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For any two languages L1 and L2 such that L1 is context-free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true? I. L̅1 (complement of L1) is recursive II. L̅2 (complement of L2) is recursive III. L̅1 is context-free IV. L̅1 ∪ L2 is recursively enumerable
Consider the following statements in respect of sets: 1. The union over the intersection of sets is distributive. 2. The complement of the union of two sets is equal to the intersection of their complements. 3. If the difference between the two sets is equal to the empty set, then the two sets must be equal. Which of the above statements are correct?
Which of the following statements about Regular Expression is/are incorrect? A. The union of two regular expressions is also a regular expression B. The concatenation of two regular expressions is also a regular expression C. The iteration of a regular expression is also a regular expression
Let L1, L2 be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT? I. L1 ∪ L2 is context-free II. L̅1 is context-free III. L1 – R is context-free IV. L1 ∩ L2 is context-free
A manufacturer of TV wants to make a profit of Tk. 300,000 on sale of 200 TV sets. It costs Tk. 10,000 each to make the first 100 TV sets and Tk. 7,500 each to make TV sets after the first 100 sets. What should be the selling price of each TV sets in Taka?
Consider the following statements: (1) If n ≥ 3 and m ≥ 3 are distinct positive integers, then the sum of exterior angles of a regular polygon of m sides is different from the sum of exterior angles of regular polygon of n sides (2) Let m, n be integers such that m > n ≥ 3. Then the sum of the interior angles of regular polygon of sides is greater than the sum of interior angles of a regular polygon of n sides, and their sum is (m + n)π/2 Which of the above statements is/are correct?
A manufacturing company produces 5 types of chairs in two sizes - Regular" and "Large". The pie charts represent the total number of five types of chairs produced and the table shows the ratio between the number of regular sized and large sized chairs of five types. Type of Chair A B C D E Ration between Number of Regular Size and Large Size Chairs 3 : 2 4 : 5 3 : 1 5 : 3 3 : 8   If the total number of all types of chairs produced is 7200, what is the total number of regular size chairs of all types produced.
A person is at the intersection of Town road and moon drive. He drives towards the north of Moon Drive, takes a left on the second road,  then right, and then left again, and then takes a left on the first road. Then he drives towards the east on the second road, takes a right on the first road, drives towards the west on the first road, and then stops at the first intersection. Which place is closest to his new position?
If from any external point, two tangents are drawn, then find the addition of angles made by the intersection of two tangents and the angle made by the intersection of two radii at the center facing the same external point  
Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statement. Statement: All refrigerators are television sets. Some speakers are television sets. All speakers are fans. Conclusion: I. Some fans are television sets. II. Some television sets are refrigerators. III. No fans is a speaker