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Use the function f(x) = x^(1//x), x gt 0...

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

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MODERN PUBLICATION-SAMPLE 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. Maximise Z=50x(1)+60x(2) Subject to 2x(1)+3x(2)le6,x(1),x(2)ge0.

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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 int0^1frac[ln(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 vec a=...

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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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