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Recent questions tagged algebra

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GATE Civil 2026 Set 1 | Question: 18
It is given that $x$ and $y$ are integers in the following equation:\[(x+y-7)^{2}+(y+3 x-13)^{2}=0\]The value of $\left(x^{3}+y^{3}\right)$ is $\_\_\_\_$ (in integer).
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1 1 answer
GATE Civil 2024 Set 1 | Question: 1
​​​​​The smallest positive root of the equation\[x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0\]lies in the range$0 < x \leq 2$$2 < x \leq 4$$6 \leq x \leq 8$$10 \leq x \leq 1...
9 9 votes
2 answers 2 answers
GATE Civil 2021 Set 2 | GA | Question: 4
$\oplus$ and $\odot$ are two operators on numbers $p$ and $q$ such that $p \odot q = p-q,$ and $p \oplus q = p\times q$Then, $\left ( 9\odot \left ( 6\oplus 7 \right ) \r...
10 10 votes
2 answers 2 answers
GATE Civil 2021 Set 1 | GA | Question: 4
​​​​​​$\bigoplus$ and $\bigodot$ are two operators on numbers $\text{p}$ and $\text{q}$ such that $p \bigoplus q=\dfrac{p^{2}+q^{2}}{pq}$ and $p \bigodot q=\dfrac{p^{2}}{...
21 21 votes
1 answers 1 answer
GATE Civil 2018 Set 2 | GA | Question: 3
$\underbrace{a+a+a+ \dots +a}_{\text{n times}}=a^2b$ and $\underbrace{b+b+b+ \dots +b}_{\text{m times}} = ab^2$, where $a, b, n, m$ are natural numbers. What is the value...
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