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ISI2018PCBA3
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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 $s$.
isi2018pcba
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numericalability
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May 12
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Numerical Ability
by
akash.dinkar12
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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
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Numerical Ability
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isi2018pcba
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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 $A+B\geq A +B 1 $, where $S$ denotes the cardinality of finite set $S$.
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May 12
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Set Theory & Algebra
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akash.dinkar12
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isi2018pcba
engineeringmathematics
discretemathematics
settheory&algebra
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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 $A^2=A$.
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May 12
in
Linear Algebra
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akash.dinkar12
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59
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isi2018pcba
engineeringmathematics
linearalgebra
matrices
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ISI2018MMA27
Number of real solutions of the equation $x^7 + 2x^5 + 3x^3 + 4x = 2018$ is $1$ $3$ $5$ $7$
asked
May 11
in
Numerical Ability
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akash.dinkar12
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41.3k
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32
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isi2018
generalaptitude
numericalability
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1
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5
ISI2018MMA24
The sum of the infinite series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+….$ is $2$ $3$ $4$ $6$
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May 11
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Numerical Ability
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akash.dinkar12
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generalaptitude
numericalability
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ISI2018MMA23
For $n\geq 1$,let $a_n=\frac{1}{2^2} + \frac{2}{3^2}+ +\frac{n}{(n+1)^2}$ and $b_n=c_0 + c_1r + c_2r^2 + · · · + c_nr^n$,where $c_k \leq M$ for all integer $k$ and $r<1$.Then both $\{a_n\}$ and $\{b_n\}$ are Cauchy ... $\{a_n\}$ is not a Cauchy sequence,and $\{b_n\}$ is Cauchy sequence neither $\{a_n\}$ nor $\{b_n\}$ is a Cauchy sequence.
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Numerical Ability
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0
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ISI2018MMA22
The xaxis divides the circle $x^2 + y^2 − 6x − 4y + 5 = 0$ into two parts. The area of the smaller part is $2\pi1$ $2(\pi1)$ $2\pi3$ $2(\pi2)$
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May 11
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Numerical Ability
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13
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isi2018
generalaptitude
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