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2 votes
1 answer
1
OS NPTEL ASSIGNMENT QUESTION
Degree of concurrency in threads can be arranged in the manner One-to-one > many-to-one > many-to-many One-to-one > many-to-many > many-to-one Many-to-many > many-to-one > one-to-one None of the above answer given is A but according to me answer is B. Someone please confirm
Degree of concurrency in threads can be arranged in the manner One-to-one > many-to-one > many-to-many One-to-one > many-to-many > many-to-one Many-to-many > many-to-one > one-to-one None of the above answer given is A but according to me answer is B. Someone please confirm
asked Sep 7 Akanksha Agrawal 87 views
0 votes
2 answers
2
nptel assignment
is given ans correct ?
is given ans correct ?
asked Aug 31 in Digital Logic Sanjay Sharma 117 views
1 vote
1 answer
3
TIFR-2012-Maths-D: 31
$f : \left [ 0,\infty \right ]\rightarrow \left [ 0,\infty \right ]$ is continuous and bounded then $f$ has a fixed point.
$f : \left [ 0,\infty \right ]\rightarrow \left [ 0,\infty \right ]$ is continuous and bounded then $f$ has a fixed point.
asked Aug 30 in TIFR soujanyareddy13 82 views
0 votes
1 answer
4
TIFR-2012-Maths-D: 32
The polynomial $X^{8}+1$ is irreducible in $\mathbb{R}\left [ X \right ]$.
The polynomial $X^{8}+1$ is irreducible in $\mathbb{R}\left [ X \right ]$.
asked Aug 30 in TIFR soujanyareddy13 35 views
0 votes
1 answer
5
TIFR-2012-Maths-D: 33
The matrix $\begin{pmatrix} 1 & \pi &3 \\ 0& 2&4 \\ 0&0 &3 \end{pmatrix}$ is diagonalisable
The matrix $\begin{pmatrix} 1 & \pi &3 \\ 0& 2&4 \\ 0&0 &3 \end{pmatrix}$ is diagonalisable
asked Aug 30 in TIFR soujanyareddy13 32 views
0 votes
0 answers
6
TIFR-2012-Maths-D: 34
If a rectangle $R:=\left \{ \left ( x,y \right ) \in \mathbb{R}^{2}\mid A\leq x\leq B,C\leq y\leq D\right \}$ can be covered (allowing overlaps ) by $25$ discs of radius $1$ then it can also be covered by $101$ dics of radius $\frac{1}{2}.$
If a rectangle $R:=\left \{ \left ( x,y \right ) \in \mathbb{R}^{2}\mid A\leq x\leq B,C\leq y\leq D\right \}$ can be covered (allowing overlaps ) by $25$ discs of radius $1$ then it can also be covered by $101$ dics of radius $\frac{1}{2}.$
asked Aug 30 in TIFR soujanyareddy13 17 views
0 votes
0 answers
7
TIFR-2012-Maths-D: 35
Given any integer $n\geq 2$, we can always finds an integer $m$ such that each of the $n-1$ consecutive integers $m+2,m+3,\dots,m+n$are composite.
Given any integer $n\geq 2$, we can always finds an integer $m$ such that each of the $n-1$ consecutive integers $m+2,m+3,\dots,m+n$are composite.
asked Aug 30 in TIFR soujanyareddy13 16 views
0 votes
0 answers
8
TIFR-2012-Maths-D: 36
The $10 \times 10 $ matrix $\begin{pmatrix} v_{1}w_{1} & \cdots&v_{1}w_{10} \\ v_{2}w_{2}& \cdots & v_{2}w_{10}\\ v_{10}w_{1}&\cdots & v_{10}w_{10} \end{pmatrix}$has rank $2$, where $v_{i},w_{i}\in \mathbb{C}.$
The $10 \times 10 $ matrix $\begin{pmatrix} v_{1}w_{1} & \cdots&v_{1}w_{10} \\ v_{2}w_{2}& \cdots & v_{2}w_{10}\\ v_{10}w_{1}&\cdots & v_{10}w_{10} \end{pmatrix}$has rank $2$, where $v_{i},w_{i}\in \mathbb{C}.$
asked Aug 30 in TIFR soujanyareddy13 13 views
0 votes
0 answers
9
TIFR-2012-Maths-D: 37
If every continuous function on $X\subset \mathbb{R}^{2}$ is bounded, then $X$ is compact.
If every continuous function on $X\subset \mathbb{R}^{2}$ is bounded, then $X$ is compact.
asked Aug 30 in TIFR soujanyareddy13 11 views
0 votes
0 answers
10
TIFR-2012-Maths-D: 38
The graph of $xy=1$ is $\mathbb{C}^{2}$ is connected.
The graph of $xy=1$ is $\mathbb{C}^{2}$ is connected.
asked Aug 30 in TIFR soujanyareddy13 13 views
0 votes
1 answer
11
TIFR-2012-Maths-D: 39
If $z_{1},z_{2},z_{3},z_{4}\in \mathbb{C}$ satisfy $z_{1}+z_{2}+z_{3}+z_{4}=0$ and $\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+\left | z_{3} \right |^{2}+\left | z_{4} \right |^{2}=1$, then the least value of $\left | z_{1} -z_{2}\right |^{2}+\left | z_{1} -z_{4}\right |^{2}+\left | z_{2}-z_{3} \right |^{2}+\left | z_{3} -z_{4}\right |^{2}$ is $2$.
