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GATE 2016 General Aptitude - GA Set- 5
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Q. 1 – Q. 5 carry one mark each.
Q.1 Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.
(A) I will not leave the place until the minister does not meet me.
(B) I will not leave the place until the minister doesn’t meet me.
(C) I will not leave the place until the minister meet me.
(D) I will not leave the place until the minister meets me.
Q.2 A rewording of something written or spoken is a ______________.
(A) paraphrase (B) paradox (C) paradigm (D) paraffin
Q.3 Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.”
The sentence above is an example of a ___________ statement.
(A) figurative (B) collateral
(C) literal (D) figurine
Q.4 If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?
(A) zentaga (B) tagafer (C) tagazen (D) relffer
Q.5 A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________.
(A) 56 (B) 64 (C) 72 (D) 96
GATE 2016 General Aptitude - GA Set- 5
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Q. 6 – Q. 10 carry two marks each.
Q.6 A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.
Quarter \ Product Elegance Smooth Soft Executive Q1 27300 20009 17602 9999 Q2 25222 19392 18445 8942 Q3 28976 22429 19544 10234 Q4 21012 18229 16595 10109
Which product contributes the greatest fraction to the revenue of the company in that year?
(A) Elegance (B) Executive (C) Smooth (D) Soft
Q.7 Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is.
Which of the following can be logically inferred from the above sentences? (A) India is a country of exactly seventeen languages.
(B) Linguistic pluralism is the only indicator of a nation’s diversity.
(C) Indian currency notes have sufficient space for all the Indian languages.
(D) Linguistic pluralism is strong evidence of India’s diversity.
Q.8 Consider the following statements relating to the level of poker play of four players P , Q , R and S.
I. P always beats Q II. R always beats S III. S loses to P only sometimes IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players (ii) S is the absolute worst player in the set
(A) (i) only (B) (ii) only (C) (i) and (ii) (D) neither (i) nor (ii)
Q.9 (^) If f(𝑥𝑥) = 2 𝑥𝑥^7 + 3 𝑥𝑥 − 5 , which of the following is a factor of f( x )?
(A) ( x^3 +8) (B)^ ( x - 1)^ (C)^ (2 x - 5)^ (D)^ ( x +1)
Q. 1 - Q. 25 carry one mark each.
Q.1 Let p, q, r, s represent the following propositions.
p: x ∈ { 8 , 9 , 10 , 11 , 12 } q: x is a composite number r: x is a perfect square s: x is a prime number
The integer x ≥ 2 which satisfies ¬((p ⇒ q) ∧ (¬r ∨ ¬s)) is.
Q.2 Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for an? (A) an = an− 1 + 2 an− 2 (B) an = an− 1 + an− 2 (C) an = 2 an− 1 + an− 2 (D) an = 2 an− 1 + 2 an− 2
Q.
lim x→ 4
sin(x − 4 ) x − 4
Q.4 A probability density function on the interval [a, 1 ] is given by 1/x^2 and outside this interval the value of the function is zero. The value of a is.
Q.5 Two eigenvalues of a 3 × 3 real matrix P are ( 2 +
− 1 ) and 3. The determinant of P is .
Q.6 Consider the Boolean operator # with the following properties: x # 0 = x, x # 1 = x¯, x # x = 0 and x # ¯x = 1. Then x # y is equivalent to (A) x y¯ + xy¯ (B) x y¯ + x¯ y¯ (C) xy¯ + xy (D) xy + x¯ y¯
Q.7 The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is.
Q.8 We want to design a synchronous counter that counts the sequence 0-1-0-2-0-3 and then repeats. The minimum number of J-K flip-flops required to implement this counter is .
Q.9 A processor can support a maximum memory of 4 GB, where the memory is word-addressable (a word consists of two bytes). The size of the address bus of the processor is at least bits.
Q.10 A queue is implemented using an array such that ENQUEUE and DEQUEUE operations are performed efficiently. Which one of the following statements is CORRECT (n refers to the number of items in the queue)? (A) Both operations can be performed in O( 1 ) time (B) At most one operation can be performed in O( 1 ) time but the worst case time for the other operation will be Ω(n) (C) The worst case time complexity for both operations will be Ω(n) (D) Worst case time complexity for both operations will be Ω(log n)
Q.13 The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:
(A) Θ(n log n), Θ(n log n), and Θ(n^2 ) (B) Θ(n^2 ), Θ(n^2 ), and Θ(n log n) (C) Θ(n^2 ), Θ(n log n), and Θ(n log n) (D) Θ(n^2 ), Θ(n log n), and Θ(n^2 )
Q.14 Let G be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE?
P: Minimum spanning tree of G does not change Q: Shortest path between any pair of vertices does not change
(A) P only (B) Q only (C) Neither P nor Q (D) Both P and Q
Q.15 Consider the following C program.
