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41
TIFR CSE 2024 | Part A | Question: 10
Let $\text{M}$ be a $3 \times 3$ matrix over the real numbers such that $\text{M}^{\text{T}} \text{M}=\mathbf{I}$. Consider the following statements. There exists a non-zero vector $x \in \mathbb{R}^{3}$ such that $M x=\mathbf{0}$. There ... /are true? Only $\text{(i)}$ Only $\text{(ii)}$. Only $\text{(iii)}$. All three statements. None of the three statements.
Let $\text{M}$ be a $3 \times 3$ matrix over the real numbers such that $\text{M}^{\text{T}} \text{M}=\mathbf{I}$. Consider the following statements.There exists a non-ze...
admin
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admin
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Jan 12
Others
tifr2024
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42
TIFR CSE 2024 | Part A | Question: 11
Consider the following sequence of polynomials with real coefficients. \[ \begin{aligned} P_{0}(x) & =1 \\ P_{1}(x) & =2 x \\ P_{n+1}(x) & =2 x P_{n}(x)-P_{n-1}(x), \text { for all natural numbers } n \geq 1 . \end{aligned} \] ... }(x), P_{4}(x)\right\} \] in the vector space of polynomials in variable $x$ with real coefficients? $1$ $2$ $3$ $4$ $5$
Consider the following sequence of polynomials with real coefficients.\[\begin{aligned}P_{0}(x) & =1 \\P_{1}(x) & =2 x \\P_{n+1}(x) & =2 x P_{n}(x)-P_{n-1}(x), \text { fo...
admin
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admin
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Jan 12
Others
tifr2024
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43
TIFR CSE 2024 | Part A | Question: 12
A subset $\text{S}$ of the rational numbers is said to be "nice" if for every infinite sequence of $x_1, x_2, \ldots$ of elements from $\text{S}$, there is always two indices $i<j$ such that $x_i \leq x_j$. Consider the following ... $\text{(i)}$ and $\text{(iii)}$. All three statements are true. None of the three statements is true.
A subset $\text{S}$ of the rational numbers is said to be "nice" if for every infinite sequence of $x_1, x_2, \ldots$ of elements from $\text{S}$, there is always two ind...
admin
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admin
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Jan 12
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44
TIFR CSE 2024 | Part A | Question: 13
Let $n \geq 100$ be a positive integer. Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables, each taking values in the set $\{0,1\}$ such that $\operatorname{Pr}\left[X_{i}=1\right]=\frac{2}{3}$ for each $1 \leq i \leq n$ ... with respect to $x$. $0$ $n$ $\frac{2 n}{3}$ $\frac{4 n^{2}+2 n}{9}$ $\frac{4 n^{2}-4 n}{9}$
Let $n \geq 100$ be a positive integer. Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables, each taking values in the set $\{0,1\}$ such that $\operatornam...
admin
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admin
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Jan 12
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tifr2024
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45
TIFR CSE 2024 | Part A | Question: 14
Let $\text{A}$ and $\text{B}$ be two $n \times n$ invertible matrices with real entries such that every row in $\text{A}$ sums to $1$ and every row in $\text{B}$ sums to $2$ ... $\text{(iii)}$. Statements $\text{(i)}$ and $\text{(iii)}$ are true but not necessarily statement $\text{(ii)}$.
Let $\text{A}$ and $\text{B}$ be two $n \times n$ invertible matrices with real entries such that every row in $\text{A}$ sums to $1$ and every row in $\text{B}$ sums to ...
admin
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Jan 12
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tifr2024
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46
TIFR CSE 2024 | Part A | Question: 15
Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only their own number and that it is different from the other one. The following conversation ensues ... was given $3$, Badri was given $4$. Asna was given $4$, Badri was given $3$. None of the above.
Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only thei...
admin
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Jan 12
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47
Made Easy Mock Test
Rohit Chakraborty
220
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Rohit Chakraborty
asked
Jan 7
GATE
made-easy-test-series
programming-in-c
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48
Made Easy Test Series Mock Test
How to calculate the third option?
How to calculate the third option?
Rohit Chakraborty
228
views
Rohit Chakraborty
asked
Jan 7
GATE
made-easy-test-series
digital-logic
adder
multiple-selects
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49
made-easy
Rohit Chakraborty
155
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Rohit Chakraborty
asked
Jan 7
GATE
made-easy-test-series
time-complexity
functions
multiple-selects
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50
can we write the same exam more than one time
Lokesh Budela
87
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Lokesh Budela
asked
Jan 1
1
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51
From where to practice questions for Data Science and AI paper of GATE 2024?
