Q3➡| Engineering Mathematics Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L ≠ G and that the size of L is at least 4. The size of L is ________.
Q5➡| Engineering Mathematics If V1 and V2 are 4-dimensional subspace of a 6-dimensional vector space V, then the smallest possible dimension of V1∩V2 is ______.
Q7➡| Digital Logic Design Consider the following minterm expression for F: F(P,Q,R,S) = Σ0,2,5,7,8,10,13,15 The minterms 2, 7, 8 and 13 are ‘do not care’ terms. The minimal sum-of-products form for F is:
Q8➡| Digital Logic Design Consider the following combinational function block involving four Boolean variables x, y, a, b where x, a, b are inputs and y is the output. Which one of the following digital logic blocks is the most suitable for implementing this function?
Q9➡| Computer-Organization Consider the following processors (ns stands for nanoseconds). Assume that the pipeline registers have zero latency. P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns. P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns. P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns. P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns. Which processor has the highest peak clock frequency?
Q11➡| Data Structure The minimum number of arithmetic operations required to evaluate the polynomial P(X) = X5 + 4X3 + 6X + 5 for a given value of X, using only one temporary variable is _________.
Q12➡| Data Structure Consider the following rooted tree with the vertex labeled P as t he root: The order in which the nodes are visited during in-order traversal is
Q13➡| Data Structure Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _______.
Q14➡| Algorithms You have an array of n elements. Suppose you implement quicksort by always choosing the central element of the array as the pivot. Then the tightest upper bound for the worst case performance is
Q15➡| Theory of Computation The length of the shortest string NOT in the language (over Σ = {a b,}) of the following regular is expression is _______. a*b*(ba)*a*
Q18➡| Compiler Design Which of the following statements are CORRECT? 1) Static allocation of all data areas by a compiler makes it impossible to implement recursion. 2) Automatic garbage collection is essential to implement recursion. 3) Dynamic allocation of activation records is essential to implement recursion. 4) Both heap and stack are essential to implement recursion.
Q20➡| Operating System A system uses 3 page frames for storing process pages in main memory. It uses the Least Recently Used (LRU) page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? 4, 7, 6, 1, 7, 6, 1, 2, 7, 2
Q21➡| Database Management System What is the optimized version of the relation algebra expression πA1(πA2(σF1(σF2(r)))), where A1, A2 are sets of attributes in with A1 ⊂ A2 and F1, F2 are Boolean expressions based on the attributes in r?
Q24➡| Computer Network A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. If the output bit-string after stuffing is 01111100101, then the input bit-string is
Q25➡| Computer Network Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP v4 network B). Assume that no error occurred during the transmission of D. When D reaches B, which of the following IP header field(s) may be different from that of the original datagram D? (i) TTL (ii) Checksum (iii) Fragment Offset
Q26➡| Computer Network An IP router implementing Classless Inter Domain Routing (CIDR) receives a packet with address 131.23.151.76. The router’s routing table has the following entries: The identifier of the output interface on which this packet will be forwarded is ________.
Q27➡|Computer Network Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup. Each host needs to generate up to 1000 unique identifiers per second. Assume that each host has a globally unique IPv4 address. Design a 50-bit globally unique ID for this purpose. After what period (in seconds) will the identifiers generated by a host wrap around?
Q28➡| Computer Network An IP router with a Maximum Transmission Unit (MTU) of 1500 bytes has received an IP packet of size 4404 bytes with an IP header of length 20 bytes. The values of the relevant fields in the header of the third IP fragment generated by the router for this packet are
i ➥ MF bit: 0, Datagram Length: 1444; Offset: 370
ii ➥ MF bit: 1, Datagram Length: 1424; Offset: 185
iii ➥ MF bit: 1, Datagram Length: 1500; Offset: 370
iv ➥ MF bit: 0, Datagram Length: 1424; Offset: 2960
Q30➡|Database Managemnt System Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation.
Q31➡| Operating Systems A system contains three programs and each requires three tape units for its operation. The minimum number of tape units which the system must have such that deadlocks never arise is .
Q32➡| Operating Systems An operating system uses shortest remaining time first scheduling algorithm for pre-emptive scheduling of processes. Consider the following set of processes with their arrival times and CPU burst times (in milliseconds): The average waiting time (in milliseconds) of the processes is_____.
Q33➡| Operating Systems Consider a paging hardware with a TLB. Assume that the entire page table and all the pages are in the physical memory. It takes 10 milliseconds to search the TLB and 80 milliseconds to access the physical memory. If the TLB hit ratio is 0.6, the effective memory access time (in milliseconds) is____. .
Q34➡| Compiler Design Consider the basic block given below. a = b + c c = a + d d = b + c e = d – b a= e + b The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are
Q36➡| Theory of Computation Consider the following languages over the alphabet Σ = {0,1, c}: L1= {0n1n | n ≥ 0} L2 = {wcwr |w ∈ {0,1}∗} L3 = {wwr |w ∈ {0,1}∗} Here, wris the reverse of the string w. Which of these languages are deterministic Context-free languages?
Q37➡|Algorithms Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of integers i, j with i < j. Given a shortcut i, j if you are at position i on the number line, you may directly move to j. Suppose T(k) denotes the smallest number of steps needed to move from k to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that T(9) = 1 + min(T(y), T(z)). Then the value of the product yz is_______________.
