Answers by jatinmittal199510 / GATE Overflow for GATE CSE

4 votes

1

GATE CSE 2000 | Question: 9
Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input): Write the truth table for all bits. Label the input bits $I_1, I_2, \ldots$ with $I_1$ as the least significant bit. ... Draw one circuit for each output bit using, altogether, two two-input AND gates, one two-input OR gate and two NOT gates.

Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input):Write the truth table for all bits. Label th...

2.9k views

answered Apr 10, 2021

0 votes

2

B+ tree maximum number of records.
What is the maximum number of records that can be indexed in B+ tree of level $4$ ,order $10$ where root is at level $1$ ? As the order of tree is $10$, nodes in the last level of b+ tree should contain $10$ record pointers (number of ... $10-1 = 9$ record pointers. Which one is correct?

What is the maximum number of records that can be indexed in B+ tree of level $4$ ,order $10$ where root is at level $1$ ?As the order of tree is $10$, nodes in the last ...

4.8k views

answered Apr 5, 2021

0 votes

3

minimum number of registers
Consider the following expression and identify minimum number of registers required to implement the following expression : (a-b)+(e+(c-d))/f Can anyone please give the theory or notes of prerequisites -, how to solve these questions. The solution of the above ... adding R1 to the R2 and result is stored back into R1 since R1=R1+R2. Number of registers used is only 3.

Consider the following expression and identify minimum number of registers required to implement the following expression : (a-b)+(e+(c-d))/fCan anyone please give the th...

1.3k views

answered Mar 27, 2021

1 votes

4

TIFR CSE 2021 | Part B | Question: 7
Which of the following regular expressions defines a language that is different from the other choices? $b^{\ast }\left ( a+b \right )^\ast a\left ( a+b \right )^ \ast ab^\ast \left ( a+b \right )^{\ast }$ ...

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^...

601 views

answered Mar 25, 2021

2 votes

5

TIFR CSE 2021 | Part A | Question: 13
What are the last two digits of $7^{2021}$? $67$ $07$ $27$ $01$ $77$

What are the last two digits of $7^{2021}$?$67$$07$$27$$01$$77$

529 views

answered Mar 25, 2021

0 votes

6

TIFR CSE 2021 | Part B | Question: 5
For a language $L$ over the alphabet $\{a, b\}$, let $\overline{L}$ denote the complement of $L$ and let $L^{\ast}$ denote the Kleene-closure of $L$. Consider the following sentences. $\overline{L}$ and $L^{\ast}$ are both context-free. $\overline{L}$ is not ... ? Both (i) and (iii) Only (i) Only (iii) Only (ii) None of the above

For a language $L$ over the alphabet $\{a, b\}$, let $\overline{L}$ denote the complement of $L$ and let $L^{\ast}$ denote the Kleene-closure of $L$. Consider the followi...

677 views

answered Mar 25, 2021

1 votes

7

TIFR CSE 2021 | Part B | Question: 6
Consider the following pseudocode: procedure HowManyDash(n) if n=0 then print '-' else if n=1 then print '-' else HowManyDash(n-1) HowManyDash(n-2) end if end procedure How many ‘-’ does HowManyDash$(10)$ print? $9$ $10$ $55$ $89$ $1024$

Consider the following pseudocode:procedure HowManyDash(n) if n=0 then print '-' else if n=1 then print '-' else HowManyDash(n-1) HowManyDash(n-2) end if end procedureHow...

546 views

answered Mar 25, 2021

0 votes

8

TIFR CSE 2021 | Part B | Question: 3
What is the prefix expression corresponding to the expression: $\left ( \left ( 9+8 \right ) \ast 7+\left ( 6\ast \left ( 5+4 \right ) \right )\ast 3\right )+2?$ You may assume that $\ast$ has precedence over $+$? $\ast + +\: 987 \ast \ast \: 6 + + \:5432$ ... $+ + \ast +\: 987 \ast \ast \: 6 + \:5432$ $+ \ast + \ast \: 987+ + \: 6 \ast \:5432$

What is the prefix expression corresponding to the expression:$\left ( \left ( 9+8 \right ) \ast 7+\left ( 6\ast \left ( 5+4 \right ) \right )\ast 3\right )+2?$You may as...

