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ISI2018PCBA4
Let $A$ and $B$ are two nonempty 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 $S$.
asked
May 12
in
Set Theory & Algebra
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akash.dinkar12
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isi2018pcba
settheory&algebra
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ISI2018PCBA3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r1$ divides $n^s1$ if and only if $r$ divides $s$.
asked
May 12
in
Numerical Ability
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akash.dinkar12
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isi2018pcba
generalaptitude
numericalability
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ISI2018PCBA2
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.
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May 12
in
Numerical Ability
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akash.dinkar12
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isi2018pcba
generalaptitude
numericalability
logicalreasoning
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ISI2018PCBA1
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 $A^2=A$.
asked
May 12
in
Linear Algebra
by
akash.dinkar12
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isi2018pcba
engineeringmathematics
linearalgebra
matrices
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Not really. It was excluding shipping I guess....
Ok sir. Actually pricing on Flipkart is 200 less...
NO.
Is this application open for 2020 graduates i.e....
@Ayush Upadhyaya sir any approximate idea...
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