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CBSE Questions for Class 12 Commerce Maths Determinants Quiz 9 - MCQExams.com

|abcc+ba+cbcaabb+ac| =
  • abc(a2+b2+c2)
  • abc(a+b+c)
  • a+b+c(a2+b2+c2)
  • abc(1+1a+1b+1c)
If A=[1221] then  adj(A)=?
  • [1221]
  • [2111]
  • [1221]
  • [1221]
To solve  x+y=3:3x2y4=0  by determinant method find  D.
  • 5
  • 1
  • 5
  • 1
The number of distinct real roots of the equation,|cosxsinxsinxsinxcosxsinxsinxsinxcosx|=0In t interval [π4π4] is/are:
  • 3
  • 2
  • 1
  • 4
If the point (λ+1,1),(2λ+1,3) and (2λ+2,2λ) are collinear then the possible value of λ is
  • 2
  • 1/2
  • 3
  • 1/3
Solve |11111+x1111+y|
  • 1
  • 0
  • x
  • xy
If (k,22k),(k+1,2k),(4k,62k) are collinear, then k=
  • +1
  • 1
  • 2
  • 2
If DP=|P158P2359P32510|, then D1+D2+D3+D4+D5 is equal to -
  • 29000
  • 25000
  • 25000
  • none of these
The value of determinant |bca2acb2abc2acb2abc2bca2abc2bca2acb2| is
  • always non-negative
  • always non-positive
  • always zero
  • can't say anything
If A=[2341], then adj (3A2+12A) is equal to 
  • [51638472]
  • [51846372]
  • [72638451]
  • [72846351]
If a,b,c are distinct and |aa2a31bb2b31cc2c31|=0 then
  • a+b+c=1
  • ab+bc+ca=0
  • a+b+c=0
  • abc=1
If [1α3133244] is the adjoint of a 3×3 matrix A and |A|=4, then α is equal to:
  • 4
  • 11
  • 5
  • 0
If f(x), g(x), h(x) are polynomials in x of degree 2 and F(x)=|fghfghf"g"h"|, , then F(x) is equal to
  • 1
  • 0
  • -1
  • f(x).g(x).h(x)
If  |1sinxsin2x1cosxcos2x1tanxtan2x|=0,x[0,2π], then number of possible values of  x  is.
  • 4
  • 5
  • 6
  • None of these
If  |x42x2x2xx42x2x2xx4| = (A+Bx)(xA)2,
then the ordered pair (A,B) is equal to:  
  • ( -4 , -5 )
  • ( -4 , 3 )
  • ( -4 , 5 )
  • ( 4 , 5 )
If A=|102306| then |A|=
  • 0
  • 10
  • 12
  • 60
If |(adjA)|=81, for 3×3 matrix, then det A is equal to 
  • 1
  • 2
  • 4
  • 9
For what value of x, will the points (-1,x),(-3,2) and (-4,4) lie on a line?
  • -3
  • 3
  • -2
  • 2
|1aa2bc1bb2ca1cc2ab|=
  • abc
  • a+b+c
  • 0
  • 4abc
The point (x1,y1),(x2,y2),(x1,y2) & (x2,y1) are always
  • Collinear
  • Concyclic
  • Vertices of a square
  • Vertices of a rhombus.
Find the value of |5374|
  • -1
  • -41
  • 41
  • 1
If a,b,c are pth,qthand rth terms of a GP, then |logap1logbq1logcr1| is equal to
  • 0
  • 1
  • logabc
  • none of these
|A|=6 and A is 3×3 matrix then det(2 adj(2(A1)T))=
  • 162
  • 36
  • 216
  • 512
If Δ(x)=|exsin2xtanx2ln(1+x)cosxsinxcosx2ex1sinx2|=A+Bx+Cx2+..... then B is equal to
  • 0
  • 1
  • 2
  • 4
If A=[55xx0x5x005] and |A2|=25, then |x| is equal to?
