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ISI-2017

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jjayantamahata asked Mar 28, 2018
985 views
ISI-2017-23
What is the smallest degree of a polynomial with real coefficients and having roots $2\omega, 2+3\omega, 2{\omega}^2, -1-3\omega \text{ and } 2-\omega-{\omega}^2$? [Here $\omega \neq 1$ is a cube root of unity.] $5$ $7$ $9$ $10$
What is the smallest degree of a polynomial with real coefficients and having roots $2\omega, 2+3\omega, 2{\omega}^2, -1-3\omega \text{ and } 2-\omega-{\omega}^2$?[Here $...
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jjayantamahata asked Mar 27, 2018
1,468 views
ISI-2017-16
Let $(x_n)$ be a sequence of real numbers such that the subsequences $(x_{2n})$ and $(x_{3n})$ converge to limits $K$ and $L$ respectively. Then $(x_n)$ always converges if $K=L$, then $(x_n)$ converges $(x_n)$ may not converge, but $K=L$ it is possible to have $K \neq L$
Let $(x_n)$ be a sequence of real numbers such that the subsequences $(x_{2n})$ and $(x_{3n})$ converge to limits $K$ and $L$ respectively. Then$(x_n)$ always convergesif...
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1 answer
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jjayantamahata asked Mar 26, 2018
310 views
ISI-2017-8
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jjayantamahata asked Mar 26, 2018
1,463 views
ISI-2017-6
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible number of boys without glasses is $\{0,.....,30\}$ $\{10,....,30\}$ $\{0,.....,40\}$ $\text{none of these}$
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible number of boys without glasses is$\{...
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