Q. Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is                 . Ans: 42 According to Lagrange’s theorem, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G. Therefore, possible subgroups of group on […]

Q. The chromatic number of the following graph is  Ans: 3 Sol: Chromatic number of given graph is 3. Note that graph is Planar so Chromatic number should be less than or equal to 4 and can not be less than 3 because of odd length cycle. In other words if a graph is planar and

Q. Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and

Q. Consider the following statements regarding the slow start phase of the TCP congestion control algorithm. Note that cwnd stands for the TCP congestion window and MSS denotes the Maximum Segment Size. i. The cwnd increases by 2 MSS on every successful acknowledgment. ii. The cwnd approximately doubles on every successful acknowledgement. iii. The cwnd

Q. In an Entity-Relationship (ER) model, suppose 𝑅 is a many-to-one relationship from entity set E1 to entity set E2. Assume that E1 and E2 participate totally in 𝑅 and that the cardinality of E1 is greater than the cardinality of E2. Which one of the following is true about 𝑅? A. Every entity in

Q. Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is M units if the corresponding memory page is available in memory, and D units if the memory access causes a page fault. It has been experimentally measured that the average time

Q. The following are some events that occur after a device controller issues an interrupt while process L is under execution. P. The processor pushes the process status of L onto the control stack. Q. The processor finishes the execution of the current instruction. R. The processor executes the interrupt service routine. S. The processor

Q. The set of all recursively enumerable languages is A. closed under complementation. B. closed under intersection. C. a subset of the set of all recursive languages. D. an uncountable set. Ans: closed under intersection.

Q. Let N be an NFA with n states. Let k be the number of states of a minimal DFA which is equivalent to N. Which one of the following is necessarily true? (A) 𝑘 ≥ 2𝑛                  (B) 𝑘 ≥ 𝑛                   (C) 𝑘 ≤ 𝑛2                  (D) 𝑘 ≤ 2𝑛 Ans: 𝑘 ≤ 2𝑛

Q. Consider the following processor design characteristics. I. Register-to-register arithmetic operations only II. Fixed-length instruction format III. Hardwired control unit Which of the characteristics above are used in the design of a RISC processor? (A) I and II only          (B) II and III only       (C) I and III only         (D) I, II and III Ans: