If |(x^(lamda),x^(lamda+2),x^(lamda+3)),...

If `|(x^(lamda),x^(lamda+2),x^(lamda+3)),(y^(lamda),y^(lamda+2),y^(lamda+3)),(z^(lamda),z^(lamda+2),z^(lamda+3))|=(x-y)(y-z)(z-x)(1/x+1/y+1/z)` then `lamda` is

`-2`

`-1`

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The matrix A={:[(lamda_(1)^(2),lamda_(1)lamda_(2),lamda_(1)lamda_(3)),(lamda_(2)lamda_(1),lamda_(2)^(2),lamda_(2)lamda_(3)),(lamda_(3)lamda_(1),lamda_(3)lamda_(2),lamda_(3)^(2))]:} is idempotent if lamda_(1)^(2)+lamda_(2)^(2)+lamda_(3)^(2)=k where lamda_(1),lamda_(2),lamda_(3) are non-zero real numbers. Then the value of (10+k)^(2) is . . .

If p lamda ^(4) + q lamda ^(3) + r lamda ^(2) + s lamda +t = |{:(lamda ^(2) + 3 lamda, lamda -1, lamda +3), ( lamda +1, 2 - lamda , lamda -4), ( lamda -3, lamda+4, 3lamda):}|. then the value of t is

If (x+y)^(2)=2(x^(2)+y^(2))and(x-y+lamda)^(2)=4,lamdagt0, then lamda is equal to :

Let plamda^(4)+qlamda^(3)+rlamda^(2)+slamda+t =|(lamda^(2)+3lamda,lamda-1,lamda-3),(lamda-1,-2lamda,lamda-4),(lamda-3,lamda+4,3lamda)| where p,q,r,s, and t are constant. Then value of t is

If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(lamda) and (x-1)/(lamda)=(y-4)/(2)=(z-5)/(1) intersect then

int (dx)/(sqrt(1-tan ^(2) x))=(1)/(lamda)sin ^(-1) (lamda sin x)+C, then lamda=

If line (2x-4)/(lamda)=(lamda-1)/(2)=(z-3)/(1) and (x-1)/(1)=(3y-1)/(lamda)=(z-2)/(1) are perpendicular to each then lamda= . . .

ML KHANNA-DETERMINANTS -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)

If R be the circum radius of the triangle ABC then the value of R^3...
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If a, b, c are sides of a triangle and |(a^2,b^2,c^2),((a+1)^2,(b+1...
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If A+B+C=pi, show that |(sin^2A,sinAcosA,cos^2A),(sin^2B,sinBcosB,cos...
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If x,y,z are all distinct and |(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1...
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If |(x+a,a^2,a^3),(x+b,b^2,b^3),(x+c,c^2,c^3)| = 0 , a ne b ne c then ...
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If a,b,c be all distinct and |(a^3-1,b^3-1,c^3-1),(a,b,c),(a^2,b^2,c...
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If a,b,c are different , then the determinant |(1,1,1),((x-a)^2,(x-b...
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If |(x^(lamda),x^(lamda+2),x^(lamda+3)),(y^(lamda),y^(lamda+2),y^(lamd...
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Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx...
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If a,b,c are negative distinct real numbers then the determinant |(a,b...
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the value of the determinant |(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)| is
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If |(x,y,z),(y,z,x),(z,x,y)|=-(x+y+z)(x+yk+zk^2)(x+yk^2+zk) then k eq...
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If a,b,c are the roots of x^3+px^2+q=0 , then the value of |(a,b,c),(b...
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If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...
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If both n and r be greater than 1 and if Delta=|(""^xCr,""^(n-1)Cr,"...
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If Delta=|(""^(10)C3,""^(10)C4,""^(11)Cn),(""^(11)C5,""^(11)C6,""^(12)...
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If Delta = |(""^(5)C0,""^(5)C3,14),(""^(5)C1,""^(5)C4,1),(""^(5)C2,""^...
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The value of the determinant |(1,1,1),(.^(m)C(1),.^(m +1)C(1),.^(m+2)C...
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The determinant |(y^(2),-xy,x^(2)),(a,b,c),(a',b',c')| is equal to
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|(bc,bc'+b'c,b'c'),(ca,ca'+ac',c'a'),(ab,ab'+a'b,a'b')| is equal to
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