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Questions with numerical answers and no options. No negative marks for these questions.

Recent questions tagged numerical-answers

1 vote
1 answer
1
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
asked Apr 25 in Calculus Lakshman Patel RJIT 220 views
3 votes
2 answers
2
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid $ is _____________
asked Feb 18 in DS Arjun 1.5k views
4 votes
3 answers
3
5 votes
2 answers
4
4 votes
3 answers
5
Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $32$ -bit address is used for accessing the cache. If the width of the tag field is $22$ bits, the associativity of the cache is _________
asked Feb 18 in CO and Architecture Arjun 1.2k views
3 votes
1 answer
6
Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory through cycle stealing at regular intervals. Consider a $\text{2 MHz}$ processor. If $0.5 \%$ processor cycles are used for $\text{DMA}$, the data transfer rate of the device is __________ bits per second.
asked Feb 18 in CO and Architecture Arjun 1.3k views
2 votes
1 answer
7
A data file consisting of $1,50,000$ student-records is stored on a hard disk with block size of $4096$ bytes. The data file is sorted on the primary key $\textrm{RollNo}$. The size of a record pointer for this disk is $7$ bytes. Each student-record has ... disk. Assume that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ________
asked Feb 18 in Databases Arjun 1.1k views
4 votes
1 answer
8
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
asked Feb 18 in Probability Arjun 836 views
3 votes
2 answers
9
Consider the following $\text{ANSI C}$ function: int SomeFunction (int x, int y) { if ((x==1) || (y==1)) return 1; if (x==y) return x; if (x > y) return SomeFunction(x-y, y); if (y > x) return SomeFunction (x, y-x); } The value returned by $\textrm{SomeFunction(15, 255)}$ is __________
asked Feb 18 in Algorithms Arjun 849 views
7 votes
4 answers
10
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
asked Feb 18 in Linear Algebra Arjun 1.6k views
2 votes
2 answers
11
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
asked Feb 18 in Calculus Arjun 711 views
8 votes
3 answers
12
Consider a three-level page table to translate a $39-$bit virtual address to a physical address as shown below: The page size is $\text{4 KB} \;(1\text{KB}=2^{10}$ bytes$)$ and page table entry size at every level is $8$ bytes. A process $P$ is currently ... $2\text{GB}$ of physical memory. The minimum amount of memory required for the page table of $P$ across all levels is _________ $\text{KB}$.
asked Feb 18 in Operating System Arjun 2.6k views
4 votes
2 answers
13
Consider the following $\text{ANSI C}$ program #include <stdio.h> int foo(int x, int y, int q) { if ((x<=0) && (y<=0)) return q; if (x<=0) return foo(x, y-q, q); if (y<=0) return foo(x-q, y, q); return foo(x, y-q, q) + foo(x-q, y, q); } int main( ) { int r = foo(15, 15, 10); printf(“%d”, r); return 0; } The output of the program upon execution is _________
asked Feb 18 in Algorithms Arjun 964 views
5 votes
5 answers
14
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
asked Feb 18 in Combinatory Arjun 1.7k views
0 votes
1 answer
15
Consider the following augmented grammar with $\{ \#, @, <, >, a, b, c \}$ ... $I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\})$. The number of items in the set $\text{GOTO(GOTO}(I_0<), <)$ is ___________
asked Feb 18 in Compiler Design Arjun 715 views
4 votes
2 answers
16
Consider a Boolean function $f(w,x,y,z)$ such that $\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$The number of literals in the minimal sum-of-products expression of $f$ is _________
asked Feb 18 in Digital Logic Arjun 1.6k views
5 votes
2 answers
17
Consider a pipelined processor with $5$ stages, $\text{Instruction Fetch} (\textsf{IF})$, $\text{Instruction Decode} \textsf{(ID)}$, $\text{Execute } \textsf{(EX)}$, $\text{Memory Access } \textsf{(MEM)}$ ... $\textit{Speedup} $ achieved in executing the given instruction sequence on the pipelined processor (rounded to $2$ decimal places) is _____________
asked Feb 18 in CO and Architecture Arjun 1.9k views
3 votes
2 answers
18
Consider a network using the pure $\text{ALOHA}$ medium access control protocol, where each frame is of length $1,000$ bits. The channel transmission rate is $1$ Mbps ($=10^6$ bits per second). The aggregate number of transmissions across all ... as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ______________
asked Feb 18 in Computer Networks Arjun 1.9k views
4 votes
2 answers
19
In a directed acyclic graph with a source vertex $\textsf{s}$, the $\textit{quality-score}$ of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex $v$ other than $\textsf{s}$, the quality-score of $v$ is ... quality-score of $\textsf{s}$ is assumed to be $1$. The sum of the quality-scores of all vertices on the graph shown above is _______
asked Feb 18 in Algorithms Arjun 1.1k views
2 votes
3 answers
20
In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.
asked Feb 18 in Graph Theory Arjun 1.2k views
1 vote
3 answers
21
2 votes
2 answers
22
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
asked Feb 18 in Probability Arjun 1.1k views
6 votes
2 answers
23
There are $6$ jobs with distinct difficulty levels, and $3$ computers with distinct processing speeds. Each job is assigned to a computer such that: The fastest computer gets the toughest job and the slowest computer gets the easiest job. Every computer gets at least one job. The number of ways in which this can be done is ___________.
asked Feb 18 in Combinatory Arjun 1.5k views
0 votes
2 answers
24
Consider the following expression.$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$The value of the above expression (rounded to 2 decimal places) is ___________.
asked Feb 18 in Calculus Arjun 709 views
2 votes
2 answers
25
Consider the following sequence of operations on an empty stack.$\textsf{push}(54);\textsf{push}(52);\textsf{pop}();\textsf{push}(55);\textsf{push}(62);\textsf{s}=\textsf{pop}();$ ... $\textsf{s+q}$ is ___________.
asked Feb 18 in DS Arjun 1k views
0 votes
3 answers
26
Consider a computer system with a byte-addressable primary memory of size $2^{32}$ bytes. Assume the computer system has a direct-mapped cache of size $\text{32 KB}$ ($\text{1 KB}$ = $2^{10}$ bytes), and each cache block is of size $64$ bytes. The size of the tag field is __________ bits.
asked Feb 18 in CO and Architecture Arjun 641 views
5 votes
2 answers
27
A relation $r(A, B)$ in a relational database has $1200$ tuples. The attribute $A$ has integer values ranging from $6$ to $20$, and the attribute $B$ has integer values ranging from $1$ to $20$. Assume that the attributes $A$ and $B$ are independently distributed. The estimated number of tuples in the output of $\sigma _{(A>10)\vee(B=18)}(r)$ is ____________.
asked Feb 18 in Databases Arjun 2.1k views
2 votes
4 answers
28
Consider the following representation of a number in $\text{IEEE 754}$ single-precision floating point format with a bias of $127$.$S: 1\quad\quad E:\; 10000001\quad\quad F:\;11110000000000000000000$ Here $S, \;E$ and $F$ denote the ... components of the floating point representation. The decimal value corresponding to the above representation (rounded to $2$ decimal places) is ____________.
asked Feb 18 in Digital Logic Arjun 1.2k views
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