  • 15
  • 5
  • 52
  • 1
If a determinant of order 3×3 is formed by using the numbers 1 or 1, then the minimum value of the determinant is?
  • 2
  • 4
  • 0
  • 8
If α,β are the roots of x2+x+1=0 then |y+1βαβy+α1α1y+β|=?
  • y21
  • y(y21)
  • y2y
  • y3
|sin2θcos2θcos2θsin2θ|=
  • cos2θ
  • 12(1+cos22θ)
  • 12(1sin22θ)
  • 12sin22θ
The sum of the real roots of the equation
|x6123xx332xx+2|=0 is equal to
  • 6
  • 1
  • 0
  • 4
|a+ibc+idc+idaib|=?
  • (a2+b2c2d2)
  • (a2b2+c2d2)
  • (a2+b2+c2+d2)
  • none of these
For square matrices A and B of the same order, we have adj(AB)=?
  • (adj A)(adj B)
  • (adj B)(adj A)
  • |AB|
  • None of these
|cos70osin20osin70ocos20o|=?
  • 1
  • 0
  • cos50o
  • sin50o
Evaluate : |sin23osin7ocos23ocos7o|
  • 32
  • 12
  • sin16o
  • cos16o
If A=[abcd] then adj A=?
  • [dcba]
  • [dbca]
  • [dbca]
  • [dbca]
If A is a 3rowed square matrix and |A|=5 then |adj A|=?
  • 5
  • 25
  • 125
  • None of these
|cos15osin15osin15ocos15o|=?
  • 1
  • 12
  • 32
  • none of these
The roots of the equation
|3x2x2+xcosθ+cos2θx2+xsinθ+sin2θx2+xcosθ+cos2θ3cos2θ1+sin2θ2x2+xsinθ+sin2θ1+cos2θ23sin2θ|=0 are
  • sinθ, cosθ
  • sin2θ, cos2θ
  • sinθ, cos2θ
  • sin2θ, cosθ
When the determinant |cos2xsin2xcos4xsin2xcos2xcos2xcos4xcos2xcos2x| is expanded in powers of sinx, then the constant term in that expression is
  • 1
  • 0
  • 1
  • 2
If the determinant |cos2xsin2xcos4xsin2xcos2xcos2xcos4xcos2xcos2x| is expanded in powers of sinx then the constant term in the expansion is 
  • 1
  • 2
  • 1
  • 2
If |A|=3 and A1=[315323] then adj A=?
  • [9352]
  • [9352]
  • [9352]
  • [9352]
If |abcc+ba+cbcaaba+bc|=0, then the line ax+by+c=0 passes through the fixed point whcih is
  • (1,2)
  • (1,1)
  • (2,1)
  • (1,0)
If A=[2513] then adj A=?
  • [3512]
  • [3152]
  • [1235]
  • None of these
If A is singular matrix , then adj A is 
  • singular
  • non-singular
  • symmetric
  • not defined
If A=[112031001/3], then 
  • |A|=1
  • adjA=[112031001/3]
  • A=[11/3701/31003]
  • A=[11/37030001]
There are two values of a which makes determinant Δ=|1252a1042a|=86 then sum of these number is
  • 4
  • 5
  • 4
  • 9
If |2x58x|=|6273| then value of x is
  • 3
  • ±3
  • ±6
  • 6
Choose the correct answer from the given alternatives in the following question:
If A=[1234],adjA=[4a3b], then the values of a and b are 
  • a=2,b=1
  • a=2,b=4
  • a=2,b=1
  • a=1,b=2
Choose the correct answer from the given alternatives in the following question:
If A=[2431], then the adjoint of matrix A is 
  • [1341]
  • [1432]
  • [1342]
  • [1342]
State whether true or false:
If the value of a third order determinant is 12, then the value of determinant formed by replacing each element by its co-factor will be 144
  • True
  • False
Choose the correct answer from the given alternatives in the following question:
If A=[1221] and A(adjA)=KI , then the value of k is 
  • 1
  • 1
  • 0
  • 3
0:0:1


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