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B. Math. 2005

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vijaycs asked Mar 23, 2016
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B.Math. 2005
Let $0 < \theta < \pi$. The area of the triangle in the plane formed by the vertices $(-1,0), (1,0), (\cos\theta, \sin\theta)$ is not more than $1$ can be more than $1$ but not more than $2$ can be more than $2$ but not more than $\pi$ can be more than $\pi$ but not more than $2\pi$
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vijaycs asked Mar 22, 2016
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If $\sqrt{3}$ + 1 is a root of equation 3 x$^{3}$ + ax$^{2}$ + bx + 12 = 0 where a and b are rational numbers, then b is equal to -6 2 6 10
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admin asked Mar 14, 2023
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TIFR CSE 2023 | Part B | Question: 9
Fix a positive integer $n$, and let $n=p_{1}^{e_{1}} p_{2}^{e_{2}} \cdots p_{k}^{e_{k}}$ be the prime factorization of $n$. Here, $p_{1}, \ldots, p_{k}$ are prime numbers and $e_{i} \geq 1$ for all $1 \leq i \leq k$ ... None of the above
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admin asked Mar 14, 2023
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TIFR CSE 2023 | Part B | Question: 11
Let $m=2877426671$. It is known that $p=5754853343=2 m+1$ is a $10$ -digit prime number. What is $16^{m}(\bmod p)$ ? $1$ $4$ $16$ $2877426671$ $5754853342 \;($ which is actually $-1(\bmod p))$
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