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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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which of the following is a distributive lattice?
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R is real no(does not contain -1) ,S is subset of R then (S,*)1.not group but monoid2.not abelian group but group3.Abelian Group4.not semigroup but groupid
#603
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Please explain me with simple 1-2 examples how order of a subgroup divide order of a group and why it is always true.
#604
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What is the probability that a five-card poker hand contains two pairs (that is, two of each of two different kinds and a fifth card of a third kind)?
#606
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The function $2x^{2}+ 2xy - y^{3}$ hasa) only one stationary point at (0,0)b)two stationary points at (0,0) and (1/6,1/3)c)two stationary points at (0,0) and (1,-1)d)no stationary points
#607
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The Number of Relations, Which are both Reflexive and Symmetric but not Anti-Symmetric, on aset with 6 elements, are ____________?i got 32768 plz check
#608
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number of ways possible to form injective function from set A to setB where |A|=3 and |B|=5 where the pth element of set A cannot match with pth element of set B?
#609
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#610
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Every subset of Distributive lattice is distributive lattice.Every subset of Distributive lattice is lattice. A>>>False and B>» True ???
#611
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What is the rank of the augmented matrix and coefficient matrix here ?x + y + 2z = 3,x + y + z = 1,2x + 2y + 2z = 2The example says it' ... 2, Can someone share the solution using echelon Form?This is a question from wiki page example here
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#613
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#614
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#615
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Determine which one of the following is a partition of the set R of real numbers.a.[{x:x>4},{x:x<5}]b.[{x:x>0},{0},{x:x<0}]c.[{x:x^2>11},{x:x^2<11}]d.none
#616
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The number of totally ordered sets compatible to the given POSET are ________
#617
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Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation?$F(x) = \frac{1}{1-x-x^2}$ ... $a_n=2a_{n-1}+3, n>1, a_0=1$
#618
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If $x=cy+bz, \: y=az+cx, \: z=bx+ay,$ where $x,y,z$ are not all zero, then $a^2+b^2+c^2=$1+2abc$1-2abc$1+abc$abc-1$
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A I and IIIB II and IIIC I, II nd IIID III only
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Ans:BSymmetric closure of R1. It is symmetric2. It contains R3.Minimal relation satisfying 1 and 2If we consider B, then condition 2 may be violated. Therefore I think the answer should be D.