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UGCNET-June-2019-I-5
Which among the following best describes the Emotional Intelligence of learners? Understand the emotion of other people and your own Express oneself very strongly Being rational in thinking Adjusting one's emotion as per situation Being creative and open to criticism Accepting other people as they are ... the options given below : a, d, and f d, e and f a, b, and c b, c and d

Vishal_kumar98 answered in Others Oct 6

by Vishal_kumar98

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2

TIFR2021-B: 11
Suppose we toss a fair coin (i.e., both beads and tails have equal probability of appearing) repeatedly until the first time by which at least $\textit{two}$ heads and at least $\textit{two}$ tails have appeared in the sequence of tosses made. What is the expected number of coin tosses that we would have to make? $8$ $4$ $5.5$ $7.5$ $4.5$

PandurangaVitthal answered in Others Oct 4

by PandurangaVitthal

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3

TIFR2021-Maths-A: 1
For each positive integer $n$, let $s_n=\frac{1}{\sqrt{4n^2-1^2}}+\frac{1}{\sqrt{4n^2-2^2}}+\dots+\frac{1}{\sqrt{4n^2-n^2}}$ Then the $\displaystyle \lim_{n\rightarrow \infty}s_n$ equals $\pi/2$ $\pi/6$ $1/2$ $\infty$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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4

TIFR2021-Maths-A: 2
The number of bijective maps $g:\mathbb{N}\rightarrow\mathbb{N}$ such that $\sum_{n=1}^\infty\frac{g(n)}{n^2}<\infty$ is $0$ $1$ $2$ $\infty$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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5

TIFR2021-Maths-A: 3
The value of $\displaystyle\lim_{n\rightarrow\infty}\prod_{k=2}^{n}\left(1-\frac{1}{k^2}\right)$ is $1/2$ $1$ $1/4$ $0$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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6

TIFR2021-Maths-A: 4
The set $S=\{x\in \mathbb{R}|x>0\text{ and } (1+x^2) \tan(2x)=x\}$ is empty nonempty but finite countably infinite uncountable

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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7

TIFR2021-Maths-A: 5
The dimension of the real vector space $V=\{f:(-1,1)\rightarrow\mathbb{R}|f$ is infinitely differentiable on $(-1,1)$ and $f^{(n)}(0)=0$ for all $n\geq 0\}$ is $0$ $1$ greater than one, but finite infinite

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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8

TIFR2021-Maths-A: 6
For a positive integer $n$, let $a_n$ denote the unique positive real root of $x^n+x^{n-1}+\dots+x-1=0.$ Then the sequence $\{a_n\}^{\infty}_{n=1}$ is unbounded $\displaystyle \lim_{n\rightarrow \infty} a_n=0$ $\displaystyle \lim_{n\rightarrow \infty} a_n=1/2$ $\displaystyle \lim_{n\rightarrow \infty} a_n$ does not exist

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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9

TIFR2021-Maths-A: 7
Let $A$ be the set of all real numbers $\lambda \in [0,1]$ such that $\displaystyle\lim_{p\rightarrow 0}\frac{\log(\lambda2^p+(1-\lambda)3^p)}{p}=\lambda \log2+(1-\lambda)\log3$ Then $A=\{0,1\}$ $A=\{0,\frac{1}{2},1\}$ $A=\{0,\frac{1}{3},\frac{1}{2},\frac{2}{3},1\}$ $A=[0,1]$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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10

TIFR2021-Maths-A: 8
Let $X\subseteq \mathbb{R}$ be a subset. Let $\{f_n\}^{\infty}_{n=1}$ be a sequence of functions $f_n:X\rightarrow \mathbb{R}$, that converges uniformly to a function $f:X\rightarrow\mathbb{R}$. For each positive integer $n$ ... then $D$ has at most $7$ elements If each $D_n$ is uncountable, then $D$ is uncountable None of the other three statements is correct

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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11

TIFR2021-Maths-A: 9
Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be an aritary function. Consider the following assertions: $f$ is continuous The set $ \text{Graph}(f)=\{(x,f(x))\in \mathbb{R}^2|x\in \mathbb{R}\}$ is a connected subset of $\mathbb{R}^2.$ Which one of the following statements is ... $(\text{I})$ $(\text{I})$ does not imply $(\text{II})$, and $(\text{II})$ does not imply $(\text{I})$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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12

