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Questions by abhi18459

11 votes
3 answers
1
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^...
6 votes
3 answers
2
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.
0 votes
2 answers
3
ISI 2016
an is a n-digit number of 0's and 1's with no consecutive 0's i.e., without the occurrence of '00'. For example, a8 =10111011. Construct a recurrence relation for an(a0=1).
an is a n-digit number of 0's and 1's with no consecutive 0's i.e., without the occurrence of '00'. For example, a8 =10111011. Construct a recurrence relation for an(a0=1...
19 votes
4 answers
4
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...