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Recent questions tagged algebra

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1
GATE ECE 2024 | GA Question: 4
​​​​For a real number $x>1$, \[ \frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1 \] The value of $x$ is $4$ $12$ $24$ $36$
​​​​For a real number $x>1$,\[\frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1\]The value of $x$ is$4$$12$$24$$36$
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2 answers
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GATE ECE 2024 | GA Question: 5
The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is $13$ $17$ $3$ $11$
The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is$13$$17$$3$$11$
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GATE ECE 2024 | Question: 19
In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.
In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.
1 votes
2 answers
4
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$$3$$7$$9$$11$
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GATE ECE 2016 Set 1 | GA Question: 9
If $q^{-a} = \frac{1}{r}$ and $r^{-b}=\frac{1}{s}$ and $s^{-c} = \frac{1}{q}$ ,the value of $abc$ is______. $(rqs)^{-1}$ $0$ $1$ $r+q+s$
If $q^{-a} = \frac{1}{r}$ and $r^{-b}=\frac{1}{s}$ and $s^{-c} = \frac{1}{q}$ ,the value of $abc$ is______.$(rqs)^{-1}$$0$$1$$r+q+s$
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