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Syllabus: Sets, Relations, Functions, Partial orders, Lattices, Monoids, Groups.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&0& 1&0&1&0&0.83&1
\\\hline\textbf{2 Marks Count} &1&1&2& 0 &2&1&0&1.16&2
\\\hline\textbf{Total Marks} & 3&3&4&1&4&3&\bf{1}&\bf{3}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Set Theory & Algebra

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Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality?$n$ $2^n$2^{n/2}$2^{n-1}$Can not be determined without knowing whether $n$ is odd or even
#642
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A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is said to be $\textit{convex}$ if for all $x,y \in \mathbb{R}$ and $\lambda$ such that $0 \leq \lambda \leq1,$ ... must be convex?Only $p$Only $q$Only $r$Only $p$ and $r$Only $q$ and $r$
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Let $f$ be a function with both input and output in the set $\{0,1,2, \dots ,9\}$, and let the function $g$ be defined as $g(x) = f(9-x)$. The function $f$ ... $\text{(i)}$ and $\text{(ii)}$ Only $\text{(iii)}$ None of themAll of them
#644
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Is below always true?$\lceil 2x \rceil=2.\lceil x \rceil$
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#646
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#647
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#648
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Let G be a group of order 231. The number of elements of order 11 in G is ______
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#650
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The number of 5-Sylow subgroup(s) in a group of order 45 is ____
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#653
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Prove S1 without using venn -diagram ( using boolean algebra )
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#656
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#658
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#659
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#660
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