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3 answers
1
GATE CSE 2021 Set 1 | Question: 12
Let $\langle M \rangle$ denote an encoding of an automaton $M$. Suppose that $\Sigma = \{0,1\}$. Which of the following languages is/are $\text{NOT}$ recursive? $L= \{ \langle M \rangle \mid M$ is a $\text{DFA}$ such that $L(M)=\emptyset \}$ ... that $L(M)=\emptyset \}$ $L= \{ \langle M \rangle \mid M$ is a $\text{PDA}$ such that $L(M)=\Sigma ^* \}$
Let $\langle M \rangle$ denote an encoding of an automaton $M$. Suppose that $\Sigma = \{0,1\}$. Which of the following languages is/are $\text{NOT}$ recursive? $L= \{ \langle M \rangle \mid M$ is a $\text{DFA}$ such that $L(M)=\emptyset \}$ $L= \{ \langle M \rangle \mid M$ is ... $L(M)=\emptyset \}$ $L= \{ \langle M \rangle \mid M$ is a $\text{PDA}$ such that $L(M)=\Sigma ^* \}$
commented Apr 5 in Theory of Computation 529 views
2 answers
2
GATE CSE 2021 Set 2 | Question: 25
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
Suppose that $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function on the interval $[-3, 3]$ and a differentiable function in the interval $(-3,3)$ such that for every $x$ in the interval, $f’(x) \leq 2$. If $f(-3)=7$, then $f(3)$ is at most __________
answer selected Apr 5 in Calculus 365 views
3 answers
3
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
answer selected Apr 5 in Linear Algebra 592 views
1 answer
4
GATE CSE 2021 Set 2 | Question: 22
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________
answer edited Apr 5 in Probability 437 views
3 answers
6
NIELIT 2017 July Scientist B (IT) - Section B: 50
Which one of the following is the function of a multiplexer? To decode information To select $1$ out of $N$ input data sources and to transmit it to single channel To transmit data on $N$ lines To perform serial to parallel conversion
Which one of the following is the function of a multiplexer? To decode information To select $1$ out of $N$ input data sources and to transmit it to single channel To transmit data on $N$ lines To perform serial to parallel conversion
answer selected Apr 4 in Digital Logic 248 views
3 answers
7
GATE CSE 2020 | Question: GA-8
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ number of circles can be painted, then the unpainted area available in ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
answer selected Apr 4 in Quantitative Aptitude 2.4k views
4 answers
8
GATE CSE 2021 Set 2 | Question: 10
Consider the following $\text{ANSI C}$ program. #include <stdio.h> int main() { int arr[4][5]; int i, j; for (i=0; i<4; i++) ​​​​​​{ for (j=0; j<5; j++) { arr[i][j] = 10 * i + j; } } printf(“%d”, *(arr[1]+9)); return 0; } What is the output of the above program? $14$ $20$ $24$ $30$
Consider the following $\text{ANSI C}$ program. #include <stdio.h> int main() { int arr[4][5]; int i, j; for (i=0; i<4; i++) ​​​​​​{ for (j=0; j<5; j++) { arr[i][j] = 10 * i + j; } } printf(“%d”, *(arr[1]+9)); return 0; } What is the output of the above program? $14$ $20$ $24$ $30$
answered Apr 4 in Programming and DS 822 views
3 answers
9
GATE CSE 2021 Set 2 | Question: 12
Let $L_1$ be a regular language and $L_2$ be a context-free language. Which of the following languages is/are context-free? $L_1 \cap \overline{L_2} \\$ $\overline{\overline{L_1} \cup \overline{L_2}} \\$ $L_1 \cup (L_2 \cup \overline{L_2}) \\$ $(L_1 \cap L_2) \cup (\overline{L_1} \cap L_2)$
Let $L_1$ be a regular language and $L_2$ be a context-free language. Which of the following languages is/are context-free? $L_1 \cap \overline{L_2} \\$ $\overline{\overline{L_1} \cup \overline{L_2}} \\$ $L_1 \cup (L_2 \cup \overline{L_2}) \\$ $(L_1 \cap L_2) \cup (\overline{L_1} \cap L_2)$
answer edited Apr 4 in Theory of Computation 603 views
2 answers
10
GATE CSE 2021 Set 2 | Question: 11
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ ... There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$
Consider the following sets, where $n \geq 2$: $S_1$: Set of all $n \times n$ matrices with entries from the set $\{ a, b, c\}$ $S_2$: Set of all functions from the set $\{0,1,2, \dots, n^2-1\}$ to the set $\{0, 1, 2\}$ Which of the following ... to $S_2$ There exists a surjection from $S_1$ to $S_2$ There exists a bijection from $S_1$ to $S_2$ There does not exist an injection from $S_1$ to $S_2$
answer selected Apr 4 in Set Theory & Algebra 568 views
2 answers
11
GATE CSE 2021 Set 2 | Question: 8
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$? $\Theta ( \sqrt{n})$ $\Theta (\log _2(n))$ $\Theta(n^2)$ $\Theta(n)$
What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size $n$? $\Theta ( \sqrt{n})$ $\Theta (\log _2(n))$ $\Theta(n^2)$ $\Theta(n)$
answer selected Apr 4 in Algorithms 643 views
3 answers
12
GATE CSE 2021 Set 2 | Question: 4
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ ... and mantissa $=0000000000000000000000001$ exponent $=00000001$ and mantissa $=0000000000000000000000000$ exponent $=00000001$ and mantissa $=0000000000000000000000001$
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ ... $=00000000$ and mantissa $=0000000000000000000000001$ exponent $=00000001$ and mantissa $=0000000000000000000000000$ exponent $=00000001$ and mantissa $=0000000000000000000000001$
answered Apr 4 in Digital Logic 622 views
3 answers
13
GATE CSE 2021 Set 2 | Question: 9
Let $L \subseteq \{0,1\}^*$ be an arbitrary regular language accepted by a minimal $\text{DFA}$ with $k$ states. Which one of the following languages must necessarily be accepted by a minimal $\text{DFA}$ with $k$ states? $L-\{01\}$ $L \cup \{01\}$ $\{0,1\}^* – L$ $L \cdot L$
Let $L \subseteq \{0,1\}^*$ be an arbitrary regular language accepted by a minimal $\text{DFA}$ with $k$ states. Which one of the following languages must necessarily be accepted by a minimal $\text{DFA}$ with $k$ states? $L-\{01\}$ $L \cup \{01\}$ $\{0,1\}^* – L$ $L \cdot L$
answer selected Apr 4 in Theory of Computation 657 views
3 answers
14
GATE CSE 2021 Set 2 | Question: 7
Consider the three-way handshake mechanism followed during $\text{TCP}$ connection establishment between hosts $P$ and $Q$. Let $X$ and $Y$ be two random $32$-bit starting sequence numbers chosen by $P$ and $Q$ respectively. Suppose $P$ sends a $\text{TCP}$ connection request ... $=Y$, $\text{ACK}$ bit $=1$, $\text{ACK}$ number $=X$, $\text{FIN}$ bit $=0$
Consider the three-way handshake mechanism followed during $\text{TCP}$ connection establishment between hosts $P$ and $Q$. Let $X$ and $Y$ be two random $32$-bit starting sequence numbers chosen by $P$ and $Q$ respectively. Suppose $P$ sends a $\text{TCP}$ connection request message to $Q$ with a ... $\text{SEQ}$ number $=Y$, $\text{ACK}$ bit $=1$, $\text{ACK}$ number $=X$, $\text{FIN}$ bit $=0$
answer selected Apr 4 in Computer Networks 511 views
4 answers
15
GATE CSE 2021 Set 2 | Question: 6
Consider the following statements $S1$ and $S2$ about the relational data model: $S1$: A relation scheme can have at most one foreign key. $S2$: A foreign key in a relation scheme $R$ cannot be used to refer to tuples of $R.$ Which one of the following choices ... are true $S1$ is true and $S2$ is false $S1$ is false and $S2$ is true Both $S1$ and $S2$ are false
Consider the following statements $S1$ and $S2$ about the relational data model: $S1$: A relation scheme can have at most one foreign key. $S2$: A foreign key in a relation scheme $R$ cannot be used to refer to tuples of $R.$ Which one of the following choices is correct? Both $S1$ and $S2$ are true $S1$ is true and $S2$ is false $S1$ is false and $S2$ is true Both $S1$ and $S2$ are false
answer selected Apr 4 in Databases 604 views
4 answers
16
GATE CSE 2021 Set 2 | Question: 5
Which one of the following circuits implements the Boolean function given below? $f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$, where $m_i$ is the $i^{\text{th}}$ minterm.
Which one of the following circuits implements the Boolean function given below? $f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$, where $m_i$ is the $i^{\text{th}}$ minterm.
answer edited Apr 4 in Digital Logic 544 views
3 answers
17
GATE CSE 2021 Set 2 | Question: 2
​​​​​Let $H$ be a binary min-heap consisting of $n$ elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in $H$? $\Theta (1)$ $\Theta (\log n)$ $\Theta (n)$ $\Theta (n \log n)$
​​​​​Let $H$ be a binary min-heap consisting of $n$ elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in $H$? $\Theta (1)$ $\Theta (\log n)$ $\Theta (n)$ $\Theta (n \log n)$
answer selected Apr 4 in DS 676 views
3 answers
18
GATE CSE 2021 Set 2 | Question: 1
Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a ... are true $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false
Let $G$ be a connected undirected weighted graph. Consider the following two statements. $S_1$: There exists a minimum weight edge in $G$ which is present in every minimum spanning tree of $G$. $S_2$: If every edge in $G$ has distinct weight, then $G$ has a unique minimum spanning ... $S_1$ is true and $S_2$ is false $S_1$ is false and $S_2$ is true Both $S_1$ and $S_2$ are false
answer selected Apr 4 in Algorithms 1k views
1 answer
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GATE CSE 2021 Set 2 | GA Question: 7
A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
answer selected Apr 4 in Spatial Aptitude 516 views
3 answers
20
GATE CSE 2021 Set 2 | GA Question: 6
Listening to music during exercise improves performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for ... effect on learning in all students. Music has a positive effect only in some students who exercise
Listening to music during exercise improves performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while ... clear positive effect on learning in all students. Music has a positive effect only in some students who exercise
answer selected Apr 4 in Verbal Aptitude 524 views
3 answers
21
GATE CSE 2021 Set 2 | GA Question: 4
​​​​​​If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is: $2$ $4$ $6$ $8$
​​​​​​If $\left( x – \dfrac{1}{2} \right)^2 – \left( x- \dfrac{3}{2} \right) ^2 = x+2$, then the value of $x$ is: $2$ $4$ $6$ $8$
answer selected Apr 4 in Quantitative Aptitude 466 views
2 answers
22
GATE CSE 2021 Set 2 | GA Question: 3
If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, $\cos \theta =$ $\frac{1}{2} \\$ $\frac{1}{\sqrt{3}} \\$ $\frac{1}{\sqrt{2}} \\$ $\frac{\sqrt{3}}{2}$
If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, $\cos \theta =$ $\frac{1}{2} \\$ $\frac{1}{\sqrt{3}} \\$ $\frac{1}{\sqrt{2}} \\$ $\frac{\sqrt{3}}{2}$
answer selected Apr 4 in Quantitative Aptitude 623 views
1 answer
23
GATE CSE 2021 Set 2 | GA Question: 2
​​​​ A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.
​​​​ A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ___________.
answer selected Apr 4 in Spatial Aptitude 489 views
5 answers
24
GATE CSE 2021 Set 2 | GA Question: 1
Gauri said that she can play the keyboard __________ her sister. as well as as better as as nicest as as worse as
Gauri said that she can play the keyboard __________ her sister. as well as as better as as nicest as as worse as
answer edited Apr 4 in Verbal Aptitude 1.8k views
4 answers
25
GATE CSE 2021 Set 2 | Question: 33
A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of ...
A bag has $r$ red balls and $b$ black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will ...
answer selected Apr 4 in Probability 1k views
2 answers
26
GATE CSE 2021 Set 1 | Question: 18
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter $2$. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to $2$ decimal places) is ____________.
answer selected Mar 31 in Probability 497 views
1 answer
27
GATE ME 2021 Set 1 | GA Question: 10
Five persons $\text{P, Q, R, S and T}$ are sitting in a row not necessarily in the same order. $Q$ and $R$ are separated by one person, and $S$ should not be seated adjacent to $Q.$ The number of distinct seating arrangements possible is: $4$ $8$ $10$ $16$
Five persons $\text{P, Q, R, S and T}$ are sitting in a row not necessarily in the same order. $Q$ and $R$ are separated by one person, and $S$ should not be seated adjacent to $Q.$ The number of distinct seating arrangements possible is: $4$ $8$ $10$ $16$
answer selected Mar 30 43 views
2 answers
28
GATE CSE 2021 Set 1 | Question: 48
Consider the following $\text{ANSI C}$ function: int SimpleFunction(int Y[], int n, int x) { int total = Y[0], loopIndex; for (loopIndex=1; loopIndex<=n-1; loopIndex++) total=x*total +Y[loopIndex]; return total; } Let $\textsf{Z}$ be an array ... $i$ such that $0 \leq i \leq 9$. The value returned by $\textsf{SimpleFunction(Z},10,2)$ is __________
Consider the following $\text{ANSI C}$ function: int SimpleFunction(int Y[], int n, int x) { int total = Y[0], loopIndex; for (loopIndex=1; loopIndex<=n-1; loopIndex++) total=x*total +Y[loopIndex]; return total; } Let $\textsf{Z}$ be an array of $10$ elements with $\textsf{Z}[i]=1$, for all $i$ such that $0 \leq i \leq 9$. The value returned by $\textsf{SimpleFunction(Z},10,2)$ is __________
answered Mar 30 in Programming and DS 310 views
2 answers
29
TIFR2021-B: 7
Which of the following regular expressions defines a language that is different from the other choices? $b^{\ast }\left ( a+b \right )^\ast a\left ( a+b \right )^ \ast ab^\ast \left ( a+b \right )^{\ast }$ ... $\left ( a+b \right )^{\ast }b^{\ast }a \left ( a+b\right )^{\ast }b^{\ast }\left ( a+b \right )^{\ast }$
Which of the following regular expressions defines a language that is different from the other choices? $b^{\ast }\left ( a+b \right )^\ast a\left ( a+b \right )^ \ast ab^\ast \left ( a+b \right )^{\ast }$ ... $\left ( a+b \right )^{\ast }b^{\ast }a \left ( a+b\right )^{\ast }b^{\ast }\left ( a+b \right )^{\ast }$
answer selected Mar 25 in Others 37 views
4 answers
30
GATE CSE 2003 | Question: 5
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
$n$ couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is \(^{2n}\mathrm{C}_n\times 2^n\) \(3^n\) \(\frac{(2n)!}{2^n}\) \(^{2n}\mathrm{C}_n\)
answer edited Mar 23 in Combinatory 4.9k views
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