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Evaluate : |[0, (a-b)^3, (b-c)^3], [(b-a...

Evaluate : `|[0, (a-b)^3, (b-c)^3], [(b-a)^3, 0, (c-a)^3],[(c- b)^3, (a-c)^3, 0]|`

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(a-2b)^(3)+(c-a)^(3)+(2b-c)^(3)

|{:(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c):}|=3abc-a^3-b^3-c^3

Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)^3,(x-c)^3),((x+a)^3,(x+b)^3,(x+c)^3)| =0, a,b and c being distinct real numbers.

the value of the determinant |(0, b^(3)-a^(3),c^(3)-a^(3)),(a^(3)-b^(3),0,c^(3)-b^(3)),(a^(3)-c^(3),b^(3)-c^(3),0)| is equal to -

If (x-a)^(3)+(x-b)^(3)+(x-c)^(3)-3(x-a)(x-b)(x-c)=0 , then x =

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b)^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

Prove that ((a^(2)-b^(2))^(3)+(b^(2)-c^(2))^(3)+(c^(2)-a^(2))^(3))/((a-b)^(3)+(b-c)^(3)+(c-a)^(3))=(a+b)(b+c)(c+a)

|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)

Simplify : (a - 2b + c)^3 - (a - 2b)^3 - 3c ( a - 2b +c)(a - 2b)

UNITED BOOK HOUSE-SET 17-EXERCISE
  1. A binary operation * is defined on the set of real numbers R by a*b =...

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  2. Solve for a,b,c and d when ((b+c, c+a), (7 - d ,6 -c)) = ((9-d, 8-d),(...

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  3. Evaluate : |[0, (a-b)^3, (b-c)^3], [(b-a)^3, 0, (c-a)^3],[(c- b)^3, (a...

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  4. Examine whether the following function is continuous at x = 0 . phi(...

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  5. Find the differential co-efficient of logx10 with respect to tan^-1x.

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  6. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

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  7. Find if Lagrange's Mean Value Theorem is applicable to the function f...

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  8. Eleminating a and b, find the differential equation of all ellipse of ...

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  9. Evaluate : underset(x rarr 0) Lt (1+3x)^((x+2)/x)

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  10. If vec a, vec b, vec c are unit vectors satisfying the condition veca+...

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  11. Find the value of lambda so that the plane vecr. (veci + 2vecj + 3veck...

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  12. If P(A)=1/4,P(B)=1/3 and P(A-B)=1/6 then verify whether a and B are tw...

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  13. An unbiased coin is tossed 6 times. Find the probability of at least f...

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  14. Given A =[(1,-1,1),(1,-2,-2),(2,1,3)] & B = [(-4,4,4),(-7,1,3),(5 , -3...

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  15. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

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  16. Show that int(2x+3)/(x^2 - 3x + 2) dx

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  17. If x = sin theta and y = cos ptheta , p is constant, then find the val...

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  18. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

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  19. Show that int(2x+3)/(x^2 - 3x + 2) dx

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  20. If theta be the angle between two unit vectors vece1 and vece2 then pr...

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