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Mean Value theorem is applicable to the and continuous in open interval (a, b) b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) d) Functions differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’
Rolle’s theorem is applicable to the and continuous in open interval (a, b) only and having same value at point ‘a’ and ‘b’ b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’ d) Monotonically Increasing funtions
As per the RBI Act, 1934, the following functions are described as the functions of a Central Bank:
1. Banking functions
2. Advisory functions
3. Supervisory functions
4. Promotional functions
Identify the correct combination:
Another form of Rolle’s theorem for the continuous condition is _____ b) f is continuous on c) f is continuous on d) f is continuous on
Assertion (A) It has been suggested that while roles answer the question 'how to be interfaced with other people to reach our goals'? Functions answer the question 'what do you do to accomplish our goals'?
Reason (R) Roles are more relational while functions go beyond inter-personal relations. Functions such as planning, decision-making etc may not necessarily involve working with others and several managerial functions can be performed without communication with people.
Consider the following statements regarding continuous beam: 1. A beam is said to be a continuous beam if it is supported on more than two supports. 2. A continuous beam is a statically indeterminate structure. 3. The degree of indeterminacy depends upon the number of supports and also on the nature of the supports. Which of the above statements are correct?
Which of the following statements is/are correct? 1. A continuous-time system is a system in which, continuous-time input signals are applied, resulting in continuous-time output signals. 2. A system is said to be linear if it follows the superposition theorem. 3. A system is said to be non-linear if it follows the superposition theorem.
Directions : In each of the following questions a statement is given, followed by two conclusions. Give answer :

Statement : The integrated steel plants in India would no longer have to depend on imports for continuous casting refractories.

Assumptions :
I. Continuous casting refractories are needed by India.
II. Continuous casting refractories are in demand.
Given the following statements about a function f : R → R , select the right option:
P: If f(x) is continuous at x = x0, then it is differential at x = x0.
Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.
R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.
When are dummy variables used in continuous time convolution?