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Syllabus: Propositional and first order logic.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1}&\textbf{2024-2}&\textbf{2023}& \textbf{2022}& \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&1&1& 0 & 1&1&0&0.67&1
\\\hline\textbf{2 Marks Count}&0&0&0&0 & 0&0&0&0&0
\\\hline\textbf{Total Marks}& 0&1&1& 0 & 1&1&\bf{0}&\bf{0.67}&\bf{1}\\\hline
\end{array}}}$$

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Recent questions in Mathematical Logic

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1141
ISI-2014-21
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1142
ISI-2014-20
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1143
ISI-2014-18
Let $D_1 = det \begin{pmatrix}a & b & c\\x &y & z\\p& q & r\end{pmatrix}$ and $D_2 = det \begin{pmatrix}-x & a & -p\\y &-b & q\\z & -c & r\end{pmatrix}$ Then $D_1 = D_2$ $D_1 = 2D_2$ $D_1 = -D_2$ $D_2 = 2D_1$
Let $D_1 = det \begin{pmatrix}a & b & c\\x &y & z\\p& q & r\end{pmatrix}$ and $D_2 = det \begin{pmatrix}-x & a & -p\\y &-b & q\\z & -c & r\end{pmatrix}$Then$D_1 = D_2$$D_...
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1144
ISI-2014-17
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$? $0$ $1$ $2$ $3$
What is the minimum value of $\mid z+w \mid$ for complex numbers $z$ and $w$ with $zw = 1$?$0$$1$$2$$3$
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1145
ISI-2014-07
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is $2\sqrt2\pi^2$ $\dfrac{\pi^2}{2\sqrt2}$ $\dfrac{\pi^2}{\sqrt2}$ $\sqrt2\pi^2$
The value of the integral ${\LARGE \int} _{0}^{\pi}\dfrac{x}{1+sin^2x}dx$ is$2\sqrt2\pi^2$$\dfrac{\pi^2}{2\sqrt2}$$\dfrac{\pi^2}{\sqrt2}$$\sqrt2\pi^2$
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2 answers
1146
ISI-2014-06
The sum of an infinite geometric series of real numbers is $14$, and the sum of the cubes of the terms of this series is $392$. Then the first term of the series is $-14$ $10$ $7$ $-5$
The sum of an infinite geometric series of real numbers is $14$, and the sum of the cubes of the terms of this series is $392$. Then the first term of the series is$-14$$...
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2 answers
1147
ISI-2014-5
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$ $\text{is 0}$ $\text{is 1}$ $\text{is 2}$ $\text{does not exist}$
The value of $\displaystyle{\lim_{x\to 0}}$ $\sin x \sin(\dfrac{1}{x})$$\text{is 0}$$\text{is 1}$$\text{is 2}$$\text{does not exist}$
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1 votes
1 answer
1148
ISI-2014-4
How many pair of positive integers of $(m,n)$ are there satisfying $\displaystyle{\sum_{i=1}^{n}i! = m!}$ $0$ $1$ $2$ $3$
How many pair of positive integers of $(m,n)$ are there satisfying$$\displaystyle{\sum_{i=1}^{n}i! = m!}$$$0$$1$$2$$3$
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1149
ISI-2014-3
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true $Re(z)=0$ $\mid z \mid =1$ $Re(z) = 1$ $\text{No such z exists}$
If $\mid 2^z \mid = 1$ for a non-zero complex number $z$ then which one of the following is necessarily true$Re(z)=0$$\mid z \mid =1$$Re(z) = 1$$\text{No such z exists}$
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0 votes
2 answers
1150
ISI-2014-2
Two integers $m$ and $n$ are chosen at random with replacement from the natural numbers $1,2,.....9$. The probability that $m^2-n^2$ is divisible by $4$ is $\dfrac{41}{81}$ $\dfrac{37}{81}$ $\dfrac{2}{3}$ $\dfrac{4}{9}$
Two integers $m$ and $n$ are chosen at random with replacement from the natural numbers $1,2,.....9$. The probability that $m^2-n^2$ is divisible by $4$ is$\dfrac{41}{81}...
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2 answers
1151
ISI-2014-1
The four distinct points $(-a,-b),(0,0),(a,b),(a^2,ab)$ are vertices of parallelogram vertices of rectangle collinear lying on a circle
The four distinct points $(-a,-b),(0,0),(a,b),(a^2,ab)$ arevertices of parallelogramvertices of rectanglecollinearlying on a circle
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1152
ISI-2014-14
The locus of the center of a circle that passes through origin and cuts off a length $2a$ from the line $y=c$ is $x^2+2cx=a^2+c^2$ $x^2+2cy=a^2+c^2$ $y^2+cx=a^2+c^2$ $y^2+2cy=a^2+c^2$
The locus of the center of a circle that passes through origin and cuts off a length $2a$ from the line $y=c$ is$x^2+2cx=a^2+c^2$$x^2+2cy=a^2+c^2$$y^2+cx=a^2+c^2$$y^2+2cy...
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1153
ISI-2014-13
The area bounded by the curves $arg(z) = \pi/3, arg(z) = 2\pi/3$ and $arg(z-2-2\sqrt3i)=\pi$ on the complex plane is given by $2\sqrt3$ $4\sqrt3$ $\sqrt3$ $3\sqrt3$
The area bounded by the curves $arg(z) = \pi/3, arg(z) = 2\pi/3$ and $arg(z-2-2\sqrt3i)=\pi$ on the complex plane is given by$2\sqrt3$$4\sqrt3$$\sqrt3$$3\sqrt3$
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1 votes
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1154
ISI 2014-10
$E1$ and $E2$ are two events such that $P(E1) = 0.2$ and $P(E2) = 0.5$. What are the minimum and maximum possible values of $P(\dfrac{\text{complement of (E1)}}{\text{complement of (E2)}})$? $\text{0 and 0.6}$ $\text{0.4 and 0.6}$ $\text{0.4 and 1}$ $\text{0.6 and 1}$
$E1$ and $E2$ are two events such that $P(E1) = 0.2$ and $P(E2) = 0.5$.What are the minimum and maximum possible values of $P(\dfrac{\text{complement of (E1)}}{\text{comp...
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2 votes
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1156
ISI 2014
Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is $0$ $7$ $8$ $11$
Number of integers $x$ between $1$ and $95$ such that $96$ divides $60x$ is$0$$7$$8$$11$
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1157
Discrete mathematics C.L.Liu Solutions
Can I have solutions of ELEMENTS OF DISCRETE MATHEMATICS by C.L.Liu Solutions. Pls help
Can I have solutions of ELEMENTS OF DISCRETE MATHEMATICS by C.L.Liu Solutions. Pls help
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1158
Transpose symmetric
What is transpose symmetric in algorithm
What is transpose symmetric in algorithm
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1 votes
1 answer
1159
eigen vector
An arbitrary vector X is an eigen vector of the vector of the matrix A=[1 0 0 a 0 0 0 0 b], if (a, b)= (a) (0, 0) (b) (1, 1) (c) (0, 1) (d) (1, 2)
An arbitrary vector X is an eigen vector of the vector of the matrix A=[1 0 0 a 0 0 0 0 b], if (a, b)=(a) (0, 0) (b) (1, 1)(c) (0, 1) (d) (1, 2)
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