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GATE 2016 General Aptitude - GA Set- 6
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Q. 1 – Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of
𝛼𝛼𝑛𝑛^ + 𝛽𝛽𝑛𝑛 𝛼𝛼−𝑛𝑛^ + 𝛽𝛽−𝑛𝑛
(A) n 4 (B) 4 n (C) 2 2n- 1 (D) 4 n- 1
Q. 6 – Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook®^ or WhatsApp®^ accounts. The number of faculty members connected only through Facebook®^ accounts is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
GATE 2016 General Aptitude - GA Set- 6
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Q.7 Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?
(i) The author believes that computers are not good for us. (ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?
(i) Ooty is not a hill-station. (ii) No hill-station can have more than one lake.
(A) (i) only (B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
Q. 1 - Q. 25 carry one mark each.
Q.1 Consider the following expressions:
(i) false (ii) Q (iii) true (iv) P ∨ Q (v) ¬Q ∨ P
The number of expressions given above that are logically implied by P ∧ (P ⇒ Q) is .
Q.2 Let f (x) be a polynomial and g(x) = f ′(x) be its derivative. If the degree of ( f (x) + f (−x)) is 10, then the degree of (g(x) − g(−x)) is.
Q.3 The minimum number of colours that is sufficient to vertex-colour any planar graph is .
Q.4 Consider the systems, each consisting of m linear equations in n variables.
I. If m < n, then all such systems have a solution II. If m > n, then none of these systems has a solution III. If m = n, then there exists a system which has a solution
Which one of the following is CORRECT? (A) I, II and III are true (B) Only II and III are true (C) Only III is true (D) None of them is true
Q.5 Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is.
Q.6 Suppose that the eigenvalues of matrix A are 1, 2 , 4. The determinant of (A−^1 )T^ is .
Q.7 Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is.
Q.8 Let, x 1 ⊕x 2 ⊕x 3 ⊕x 4 = 0 where x 1 , x 2 , x 3 , x 4 are Boolean variables, and ⊕ is the XOR operator. Which one of the following must always be TRUE? (A) x 1 x 2 x 3 x 4 = 0 (B) x 1 x 3 + x 2 = 0 (C) x¯ 1 ⊕ x¯ 3 = x¯ 2 ⊕ x¯ 4 (D) x 1 + x 2 + x 3 + x 4 = 0
Q.9 Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X −Y is.
Q.10 A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is.
Q.14 The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
(A) Greedy paradigm. (B) Divide-and-Conquer paradigm. (C) Dynamic Programming paradigm. (D) neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
Q.15 N items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on which the operation is to be performed. An algorithm performs the following operations on the list in this order: Θ(N) delete, O(log N) insert, O(log N) find, and Θ(N) decrease-key. What is the time complexity of all these operations put together? (A) O(log^2 N) (B) O(N) (C) O(N^2 ) (D) Θ(N^2 log N)
Q.16 The number of states in the minimum sized DFA that accepts the language defined by the regular expression ( 0 + 1 )∗( 0 + 1 )( 0 + 1 )∗ is.
Q.17 Language L 1 is defined by the grammar: S 1 → aS 1 b|ε Language L 2 is defined by the grammar: S 2 → abS 2 |ε Consider the following statements: P: L 1 is regular Q: L 2 is regular
Which one of the following is TRUE? (A) Both P and Q are true (B) P is true and Q is false (C) P is false and Q is true (D) Both P and Q are false
Q.18 Consider the following types of languages: L 1 : Regular, L 2 : Context-free, L 3 : Recursive, L 4 : Recursively enumerable. Which of the following is/are TRUE?
