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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1&0&1&2&1&1&0&2&0&0&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&1&0&0&1&1&0&1&2&0&0.8&2
\\\hline\textbf{Total Marks} & 1&4&3&2&1&3&2&2&2&4&\bf{1}&\bf{2.4}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Set Theory & Algebra

4 votes
1 answer
1482
A set  S has 5 elements .How many ways we can choose subset P and Q of S so that P∩Q=∅
40 votes
5 answers
1483
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ?$2^{n+1}$$2^{2n}$$3^{n}$$2^{n} + 1$$3^{n + 1}...
1 votes
4 answers
1485
2 votes
1 answer
1486
IF function f(x)=1+kx is its own inverse then find value of k
1 votes
2 answers
1487
IF A B C are three sets which of following statement is not true?1)(A-B)-C=A-(C-B)2)A-(B∪C)=(A-B)∩(A-C)3)A-(B-C)=(A-B)-(A-C)4)A∆(B∪C)=(A∆B)∪(A∆C)
3 votes
3 answers
1488
If A and B are subsets  of set X={1,2,3........100} and A∆B denotes set of all elements of X which belong to exactly one of A or B.Then total no of subsets of X such t...
2 votes
1 answer
1489
If $f:X→Y$ and $a, b \subseteq X$, then$f(a \cap b)$ is equal to$f(a) –f(b)$$f(a) \cap f(b)$a proper subset of $f(a)\cap f(b)$$f(b)–f(a)$
0 votes
1 answer
1490
If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is Rcomposite R?(a) ((1,1), (3, 1), (2, 3), (4, 2))(b) ((1, 1), (9, 1), (4, 9...
1 votes
1 answer
1491
which of the following is wrong?A)group of order is 27 is cyclicB)group of order is 14 is cyclicC)group of order is 21 is cyclic  group of order is 30 is cyclic
1 votes
2 answers
1492
let f and g be two functions f :A->B and g: B->C g0f :A->C is surjection  g is injection then f is1)injection2) surjection3)bijection4)none
2 votes
2 answers
1495
Determine the cardinality of the following set:$$\{x \mid x\text{ is an integer and } 1/8 < x < 17/2\}$$
2 votes
1 answer
1496
difference between {} , ∅ , {∅} ???
0 votes
1 answer
1497
every total ordered set is distributive.