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If a,b,c are in A.P., then the determina...

If a,b,c are in A.P., then the determinant
`|[x+2, x+3, x+2a],[x+3,x+4,x+2b],[x+4,x+5,x+2c]|` is

A

0

B

1

C

x

D

2x

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The correct Answer is:
A
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The maximum degree of x by which determinant |(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)| divisible is a)0 b)1 c)2 d)3

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

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A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Solve the following system of linear equations using matrix method. 2x...

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  2. Solve the following system of linear equations using matrix method. x-...

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  3. If A=[[2,-3,5],[3,2,-4],[1,1,-2]]find A^(-1)Using A^(-1)solve the syst...

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  4. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs.60.The cost of ...

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  5. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  6. Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca...

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  7. Evaluate|[cosalpha cosbeta,cosalpha sinbeta,-sinalpha],[-sinbeta,cosbe...

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  8. If a,b,c are real numbers and abs[[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+...

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  9. Solve the equation |[x+a,x,x],[x,x+a,x],[x,x,x+a]|=0, a ne0

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  10. Prove that |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c^...

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  11. If A^(-1)=[[3,-1,1],[-15,6,-5],[5,-2,2]] and B=[[1,2,-2],[-1,3,0],[0,-...

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  12. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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  13. Let A=[[1,-2,1],[-2,3,1],[1,1,5]] verify that (A^(-1))^(-1)=A

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  14. Using properties of determinants prove abs[[x,y,x+y],[y,x+y,x],[x+y,...

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  15. evaluate | [1,x,y],[1,x+y,y],[1,x,x+y] |

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  16. Using properties of determinants, prove that |[alpha, alpha^2, beta+g...

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  17. Given Delta=|(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3)| Prove that ...

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  18. Consider a system of linear equations which is given below, 2/x+3/y+10...

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  19. If a,b,c are in A.P., then the determinant |[x+2, x+3, x+2a],[x+3,x+...

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  20. If x,y,z are non-zero real numbers, then the inverse of A=[[x,0,0],[0,...

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