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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=sinθ1t1+t2dt and
B=cosecθ11t(1+t2)dt, then the value of determinant  |AA2BeA+BB211A2+B21| is 

  • sinθ
  • cosecθ
  • 0
  • 1
I. If A,B,C are angles of angle and |1111+sinA1+sinB1+sinCsinA+sin2AsinB+sin2BsinC+sin2C| =0  then triangle is isosceles
 II. lf a=1+2+4+ upto n terms b=1+3+9+ up to n terms c=1+5+25+up to n terms  then Δ|a2b4c2222n3n5n| =0
  • I, II both are true
  • only I is true
  • only II is true
  • neither of them are true
1fA=[156804372] then the cofactors of the elements 3,7,2 are p,q,r respectively their ascending order is 
  • p, r,q
  • q,r, p
  • p,q,r
  • r,p, q
If f(x)= |sinx1012sinx1012sinx| then π2π2f(x) equals 

  • 0
  • 1
  • 1
  • 3π2
|1cosαcosβcosα1cosγcosβcosγ1| = |0cosαcosβcosα0cosγcosβcosγ0| then 


  • cosα+cosβ+cosγ=0
  • cosα.cosβ.cosγ=0
  • cos2α+cos2β+cos2γ=1
  • cosαcosβ=0
Match the following elements of |110042346| 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
  • Ib,IId,IIIa,IVc
  • Ib,IId,IIIc,IVa
  • Id,IIb,IIIa,IVc
  • Id,IIa,IIIb,IVc
If A=[cosθsinθsinθcosθ] then limn1n|An|=
  • 1
  • 0
  • A
  • 1nA
Det{2aa+bc+ab+a2bb+cc+ac+b2c}= 

  • (a+b)(b+c)(c+a)
  • (ab)(bc)(ca)
  • 4(a+b)(b+c)(c+a)
  • 4(ab)(bc)(ca)
The sum of infinite series |1264|+|12224|+|142234|+ ....... is 
  • 10
  • 0
  • 10
lf f(x)=|secxcosxcos2xcos2x|, then π/20f(x)dx=
  • 1/2
  • 1/3
  • 0
  • 1
lf abc Then one value of x which satisfies the equation |0xaxbx+a0xcx+bx+c0| = 0 is given by 

  • x = a
  • x = b
  • x = c
  • x = 0
.Let |x2xx2x6xx6| =ax4+bx3+cx2+dx+e ,then the value of 5a + 4b + 3c + 2d + e is
equal to 

  • 0
  • 16
  • -16
  • -11
|1+i1i11ii1+ii1+i1i| is a 
  • real number
  • irrational number
  • complex member
  • Purely imaginary
A=[122212221] then Adj(A)= 

  • AT
  • 3AT
  • A1
  • AT
If Δ = |cosθ2111cosθ2cosθ2cosθ211| the minimum of Δ is m1 and maximum of Δ is m2 then [m1,m2] is
  • [ 4, 2]
  • [2,4]
  • [4,0]
  • [0,2]
f(x)= |cosxx12sinxx22xtanxx1| then limx0f(x)=
  • 0
  • -1
  • -2
  • 2
The value of |1+x2312+x3123+x| is 
  • (x6)x2
  • (x6)x
  • x2(x+6)
  • (x6)
If [x] stands greatest integer x then the value of |[e][π][π26][π]π26[e][π26][e][π]| equals 
  • -8
  • 8
  • -1
  • 1
lf adjA={110231211} then adj 2 A= 

  • {220462422}
  • {4408124844}
  • {880162481688}
  • {110231211}
A=[425], B= [203], then Adj(BA)= 
  • {000000000}
  • {841000012615}
  • {80124061005}
  • None of the above
.Let Δ (x)=|x+ax+bx+acx+bx+cx1x+cx+dxb+d| and 20Δ(x)dx=16, where a, b,c,d are in A.P. then the common difference of the A.P. is 

  • ±1
  • ±2
  • ±3
  • ±4
A= [b2c2bcb+cc2a2cac+aa2b2aba+b] then |A| =?
  • abc
  • abc1
  • abc+1
  • 0
The straight lines x+2y9=0,3x+5y5=0 and ax+by1=0 are concurrent if the straight line 22x35y1=0 passes through the point 

  • (a, b)
  • (b,a)
  • (-a,b)
  • (-a, -b)
If maximum and minimum values of the determinant |1+sin2xcos2xsin2xsin2x1+cos2xsin2xsin2xcos2x1+sin2x| are α and β, then 
  • α+β99=4
  • α3β17=26
  • (α2nβ2n) is always an even integer for nN
  • a triangle can be constructed having its sides as αβ,α+β and α+3β

y=sinx, yn=dn(sinx)dxn
then |yy1y2y3y4y5y6y7y8| =?



  • -sin x
  • 0
  • sin x
  • cos x
If f (x) = tan x and A, B, C are the angles of ΔABC, then |f(A)f(π/4)f(π/4)f(π/4)f(B)f(π/4)f(π/4)f(π/4)f(C)| 

  • 0
  • -2
  • 2
  • 1
If the lines 2xay+1=0, 3xby+1=0, 4xcy+1=0 are concurrent then a,b,c are in ?

.
  • G.P.
  • A.P.
  • H.P.
  • A.G.P.
If abc and if ax+by+c=0 bx+cy+a=0 and cx+ay+b=0 are concurrent, 
then find the value of 
2a2b1c12b2c1a12c2a1b1
  • 1
  • 4
  • 8
  • 16
lf the lines 3x+2y5=0, 2x5y+3=0, 5x+by+c=0 are concurrent then b+c=
  • 7
  • -5
  • 6
  • 9
If α, β are the roots of  |x120111x2| = 0 then αn+βn=? 


  • 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
  • 12
  • 12
  • 2
If ap,bq,cr and |pbcaqcabr|=0, then the value of ppa+qqb+rrc is
  • 0
  • 1
  • 1
  • 2
If the points (0,0),(1,2) and (x,y) are collinear, then
  • x=y
  • 2x=y
  • x=2y
  • 2x=y
|sin2xcos2x1cos2xsin2x110122|=
  • 0
  • 12cos2x10sin2x
  • 12sin2x10cos2x2
  • 10sin2x
Ifa2+b2+c2=2 and f(x)= |1+a2x(1+b2)x(1+c2)x(1+a2)x1+b2x(1+c2)x(1+a2)x(1+b2)x1+c2x|  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
  • 12
  • 2
  • 2.5
If A is a square matrix, then adjAT(adjA)T is equal to
  • 2 |A|
  • 2 |A| I
  • null matrix
  • unit matrix
If B=A, |P|=|Q|=1, then adj(Q1BP1) is
  • P.Q
  • Q.adj(A).P
  • P.adj(A).Q
  • P.A1.Q
If A=[5213], then adj A is equal to
  • [3215]
  • [3215]
  • [5123]
  • [3215]
If P is a non singular matrix, then value of adj(P1) in terms of P is

  • P/|P|
  • P|P|
  • P
  • none of these
The adjoint of [111123213] is
  • [395413541]
  • [345914531]
  • [345914531]
  • None of these
If (3,2), (x,225),(8,8) lie on a line, then x is equal to
  • 5
  • 2
  • 4
  • 5
Given the matrix A=[x321y422z]. If xyz=60 and 8x+4y+3z=20, then A(adj A) is equal to
  • A=[640006400064]
  • A=[880008800088]
  • A=[680006800068]
  • A=[340003400034]
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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