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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’
Directions : In each of the following questions a statement is given, followed by two conclusions. Give answer :

Statement : Never before such a lucid book was available on the topic.

Assumptions :
I. Some other books were available on this topic.
II. You can write lucid books on very few topics.
The marks of 30 students in a test is shown as follows: 12, 16, 22, 24, 11, 7, 9, 11, 13, 14, 17, 19, 18, 21, 22, 23, 8, 9, 17, 16, 14, 23, 24, 24, 23, 17, 18, 16, 11, 9  Which Tally table represent the correct data of the marks of the students. (A) Interval of marks Tally marks of students 0-5 0 5-10 ||||  10-15 |||| || 15-20 |||| |||| 20-25 |||| ||||   (B)  Interval of marks Tally marks of students 0-5 0 5-10 |||| | 10-15 |||| ||| 15-20 |||| |||| 20-25 |||| || (C) Interval of marks Tally marks of students 0-5 0 5-10 |||| | 10-15 |||| || 15-20 |||| |||| 20-25 |||| || (D) Interval of marks Tally marks of students 0-5 0 5-10 ||||  10-15 |||| || 15-20 |||| ||| 20-25 |||| ||||
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
Three alarms are ringed on an interval. If the time interval between 1st and 2nd alarm is 220 secs, 2nd and 3rd alarm is 180 secs and time interval between 3rd and 1st alarm is 88.88% of 2nd and 3rd alarm. After how much time does they ringed together?
Which of the following statements will be considered true in the case of good hypothesis? Choose the correct answer from the code given below. i) It should be derived from the existing theory of knowledge. ii) It should clearly indicate the relation between variables postulated. iii) It should test a theory. iv) It should be related to a current issue. v) It should be stated in a concise and lucid manner.
Choose the appropriate word as synonym : Lucid :
Choose the word which is most nearly opposite in meaning to the word given. LUCID
Choose word opposite : "Lucid"-
The correct synonym of the word Lucid is -