If a, b, c are sides of a triangle and...

If `a, b, c` are sides of a triangle and `|(a^2,b^2,c^2),((a+1)^2,(b+1)^2,(c+1)^2),((a-1)^2,(b-1)^2,(c-1)^2)|=` then

`DeltaABC` is an equilateral triangle

`Delta ABC` is a right angled isosceles triangle

`DeltaABC` is an isosceles triangle

none of these

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If the sides of a DeltaABC and a, b, c and |{:(a^(2),b^(2),c^(2)),((a+1)^(2),(b+1)^(2),(c+1)^(2)),((a-1)^(2),(b-1)^(2),(c-1)^(2)):}|=0 then prove that DeltaABC is an isosceles triangle.

If |(a^2,b^2,c^2),((a+b)^2 ,(b+1)^2,(c+1)^2),((a-1)^2 ,(b-1)^2,(c-1)^2)| =k(a-b)(b-c)(c-a) then the value of k is a. 4 b. -2 c.-4 d. 2

|[a^(2), b^(2), c^(2)], [(a+1)^(2), (b+1)^(2), (c+1)^(2)], [(a-1)^(2), (b-1)^(2), (c-1)^(2)]| =-4(a-b)(b-c)(c-a)

det[[ Prove that :,c^(2)a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),[c-1)^(2)]]=4det[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

If a, b, c are the sides of a triangle ABC and |(1,a,b),(1,c,a),(1,b,c)|=0, then the value of cos^2 A + cos^2 B +cos^2 C is equal to

If a, b, c are sides of the triangle ABC and |(1,a, b),(1,c,a),(1,b,c)|=0 , then the value of cos 2A+cos 2B+cos 2C is equal to

If |((a_1 - a)^2,(a_1 - b)^2,(a_1 - c)^2),((b_1 - a)^2,(b_1 - b)^2,(b_1 - c)^2),((c_1 - a)^2,(c_1-b)^2,(c_1-c)^2)|=0 and if the vectors vec alpha = (1, a, a^2), vec beta = (1,b,b^2),vec gamma=(1,c,c^2) are non coplanar, show that the vectors vec alpha_1 =(1,a,a_1^2) ,vec beta_1=(1,b_1,b_1^2),vec gamma_1=(1,c_1,c_1^2) are coplanar.

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

[[a^(2),b^(2),c^(2)(a+1)^(2),(b+1)^(2),(c+1)^(2)(a-1)^(2),(b-1)^(2),(c-1)^(2)]]=k[[a^(2),b^(2),c^(2)a,b,c1,1,1]]

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

If A,B and C are the angles of a triangle and |{:(1,1,1),(1+sinA,1+s...
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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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