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31. Integration ∫ log x dx has the value

x log x - 1

log x - x

x(log x -1)

none of these

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32. The integral

diverges

converges to 1/3

converges to - 1 / a^{3}

converges to 0

33. If f(x), φ(x) and ψ (x) have derivatives when a ≤ x ≤ b, then E a value of c of x lying between a and b such that

34. The limit of the function f(x) = [ 1 - a^{4} / x^{4} ] as x ---> ∞ is given by

1

exp[ -a^{4} ]

∞

zero

35. The following function has a local minima at which value of x

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