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Recent questions tagged isi2016

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1 answer
2
ISI-2016-05
Let $f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0)\end{cases}$ Then $\displaystyle{\lim_{(x,y)\rightarrow(0,0)}}f (x,y)$ equals $0$ equals $1$ equals $2$ does not exist
Let $$f(x,y) = \begin{cases} \dfrac{x^2y}{x^4+y^2}, & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0)\end{cases}$$Then $\displaystyle{\lim_{(x,y)...
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3 votes
4 answers
3
ISI-2016-04
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 $-4$ $0$ $16$ $-16$
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$
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15 votes
3 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 $k$?
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 $k$?
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11 votes
3 answers
5
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
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^...
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6 votes
3 answers
6
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
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19 votes
4 answers
7
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?
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 ma...
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