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1231

NIELIT 2021 Dec Scientist B - Section A: 40
“Going by the ____________ that many hands make light work, the school ____________ involved all the students in the task.” The words that best fill the blanks in the above sentence are $:$ principle, principal principal, principle principle, principle principal, principal

“Going by the ____________ that many hands make light work, the school ____________ involved all the students in the task.” The words that best fill the blanks in the...

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soujanyareddy13 asked Dec 7, 2021

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1232

NIELIT 2021 Dec Scientist B - Section A: 41
Which of the following options is the closest in meaning to the word below $?$ $\text{DELETERIOUS}$ delaying glorious harmful graduating

Which of the following options is the closest in meaning to the word below $?$ $\text{DELETERIOUS}$delayinggloriousharmfulgraduating

soujanyareddy13

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soujanyareddy13 asked Dec 7, 2021

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1233

NIELIT 2021 Dec Scientist B - Section A: 42
The fisherman, ___________ the flood victims owed their lives, were rewarded by the govt. whom to which to whom to that

The fisherman, ___________ the flood victims owed their lives, were rewarded by the govt.whomto whichto whomto that

soujanyareddy13

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soujanyareddy13 asked Dec 7, 2021

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1234

IITB Practice Set: 1
Given four distinct points $A, B, C,$ and $D$ on the directed ray denoting the positive $x$-axis, the cross ratio of $A,B$ with respect to $C,D$ denoted by $(A,B;C,D)$ is defined to be $\frac{AC}{BC}/\frac{AD}{BD}$. Here, $AC$, for example, ... A colleague pretends that this ray of slope $1$ is the $x$-axis and computes the cross-ratio as $p$. The value of of $r/p$ is ______.

Given four distinct points $A, B, C,$ and $D$ on the directed ray denoting the positive $x$-axis, the cross ratio of$A,B$ with respect to $C,D$ denoted by $(A,B;C,D)$ is ...

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1235

IITB Practice Set: 2
Consider the following in $2D:$ Two lines $AB$ and $CD$ intersect at a point $K$, such that the angle between them is $t$ degrees. A triangle $\Delta PQR$ is first reflected about line $AB$, then about line $CD$. After the reflections, the ... $2\times 2$ rotation transformation $T_R$. $T_R$ rotates the triangle by an angle _____ degrees, about the point _____.

Consider the following in $2D:$ Two lines $AB$ and $CD$ intersect at a point $K$, such that the angle between them is $t$ degrees. A triangle $\Delta PQR$ is first reflec...

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1236

IITB Practice Set: 3
Consider the real-valued function $f(x, y):= x + y$ defined on points $(x, y)$ in a $2-$dimensional Euclidean plane. Suppose you want to find all possible $(x^{\ast}, y^{\ast})$ that maximize the value of the function $f\left(\cdot,\cdot\right)$ ... $f(\cdot,\cdot)$ at all possible solutions $(x', y'):$______

Consider the real-valued function $f(x, y):= x + y$ defined on points $(x, y)$ in a $2-$dimensional Euclidean plane.Suppose you want to find all possible $(x^{\ast}, y^{\...

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1237

IITB Practice Set: 4
Kamala tosses $11$ fair coins and Rajani tosses $10$ fair coins. The probability that the number of heads obtained by Kamala is more than the number of tails obtained by Rajani is _____.

Kamala tosses $11$ fair coins and Rajani tosses $10$ fair coins. The probability that the number of heads obtained by Kamala is more than the number of tails obtained by ...

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1238

IITB Practice Set: 5
Let matrix $X = \begin{bmatrix}x_1 & x_2 \end{bmatrix}, \; \Sigma = \begin{bmatrix}a_{1,1} & a_{1,2} a_{2,1} & a_{2,2}\end{bmatrix}$. Assume none of the elements are zero in $X,\Sigma$. Let $X^T$ denote the transpose of vector $X.$ Select all ... $X^T \Sigma X$. It is non-singular. None of the above are true.

Let matrix $X = \begin{bmatrix}x_1 & x_2 \end{bmatrix}, \; \Sigma = \begin{bmatrix}a_{1,1} & a_{1,2}a_{2,1} & a_{2,2}\end{bmatrix}$. Assume none of the elements are zero ...

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1239

IITB Practice Set: 6
Consider a binary classification problem $(y \in \{0,1\})$ and two dimensional data where both dimensions $x_1$ and $x_2$ are binary. Let $n^y_{00},n^y_{10},n^y_{01},n^y_{11}$ denote the number of training instances in class $y$ where $[x_1 \; x_2]$ ... $\dfrac{n^1_{00}+n^1_{01}}{n^1_{00}+n^1_{10}+n^1_{01}+n^1_{11}}$

Consider a binary classification problem $(y \in \{0,1\})$ and two dimensional data where both dimensions $x_1$and $x_2$ are binary. Let $n^y_{00},n^y_{10},n^y_{01},n^y_{...

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1240

IITB Practice Set: 7
This question is about the behaviour of lexical analysers generated by Lex. Consider the following Lex-like specification of two tokens: %% abc printf("Token 1"); (abc)*d printf("Token 2"); %% The time taken for the complete tokenization (extraction of all tokens) of the input string ... alternatives: $(a) O(1), (b) O(m), (c) O(m^2) \text{ and } (d) O(m^3).$

This question is about the behaviour of lexical analysers generated by Lex. Consider the following Lex-likespecification of two tokens:%% abc printf("Token 1"); (abc)*d p...