Q38➡|Algorithms Consider the decision problem 2CNFSAT defined as follows: { 0 | 0 is a satisfiable propositional formula in CNF with at most two literals per clause } For example, 0 = (x1 ˅ x2)⋀(x1 ˅ x3‘)⋀(x2 ˅ x4) is a Boolean formula and it is in 2CNFSAT. The decision problem 2CNFSAT is____.
i ➥ NP-Complete.
ii ➥ solvable in polynomial time by reduction to directed graph reachability.
iii ➥ solvable in constant time since any input instance is satisfiable.
Q39➡|Data Structure Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up all the numbers in T that lie between L and H. Suppose there are N such numbers in T. If the tightest upper bound on the time to compute the sum is 0(na logb n+ mc logd n), the value of a + 10b + 100c + 1000d is_____. .
Q40➡| Data Structure Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions?
Q41➡|Programming in C Consider the pseudocode given below. The function DoSomething() takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. Each node of the tree is of type treeNode. When the pointer to the root of a tree is passed as the argument to DoSomething, the value returned by the function corresponds to the
i ➥ number of internal nodes in the tree.
ii ➥ height of the tree.
iii ➥ number of nodes without a right sibling in the tree.
Q42➡| Programming Consider the C function given below. Assume that the array listA contains n (> 0) elements, sorted in ascending order. Which one of the following statements about the function ProcessArray is CORRECT?
i ➥ It will run into an infinite loop when x is not in listA.
ii ➥ It is an implementation of binary search.
iii ➥ It will always find the maximum element in listA.
iv ➥ It will return −1 even when x is present in listA.
Q43➡| Computer Organization An instruction pipeline has five stages, namely, instruction fetch (IF), instruction decode and register fetch (ID/RF), instruction execution (EX), memory access (MEM), and register writeback (WB) with stage latencies 1 ns, 2.2 ns, 2 ns, 1 ns, and 0.75 ns, respectively (ns stands for nanoseconds). To gain in terms of frequency, the designers have decided to split the ID/RF stage into three stages (ID, RF1, RF2) each of latency 2.2/3 ns. Also, the EX stage is split into two stages (EX1, EX2) each of latency 1 ns. The new design has a total of eight pipeline stages. A program has 20% branch instructions which execute in the EX stage and produce the next instruction pointer at the end of the EX stage in the old design and at the end of the EX2 stage in the new design. The IF stage stalls after fetching a branch instruction until the next instruction pointer is computed. All instructions other than the branch instruction have an average CPI of one in both the designs. The execution times of this program on the old and the new design are P and Q nanoseconds, respectively. The value of P/Q is__________________.
Q44➡| Computer Organization The memory access time is 1 nanosecond for a read operation with a hit in cache, 5 nanoseconds for a read operation with a miss in cache, 2 nanoseconds for a write operation with a hit in cache and 10 nanoseconds for a write operation with a miss in cache. Execution of a sequence of instructions involves 100 instruction fetch operations, 60 memory operand read operations and 40 memory operand write operations. The cache hit-ratio is 0.9. The average memory access time (in nanoseconds) in executing the sequence of instructions is .
Q45➡|Digital Logic Design The above synchronous sequential circuit built using JK flip-flops is initialized with Q2Q1QO = 000. The state sequence for this circuit for the next 3 clock cycles is
Q46➡| Engineering Mathematics With respect to the numerical evaluation of the definite integral, K = where a and b are given, which of the following statements is/are TRUE? I) The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral. II) The value of K obtained using the Simpson’s rule is always equal to the exact value of the definite integral.
Q48➡|Engineering Mathematics Let S be a sample space and two mutually exclusive events A and B be such that A ∪ B = S. If P(∙) denotes the probability of the event, the maximum value of P(A)P(B) is .
Q49➡|Engineering Mathematics Consider the set of all functions ƒ: {0,1, … ,2014} → {0,1, … ,2014} such that ƒ(ƒ(i)) = i, for all 0 ≤ i ≤ 2014. Consider the following statements: P. For each such function it must be the case that for every i, ƒ(i) = i. Q. For each such function it must be the case that for some i, ƒ(i) = i. R. Each such function must be onto. Which one of the following is CORRECT?
Q50➡| Engineering Mathematics There are two elements x, y in a group (G,∗) such that every element in the group can be written as a product of some number of x’s and y’s in some order. It is known that x ∗ x = y ∗ y = x ∗ y ∗ x ∗ y = y ∗ x ∗ y ∗ x = e where e is the identity element. The maximum number of elements in such a group is_________. .
Q52➡| Discrete Mathematics Let δ denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with δ ≥ 3, which one of the following is TRUE?
i ➥ In any planar embedding, the number of faces is at least n/2+2
ii ➥ In any planar embedding, the number of faces is less than n/2+2
iii ➥ There is a planar embedding in which the number of faces is less than n/2+2
iv ➥ There is a planar embedding in which the number of faces is at most n/ δ +1
Q54➡|Database-Management-System Consider the following relational schema: employee(empId,empName,empDept) customer(custId,custName,salesRepId,rating) salesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return?
SELECT empName FROM employee E WHERE NOT EXISTS (SELECT custId FROM customer C WHERE C.salesRepId = E.empId AND C.rating <> ’GOOD’);
i ➥ Names of all the employees with at least one of their customers having a ‘GOOD’ rating.
ii ➥ Names of all the employees with at most one of their customers having a ‘GOOD’ rating.
iii ➥ Names of all the employees with none of their customers having a ‘GOOD’ rating.
iv ➥ Names of all the employees with all their customers having a ‘GOOD’ rating
Q55➡|Digital Logic Design Let ⊕ denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for F over two variables P and Q: F(P, Q) = ((1⨁P)⨁(P⨁Q)) ⨁ ((P⨁Q)⨁(Q⨁0)) The equivalent expression for F is
where a and b are given, 
