Processing math: 49%

CBSE Questions for Class 12 Commerce Maths Determinants Quiz 8 - MCQExams.com

If xayb=em,xcyd=en,1=|mbnd|,2=|amcn| and 3=|abcd| the value of x and y are respectively
  • 13 and 23
  • 21 and 31
  • log(13)andlog(23)
  • e1/3 and e2/3
The value of 1xy|1003x315y31| is-
  • x+y
  • x2xy+y2
  • x2+xy+y2
  • x3y3
One of the roots of |x+abcax+bcabx+c|=0 is
  • abc
  • a+b+c
  • (a+b+c)
  • abc
Three straight lines 2x+11y5=0,24x+7y20=0 and 4x3y2=0
  • form a triangle
  • are only congruent
  • are concurrent with one line bisecting the angle between the other two
  • None of above
If Δ=|x2yzzy2xzzy2yz2x2yz|,then
  • x-y is a factor of Δ
  • (xy)2 is a factor of Δ
  • (x-y)^3 is a factor of Δ
  • Δ is independent of z
For distinct numbers a,b,c,x,y,z ϵR if Δ1|(ax)2(bx)2(cx)2(ay)2(by)2(cy)2(az)2(bz)2(cz)2|Δ2|(ax+1)2(bx+1)2(cx+1)2(ay+1)2(by+1)2(cy+1)2(az+1)2(bz+1)2(cz+1)2| then Δ21Δ22+Δ22Δ21=
  • 54
  • 103
  • 14
  • None of these
Let Δ=|sinθcosϕsinθsinϕcosθcosθcosϕcosθsinϕsinθsinθsinϕsinθcosϕ0|, then
  • Δ is independent of θ
  • Δ is independent of ϕ
  • Δ is a constant
  • none of these
The determinant Δ=|a2(1+x)abacabb2(1+x)bcacbcc2(1+x)| is divisible by
  • (x+3)
  • (1+x)2
  • x2
  • (x2+1)
The determinant Δ=|bcbα+ccdcα+dbα+ccα+daα3cα| is equal to zero if 
  • b,c,d are in A.P
  • b,c,d are in G.P
  • b,c,d are in H.P
  • α is a root of ax3bx23cxd=0
Find the values of a and b so that the points (a,b,3),(2,0,1) and (1,1,3) are collinear.
  • a=4,b=2
  • a=0,b=2
  • a=4,b=2
  • a=4,b=2
Δ=|0i100i500100i01000i500ii10000| is equal to
  • 100
  • 500
  • 1000
  • 0
Let A=|abcpqrxyz| and suppose that det.(A) =2 then the det.(B) equals, where B=|4x2ap4y2bq4z2ct| 
  • det(B)=2
  • det(B)=8
  • det(B)=16
  • det(B)=8
The value of determinant |a2a1cos(nx)cos(n+1)xcos(n+2)xsin(nx)sin(n+1)xsin(n+2)x| is independent of 
  • n
  • a
  • x
  • a , n and x
In |127375143|, cofactor of 2=___________ and cofactor of -1=___________.
  • 4,59
  • 4,59
  • 4,59
  • 59,4
If f(x)=|x32x2183x381x52x2504x3500123| then f(1).f(3)+f(3).f(5)+f(5).f(1) is equal to-
  • f(1)
  • f(3)
  • f(1)+f(3)
  • f(1)+f(5)
The points (X1,Y1), (X2,Y2), (X1,Y2) and (X2,Y1) are always
  • Collinear
  • Concyclic
  • Vertices of a square
  • Vertices of rectangle
If a,b,c are non-zeros, then the system of equation : (α+a)x+α+αz=0; αx+(a+b)y+αz=0; αx+αy+(α+c)z=0 has a non-trivial solution if
  •  1α=(1a+1b+1c)
  • α1=a+b+c
  • α+a+b+c=1
  • None of the above
If pλ4+pλ3+pλ2+sλ+t= |λ2+3λλ+1λ+3λ+12λλ4λ3λ+43λ|, then value of t is 
  • 16
  • 18
  • 17
  • 19
State whether following statement is true or false.
If A is a square matrix of order n, then |Adj(AdjA)| is of order (n2).
  • True
  • False
A=[55αα0α5α005]; If |A2|=25, then |α|=
  • 5
  • 52
  • 1
  • 15
the following relation is |aa+ba+b+c2a3a+2b4a+3b+2c=a33a6a+2b10a+6b+3c|=a3 
  • True
  • False
If |λ2+3λλ1λ+3λ+12λλ4λ3λ+43λ|=pλ4+qλ3+rλ2+sλ+t then t=
  • 16
  • 17
  • 18
  • 19
|1abca21bcab21cabc2| is equal to -
  • (ab)(bc)(ca)
  • abc(ab)(bc)(ca)
  • 0
  • 1
|logeloge2loge3loge2loge3loge4loge3loge4loge5|=?
  • 0
  • 1
  • 4 log e
  • 5 log e
If f(x)=|1xx+12xx(x1)(x+1)x3x(x1)x(x1)(x2)(x+1)x(x1)| then f(100) is equal to?
  • 0
  • 1
  • 100
  • 100
the value of the determinant of order 3 remains unchanged if its rows and columns are interchanged. that statement is ___
  • True
  • False
If none of a,b,c is zero,  Whether the given equation  |bcb2+bcc2+bca2+acacc2+aca2+abb2+abab|=(bc+ca+ab)3 is ?

  • True
  • False
The value of the determinant \left| \begin{matrix} { b }^{ 2 }-ab & b-c & bc-ac \\ ab-{ b }^{ 2 } & a-b & { b }^{ 2 }-ab \\ bc-ac & c-a & ab-{ b }^{ 2 } \end{matrix} \right| 
  • abc
  • a+b+c
  • 0
  • ab+bc+ca
if a>0 and discriminant of {ax}^{2}+{2bx}+{c} is -ve, then \left| \begin{matrix} a & b & ax+b \\ b & c & bx+c \\ ax+b & bx+c & 0 \end{matrix} \right| is
  • +ve
  • {(ac-b^2)(ax^2+2bx+c)}
  • -ve
  • 0
\left| \begin{matrix} \sqrt { 13 } +\sqrt { 3 }  & 2\sqrt { 5 }  & \sqrt { 5 }  \\ \sqrt { 15 } +\sqrt { 26 }  & 5 & \sqrt { 10 }  \\ 3+\sqrt { 65 }  & \sqrt { 15 }  & 5 \end{matrix} \right| = 
  • 15\sqrt{2}-25\sqrt{3}
  • 15\sqrt{5}-25\sqrt{6}
  • 25\sqrt{2}-15\sqrt{3}
  • 0
The value of \left| \begin{matrix} 1+w & { w }^{ 2 } & -w \\ 1+{ w }^{ 2 } & w & -{ w }^{ 2 } \\ { w }^{ 2 }+w & w & -{ w }^{ 2 } \end{matrix} \right| is equal to 
  • 0
  • 2 \omega
  • 2 {\omega}^{2}
  • -3 {\omega}^{2}
If the points A(at^{2}_{1},2at_{1}), B(at^{2}_{2},2at_{2}) and C(\alpha,0) are collinear, then t_{1} t_{2} equals
  • 2
  • -1
  • 1
  • None\ of\ these
Let F(x)=\left | \left|  \right| \begin{matrix}1  &1+sin\ x  &1+sin\ x+cos\ x \\  2 &3+2\ sin\ x  &4+3\ sin\ x+2\ cos\ x  \\  3&6+3\ sin\ x&10+6\ sin\ x+3\ cos\ x  \end{matrix} \right |  then F'\ \left ( \dfrac{\pi}{2} \right ) is equal to
  • -1
  • 0
  • 1
  • 2
If A = \left[ {\begin{array}{*{20}{c}}a&0&0\\0&a&0\\0&0&a\end{array}} \right] then find the value of \left| A \right|\left| {adjA} \right|
  • {a^3}
  • {a^6}
  • {a^9}
  • a
If \begin{vmatrix} 1+x & 2 & 3 \\ 1 & 2+x & 3 \\ 1 & 2 & 3+x \end{vmatrix}=0 then x=
  • 1
  • -1
  • -6
  • 6
If A = {\left[ {\begin{array}{*{20}{c}}a\\b\\c\end{array}\begin{array}{*{20}{c}}p\\q\\r\end{array}} \right]_{3 \times 2}} then determinant \left( {A{A^T}} \right) is equal to
  • 0
  • {a^2} + {b^2} + {c^2}
  • {p^2} + {q^2} + {r^2}
  • {p^2} + {q^2}
