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Syllabus: Propositional and first order logic.

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&0&0&2&1&1&1&0&0.8&2
\\\hline\textbf{2 Marks Count}&1&1&1&0&0&1&0&0.7&1
\\\hline\textbf{Total Marks}&2&2&4&1&1&3&\bf{1}&\bf{2.2}&\bf{4}\\\hline
\end{array}}}$$

Recent questions in Mathematical Logic

1 vote
0 answers
1
Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 69 views
0 votes
1 answer
2
If $A$ and $B$ are two related events, and $P(A \mid B)$ represents the conditional probability, Bayes’ theorem states that $P(A\mid B) = \dfrac{P(A)}{P(B)} P(B\mid A)$ $P(A\mid B) = P(A) P(B) P(B\mid A)$ $P(A\mid B) = \dfrac{P(A)}{P(B)}$ $P(A\mid B) = P(A)+P(B)$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 44 views
1 vote
0 answers
3
If $y=f(x)$, in the interval $[a,b]$ is rotated about the $x$-axis, the Volume of the solid of revolution is $(f’(x)=dy/dx)$ $\int_{a}^{b} \pi [f(x)]^{2} dx \\$ $\int_{a}^{b}[f(x)]^{3} dx \\$ $\int_{a}^{b} \pi [{f}'(x)]^{2} dx \\$ $\int_{a}^{b} \pi^{2} f(x)dx \\$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 19 views
0 votes
0 answers
4
The area under the curve $y(x)=3e^{-5x}$ from $x=0 \text{ to } x=\infty$ is $\dfrac{3}{5}$ $\dfrac{-3}{5}$ ${5}$ $\dfrac{5}{3}$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 23 views
0 votes
1 answer
5
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 34 views
0 votes
1 answer
6
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 29 views
0 votes
1 answer
7
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 21 views
0 votes
1 answer
8
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 26 views
0 votes
0 answers
9
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 21 views
0 votes
0 answers
10
Find the area bounded by the curve $y=\sqrt{5-x^{2}}$ and $y=\mid x-1 \mid$ $\dfrac{2}{0}(2\sqrt{6}-\sqrt{3})-\dfrac{5}{2}$ $\dfrac{2}{3}(6\sqrt{6}+3\sqrt{3})+\dfrac{5}{2}$ $2(\sqrt{6}-\sqrt{3})-5$ $\dfrac{2}{3}(\sqrt{6}-\sqrt{3})+5$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 20 views
0 votes
0 answers
11
The equation of the plane through the point $(-1,3,2)$ and perpendicular to each of the planes $x+2y+3z=5$ and $3x+3y+z=0$ is $7x-8y+3z+25=0$ $7x+8y+3z+25=0$ $7x-8y+3z-25=0$ $7x-8y-3z-25=0$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 19 views
0 votes
0 answers
12
0 votes
1 answer
13
A ladder $13$ feet long rests against the side of a house. The bottom of the ladder slides away from the house at a rate of $0.5$ ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is $5$ feet from the house? $\dfrac{5}{24} \text{ ft/s} \\$ $\dfrac{5}{12} \text{ ft/s} \\$ $-\dfrac{5}{24} \text {ft/s} \\$ $-\dfrac{5}{12} \text{ ft/s}$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 27 views
0 votes
0 answers
14
Find the volume of the solid obtained by rotating the region bound by the curves $y=x^3+1, \: x=1$, and $y=0$ about the $x$-axis $\dfrac{23\pi}{7} \\$ $\dfrac{16\pi}{7} \\$ $2\pi \\$ $\dfrac{19\pi}{7}$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 21 views
0 votes
0 answers
15
If product of matrix $A=\begin{bmatrix}\cos^{2}\theta &\cos \theta \sin \theta \\ \cos \theta \sin \theta &\sin ^{2} \theta& \end{bmatrix}$ and $B=\begin{bmatrix}\cos^{2}\phi &\cos \phi \sin \phi \\ \cos \phi \sin \phi &\sin ^{2} \phi& \end{bmatrix}$ is a ... and $\phi$ differ by an odd multiple of $\pi$ even multiple of $\pi$ odd multiple of $\dfrac{\pi}{2}$ even multiple of $\dfrac{\pi}{2}$
asked Apr 2 in Mathematical Logic Lakshman Patel RJIT 27 views
1 vote
2 answers
17
Which of the following statements is false? $(P\land Q)\lor(\sim P\land Q)\lor(P \land \sim Q)$ is equal to $\sim Q\land \sim P$ $(P\land Q)\lor(\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor P$ $(P\wedge Q)\lor (\sim P\land Q)\lor(P \wedge \sim Q)$ is equal to $Q\lor (P\wedge \sim Q)$ $(P\land Q)\lor(\sim P\land Q)\lor (P \land \sim Q)$ is equal to $P\lor (Q\land \sim P)$
asked Mar 30 in Mathematical Logic Lakshman Patel RJIT 55 views
0 votes
2 answers
18
0 votes
3 answers
19
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
asked Mar 30 in Mathematical Logic Lakshman Patel RJIT 120 views
0 votes
1 answer
20
The proposition ~ q ∨ p is equivalent to :
asked Mar 27 in Mathematical Logic jothee 58 views
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