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61
ISI 2021 | PCB CS | Question: 3
Let $G$ be a simple undirected graph having $n$ vertices with the property that the average of the degrees of the vertices in $G$ is at least $4.$ ... $\textsf{deg(x)}$ denotes the degree of the vertex $\textsf{x}$.
Let $G$ be a simple undirected graph having $n$ vertices with the property that the average of the degrees of the vertices in $G$ is at least $4.$ Consider the following ...
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62
ISI 2021 | PCB CS | Question: 8
Consider the following language $L$ over the alphabet $\Sigma=\{a, b, c\}$. $ L=\left\{a^{i} b^{j} c^{k} \mid i, j, k \geq 0 \text {, and if } i=1 \text { then } j=k\right\} $ Show that $L$ is not regular. Show that $L$ is a context-free language.
Consider the following language $L$ over the alphabet $\Sigma=\{a, b, c\}$. $$ L=\left\{a^{i} b^{j} c^{k} \mid i, j, k \geq 0 \text {, and if } i=1 \text { then } j=k\rig...
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63
ISI2021-MMA: 1
Suppose $f : \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function such that $f(x) = \frac{2 – \sqrt{x+4}}{\sin 2x}$ for all $x \neq 0.$ Then the value of $f(0)$ is $ – \frac{1}{8}$ $\frac{1}{8}$ $0$ $ – \frac{1}{4}$
Suppose $f : \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function such that $f(x) = \frac{2 – \sqrt{x+4}}{\sin 2x}$ for all $x \neq 0.$ Then the value of $f(0)$ ...
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64
ISI2021-MMA: 2
A person throws a pair of fair dice. If the sum of the numbers on the dice is a perfect square, then the probability that the number $3$ appeared on at least one of the dice is $1 / 9$ $4 / 7$ $1 / 18$ $7 / 36$
A person throws a pair of fair dice. If the sum of the numbers on the dice is a perfect square, then the probability that the number $3$ appeared on at least one of the d...
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65
ISI2021-MMA: 3
Consider the system of linear equations: $x + y + z = 5, \quad 2x + 2y + 3z = 4$. Then the system is inconsistent the system has a unique solution the system has infinitely many solutions none of the above is true
Consider the system of linear equations: $x + y + z = 5, \quad 2x + 2y + 3z = 4$. Thenthe system is inconsistentthe system has a unique solutionthe system has infinitely ...
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68
CMI-2021-DataScience-A: 2
The roots of the polynomial $p(x)=x^{4}-2x^{3}-2x^{2}+8x-8$ are: $1, -1, 2, 2+3 i$ $1+i, 1-i, 2, -2$ $1, -1+i, 2, 2+3 i$ $1+i, -1+i, 2, -2$
The roots of the polynomial $p(x)=x^{4}-2x^{3}-2x^{2}+8x-8$ are:$1, -1, 2, 2+3 i$$1+i, 1-i, 2, -2$$1, -1+i, 2, 2+3 i$$1+i, -1+i, 2, -2$
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69
NIELIT 2021 Dec Scientist B - Section B: 28
Which $\text{TCP/IP}$ protocol is used for file transfer with minimal capability and minimal overhead? $\text{RARP}$ $\text{FTP}$ $\text{TFTP}$ $\text{TELNET}$
Which $\text{TCP/IP}$ protocol is used for file transfer with minimal capability and minimal overhead?$\text{RARP}$$\text{FTP}$$\text{TFTP}$$\text{TELNET}$
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2 answers
71
NIELIT 2022 April Scientist B | Section B | Question: 65
Let $\text{G}$ be a multiplicative group and $a \in \text{G.}$ If the order of $a$ is $6,$ then the order of $a^{5}$ is equal to : $1$ $5$ $6$ $30$
Let $\text{G}$ be a multiplicative group and $a \in \text{G.}$ If the order of $a$ is $6,$ then the order of $a^{5}$ is equal to :$1$$5$$6$$30$
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2 answers
72
NIELIT 2022 April Scientist B | Section B | Question: 67
The first order logic statement $((\text{R} \vee \text{Q}) \wedge (\text{P} \; \vee \sim \text{Q}))$ ...
The first order logic statement $((\text{R} \vee \text{Q}) \wedge (\text{P} \; \vee \sim \text{Q}))$ is equivalent to which of the following?$((\text{R} \vee \sim \text{Q...
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2 answers
73
NIELIT 2022 April Scientist B | Section B | Question: 72
The Eigen values of a matrix $\text{A} = \begin{bmatrix} -2 & 2 & -3 \\ 2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}$ are $-3, -3$ and $5,$ then the trace of the matrix $A^{3} – 3A^{2}$ is: $200$ $71$ $-58$ $-200$
The Eigen values of a matrix$\text{A} = \begin{bmatrix} -2 & 2 & -3 \\ 2 & 1 & -6 \\ -1 & -2 & 0 \end{bmatrix}$ are $-3, -3$ and $5,$ then the trace of the matrix $A^{3} ...
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75
NIELIT 2022 April Scientist B | Section A | Question: 3
In the following question, a statement is followed by two assumptions numbered $\text{I}$ and $\text{II}.$ ... If only assumption $\text{II}$ is implicit; If neither $\text{I}$ nor $\text{II}$ is implicit.
In the following question, a statement is followed by two assumptions numbered $\text{I}$ and $\text{II}.$ Consider the statement and the following assumptions to decide ...
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79
NIELIT 2021 Dec Scientist A - Section B: 48
The addressing mode/s, which uses the $\text{PC}$ instead of a general-purpose register is : Indexed with offset Relative Direct Both Indexed with offset and direct
The addressing mode/s, which uses the $\text{PC}$ instead of a general-purpose register is :Indexed with offsetRelativeDirectBoth Indexed with offset and direct
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80
NIELIT 2021 Dec Scientist A - Section B: 87
The postfix equivalent of the infix expression $(a+b)^{*}(c^{*}d-e)^{*}f/g$ is : $ab + cd^{*}e – fg^{*}/^{*}$ $ab + cd^{*}e - fg/^{**}$ $ab + cde^{*} – fg/^{**}$ $abcd + e^{*} fg – /^{**}$
The postfix equivalent of the infix expression $(a+b)^{*}(c^{*}d-e)^{*}f/g$ is :$ab + cd^{*}e – fg^{*}/^{*}$$ab + cd^{*}e - fg/^{ }$$ab + cde^{*} – fg/^{ }$$abcd + e^...
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