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AIEEE 2003 (Maths) Mock Test

Medium 75 Questions 180 min 75 marks

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180 min · 75 marks · Full test mode with leaderboard

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Question No: 31Difficulty: mediumMarks: 1mcq

Let f (a) = g (a) = k and their n th derivatives f^{n} (a), g^{n} (a) exist and are not equal for some n . Further if lim_{x \to a} \frac{f ( a ) g ( x ) - f ( a ) g ( a ) - g ( a ) f ( x ) + g ( a ) f ( a )}{f ( x ) - g ( x )} = 4, then the value of k is:

Question No: 32Difficulty: mediumMarks: 1mcq

The function f (x) = lo g (x + x^{2} + 1) is:

Question No: 33Difficulty: mediumMarks: 1mcq

If f (x) = {x e^{- (\frac{1}{∣ x ∣} + \frac{1}{x})}, 0, x \neq = 0 x = 0 then f (x) is:

Question No: 34Difficulty: mediumMarks: 1mcq

If the function f (x) = 2 x^{3} - 9 a x^{2} + 12 a^{2} x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p^{2} = q, then a equals:

Question No: 35Difficulty: mediumMarks: 1mcq

If f (y) = e^{y}, g (y) = y for y > 0 and F (t) = \int_{0}^{t} f (t - y) g (y) d y, then:

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