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Prove that "^(2n)C0 + ^(2n)C2 + .... + ^...

Prove that `"^(2n)C_0 + ^(2n)C_2 + .... + ^(2n)C_(2n) = 2^(2n-1)`

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SHARAM PUBLICATION-QUESTION PAPER 2013-EXERCISE
  1. Show that the points (3,-2,4)(1,1,1) and (-1,4,-1) are collinear.

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  2. Find the equation of a plane biscting the line segment joining (-1,4,3...

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  3. Find the value of r, if the line  (x-1)/(1) = (y+2)/(3) = (z-1)/(-1) =...

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  4. Find equation of the sphere if the line segment joining the Points (4,...

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  5. Find the maixmum value of z =50x1+60x2 subject to 2x1+3x2le6,x1,x2ge0

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  6. Find the value of |{:(17,58,97),(19,60,99),(18,59,98):}| without expan...

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  7. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  8. Find the product [{:(1,2,3),(2,3,4):}][{:(1,-2),(-2,3):}]

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  9. Prove that "^(2n)C0 + ^(2n)C2 + .... + ^(2n)C(2n) = 2^(2n-1)

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  10. C(3)^(2n):C(3)^(n)= 44:5, find the value of n.

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  11. In how many ways can 2 boys and 3 girls sit in a row so that no two gi...

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  12. If 8 person are to sit around a table what is the probability that X a...

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  13. A class consists of 25 boys and 15 girls. If a committee of 6 is to be...

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  14. If y = e^(ax) cos bx then find y(n)(0).

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  15. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

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  16. Evaluate : overset(1)underset(0)intln(1+x)/(1+x^2)dx.

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  17. Solve dy/dx+y/x=xy^2.

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  18. Obtain the volume of the parallelopiped whose sides are vectors veca=2...

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  19. Solve the matrix inversion method x+2y+3z=8,2x+y+z=8 and x+y+2z=6

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  20. If P (A) = 0.4,P (B | A)= 0.3 and P (B^c | A^c)=0.2. find P(B)

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