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61
TIFR-2012-Maths-C: 21
True/False Question: Let $f : \mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous function. Then the derivative $\frac{\partial ^{2}f}{\partial x\partial y}$ can exist without $\frac{\partial f}{\partial x}$ existing.
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Aug 30, 2020
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199
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tifrmaths2012
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62
TIFR-2019-Maths-B: 13
True/False Question : Let $A$ be a commutative ring with $1$, and let $a,b,c\in A$. Suppose there exist $x,y,z\in A$ such that $ax+by+cz=1.$ Then there exist ${x}',{y}',{z}'\in A$ such that $a^{50}{x}'+b^{20}{y}'+c^{15}{z}'=1$.
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TIFR
Aug 29, 2020
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198
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tifrmaths2019
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63
TIFR-2020-Maths-A: 6
Let $C = \{ f:\mathbb{R}\rightarrow \mathbb{R}| f$ is differentiable, and $\lim_{x\rightarrow \infty }\left ( 2f\left ( x \right ) +f{}'\left ( x \right )\right )=0\left \} \right.$. Which of the following statements is correct? For each $L$ ... $f \in C$ such that $\lim_{x\rightarrow \infty }f\left ( x \right )\frac{1}{2}$
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TIFR
Aug 28, 2020
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198
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tifrmaths2020
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64
TIFR-2016-Maths-A: 7
Let $A=\left \{ \sum _{i=1}^{\infty } \frac{a_{i}}{5^{i}}:a_{i}=0,1,2,3\:or \:4\right \}\subset \mathbb{R}$. Then $A$ is a finite set $A$ is countably infinite $A$ is uncountable but does not contain an open interval $A$ contains an open interval
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TIFR
Aug 30, 2020
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soujanyareddy13
197
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tifrmaths2016
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65
TIFR-2012-Maths-C: 25
True/False Question: If $A\subset \mathbb{R}$ and open then the interior of the closure $\overset{-0}{A}$is $A$.
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TIFR
Aug 30, 2020
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soujanyareddy13
196
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tifrmaths2012
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66
TIFR-2018-Maths-A: 1
True/False Question : Let $A$ be a countable subset of $\mathbb{R}$ which is well-ordered with respect to the usual ordering on $\mathbb{R}$ (where ‘well-ordered’ means that every nonempty subset has a minimum element in it). Then $A$ an order perserving bijection with a subset of $\mathbb{N}$.
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Aug 29, 2020
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soujanyareddy13
194
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tifrmaths2018
true-false
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67
TIFR-2012-Maths-B: 18
True/False Question: Any $3\times3$ and $5\times5$ skew-symmetric matrices have always zero determinants.
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TIFR
Aug 30, 2020
by
soujanyareddy13
193
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tifrmaths2012
0
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68
TIFR-2016-Maths-B: 21
Let $A_{1}\supset A_{2}\supset \cdots \supset A_{n}\supset A_{n+1}\supset \cdots$ be an infinite sequence of non-empty subsets of $\mathbb{R}^{3}$. which of the following conditions ensures that their intersection is non-empty ? Each $A_{i}$ is uncountable Each $A_{i}$ is open Each $A_{i}$ is connected Each $A_{i}$ is compact.
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TIFR
Aug 30, 2020
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soujanyareddy13
191
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tifrmaths2016
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69
TIFR-2018-Maths-B: 1
The set of real numbers in the open interval $(0,1)$ which have more than one decimal expansion is empty non-empty but finite countably infinite uncountable
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Aug 30, 2020
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189
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tifrmaths2018
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70
TIFR-2016-Maths-A: 18
Let A be a $3\times3$ matrix with integer entries such that det $\left ( A \right )=1$. What is the maximum possible number of entries of $A$ that are even ? $2$ $3$ $6$ $8$
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TIFR
Aug 30, 2020
by
soujanyareddy13
187
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tifrmaths2016
0
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71
TIFR-2018-Maths-A: 13
True/False Question : Let $V$ be the vector space over $\mathbb{R}$ consisting of polynomials of degree less than or equal to $3$. Let $T:V \rightarrow V$ be the operator sending $f\left(t\right)$ to $f\left(t+1 \right)$, and $D:V \rightarrow V$ the operator sending $f\left(t \right)$ to $df\left(t \right)/dt$. Then $T$ is a polynomial in $D$.