TIFR2021-Maths-A: 10
Let $\mathcal{C}$ denote the set of colorings of an $8\times 8$ chessboard, where each square is colored either black or white. Let $\thicksim$ denote the equivalence relation on $\mathcal{C}$ defined as follows: two colorings are equivalent if and only if one of them can be obtained from the other by a ... $2^{62}+2^{30}+2^{15}$ $2^{64}-2^{32}+2^{16}$ $2^{63}-2^{31}+2^{15}$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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13

TIFR2021-Maths-A: 11
What is the number of surjective maps from the set $\{1,\dots,10\}$ to the set $\{1,2\}$? $90$ $1022$ $98$ $1024$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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14

TIFR2021-Maths-A: 12
Let $V$ be a vector space over a field $F$. Consider the following assertions: $V$ is finite dimensional For every linear transformation $T:V\rightarrow V$, there exists a nonzero polynomial $p(x)\in F[x]$ such that $p(T):V\rightarrow V$ is the zero map. Which one of the ... $(\text{I})$ does not imply $(\text{II})$, and $(\text{II})$ does not imply $(\text{I})$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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15

TIFR2021-Maths-A: 13
$T:\mathbb{C}[x]\rightarrow\mathbb{C}[x]$ be the $\mathbb{C}-$linear transformation defined on the complex vector space $\mathbb{C}[x]$ of one variable complex polynomials by $Tf(x)=f(x+1)$. How many eigenvalues does $T$ have? $1$ finite but more than $1$ countably infinite uncountable

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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16

TIFR2021-Maths-A: 14
Let $\mathbb{R}^{\mathbb{N}}$ denote the real vector space of sequences $(x_0,x_1,x_2,\dots)$ of real numbers. Define a linear transformation $T:\mathbb{R}^{\mathbb{N}}\rightarrow\mathbb{R}^{\mathbb{N}}$ ... space $\mathbb{R}^{\mathbb{N}}/T(\mathbb{R}^{\mathbb{N}})$ is infinite dimensional None of the other three statements is correct

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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17

TIFR2021-Maths-A: 15
Which one of the following statements is correct? There Exists a $\mathbb{C}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$ There exists no $\mathbb{C}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$ ... there exists a $\mathbb{Q}-$linear isomorphism $\mathbb{C}^2\rightarrow\mathbb{C}$ None of the other three statements is correct

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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18

TIFR2021-Maths-A: 16
The matrix $\begin{pmatrix} 4 & -3 & -3\\3 & -2 & -3\\ -1 & 1& 2 \end{pmatrix}$ is diagonalizable nilpotent idempotent none of the other three options

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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19

TIFR2021-Maths-A: 17
Which of the following is a necessary and sufficient condition for two real $3\times 3$ matrices $A$ and $B$ to be similar $($i.e., $PAP^{-1}=B$ for an invertible real $3\times 3$ matrix $P)$? They have the same characteristic polynomial They have the same minimal polynomial They have the same minimal and characteristic polynomials None of the other three conditions

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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20

TIFR2021-Maths-A: 18
Consider the following two subgroups $A,B$ of the group $\mathbb{Q}[x]$ of one variable rational polynomials under addition: $A=\{p(x)\in \mathbb{Z}[x]|p \text{ has degree at most } 2\}, \text{ and} $ ... $[B:A]$ of $A$ in $B$ equals $1$ $2$ $4$ none of the other three options

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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21

TIFR2021-Maths-A: 19
Let $G$ be any finite group of order $2021$. For which of the following positive integers $m$ is the map $G\rightarrow G$, given by $g\mapsto g^m$, a bijection? $43$ $45$ $47$ none of the other three options

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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22

TIFR2021-Maths-A: 20
How many subgroups does $(\mathbb{Z}/13\mathbb{Z})\times (\mathbb{Z}/13\mathbb{Z})$ have? $13$ $16$ $4$ $25$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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23

TIFR2021-Maths-B: 1
Let $f_n:[0,1]\rightarrow \mathbb{R}$ be a continuous function for each positive integer $n$. If $\displaystyle\lim_{n\rightarrow \infty} \displaystyle \int_0^1 f_n(x)^2 dx=0,$ then $\displaystyle\lim_{n\rightarrow \infty} f_n\left(\frac{1}{2}\right)=0.$

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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24

TIFR2021-Maths-B: 2
Let $(X,d)$ be an infinite compact metric space. Then there exists no function $f:X\rightarrow X$, continuous or otherwise, with the property that $d(f(x),f(y))>d(x,y)$ for all $x\neq y$.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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25

TIFR2021-Maths-B: 3
Every infinite closed subset of $\mathbb{R}^n$ is the closure of a countable set.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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26

