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Events A and B are such that P(A) =(1)/(...

Events A and B are such that `P(A) =(1)/(2), P(B) =(7)/(12)` and `"P(not A or not B)"=(1)/(4)`. State whether A and B are independent ?

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UNITED BOOK HOUSE-SET 3-EXERCISE
  1. If |veca+vecb|= |veca-vecb| ,(where veca and vec b are any vector) the...

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

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

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

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

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

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

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

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

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

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

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

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  14. Solve: (dy)/(dx) = (2x+3y)/(3x+2y)

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  15. If veca = hati+hatj + hat k, vecb=hati+hatj,vec c= hati and (vec axxve...

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  16. If vec a= hat i+hat j- hat k, vec b= -hat i+2 hat j+ hat k and vec c =...

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  17. Prove that overset(2)underset(-2)int |1-x^2|dx=4

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  18. Evaluate (with the help of definite integral) underset(n rarr infty)...

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  19. If two dice are rolled 12 times, obtain the mean and varianve of the d...

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