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TIFR
Aug 29, 2020
by
soujanyareddy13
184
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tifrmaths2018
true-false
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72
TIFR-2012-Maths-C: 24
True/False Question: The Integral $\int_{-\infty }^{+\infty }\frac{e^{-x}}{1+x^{2}}\:dx$ is convergent.
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TIFR
Aug 30, 2020
by
soujanyareddy13
183
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tifrmaths2012
0
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73
TIFR-2013-Maths-D: 31
True/False Question : The inequality $\sqrt{n+1}-\sqrt{n}< \frac{1}{\sqrt{n}}$ is false for all $n$ such that $101\leq n\leq 2000.$
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TIFR
Aug 30, 2020
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soujanyareddy13
183
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tifrmaths2013
true-false
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74
TIFR-2016-Maths-A: 8
The number of group homomorphisms from $\mathbb{Z}/20\mathbb{Z}$ to $\mathbb{Z}/29\mathbb{Z}$ is $1$ $20$ $29$ $580$
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TIFR
Aug 30, 2020
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soujanyareddy13
183
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tifrmaths2016
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75
TIFR-2020-Maths-A: 10
Consider the following sentences: $\left ( I \right )$ For every connected subset $Y$ of a metric space $X$, its interior $Y^{\circ}$ is connected. $\left ( II \right )$ For every connected subset $Y$ of a metric space $X$, its boundary $\partial Y$ is connected. Which ... $\left ( II \right )$ are both true. $\left ( I \right )$and $\left ( II \right )$ are both true.
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TIFR
Aug 28, 2020
by
soujanyareddy13
182
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tifrmaths2020
0
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76
TIFR-2012-Maths-C: 30
True/False Question: The composition of two uniformly continuous functions need not always be uniformly continuous.
soujanyareddy13
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TIFR
Aug 30, 2020
by
soujanyareddy13
181
views
tifrmaths2012
0
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0
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77
TIFR-2012-Maths-B: 15
True/False Question: Let $P$ be an $n \times n $ matrix whose row sums equal $1$. Then for any positive integer $m$ the row sums of the matrix $p^{m}$ equal $1$.
soujanyareddy13
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TIFR
Aug 30, 2020
by
soujanyareddy13
181
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tifrmaths2012
0
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78
TIFR-2012-Maths-A: 6
True/False Question: Let $u_{1},u_{2},u_{3},u_{4}$ be vectors in $\mathbb{R}^{2}$ and $u=\sum_{j=1}^{4}t_{i}u_{j}\:\:\: ; \:\:\:t_{j}> 0 \:\: and \sum_{j=1}^{4}t_{j}=1.$ Then three vectors $v_{1},v_{2},v_{3}\in \mathbb{R}^{2}$may be chosen from $\left \{ u_{1},u_{2},u_{3},u_{4} \right \}$ such that $u=\sum_{j=1}^{3}s_{i}v_{j}, \:\:\:s_{j}\geq 0 ,\:\: \sum_{j=1}^{3}s_{j}=1.$
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TIFR
Aug 30, 2020
by
soujanyareddy13
180
views
tifrmaths2012
0
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0
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79
TIFR-2016-Maths-A: 17
Let $S$ be the set of all $3 \times3$ matrices $A$ with integer entries such that the product $AA^{t}$ is the identity matrix. Here $A^{t}$ denotes the transpose of $A$. Then $\left | S \right |$ = $12$ $24$ $48$ $60$
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TIFR
Aug 30, 2020
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soujanyareddy13
179
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tifrmaths2016
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80
TIFR-2017-Maths-B: 6
How many isomorphism classes of associative rings (with identity) are there with $35$ elements? Prove your answer.
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Aug 30, 2020
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179
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tifrmaths2017
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