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Recent questions tagged isi2016
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ISI 2016 MMA 24
let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one of the following is always true? A) The limits $\lim_{x\rightarrow a+} f(X)$ and $\lim_{x\rightarrow a} f(X)$ exist for all real number a B) if $f$ is differentiable at a ... that $f(x) < B$ for all real $x$ D) There cannot not be a real number $L$ such that $f(x) > L$ for all real $x$
asked
Apr 30
in
Calculus
by
Tesla!
Boss
(
16.1k
points)

42
views
isi2016
functions
0
votes
1
answer
2
ISI201605
Let $$f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if (x,y) }\neq\text{(0,0) }\\ 0 & \text{ if (x,y) = (0,0)}\end{cases}$$ Then $\displaystyle{\lim_{(x,y)\rightarrow(0,0)}}f (x,y)$ $\text{equals 0}$ $\text{equals 1}$ $\text{equals 2}$ $\text{does not exist}$
asked
Mar 31
in
Mathematical Logic
by
jjayantamahata
Active
(
1.5k
points)

47
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isi2016
engineeringmathematics
limits
+1
vote
3
answers
3
ISI201604
If $a,b,c$ and $d$ satisfy the equations $$a+7b+3c+5d =16\\8a+4b+6c+2d = 16\\ 2a+6b+4c+8d = 16 \\ 5a+3b+7c+d= 16$$ Then $(a+d)(b+c)$ equals $4$ $0$ $16$ $16$
asked
Mar 31
in
Linear Algebra
by
jjayantamahata
Active
(
1.5k
points)

106
views
isi2016
engineeringmathematics
systemofequations
+10
votes
2
answers
4
ISI Entrance Exam MTech (CS)
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than $1$ in a given tree. What is the maximum possible value of $k$?
asked
Apr 6, 2017
in
Graph Theory
by
Shreya Roy
Active
(
4.3k
points)

632
views
isi2016
graphtheory
trees
descriptive
+2
votes
1
answer
5
ISI 2016 PCB C8
Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.
asked
Mar 5, 2017
in
Others
by
Devasish Ghosh
Junior
(
667
points)

145
views
datastructure
engineeringmathematics
isi2016
descriptive
graphtheory
+7
votes
2
answers
6
ISI2016
Let $A$ be a matrix such that: $A=\begin{pmatrix} 1 & 2\\ 0 & 1 \end{pmatrix}$ and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true? $B^{2}=I$ $B^{2}=0$ $B^{2}=B$ None of the above
asked
May 9, 2016
in
Linear Algebra
by
abhi18459
(
251
points)

359
views
isi2016
matrices
+2
votes
2
answers
7
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
asked
May 9, 2016
in
Set Theory & Algebra
by
abhi18459
(
251
points)

266
views
isi2016
settheory&algebra
numbertheory
numericalanswers
+11
votes
4
answers
8
ISI2016
A palindrome is a sequence of digits which reads the same backward or forward. For example, $7447$, $1001$ are palindromes, but $7455$, $1201$ are not palindromes. How many $8$ digit prime palindromes are there?
asked
May 8, 2016
in
Combinatory
by
abhi18459
(
251
points)

432
views
isi2016
permutationsandcombinations
discretemathematics
normal
descriptive
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