GATE CSE 2014 Set 3
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## GATE CSE

The minimum number of arithmetic operations required to evaluate the polynomial P(X) = X5 + 4X3 + 6X + 5 for a given val
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You have an array of n elements. Suppose you implement quicksort by always choosing the central element of the array as
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Consider the decision problem 2CNFSAT defined as follows: { $$\Phi$$ | $$\Phi$$ is a satisfiable propositional formula
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One of the purposes of using intermediate code in compilers is to
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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
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In the following pairs of OSI protocol layer/sub-layer and its functionality, the INCORRECT pair is
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A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. If the output bit-string after stuffi
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Host A (on TCP/IPv4 network A) sends an IP datagram D to host B (also on TCP/IPv4 network B). Assume that no error occur
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Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup. Each host needs to generate
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An IP router with a Maximum Transmission Unit (MTU) of 1500 bytes has received an IP packet of size 4404 bytes with an I
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An IP router implementing Classless Inter-domain Routing (CIDR) receives a packet with address 131.23.151.76. The router
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The memory access time is $$1$$ nanosecond for a read operation with a hit in cache, $$5$$ nanoseconds for a read operat
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Consider the following processors ($$ns$$ stands for nanoseconds). Assume that the pipeline registers have zero latency.
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An instruction pipeline has five stages, namely, instruction fetch $$(IF),$$ instruction decode and register fetch $$(ID View Question Consider the following rooted tree with the vertex labelled P as the root The order in which the nodes are visited duri View Question Consider the C function given below. Assume that the array listA contains n (&gt; 0) elements, sored in ascending order. View Question Consider the pseudocode given below. The function Dosomething () takes as argument a pointer to the root of an arbitrary View Question Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call View Question Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is t View Question Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up a View Question A prime attribute of a relation scheme$$R$$is an attribute that appears View Question Consider the following relational schema: employee (empId, empName, empDept ) customer (custId, custName, salesRepId, ra View Question What is the optimized version of the relation algebra expression$$\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$$, wh View Question Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of t View Question Consider the transactions T1, T2, and T3 and the schedules S1 and S2 given below. T1 : r1 (X) ; r1 (Z) ; w1 (X) ; w1 (Z) View Question Consider the following combinational function block involving four Boolean variables$$x, y, a,b$$where$$x, a, b
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Let $$\oplus$$ denote the exclusive $$OR\left( {XOR} \right)$$ operation. Let $$'1'$$ and $$'0'$$ denote the binary co
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Consider the following interm expression of $$F:$$ $$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15}$$ Th
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The above synchronous sequential circuit built using $$JK$$ flip-flops is initialized with $${Q_2}{Q_1}{Q_0} = 000.\,\, View Question Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies View Question Let S be a sample space and two mutually exclusive events A and B be such that$$A\, \cup \,B = \,S$$. If P(.) denotes t View Question The CORRECT formula for the sentence, "not all rainy days are cold" is View Question Let$$X$$and$$Y$$be finite sets and$$f:X \to Y$$be a function. Which one of the following statements is TRUE? View Question Which one of the following statements is TRUE about every$$n\,\, \times \,n$$matrix with only real eigen values? View Question If$${V_1}$$and$${V_2}$$are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dim View Question If$$\int_0^{2\pi } {\left| {x\sin x} \right|dx = k\pi ,} $$then the values of$$k$$is equal to _________ . View Question The value of the integral given below is$$\$\int_0^\pi {{x^2}\,\cos \,x\,dx} $$View Question Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you View Question Consider the set of all functions$$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$such View Question There are two elements$$x, y$$in a group$$\left( {G,\, * } \right)$$such that every elements in the group can be wri View Question let$$G$$be a group with$$15$$elements. Let$$L$$be a subgroup of$$G$$. It is known that$$L \ne G$$and that the s View Question Let$$\delta $$denote the minimum degree of a vertex in a graph. For all planar graphs on$$n$$vertices with$$\delta
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If $$G$$ is a forest with $$n$$ vertices and $$k$$ connected components, how many edges does $$G$$ have?
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An operating system uses $$shortest$$ $$remaining$$ $$time$$ $$first$$ scheduling algorithm for pre-emptive scheduling o
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A system uses $$3$$ page frames for storing process pages in main memory. It uses the Least Recently Used $$(LRU)$$ page
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Consider a paging hardware with a TLB. Assume that the entire page table and all the pages are in the physical memory. I
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A system contains three programs and each requires three tape units for its operation. The Minimum number of tape units
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Which of the following statements are CORRECT? 1) Static allocation of all data areas by a compiler makes it impossible
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Let A be a square matrix size $$n \times n$$. Consider the following pseudocode. What is the expected output? C = 100;
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In the context of modular software design, which one of the following combinations is desirable?
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The length of the shortest string NOT in the language (over $$\sum { = \left\{ {a,\,\,b} \right\}}$$) of the following
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Consider the following languages over the alphabet $$\sum { = \left\{ {0,\,1,\,c} \right\}:}$$ \eqalign{ &amp; {L_ View Question Let\sum \, $$be a finite non - empty alphabet and let$${2^{\sum {{}^ * } }}$$be the power set of$$\sum {{}^ * .\,
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Which one of the following problems is un-decidable?
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