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  • Question 1
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  • Question 2
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    It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = kex – x for all real x where k is a real constant.
    The line y = x meets y = kex for k ≤ 0 at

  • Question 3
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    It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = kex – x for all real x where k is a real constant.
    The positive value of k for which kex – x = 0 has only one root is

  • Question 4
    4 / -1

    It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = kex – x for all real x where k is a real constant.

  • Question 5
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  • Question 6
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  • Question 7
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    This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
    The minimum value of the sum of real numbers a–5, a–4, 3a–3,1,a8 and a10, where a > 0 is

  • Question 8
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    This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9

  • Question 9
    4 / -1

    This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9

  • Question 10
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    This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
    Let p(x) be real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p’(0) is

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