If $z_{1},z_{2},z_{3},z_{4}\in \mathbb{C}$ satisfy $z_{1}+z_{2}+z_{3}+z_{4}=0$ and $\left | z_{1} \right |^{2}+\left | z_{2} \right |^{2}+\left | z_{3} \right |^{2}+\left | z_{4} \right |^{2}=1$, then the least value of $\left | z_{1} -z_{2}\right |^{2}+\left | z_{1} -z_{4}\right |^{2}+\left | z_{2}-z_{3} \right |^{2}+\left | z_{3} -z_{4}\right |^{2}$ is $2$.
asked Aug 30 in TIFR soujanyareddy13 19 views
0 votes
0 answers
12
TIFR-2012-Maths-D: 40
Consider the differential equations (with $y$ is a function of $x$) $\begin{matrix} \frac{dy}{dx} & = & y\\ y\left ( 0 \right ) & = & 0 \end{matrix}$ $\begin{matrix} \frac{dy}{dx} & = & \left | y \right |^{\frac{1}{3}}\\ y\left ( 0 \right ) & = & 0. \end{matrix}$ Then $(1)$ has infinitely many solutions but $(2)$ has finite number of solutions.
Consider the differential equations (with $y$ is a function of $x$) $\begin{matrix} \frac{dy}{dx} & = & y\\ y\left ( 0 \right ) & = & 0 \end{matrix}$ $\begin{matrix} \frac{dy}{dx} & = & \left | y \right |^{\frac{1}{3}}\\ y\left ( 0 \right ) & = & 0. \end{matrix}$ Then $(1)$ has infinitely many solutions but $(2)$ has finite number of solutions.
asked Aug 30 in TIFR soujanyareddy13 13 views
0 votes
0 answers
13
TIFR-2012-Maths-C: 21
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.
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.
asked Aug 30 in TIFR soujanyareddy13 13 views
0 votes
0 answers
14
TIFR-2012-Maths-C: 22
If $f$ is continuous on $\left [ 0,1 \right ]$ and if $\int_{0}^{1}f\left ( x \right )x^{n}dx=0$ for $n=1,2,3,\cdots .$ .Then $\int_{0}^{1}f^{2}\left ( x \right )dx=0.$
If $f$ is continuous on $\left [ 0,1 \right ]$ and if $\int_{0}^{1}f\left ( x \right )x^{n}dx=0$ for $n=1,2,3,\cdots .$ .Then $\int_{0}^{1}f^{2}\left ( x \right )dx=0.$
asked Aug 30 in TIFR soujanyareddy13 15 views
0 votes
0 answers
15
TIFR-2012-Maths-C: 23
Suppose that $f \in \mathfrak{L}^{2} \left ( \mathbb{R} \right )$. Then $f \in \mathfrak{L}^{1} \left ( \mathbb{R} \right )$.
Suppose that $f \in \mathfrak{L}^{2} \left ( \mathbb{R} \right )$. Then $f \in \mathfrak{L}^{1} \left ( \mathbb{R} \right )$.
asked Aug 30 in TIFR soujanyareddy13 14 views
0 votes
0 answers
16
TIFR-2012-Maths-C: 24
The Integral $\int_{-\infty }^{+\infty }\frac{e^{-x}}{1+x^{2}}\:dx$ is convergent.
The Integral $\int_{-\infty }^{+\infty }\frac{e^{-x}}{1+x^{2}}\:dx$ is convergent.
asked Aug 30 in TIFR soujanyareddy13 19 views
0 votes
0 answers
17
TIFR-2012-Maths-C: 25
If $A\subset \mathbb{R}$ and open then the interior of the closure $\overset{-0}{A}$is $A$.
If $A\subset \mathbb{R}$ and open then the interior of the closure $\overset{-0}{A}$is $A$.
asked Aug 30 in TIFR soujanyareddy13 11 views
0 votes
0 answers
18
TIFR-2012-Maths-C: 26
If $f \in C^{\infty }$ and $f^{\left ( k \right )}\left ( 0 \right )=0$ for all integer $k\geq 0$, then $f\equiv 0$.
If $f \in C^{\infty }$ and $f^{\left ( k \right )}\left ( 0 \right )=0$ for all integer $k\geq 0$, then $f\equiv 0$.
asked Aug 30 in TIFR soujanyareddy13 11 views
0 votes
0 answers
19
TIFR-2012-Maths-C: 27
Let $f:\left [ 0,1 \right ]\rightarrow \left [ 0,1 \right ]$be continuous then $f$ assumes the value $\int_{0}^{1}f^{2}\left ( t \right )dt$ somewhere in $\left [ 0,1 \right ]$.
Let $f:\left [ 0,1 \right ]\rightarrow \left [ 0,1 \right ]$be continuous then $f$ assumes the value $\int_{0}^{1}f^{2}\left ( t \right )dt$ somewhere in $\left [ 0,1 \right ]$.
asked Aug 30 in TIFR soujanyareddy13 10 views
0 votes
0 answers
20
TIFR-2012-Maths-C: 28
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function such that $\underset{h\rightarrow 0}{lim }\:\frac{f\left ( x+h \right )-f\left ( x-h \right )}{h}$ exists for all $x \in \mathbb{R}$. Then $f$ is differentiable in $\mathbb{R}.$
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function such that $\underset{h\rightarrow 0}{lim }\:\frac{f\left ( x+h \right )-f\left ( x-h \right )}{h}$ exists for all $x \in \mathbb{R}$. Then $f$ is differentiable in $\mathbb{R}.$
asked Aug 30 in TIFR soujanyareddy13 12 views
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