#include<stdio.h> void mystery(int *ptra, int *ptrb) { int *temp; temp = ptrb; ptrb = ptra; ptra = temp; } int main() { int a=2016, b=0, c=4, d=42; mystery(&a, &b); if (a < c) mystery(&c, &a); mystery(&a, &d); printf("%d\n", a); }
The output of the program is.
Q.16 Which of the following languages is generated by the given grammar?
S −→ aS | bS | ε
(A) {anbm^ | n, m ≥ 0 } (B) {w ∈ {a, b}∗^ | w has equal number of a’s and b’s } (C) {an^ | n ≥ 0 } ∪ {bn^ | n ≥ 0 } ∪ {anbn^ | n ≥ 0 } (D) {a, b}∗
Q.20 Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths submitted at the same time to a computer system. Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue? (A) Shortest remaining time first (B) Round-robin with time quantum less than the shortest CPU burst (C) Uniform random (D) Highest priority first with priority proportional to CPU burst length
Q.21 Which of the following is NOT a superkey in a relational schema with attributes V , W , X, Y , Z and primary key V Y? (A) V XY Z (B) VW XZ (C) VW XY (D) VW XY Z
Q.22 Which one of the following is NOT a part of the ACID properties of database transactions?
(A) Atomicity (B) Consistency (C) Isolation (D) Deadlock-freedom
Q.23 A database of research articles in a journal uses the following schema.
(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE) The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE) → TITLE (VOLUME, NUMBER) → YEAR (VOLUME, NUMBER, STARTPAGE, ENDPAGE) → PRICE The database is redesigned to use the following schemas. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE) (VOLUME, NUMBER, YEAR) Which is the weakest normal form that the new database satisfies, but the old one does not? (A) 1NF (B) 2NF (C) 3NF (D) BCNF
Q.24 Which one of the following protocols is NOT used to resolve one form of address to another one? (A) DNS (B) ARP (C) DHCP (D) RARP
Q.25 Which of the following is/are example(s) of stateful application layer protocols?
(i) HTTP (ii) FTP (iii) TCP (iv) POP
(A) (i) and (ii) only (B) (ii) and (iii) only (C) (ii) and (iv) only (D) (iv) only
Q.30 Consider the two cascaded 2-to-1 multiplexers as shown in the figure.
MUX
(^0) 2−to− 1
0 1
0 MUX
2−to−1^ X
R
R
P Q
s s
The minimal sum of products form of the output X is (A) P¯ Q¯ + PQR (B) PQ¯ + QR (C) PQ + P¯ QR¯ (D) Q¯ R¯ + PQR
Q.31 The size of the data count register of a DMA controller is 16 bits. The processor needs to transfer a file of 29,154 kilobytes from disk to main memory. The memory is byte addressable. The minimum number of times the DMA controller needs to get the control of the system bus from the processor to transfer the file from the disk to main memory is.
Q.32 The stage delays in a 4-stage pipeline are 800, 500, 400 and 300 picoseconds. The first stage (with delay 800 picoseconds) is replaced with a functionally equivalent design involving two stages with respective delays 600 and 350 picoseconds. The throughput increase of the pipeline is percent.
Q.33 Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is (A) Θ( 1 ) (B) Θ(log(n)) (C) Θ(
n) (D) Θ(n)
Q.34 The following function computes the maximum value contained in an integer array p[] of size n (n >= 1).
int max(int *p, int n) { int a=0, b=n-1;
while (__________) { if (p[a] <= p[b]) { a = a+1; } else { b = b-1; } }
return p[a]; }
The missing loop condition is (A) a != n (B) b != 0 (C) b > (a + 1) (D) b != a
Q.35 What will be the output of the following C program?
void count(int n){ static int d=1;
printf("%d ", n); printf("%d ", d); d++; if(n>1) count(n-1); printf("%d ", d); }
void main(){ count(3); }
(A) 3 1 2 2 1 3 4 4 4 (B) 3 1 2 1 1 1 2 2 2 (C) 3 1 2 2 1 3 4 (D) 3 1 2 1 1 1 2
Q.40 G = (V, E) is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE?
I. If e is the lightest edge of some cycle in G, then every MST of G includes e II. If e is the heaviest edge of some cycle in G, then every MST of G excludes e
(A) I only (B) II only (C) both I and II (D) neither I nor II
Q.41 Let Q denote a queue containing sixteen numbers and S be an empty stack. Head(Q) returns the element at the head of the queue Q without removing it from Q. Similarly Top(S) returns the element at the top of S without removing it from S. Consider the algorithm given below.
while Q is not Empty do if S is Empty OR Top(S) ≤ Head(Q) then x := Dequeue(Q); Push(S, x); else x := Pop(S); Enqueue(Q, x); end end
The maximum possible number of iterations of the while loop in the algorithm is .
