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Without expanding show that |[1/a,1,bc],...

Without expanding show that `|[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0`

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Without expanding prove that, |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

Without expanding prove that , |{:(1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1/c+1/a):}|=0

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UNITED BOOK HOUSE-SET 3-EXERCISE
  1. Solve: sin^(-1)x-cos^(-1)x = pi/6

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  2. If A= [[0,2],[3,-4]],kA = [[0,3a],[2b,24]] then find the value of k+a+...

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  3. Without expanding show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

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  4. Show that , d/(dx)[x/2sqrt(a^2-x^2)+a^2/2 sin^(-1)x/a]=sqrt(a^2-x^2)

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  5. Evaluate the following integral: int (tan^-1)sqrt((1-sinx)/(1+sinx)...

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  6. Find the value of C that occurs in the conclusion of largranges's MVT ...

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  7. Solve the following differential equations: dy/dx=e^(x+y)+x^2 e^y

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  8. If |veca+vecb|= |veca-vecb| ,(where veca and vec b are any vector) the...

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  9. The cartesian equations of a line are x= ay+b,z= cy+d . Find its direc...

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  10. Events A and B are such that P(A) =(1)/(2), P(B) =(7)/(12) and "P(not ...

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  11. A binomial distribution B(n,p) has the mean 8 and variance 8/3. Find ...

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  12. Show that cos^(-1) ((cosx+cos y)/(1+cos x.cosy))= 2tan^(-1)(tan(x/2).t...

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  13. By row transformation find inverse of the matrix A= [[1,3,2],[-3,-3,-1...

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  14. Show that, A = 1/3[[1,2,2],[2,1,-2],[-2,2,-1]] are orthogonal matrix a...

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  15. Prove that, |[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3)(a+4),a+4,1]|...

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  16. If y = 3e^(2x)+2e^(3x) then show that y2-5y1 +6y=0

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  17. If x = sqrt(a^(sin^(-1)t)) and y= sqrt(a^(cos^(-1)t) show that (dy)/(...

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  18. Evaluate: int(sin^(-1)x)/(x^2 dx

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  19. Evaluate: int (dx)/(x(x^n+1))

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  20. Solve: (dy)/(dx)+y/x = e^x

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