I. L 3 ∪ L 4 is recursively enumerable II. L 2 ∪ L 3 is recursive III. L∗ 1 ∩ L 2 is context-free IV. L 1 ∪ L 2 is context-free
(A) I only (B) I and III only (C) I and IV only (D) I, II and III only
Q.19 Match the following:
(P) Lexical analysis (i) Leftmost derivation (Q) Top down parsing (ii) Type checking (R) Semantic analysis (iii) Regular expressions (S) Runtime environments (iv) Activation records
(A) P ↔ i, Q ↔ ii, R ↔ iv, S ↔ iii (B) P ↔ iii, Q ↔ i, R ↔ ii, S ↔ iv (C) P ↔ ii, Q ↔ iii, R ↔ i, S ↔ iv (D) P ↔ iv, Q ↔ i, R ↔ ii, S ↔ iii
Q.20 In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases? (A) LRU (Least Recently Used) (B) OPT (Optimal Page Replacement) (C) MRU (Most Recently Used) (D) FIFO (First In First Out)
Q.25 Identify the correct sequence in which the following packets are transmitted on the network by a host when a browser requests a webpage from a remote server, assuming that the host has just been restarted. (A) HTTP GET request, DNS query, TCP SYN (B) DNS query, HTTP GET request, TCP SYN (C) DNS query, TCP SYN, HTTP GET request (D) TCP SYN, DNS query, HTTP GET request
Q. 26 - Q. 55 carry two marks each.
Q.26 A binary relation R on N × N is defined as follows: (a, b)R(c, d) if a ≤ c or b ≤ d. Consider the following propositions: P: R is reflexive Q: R is transitive
Which one of the following statements is TRUE? (A) Both P and Q are true. (B) P is true and Q is false. (C) P is false and Q is true. (D) Both P and Q are false.
Q.27 Which one of the following well-formed formulae in predicate calculus is NOT valid?
(A) (∀x p(x) ⇒ ∀x q(x)) ⇒ (∃x ¬p(x) ∨ ∀x q(x)) (B) (∃x p(x) ∨ ∃x q(x)) ⇒ ∃x (p(x) ∨ q(x)) (C) ∃x (p(x) ∧ q(x)) ⇒ (∃x p(x) ∧ ∃x q(x)) (D) ∀x (p(x) ∨ q(x)) ⇒ (∀x p(x) ∨ ∀x q(x))
Q.28 Consider a set U of 23 different compounds in a Chemistry lab. There is a subset S of U of 9 compounds, each of which reacts with exactly 3 compounds of U. Consider the following statements:
I. Each compound in U \ S reacts with an odd number of compounds. II. At least one compound in U \ S reacts with an odd number of compounds. III. Each compound in U \ S reacts with an even number of compounds.
Which one of the above statements is ALWAYS TRUE? (A) Only I (B) Only II (C) Only III (D) None
Q.29 The value of the expression 13^99 (mod 17), in the range 0 to 16, is.
Q.30 Suppose the functions F and G can be computed in 5 and 3 nanoseconds by functional units UF and UG, respectively. Given two instances of UF and two instances of UG, it is required to implement the computation F(G(Xi)) for 1 ≤ i ≤ 10. Ignoring all other delays, the minimum time required to complete this computation is nanoseconds.
Q.31 Consider a processor with 64 registers and an instruction set of size twelve. Each instruction has five distinct fields, namely, opcode, two source register identifiers, one destination register identifier, and a twelve-bit immediate value. Each instruction must be stored in memory in a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes) consumed by the program text is.
Q.32 The width of the physical address on a machine is 40 bits. The width of the tag field in a 512 KB 8-way set associative cache is bits.
Q.36 Consider the following New-order strategy for traversing a binary tree:
- Visit the root;
- Visit the right subtree using New-order;
- Visit the left subtree using New-order;
The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 * 5 - 2 ˆ 6 7 * 1 + - is given by: (A) + - 1 6 7 * 2 ˆ 5 - 3 4 * (B) - + 1 * 6 7 ˆ 2 - 5 * 3 4 (C) - + 1 * 7 6 ˆ 2 - 5 * 4 3 (D) 1 7 6 * + 2 5 4 3 * - ˆ -
Q.37 Consider the following program:
int f(int *p, int n) { if (n <= 1) return 0; else return max(f(p+1,n-1),p[0]-p[1]); }
int main() { int a[] = {3,5,2,6,4}; printf("%d", f(a,5)); }
Note: max(x,y) returns the maximum of x and y.
The value printed by this program is.