Q.42 Consider the following context-free grammars:
G 1 : S → aS|B, B → b|bB G 2 : S → aA|bB, A → aA|B|ε, B → bB|ε Which one of the following pairs of languages is generated by G 1 and G 2 , respectively? (A) {ambn|m > 0 or n > 0 } and {ambn|m > 0 and n > 0 } (B) {ambn|m > 0 and n > 0 } and {ambn|m > 0 or n ≥ 0 } (C) {ambn|m ≥ 0 or n > 0 } and {ambn|m > 0 and n > 0 } (D) {ambn|m ≥ 0 and n > 0 } and {ambn|m > 0 or n > 0 }
Q.43 Consider the transition diagram of a PDA given below with input alphabet Σ = {a, b} and stack alphabet Γ = {X, Z}. Z is the initial stack symbol. Let L denote the language accepted by the PDA.
b, X/ε (^) ε, Z/Z
a, Z/XZ b, X/ε
a, X/XX
Which one of the following is TRUE? (A) L = {anbn|n ≥ 0 } and is not accepted by any finite automata (B) L = {an|n ≥ 0 } ∪ {anbn|n ≥ 0 } and is not accepted by any deterministic PDA (C) L is not accepted by any Turing machine that halts on every input (D) L = {an|n ≥ 0 } ∪ {anbn|n ≥ 0 } and is deterministic context-free
Q.44 Let X be a recursive language and Y be a recursively enumerable but not recursive language. Let W and Z be two languages such that Y reduces to W , and Z reduces to X (reduction means the standard many-one reduction). Which one of the following statements is TRUE? (A) W can be recursively enumerable and Z is recursive. (B) W can be recursive and Z is recursively enumerable. (C) W is not recursively enumerable and Z is recursive. (D) W is not recursively enumerable and Z is not recursive.
Q.45 The attributes of three arithmetic operators in some programming language are given below.
Operator Precedence Associativity Arity
- High Left Binary − Medium Right Binary ∗ Low Left Binary The value of the expression 2 − 5 + 1 − 7 ∗ 3 in this language is.
Q.50 Consider the following proposed solution for the critical section problem. There are n processes: P 0... Pn− 1. In the code, function pmax returns an integer not smaller than any of its arguments. For all i, t[i] is initialized to zero.
Code for Pi:
do { c[i]=1; t[i] = pmax(t[0],.. .,t[n-1])+1; c[i]=0; for every j 6 = i in {0,.. .,n-1} { while (c[j]); while (t[j] != 0 && t[j]<=t[i]); } Critical Section; t[i]=0; Remainder Section; } while (true);
Which one of the following is TRUE about the above solution? (A) At most one process can be in the critical section at any time (B) The bounded wait condition is satisfied (C) The progress condition is satisfied (D) It cannot cause a deadlock
Q.51 Consider the following two phase locking protocol. Suppose a transaction T accesses (for read or write operations), a certain set of objects {O 1 ,... , Ok}. This is done in the following manner:
Step 1. T acquires exclusive locks to O 1 ,... , Ok in increasing order of their addresses. Step 2. The required operations are performed. Step 3. All locks are released.
This protocol will (A) guarantee serializability and deadlock-freedom (B) guarantee neither serializability nor deadlock-freedom (C) guarantee serializability but not deadlock-freedom (D) guarantee deadlock-freedom but not serializability
Q.52 Consider that B wants to send a message m that is digitally signed to A. Let the pair of private and public keys for A and B be denoted by K x− and K x+ for x = A, B, respectively. Let Kx(m) represent the operation of encrypting m with a key Kx and H(m) represent the message digest. Which one of the following indicates the CORRECT way of sending the message m along with the digital signature to A? (A) {m, K B+ (H(m))} (B) {m, K B− (H(m))} (C) {m, K A− (H(m))} (D) {m, K A+ (m)}
Q.53 An IP datagram of size 1000 bytes arrives at a router. The router has to forward this packet on a link whose MTU (maximum transmission unit) is 100 bytes. Assume that the size of the IP header is 20 bytes. The number of fragments that the IP datagram will be divided into for transmission is .
Q.54 For a host machine that uses the token bucket algorithm for congestion control, the token bucket has a capacity of 1 megabyte and the maximum output rate is 20 megabytes per second. Tokens arrive at a rate to sustain output at a rate of 10 megabytes per second. The token bucket is currently full and the machine needs to send 12 megabytes of data. The minimum time required to transmit the data is seconds.
Q.55 A sender uses the Stop-and-Wait ARQ protocol for reliable transmission of frames. Frames are of size 1000 bytes and the transmission rate at the sender is 80 Kbps (1Kbps = 1000 bits/second). Size of an acknowledgement is 100 bytes and the transmission rate at the receiver is 8 Kbps. The one-way propagation delay is 100 milliseconds. Assuming no frame is lost, the sender throughput is bytes/second.