TIFR2021-Maths-B: 4
If $X$ is a compact metric space, there exists a surjective (not necessarily continuos) function $\mathbb{R}\rightarrow X$.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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27

TIFR2021-Maths-B: 5
If $X$ is a compact metric space, then every isometry $f:X\rightarrow X$ is surjective.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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28

TIFR2021-Maths-B: 6
Define a metric on the set of finite subsets of $\mathbb{Z}$ as ollows: $d(A,B)=\text{the cardinality of } (A\cup B \backslash (A\cap B)).$ The resulting metric space admits an isometry into $\mathbb{R}^n,$ for some positive integer $n$.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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29

TIFR2021-Maths-B: 7
There exists a continuous function $f:[0,1]\rightarrow \{A\in M_2(\mathbb{R})|A^2=A\}$ such that $f(0)=0$ and $f(1)=\text{Id}$.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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30

TIFR2021-Maths-B: 8
Let $f:[0,1]\rightarrow{\mathbb{R}}$ be a monotone increasing (not necessarily continuous) function such that $f(0)>0$ and $f(1)<1$. Then there exists $x\in[0,1]$ such that $f(x)=x$.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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31

TIFR2021-Maths-B: 9
The set $\{(x,y)\in \mathbb{N}\times\mathbb{N}| x^y \text{ divides } y^x,\:x\neq y,\:xy\neq0,\:x\neq1\}$ is finite.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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32

TIFR2021-Maths-B: 10
Suppose a line segment of a fixed length $L$ is given. It is possible to construct a triangle of perimeter $L$, whose angles are $105^{\circ},\: 45^{\circ} \text{ and } 30^{\circ}$, using only a straight edge and a compass.

soujanyareddy13 asked in Others Sep 27

by soujanyareddy13

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33

UGCNET-Dec2019-II: 34
An _______ chart is a project schedule representation that presents project plan as a directed graph. The critical path is the __________ sequence of ________ tasks and it defines project ________. Activity, Shortest, Independent, Cost Activity, Longest, Dependent, Duration Activity, Longest, Independent, Duration Activity, Shortest, Dependent, Duration

air11 answered in Others Sep 24

by air11

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34

GATE 2022 PSUs
I am a 30 year old guy without any job and work experience. I was very casual and lazy. I am 2013 passout in Btech Electrical Engg. This year I have prepared really hard for GATE 2022. But only one thing I am getting worried is about the PSUs interview. Will the PSUs reject me straightforward ? I have no justification for my 9 year gap.

minalBallav answered in Others Sep 19

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35

UGCNET-Dec2019-II: 54
Consider a subnet with $720$ routers. If a three-level hierarchy is chosen, with eight clusters, each containing $9$ regions of $10$ routers, then total number of entries in hierarchical table of each router is $25$ $27$ $53$ $72$

prakash007 answered in Others Sep 19

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36

UGCNET-Dec2019-II: 56
A network with bandwidth of $10 \text{ Mbps}$ can pass only an average of $12, 000$ frames per minute with each frame carrying an average of $10,000$ bits. What is the throughput of this network? $1, 000, 000 \text{ bps}$ $2, 000, 000 \text{ bps}$ $12, 000, 000 \text{ bps}$ $1, 200, 00, 000 \text{ bps}$

prakash007 answered in Others Sep 19

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37

UGCNET-Dec2019-II: 74
Identify the circumstances under which pre-emptive $\text{CPU}$ scheduling is used: A process switches from Running state to Ready state A process switches from Waiting state to Ready state A process completes its execution A process switches from Ready to Waiting state Choose the correct option: (a) and (b) only (a) and (d) only (c) and (d) only (a), (b), (c) only

minalBallav answered in Others Sep 18

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38

UGCNET-June2005-II: 4
Consider the relation on the set of non-negative integers defined by $x \equiv y$ if and only if: $x$ $\text{mod}$ $3=3$ $\text{mod}$ $y$ $3$ $\text{mod}$ $x \equiv 3$ $\text{mod}$ $y$ $x$ $\text{mod}$ $3=y$ $\text{mod}$ $3$ None of the above

anis7860 answered in Others Sep 15

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39

UGCNET-Dec2019-II: 71
Which of the following statements are true regarding $\text{C++}$? Overloading gives the capability to an existing operator to operate on other data types Inheritance in object oriented programming provides support to reusability When object of a derived class is defined, first the constructor of derived ... (a), (b) and (c) only (a), (b) and (d) only (b), (c) and (d) only

Nibchee answered in Others Sep 15

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40

all tests and quiz are paid or not
all test is paid or not

Arjun answered in Others Sep 10

by Arjun

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