Q.38 Let A 1 , A 2 , A 3 , and A 4 be four matrices of dimensions 10 × 5 , 5 × 20 , 20 × 10, and 10 × 5, respectively. The minimum number of scalar multiplications required to find the product A 1 A 2 A 3 A 4 using the basic matrix multiplication method is.
Q.39 The given diagram shows the flowchart for a recursive function A(n). Assume that all statements, except for the recursive calls, have O( 1 ) time complexity. If the worst case time complexity of this function is O(nα^ ), then the least possible value (accurate up to two decimal positions) of α is.
Start
A(n/ 2 )
Return A(n/^2 ) A(n/^2 )^ A(n/^2 )^ Return
A(n/ 2 )
Return A(n/^2 ) Return
Flowchart for Recursive Function A(n)
Q.40 The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary search tree, such that the resulting tree has height 6, is. Note: The height of a tree with a single node is 0.
Q.44 Consider the following languages.
L 1 = {〈M〉 | M takes at least 2016 steps on some input}, L 2 = {〈M〉 | M takes at least 2016 steps on all inputs} and L 3 = {〈M〉 | M accepts ε},
where for each Turing machine M, 〈M〉 denotes a specific encoding of M. Which one of the following is TRUE? (A) L 1 is recursive and L 2 , L 3 are not recursive (B) L 2 is recursive and L 1 , L 3 are not recursive (C) L 1 , L 2 are recursive and L 3 is not recursive (D) L 1 , L 2 , L 3 are recursive
Q.45 Which one of the following grammars is free from left recursion?
(A) S → AB A → Aa | b B → c
(B) S → Ab | Bb | c A → Bd | ε B → e
(C) S → Aa | B A → Bb | Sc | ε B → d
(D) S → Aa | Bb | c A → Bd | ε B → Ae | ε
Q.46 A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example, int a[10][3]; The grammars use D as the start symbol, and use six terminal symbols int ; id [ ] num. Grammar G1 Grammar G D → int L; D → int L; L → id [E L → id E E → num] E → E[num] E → num] [E E → [num]
Which of the grammars correctly generate the declaration mentioned above? (A) Both G1 and G (B) Only G (C) Only G (D) Neither G1 nor G
Q.47 Consider the following processes, with the arrival time and the length of the CPU burst given in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time first.
Process Arrival Time Burst Time P 1 0 10 P 2 3 6 P 3 7 1 P 4 8 3
The average turn around time of these processes is milliseconds.
Q.50 A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is 1 ms and to read a block from the disk is 10 ms. Assume that the cost of checking whether a block exists in the cache is negligible. Available cache sizes are in multiples of 10 MB.
Miss rate (%)
Cache size (MB)
The smallest cache size required to ensure an average read latency of less than 6 ms is MB.
Q.51 Consider the following database schedule with two transactions, T 1 and T 2.
S = r 2 (X); r 1 (X); r 2 (Y ); w 1 (X); r 1 (Y ); w 2 (X); a 1 ; a 2
where ri(Z) denotes a read operation by transaction Ti on a variable Z, wi(Z) denotes a write operation by Ti on a variable Z and ai denotes an abort by transaction Ti. Which one of the following statements about the above schedule is TRUE?
(A) S is non-recoverable (B) S is recoverable, but has a cascading abort (C) S does not have a cascading abort (D) S is strict
Q.52 Consider the following database table named water_schemes :
water_schemes scheme_no district_name capacity 1 Ajmer 20 1 Bikaner 10 2 Bikaner 10 3 Bikaner 20 1 Churu 10 2 Churu 20 1 Dungargarh 10
The number of tuples returned by the following SQL query is.
with total(name, capacity) as select district_name, sum(capacity) from water_schemes group by district_name with total_avg(capacity) as select avg(capacity) from total select name from total, total_avg where total.capacity ≥ total_avg.capacity
Q.53 A network has a data transmission bandwidth of 20 × 106 bits per second. It uses CSMA/CD in the MAC layer. The maximum signal propagation time from one node to another node is 40 microseconds. The minimum size of a frame in the network is bytes.