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1241

IITB Practice Set: 8
Consider the grammar: $S \rightarrow aSB$ $S \rightarrow d$ $B \rightarrow b$ During a bottom-up parsing of the sentence $aaadbbb$, consider all the states of the parser in which the contents of the stack, read as a string from the bottom of the stack to the ... for $\textit{shift symbol x,} \text{ or } \textit{r n}$, standing for $\textit{reduce using production number n}$.

Consider the grammar:$S \rightarrow aSB$$S \rightarrow d$$B \rightarrow b$During a bottom-up parsing of the sentence $aaadbbb$, consider all the states of the parser in w...

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1242

IITB Practice Set: 9
Consider expression trees made up of variables and the operator $+$ ... $4$ registers to evaluate is _______.

Consider expression trees made up of variables and the operator $+$. Let the size of a tree be defined as the number of nodes in the tree, counting both internal and leaf...

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1243

IITB Practice Set: 10
Let $\Sigma = \{0,1\}$ and $L$ be the language given by the regular expression $(01)^\ast$. We define the following equivalence relation $\sim_L$ on $\Sigma ^{\ast}$: given two words $x, y,$ we say $x \sim_L$ y iff $\text{for all } z \in \Sigma^{\ast}: xz \in L \text{ iff } yz \in L.$ The number of equivalence classes for $\sim_L$ is ______.

Let $\Sigma = \{0,1\}$ and $L$ be the language given by the regular expression $(01)^\ast$. We define the following equivalence relation $\sim_L$ on $\Sigma ^{\ast}$: giv...

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1244

IITB Practice Set: 11
Let $F$ be a propositional formula. Let $G(x)$ be a propositional formula containing propositional variable $x.$ For some propositional formula $H,$ let $G(H)$ be the formula obtained by replacing all occurrences of $x$ by $H$ ... $F \Rightarrow G(F) \equiv F \Rightarrow G\text{(False)}$

Let $F$ be a propositional formula. Let $G(x)$ be a propositional formula containing propositional variable $x.$For some propositional formula $H,$ let $G(H)$ be the form...

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1245

IITB Practice Set: 12
Which of the following identities are true for arbitrary regular languages $R$ and $S$. Choose ALL correct answers. $(R^\ast S^\ast)^{\ast}= (R+S)^{\ast}$ $(RS)^{\ast}R = R(SR)^{\ast}$ $(R+RS)^{\ast} = \left(R^{\ast} +RS^{\ast}\right)^{\ast}$ $(R+S)^{\ast} S = (R^{\ast} S)^{\ast}$

Which of the following identities are true for arbitrary regular languages $R$ and $S$. Choose ALL correct answers.$(R^\ast S^\ast)^{\ast}= (R+S)^{\ast}$$(RS)^{\ast}R = R...

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1246

IITB Practice Set: 13
A $\textbf{CFG G}$ satisfies the following properties: The number of non-terminals (variables) in $G$ is $3$. The maximum number of symbols in the right hand side of any production rule is $2$. There is a word $w \in L(G)$ ... Turing machine. $L(G)$ can be accepted (by empty-stack acceptance condition) by a Nondeterministic pushdown automaton which has only one state.

A $\textbf{CFG G}$ satisfies the following properties:The number of non-terminals (variables) in $G$ is $3$.The maximum number of symbols in the right hand side of any pr...

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1247

IITB Practice Set: 14
Suppose the ground is the $(x, y)$ plane and the sun is located at infinity in the direction of the vector $(1,2,1)$. When a flying bird is at the point $(1,1,1)$, its shadow on the ground will fall on the coordinates $(x, y)=$ ______.

Suppose the ground is the $(x, y)$ plane and the sun is located at infinity in the direction of the vector $(1,2,1)$.When a flying bird is at the point $(1,1,1)$, its sha...

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1248

IITB Practice Set: 15
Suppose G is a $\textit{group}$ formed by all $2\times 2$ matrices with the group operation being matrix addition. Which all of the following are subgroups of $G$? The set of all $2\times 2$ invertible matrices. The set of all $2\times 2$ symmetric ... $0$. The set of all $2\times2$ matrices with the top right entry being $1$.

Suppose G is a $\textit{group}$ formed by all $2\times 2$ matrices with the group operation being matrix addition. Whichall of the following are subgroups of $G$?The set ...

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1249

IITB Practice Set: 16
A $\textit{proper edge coloring}$ of a graph is an assignment of colors to the edges so that any two edges sharing a common vertex should get different colors. Let $G$ be a graph with $20$ vertices that has a proper edge coloring with $6$ colors. The maximum number of edges in $G$ can be ______.

A $\textit{proper edge coloring}$ of a graph is an assignment of colors to the edges so that any two edges sharing a common vertex should get different colors. Let $G$ be...

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1250

IITB Practice Set: 17
Let $v$ be a column vector with $n > 1$ elements of which at least one is non-zero. Consider the matrix $B = vv^t$ where $v^t$ refers to the transpose of $v$. Which of the following is true about matrix $B$? $B$ has two ... one eigenvalue which is zero and another which is strictly negative. $B$ has one eigenvalue which is zero and another which may be positive or negative.

Let $v$ be a column vector with $n 1$ elements of which at least one is non-zero. Consider the matrix $B = vv^t$ where $v^t$ refers to the transpose of $v$. Which of the...

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admin asked Nov 30, 2021

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