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Show that |[-1,b,c],[a,-1,c],[a,b,-1]|=...

Show that `|[-1,b,c],[a,-1,c],[a,b,-1]|=(a+1)(b+1)(c+1)(a/(a+1)+b/(b+1)+c/(c+1)-1)`

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Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab

Answer the foll. Question : 2.show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]| = abc(1+1/a+1/b+1/c) , (abc != 0)

Show that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+(1)/(a)+(1)/(b)+(1)/(c)),(abcne0) .

If a ,b , c are nonzero real numbers such that |[b c,c a, a b],[ c a, a b,b c],[ a b,b c,c a]|=0,t h e n 1/a+1/(bomega)+1/(comega^2)=0 b. 1/a+1/(bomega^2)+1/(comega)=0 c. 1/(aomega)+1/(bomega^2)+1/c=0 d. none of these

|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

|{:(b+c,a,1),(c+a,b,1),(a+b,c,1):}|=0

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

prove that : |{:(1,a,b),(-a,1,c),(-b,-c,1):}|=1+a^2+b^2+c^2

|{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]| = 2(a-b)(b-c)(c-a)

UNITED BOOK HOUSE-SET 7-EXERCISE
  1. Find the equation of the line passing through the point(1,2,3) and par...

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  2. Two unbiased dice are thrown. Find the probability that the sum of the...

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  3. M and E are two equally strong football teams. Findthe probability tha...

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  4. Solve: tan^(-1)sqrt(x(x+1)+sin^(-1)sqrt(1+x+x^2) = pi/2

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  5. If A = [[1,-1],[2,-1]],B = [[a,1],[b,-1]] and (A+B)^2 = A^2+B^2 find a...

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  6. Evaluate: |[alpha, beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,ga...

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  7. Show that |[-1,b,c],[a,-1,c],[a,b,-1]|=(a+1)(b+1)(c+1)(a/(a+1)+b/(b+1...

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  8. If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) ...

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  9. Evaluate: int (cos x-sinx )/sqrt(sin 2x)dx

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  10. Evaluate: int x sqrt((a^2-x^2)/(a^2+x^2))dx

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  11. Solve: cos^(-1)((dy)/(dx)) = x+y.

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  12. solve : sqrt(a^2+x^2)(dy)/(dx)+y= sqrt(a^2+x^2)-x

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  13. Find a unit vector in direction parallel to the sum of the vectors vec...

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  14. answer any one question : (ii) let vec a= hat i+4 hat j+ 2hat k , vec...

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  15. Evaluate: overset(1)underset(0)int (tan^(-1)x)/(1+x^2)dx.

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  16. Evaluate : underset(nrarrinfty)lim [1/n + 1/(n+1)+ 1/(n+2) + .... +1...

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  17. Three groups of children contain respectively 3 girls and 1 boy, 2 gir...

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  18. 5% of the electric valves are defective. 10 valves are drawn at random...

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  19. Find the area of the region bounded by the parabola y = x^(2) and y = ...

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  20. Show that the pair of lines whose direction cosines are given by 3 lm-...

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