are concurrent then \mathrm{b}+\mathrm{c}=
  • 7
  • -5
  • 6
  • 9
If \alpha,\ \beta are the roots of  \begin{vmatrix} x & 1 & 2\\ 0 & 1& 1\\ 1 & x & 2 \end{vmatrix} = 0 then \alpha^{n}+\beta^{n}=? 


  • 0
  • 1
  • 2
  • 2n
If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then
  • a=b
  • a=2b 
  • 2a=b
  • a=-b
Relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear is _____
  • x+3y=7
  • x+3y=14
  • -x+3y=7
  • -x+3y=14
Points (1, 5), (2, 3) and (-2, -11) are ____
  • Non-collinear
  • Collinear
  • Vertices of equilateral triangle
  • Vertices of right angle triangle
P, Q, R are three collinear points. The coordinates of P and R are (3, 4) and (11, 10) respectively and PQ is equal to 2.5 units. Coordinates of Q are-
  • (5, 11/2)
  • (11, 5/2)
  • (5, -11/2)
  • (-5, 11/2)
Find the value of m if the points (5, 1), (2, 3) and (8, 2m ) are collinear.
  • {-1}
  • \dfrac{1}{2}
  • -\dfrac{1}{2}
  • {2}
If a\neq p, b\neq q, c\neq r and \begin{vmatrix}p & b & c\\ a & q & c\\ a & b & r\end{vmatrix}=0, then the value of \dfrac{p}{p-a}+\dfrac{q}{q-b}+\dfrac{r}{r-c} is
  • 0
  • 1
  • -1
  • -2
If the points (0, 0), (1, 2) and (x, y) are collinear, then
  • x = y
  • 2x = y
  • x =2 y
  • 2x = -y
\left| {\begin{array}{*{20}{c}}   {{{\sin }^2}x}&{{{\cos }^2}x}&1 \\   {{{\cos }^2}x}&{{{\sin }^2}x}&1 \\   { - 10}&{12}&2 \end{array}} \right| =
  • 0
  • 12 cos^2x -10 sin^2x
  • 12 sin^2x -10 cos^2x - 2
  • 10 sin 2x
\mathrm{If}\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}=-2 and \mathrm{f}(\mathrm{x})= \begin{vmatrix}1+a^{2}x &(1+b^{2})x &(1+c^{2})x \\(1+a^{2})x&1+b^{2}x &(1+c^{2})x\\(1+a^{2})x&(1+b^{2})x & 1+c^2x\end{vmatrix}  then f(x) is a polynomial of degree 

  • 1
  • 0
  • 3
  • 2
Find the values of k, if the points A (k + 1, 2k), B (3k, 2k + 3) and C (5k +1, 5k) are collinear.
  • 1
  • \dfrac{1}{2}
  • 2
  • 2.5
If A is a square matrix, then adj A^{T} - (adj  A)^T is equal to
  • 2 |A|
  • 2 |A| I
  • null matrix
  • unit matrix
If B=A, |P|=|Q|=1, then adj({ Q }^{ -1 }{ BP }^{ -1) } is
  • P.Q
  • Q.adj(A).P
  • P.adj(A).Q
  • P.{ A }^{ -1 }.Q
If A = \begin{bmatrix}-5 & 2\\ 1 & -3\end{bmatrix}, then adj A is equal to
  • \begin{bmatrix}-3 & -2\\ -1 & -5\end{bmatrix}
  • \begin{bmatrix}3 & -2\\ -1 & 5\end{bmatrix}
  • \begin{bmatrix}5 & 1\\ 2 & 3\end{bmatrix}
  • \begin{bmatrix}3 & 2\\ 1 & 5\end{bmatrix}
If P is a non singular matrix, then value of adj({ P }^{ -1 }) in terms of P is

  • { P }/{ |P| }
  • { P }{ |P| }
  • P
  • none of these
The adjoint of \begin{bmatrix}1 & 1 & 1\\ 1 & 2 & -3\\ 2 & -1 & 3\end{bmatrix} is
  • \begin{bmatrix}3 & -9 & -5\\ -4 & 1 & 3\\ -5 & 4 & 1\end{bmatrix}
  • \begin{bmatrix}3 & -4 & -5\\ -9 & 1 & 4\\ -5 & 3 & 1\end{bmatrix}
  • \begin{bmatrix}-3 & 4 & 5\\ 9 & -1 & -4\\ 5 & -3 & -1\end{bmatrix}
  • None of these
If (3, 2), \left (x, \dfrac {22}{5}\right), (8, 8) lie on a line, then x is equal to
  • -5
  • 2
  • 4
  • 5
Given the matrix A=\begin{bmatrix} x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z \end{bmatrix}. If xyz=60 and 8x+4y+3z=20, then A(adj\ A) is equal to
  • A=\begin{bmatrix} 64 & 0 & 0 \\ 0 & 64 & 0 \\ 0 & 0 & 64 \end{bmatrix}
  • A=\begin{bmatrix} 88 & 0 & 0 \\ 0 & 88 & 0 \\ 0 & 0 & 88 \end{bmatrix}
  • A=\begin{bmatrix} 68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68 \end{bmatrix}
  • A=\begin{bmatrix} 34 & 0 & 0 \\ 0 & 34 & 0 \\ 0 & 0 & 34 \end{bmatrix}
If the points (0, 4), (4, 0) and (5,  p) are collinear, then value of p is
  • - 1
  • 7
  • 6
  • 4
0:0:1


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