Which resources to follow to practice questions for DS and AI paper of GATE 2024? Which resources to follow? where to find them Questions for Mathematics and questions for AI? A bit of help on that would be much appreciated
Which resources to follow to practice questions for DS and AI paper of GATE 2024?Which resources to follow?where to find themQuestions for Mathematics and questions for A...
rajveer43
202
views
rajveer43
asked
Dec 10, 2023
GATE
gate-preparation
virtual-gate-test-series
cmi2022-datascience
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52
How to prep for gate?
deeptigururajb
109
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deeptigururajb
asked
Dec 6, 2023
GATE
query
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53
NTA PhD Entrance Examination CS 2023| Part 2 Question: 1
Question No. 1 / Question ID 974051 Marks: 4.00 The number of divisors of 2100 is 1. 42 2. 36 3. 78 4. 72 1 (Chosen Option) 2 3 4
Question No. 1 / Question ID 974051Marks: 4.00The number of divisors of 2100 is1. 422. 363. 784. 721 (Chosen Option)234
admin
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admin
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Dec 2, 2023
Others
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 2
Suppose that a disk drive has 5000 cylinders, numbered from 0 to 4999 . The drive is assumed to be currently serving a request at cylinder 143 , provided that the previous request was at cylinder 125 . The queue of pending requests, in FIFO ... satisfy C-SCAN disk-scheduling algorithm? 1. 3363 2. 9813 3. 9769 4. 3319 1 2 (Chosen Option) 3 4
Suppose that a disk drive has 5000 cylinders, numbered from 0 to 4999 . The drive is assumed to be currently serving a request at cylinder 143 , provided that the previou...
admin
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admin
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Dec 2, 2023
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nta-phd-cs-2023
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 3
Question No. 3 / Question ID 974076 Marks: 4.00 void main() \{ int $\mathrm{i}$; for $(i=0 ; i
Question No. 3 / Question ID 974076Marks: 4.00void main()\{int $\mathrm{i}$;for $(i=0 ; i
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admin
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Dec 2, 2023
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nta-phd-cs-2023
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 4
Question No. 4 / Question ID 974060 Marks: 4.00 A group $\mathrm{G}$ has an order of 84 . The size of the largest possible proper subgroup of $\mathrm{G}$ is 1. 14 2. 12 3. 42 4. 84 1 2 3 (Chosen Option) 4
Question No. 4 / Question ID 974060Marks: 4.00A group $\mathrm{G}$ has an order of 84 . The size of the largest possible proper subgroup of $\mathrm{G}$ is1. 142. 123. 42...
admin
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admin
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Dec 2, 2023
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nta-phd-cs-2023
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 5
Question No. 5 / Question ID 974062 Marks: 4.00 Assume a page reference string for a process with $m$ frames (initially all empty). The page reference string has length $\mathrm{p}$ with $\mathrm{n}$ distinct page numbers occurring in it. Consider any page- ... $\mathrm{p}-1, \mathrm{n}$ 4. n, p 1 2 3 (Chosen Option) 4
Question No. 5 / Question ID 974062Marks: 4.00Assume a page reference string for a process with $m$ frames (initially all empty). The page reference string has length $\m...
admin
92
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admin
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Dec 2, 2023
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 6
Question No. 6 / Question ID 974081 Marks: 4.00 Some of the following statements are NOT correct about B+ tree that is used for creating an index of relational database table. $B+$ tree is also called as a height imbalanced tree. Non-leaf nodes have pointers ... given below: 1. A and B Only 2. C and E Only 3. A and D Only 4. C, D and E Only
Question No. 6 / Question ID 974081Marks: 4.00Some of the following statements are NOT correct about B+ tree that is used for creating an index of relational database tab...
admin
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admin
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Dec 2, 2023
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nta-phd-cs-2023
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 7
Question No. 7 / Question ID 974077 Marks: 4.00 Match List I with List II \begin{tabular}{|l|l|c|c|} \hline \multicolumn{2}{|c|}{ LIST I } & \multicolumn{2}{c|}{ LIST II } \\ \hline & File & & memory allocation \\ \hline & Detection ... D-IV 3. A-III, B-I, C-II, D-IV 4. A-IV, B-III, C-II, D-I 1 (Chosen Option) 2 3 4
Question No. 7 / Question ID 974077Marks: 4.00Match List I with List II\begin{tabular}{|l|l|c|c|}\hline \multicolumn{2}{|c|}{ LIST I } & \multicolumn{2}{c|}{ LIST II } \\...
admin
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admin
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Dec 2, 2023
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nta-phd-cs-2023
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NTA PhD Entrance Examination CS 2023| Part 2 Question: 8
Question No. 8 / Question ID 974068 Marks: 4.00 Match List I with List II \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{ LIST I } & \multicolumn{2}{|c|}{ LIST II } \\ \hline & RAID Level 0 & & \begin{tabular}{l} Refers a disk array ... 2. A-I, B-II, C-III, D-IV 3. A-III, B-I, C-II, D-IV 4. A-IV, B-III, C-II, D-I
Question No. 8 / Question ID 974068Marks: 4.00Match List I with List II\begin{tabular}{|l|l|l|l|}\hline \multicolumn{2}{|c|}{ LIST I } & \multicolumn{2}{|c|}{ LIST II } \...
admin
62
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admin
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Dec 2, 2023
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