836 views

answered Mar 25, 2021

1 votes

9

TIFR CSE 2021 | Part B | Question: 2
Let $L$ be a singly-linked list $X$ and $Y$ be additional pointer variables such that $X$ points to the first element of $L$ and $Y$ points to the last element of $L$. Which of the following operations cannot be done in time that is ... after the last element of $L$. Add an element before the first element of $L$. Interchange the first two elements of $L$.

Let $L$ be a singly-linked list $X$ and $Y$ be additional pointer variables such that $X$ points to the first element of $L$ and $Y$ points to the last element of $L$. Wh...

788 views

answered Mar 25, 2021

4 votes

10

TIFR CSE 2021 | Part A | Question: 12
How many numbers in the range ${0, 1, \dots , 1365}$ have exactly four $1$'s in their binary representation? (Hint: $1365_{10}$ is $10101010101_{2}$, that is, $1365=2^{10} + 2^{8}+2^{6}+2^{4}+2^{2}+2^{0}.)$ ... $\binom{11}{4}+\binom{9}{3}+\binom{7}{2}+\binom{5}{1}$ $1024$

How many numbers in the range ${0, 1, \dots , 1365}$ have exactly four $1$’s in their binary representation? (Hint: $1365_{10}$ is $10101010101_{2}$, that is, $$1365=2^...

568 views

answered Mar 25, 2021

2 votes

11

TIFR CSE 2021 | Part A | Question: 11
Find the following sum. $\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$ $\frac{20}{41}$ $\frac{10}{41}$ $\frac{10}{21}$ $\frac{20}{21}$ $1$

Find the following sum.$$\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\frac{1}{6^{2}-1}+\cdots+\frac{1}{40^{2}-1}$$$\frac{20}{41}$$\frac{10}{41}$$\frac{10}{21}$$\frac{20}{21}$$1$

673 views

answered Mar 25, 2021

2 votes

12

TIFR CSE 2021 | Part A | Question: 10
Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads than ketak? In the following, the binomial coefficient $\binom{n}{k}$ counts the number of $k$-element subsets of ... $\sum_{i=0}^{n}\frac{\binom{n}{i}}{2^{n}}$

Lavanya and Ketak each flip a fair coin (i.e., both heads and tails have equal probability of appearing) $n$ times. What is the probability that Lavanya sees more heads t...

553 views

answered Mar 25, 2021

0 votes

13

TIFR CSE 2021 | Part A | Question: 7
Let $d$ be the positive square integers (that is, it is a square of some integer) that are factors of $20^{5} \times 21^{5}$. Which of the following is true about $d$? $50\leq d< 100$ $100\leq d< 150$ $150\leq d< 200$ $200\leq d< 300$ $300\leq d$

Let $d$ be the positive square integers (that is, it is a square of some integer) that are factors of $20^{5} \times 21^{5}$. Which of the following is true about $d$?$50...

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answered Mar 25, 2021

0 votes

14

TIFR CSE 2021 | Part A | Question: 5
Let $n, m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\left \{ 1, 2,\dots, n \right \}$ of size $k$. Consider sampling a function $f$ uniformly at random from the set of all functions mapping $\left \{ 1,\dots, n \right \}$ ... $1-\frac{k!\binom{n}{k}}{n^{k}}$ $1-\frac{k!\binom{n}{k}}{m^{k}}$

Let $n, m$ and $k$ be three positive integers such that $n \geq m \geq k$. Let $S$ be a subset of $\left \{ 1, 2,\dots, n \right \}$ of size $k$. Consider sampling a func...

590 views

answered Mar 25, 2021

1 votes

15

TIFR CSE 2021 | Part A | Question: 4
What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months? $\frac{25}{48}$ $\frac{5}{8}$ $\frac{5}{12}$ $\frac{41}{96}$ $\frac{55}{96}$

What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve mo...

1.0k views

answered Mar 25, 2021

20 votes

16

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 pick...

9.3k views

answered Feb 19, 2021

2 votes

17

GATE CSE 2021 Set 1 | Question: 6
Let the representation of a number in base $3$ be $210$. What is the hexadecimal representation of the number? $15$ $21$ $\text{D}2$ $528$

Let the representation of a number in base $3$ be $210$. What is the hexadecimal representation of the number?$15$$21$$\text{D}2$$528$

8.9k views

answered Feb 18, 2021

9 votes

18

GATE CSE 2021 Set 2 | Question: 35
Consider the following $\text{ANSI C}$ program: #include <stdio.h> #include <stdlib.h> struct Node{ int value; struct Node *next;}; int main( ) { struct Node *boxE, *head, *boxN; int index=0; boxE=head= (struct ... which will be reported as an error by the compiler It dereferences an uninitialized pointer that may result in a run-time error

Consider the following $\text{ANSI C}$ program:#include <stdio.h #include <stdlib.h struct Node{ int value; struct Node *next;}; int main( ) { struct Node *boxE, *head, *...

9.6k views

answered Feb 18, 2021

8 votes

19

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 ...

10.9k views

answered Feb 18, 2021

9 votes

20

GATE CSE 2021 Set 2 | Question: 29
In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted. If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the ... $22$. First $\textsf{QuesA}$ and then $\textsf{QuesB}$. Expected marks $16$.

In an examination, a student can choose the order in which two questions ($\textsf{QuesA}$ and $\textsf{QuesB}$) must be attempted.If the first question is answered wrong...

7.5k views

answered Feb 18, 2021

2 votes

21

GATE CSE 2021 Set 2 | Question: 26
Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties: For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. ... which satisfy the above two properties, what is the minimum length of the encoded string? $21$ $23$ $25$ $30$

Consider the string $\textrm{abbccddeee}$. Each letter in the string must be assigned a binary code satisfying the following properties:For any two letters, the code assi...

9.5k views

answered Feb 18, 2021

5 votes

22

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 fo...

6.3k views

answered Feb 18, 2021

38 votes

23

GATE CSE 2021 Set 2 | Question: 20
Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory through cycle stealing at regular intervals. Consider a $\text{2 MHz}$ ... $\text{DMA}$, the data transfer rate of the device is __________ bits per second.

Consider a computer system with $\text{DMA}$ support. The $\text{DMA}$ module is transferring one $8$-bit character in one $\text{CPU}$ cycle from a device to memory thro...

11.4k views

answered Feb 18, 2021

7 votes

24

GATE CSE 2021 Set 2 | Question: 19
Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $32$ -bit address is used for accessing the cache. If the width of the tag field is $22$ bits, the associativity of the cache is _________

Consider a set-associative cache of size $\text{2KB (1KB} =2^{10}$ bytes$\text{)}$ with cache block size of $64$ bytes. Assume that the cache is byte-addressable and a $3...

7.2k views

answered Feb 18, 2021

13 votes

25

GATE CSE 2021 Set 2 | Question: 18
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________

If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________

4.9k views

answered Feb 18, 2021

28 votes

26

GATE CSE 2021 Set 2 | Question: 17
Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________

Consider the following deterministic finite automaton $\text{(DFA)}$The number of strings of length $8$ accepted by the above automaton is ___________

9.4k views

answered Feb 18, 2021

22 votes

27

GATE CSE 2021 Set 2 | Question: 16
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid $ is _____________

Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the ...

11.2k views

answered Feb 18, 2021

4 votes

28

GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$

Choose the correct choice(s) regarding the following proportional logic assertion $S$:$$S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \righta...

8.9k views

answered Feb 18, 2021

15 votes

29

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{\overlin...

9.9k views

answered Feb 18, 2021

3 votes

30

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...

30.2k views

answered Feb 18, 2021

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