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Urn A contains 1 white, 2 black and 3 re...

Urn A contains 1 white, 2 black and 3 red balls urn B contains 2 white, 1 black and 1 red ball and urn C contains 4 white, 5 black and 3 red balls. One urn is chosen at random and two balls are drawn. These happen to be one white and one red. What is the probability that they come from urnA?

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UNITED BOOK HOUSE-SET 1-EXERCISE
  1. Prove that the equation of the plane which passes through the point (2...

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  2. Show that the probability that exactly one of the events A and B occur...

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  3. Show that tan^(-1)(1/sqrt3tanx/2)=1/2 cos^(-1)(1+2cosx)/(2+cosx).

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  4. If A = [[1,x,-2],[2,2,4],[0,0,2]] and A^2+2I3=3A Find x, here I3 is th...

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  5. Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

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  6. Show that , |[(a^2+b^2)/c,c,c],[a,(b^2+c^2)/a,a],[b,b,(c^2+a^2)/b]|=4a...

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  7. If f(x)= tan^(-1)(x/(1+20x^2)) show that f'(x)=5/(1+25x^2)-4/(1+16x^2)...

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  8. Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show that (1-x^2)(d^2y)/(dx^2)-x(d...

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  9. Evaluate: int (dx)/sqrt(2/3x^3-x^2+1/3)

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  10. Solve: (6x+9y-7)dx= (2x+3y-6)dy

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  11. Solve: (1-x^2)(dy)/(dx)-xy=x^2, given y = 2 when x= 0.

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  12. If vec(AB) = 2 hati- 4 hatj +5 hatk and vec(BC)= hat i-2 hatj-3hatk in...

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  13. Find x such that the four points A(3,2,1),B(4,x,5),C(4,2,-2) and D(6,5...

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  14. Prove that overset(pi//2)underset(0)intlog(sinx)dx = -pi/2 log2

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  15. Urn A contains 1 white, 2 black and 3 red balls urn B contains 2 white...

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  16. A cylindrical tin can, open at the top, of a given capacity has to be...

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  17. If the straight line y =kx+3 is a tangent to the hyperbola 7x^2-4y^2=2...

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  18. Using calculus, find the area bounded by the curve |x|+|y|=1.

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  19. Show that the lines vecr= (hat i+hat j+hat k)+t(hat i-hat j+hat k) and...

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  20. Find the equation of the plane passing through the points (-1,1,1) an...

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