# Recent questions tagged gate2015-2

1
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
2
A computer system implements a $40-bit$ virtual address, page size of $8$ $\text{kilobytes}$, and a $128-entry$ translation look-aside buffer ($TLB$) organized into $32$ sets each having $4$ ways. Assume that the $TLB$ tag does not store any process id. The minimum length of the $TLB$ tag in bits is ____.
3
Assume that for a certain processor, a read request takes $50\:\text{nanoseconds}$ on a cache miss and $5\:\text{nanoseconds}$ on a cache hit. Suppose while running a program, it was observed that $80\%$ of the processor's read requests result in a cache hit. The average read access time in nanoseconds is ______.
4
A system has $6$ identical resources and $N$ processes competing for them. Each process can request at most $2$ requests. Which one of the following values of $N$ could lead to a deadlock? $1$ $2$ $3$ $4$
5
An unordered list contains $n$ distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is $\Theta(n \log n)$ $\Theta(n)$ $\Theta(\log n)$ $\Theta(1)$
6
Consider the following statements. The complement of every Turing decidable language is Turing decidable There exists some language which is in NP but is not Turing decidable If L is a language in NP, L is Turing decidable Which of the above statements is/are true? Only II Only III Only I and II Only I and III
7
Identify the correct order in which a server process must invoke the function calls accept, bind, listen, and recv according to UNIX socket API. listen, accept, bind, recv bind, listen, accept, recv bind, accept, listen, recv accept, listen, bind, recv
8
Match the following: ... $\text{P-2, Q-1, R-4, S-3}$ $\text{P-2, Q-4, R-1, S-3}$ $\text{P-2, Q-3, R-4, S-1}$
9
The cardinality of the power set of $\{0, 1, 2, \dots , 10\}$ is _______
10
Consider a complete binary tree where the left and right subtrees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is $\Omega(\log n)$ $\Omega(n)$ $\Omega(n \log n)$ $\Omega(n^2)$
11
Let $R$ be the relation on the set of positive integers such that $aRb$ and only if $a$ and $b$ are distinct and let have a common divisor other than 1. Which one of the following statements about $R$ is true? $R$ is symmetric and reflexive ... is reflexive but not symmetric not transitive $R$ is transitive but not reflexive and not symmetric $R$ is symmetric but not reflexive and not transitive
12
Consider the following function written in the C programming langauge : void foo(char *a) { if (*a && *a != ' ') { foo(a+1); putchar(*a); } } The output of the above function on input "$ABCD \ EFGH$" is $ABCD \ EFGH$ $ABCD$ $HGFE \ DCBA$ $DCBA$
13
In the context of abstract-syntax-tree (AST) and control-flow-graph (CFG), which one of the following is TRUE? In both AST and CFG, let node $N_2$ be the successor of node $N_1$. In the input program, the code corresponding to $N_2$ is present after the code ... node in an AST and a CFG depends on the input program Each node in AST and CFG corresponds to at most one statement in the input program
14
Which of the following statements is NOT correct about HTTP cookies? A cookie is a piece of code that has the potential to compromise the security of an Internet user A cookie gains entry to the user's work area through an HTTP header A cookie has an expiry date and time Cookies can be used to track the browsing pattern of a user at a particular site
15
Consider the basic COCOMO model where $E$ is the effort applied in person-months, $D$ is the development time in chronological months, $KLOC$ is the estimated number of delivered lines of code (in thousands) and $a_b, b_b, c_b, d_b$ have their useful meanings. The basic COCOMO equations are of the form ... $E=a_b exp(b_b), D=c_b (KLOC) exp(d_b)$ $E=a_b exp(d_b), D=c_b (KLOC) exp(b_b)$
16
Consider the following C function. int fun(int n) { int x=1, k; if (n==1) return x; for (k=1; k<n; ++k) x = x + fun(k) * fun (n-k); return x; } The return value of $fun(5)$ is ______.
17
A binary tree T has $20$ leaves. The number of nodes in T having two children is ______.
18
The number of divisors of $2100$ is ____.
19
A link has transmission speed of $10^6$ bits/sec. It uses data packets of size $1000$ $\text{bytes}$ each. Assume that the acknowledgment has negligible transmission delay and that its propagation delay is the same as the data propagation delay. Also, assume that the ... $\text{%}$. The value of the one way propagation delay (in milliseconds) is_____.
20
The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0, 0, 1, 1, 2, 2, 3, 3, 0, 0, ...) is _______.
21
With reference to the B+ tree index of order $1$ shown below, the minimum number of nodes (including the Root node) that must be fetched in order to satisfy the following query. "Get all records with a search key greater than or equal to $7$ and less than $15$ " is ______.
22
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
23
A software requirements specification (SRS) document should avoid discussing which one of the following? User interface issues Non-functional requirements Design specification Interfaces with third party software
24
Consider the following two statements. $S_1$: If a candidate is known to be corrupt, then he will not be elected $S_2$: If a candidate is kind, he will be elected Which one of the following statements follows from $S_1$ and $S_2$ as per sound inference rules of logic? If a ... is not kind If a person is kind, he is not known to be corrupt If a person is not kind, he is not known to be corrupt
25
Consider two decision problems $Q_1, Q_2$ such that $Q_1$ reduces in polynomial time to 3-SAT and 3-SAT reduces in polynomial time to $Q_2$. Then which one of the following is consistent with the above statement? $Q_1$ is in NP, $Q_2$ is NP hard. $Q_2$ is in NP, $Q_1$ is NP hard. Both $Q_1$ and $Q_2$ are in NP. Both $Q_1$ and $Q_2$ are in NP hard.
26
Consider the following transaction involving two bank accounts $x$ and $y$. read(x); x:=x-50; write (x); read(y); y:=y+50; write(y) The constraint that the sum of the accounts $x$ and $y$ should remain constant is that of Atomicity Consistency Isolation Durability
27
Out of the following 4 sentences, select the most suitable sentence with respect to grammar and usage: Since the report lacked needed information, it was of no use to them. The report was useless to them because there were no needed information in it. Since the ... needed information, it was not real useful to them. Since the report lacked needed information, it would not had been useful to them.
If p, q, r, s are distinct integers such that: $f (p, q, r, s) = \text{ max } (p, q, r, s)$ $g (p, q, r, s) = \text{ min } (p, q, r, s)$ ... Also the same operations are valid with two variable functions of the form $f(p, q)$ What is the value of $fg \left(h \left(2, 5, 7, 3\right), 4, 6, 8\right)$?
In a triangle $PQR, PS$ is the angle bisector of $\angle QPR \text{ and } \angle QPS =60^\circ$. What is the length of $PS$ ? $\left(\dfrac{(q+r)} {qr}\right)$ $\left(\dfrac {qr} {q+r}\right)$ $\large \sqrt {(q^2 + r^2)}$ $\left(\dfrac{(q+r)^2} {qr}\right)$
Four branches of a company are located at $M$, $N$, $O$ and $P$. $M$ is north of $N$ at a distance of $4 km$; $P$ is south of $O$ at a distance of $2$ $km$; $N$ is southeast of O by $1 km$. What is the distance between $M$ and $P$ in $km$? $5.34$ $6.74$ $28.5$ $45.49$