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Recent questions tagged isi2018-pcb-a

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ISI2018-PCB-A4
Let $A$ and $B$ are two non-empty finite subsets of $\mathbb{Z}$, the set of all integers. Define $A+B=\{a+b:a\in A,b\in B\}$.Prove that $\mid A+B \mid \geq \mid A \mid + \mid B \mid -1 $, where $\mid S \mid$ denotes the cardinality of finite set $S$.

akash.dinkar12 asked in Set Theory & Algebra May 12, 2019

by akash.dinkar12

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ISI2018-PCB-A3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.

akash.dinkar12 asked in Quantitative Aptitude May 12, 2019

by akash.dinkar12

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ISI2018-PCB-A2
Let there be a pile of $2018$ chips in the center of a table. Suppose there are two players who could alternately remove one, two or three chips from the pile. At least one chip must be removed, but no more than three chips can be removed in a ... game, that is, whatever moves his opponent makes, he can always make his moves in a certain way ensuring his win? Justify your answer.

akash.dinkar12 asked in Analytical Aptitude May 12, 2019

by akash.dinkar12

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4

ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.

akash.dinkar12 asked in Linear Algebra May 12, 2019

by akash.dinkar12

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Recent questions tagged isi2018-pcb-a