If {t_{1,}}{t_2}\, and {t_3} distinct. and the points \left( {{t_1}.2a{t_1} + a{t_1}^3} \right).\left( {{t_2}.2a{t_2} + a{t_2}^3} \right),\left( {{t_3}.2a{t_3} + a{t_3}^3} \right) are collinear, then {t_1} + {t_2} + {t_3} =
  • t_1 t_2 t_3 =-1
  • t_1 +t_2 +t_3 =t_1 t_2 t_3
  • t_1 +t_2 +t_3 =0
  • t_1 +t_2 +t_3 =-1
Using properties of determinants it can be proved
\begin{vmatrix} b+c & a & a \\ b & c+a & b \\ c & c & a+b \end{vmatrix}=4abc
  • True
  • False
If \Delta  = \left| {\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}} \right| for x \ne 0,\,y \ne 0 then \Delta is
  • Divisible by neither x nor y
  • Divisible by both x and y
  • Divisible by x but not y
  • Divisible by y but not x
If A=\quad \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}, B=(adj\quad A) and C=5A, then \cfrac { \left| adj\quad B \right|  }{ \left| C \right|  } is equal to
  • 5
  • 25
  • -1
  • 1
Find the value of the determinant \begin{vmatrix} 1 & 0 & 0 \\ 2 & \cos { x }  & \sin { x }  \\ 3 & \sin { x }  & \cos { x }  \end{vmatrix}.
  • \cos{2x}
  • 1
  • 0
  • \sin{2x}
If the points (k, 2-2k), (1-k, 2k) and (-k-4, 6-2k) be collinear, the number of possible values of k are 
  • 4
  • 2
  • 1
  • 3
If A=\begin{bmatrix} 1 & 2 & -2 \\ -2 & 2 & 1 \\ 2 & 1 & 2 \end{bmatrix} then {A}^{-1}=
  • A
  • \dfrac{1}{9} {A}^{T}
  • \dfrac{1}{9}A
  • \dfrac{1}{9}{A}^{-1}
The determinant \begin{bmatrix} b_{1}+c_{1} & c_{1}+a_{1} & a_{1}+b_{1} \\ b_{2}+c_{2} & c_{2}+a_{2} & a_{2}+b_{2} \\ b_{3}+c_{3} & c_{3}+a_{3} & a_{3}+b_{3}\end{bmatrix}=_____
  • \begin{bmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{bmatrix}
  • 2\begin{bmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{bmatrix}
  • 3\begin{bmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{bmatrix}
  • 4\begin{bmatrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{bmatrix}
In a triangle ABC, with usual notations, if \begin{vmatrix} 1 & a & b \\ 1 & c & a \\ 1 & b & c \end{vmatrix}=0, then 4sin^2A+24sin^2B+36sin^2C is equal to 
  • 48
  • 50
  • 44
  • 34
If adj A=\begin{bmatrix}20 & -20 \\ 10 & 10 \end{bmatrix} , then |A|=..... 
  • 400
  • 200
  • \pm 20
  • 0
29 If z=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} where 0, I are 2x2 null and identity matrix then det \left( \left[ z \right]  \right) is  _______________.
  • 1
  • -1
  • 0
  • None of these
Sum of the real roots of the equation \begin{vmatrix} 1 & 4 & 20\\ 1 & -2 & 5 \\ 1 & 2x & 5{x}^{2} \end{vmatrix}=0 is
  • -2
  • -1
  • 0
  •  1
The cofactor of the element 4 in the determinant \begin{vmatrix} 1 & 3 & 5 & 1\\ 2 & 3 & 4 & 2\\ 8 & 0 & 1 & 1\\ 0 & 2 & 1 & 1\end{vmatrix} is?
  • 4
  • 10
  • -10
  • -4
Find the values of x if, \left| \begin{matrix} 1 & 4 & 20 \\ 1 & -2 & 5 \\ 1 & 2x & 5x^{ 2 } \end{matrix} \right| =0
  • -1, 2
  • -1, -2
  • 1, -2
  • 1, 2
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers