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Answers by Bhagirathi
20
votes
91
GATE CSE 1996 | Question: 2.12
The recurrence relation $T(1) = 2$ $T(n) = 3T (\frac{n}{4}) +n$ has the solution $T(n)$ equal to $O(n)$ $O (\log n)$ $O\left(n^\frac{3}{4}\right)$ None of the above
The recurrence relation$T(1) = 2$$T(n) = 3T (\frac{n}{4}) +n$has the solution $T(n)$ equal to$O(n)$$O (\log n)$$O\left(n^\frac{3}{4}\right)$ None of the above
7.1k
views
answered
Oct 16, 2014
Algorithms
gate1996
algorithms
recurrence-relation
normal
+
–
24
votes
92
GATE CSE 1996 | Question: 1.5
Two dice are thrown simultaneously. The probability that at least one of them will have $6$ facing up is $\frac{1}{36}$ $\frac{1}{3}$ $\frac{25}{36}$ $\frac{11}{36}$
Two dice are thrown simultaneously. The probability that at least one of them will have $6$ facing up is$\frac{1}{36}$$\frac{1}{3}$$\frac{25}{36}$$\frac{11}{36}$
4.8k
views
answered
Oct 16, 2014
Probability
gate1996
probability
easy
+
–
26
votes
93
GATE CSE 1996 | Question: 2.7
The probability that top and bottom cards of a randomly shuffled deck are both aces is $\frac{4}{52} \times \frac{4}{52}$ $\frac{4}{52} \times \frac{3}{52}$ $\frac{4}{52} \times \frac{3}{51}$ $\frac{4}{52} \times \frac{4}{51}$
The probability that top and bottom cards of a randomly shuffled deck are both aces is$\frac{4}{52} \times \frac{4}{52}$$\frac{4}{52} \times \frac{3}{52}$$\frac{4}{52} \t...
4.9k
views
answered
Oct 16, 2014
Probability
gate1996
probability
easy
+
–
5
votes
94
GATE CSE 1996 | Question: 2.24
What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in Fig $B\overline{D} + \overline{B}D$ $(B + \overline{C} +D) (\overline{B} + C + \overline{D})$ $(B + {D})(\overline{B} +\overline{ D})$ $(B + \overline{D})(\overline{B} + {D})$
What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in Fig $B\overline{D} + \overline{B}D$$(B + \overline{C} +D) (\overline{B} + ...
9.0k
views
answered
Oct 16, 2014
Digital Logic
gate1996
digital-logic
k-map
easy
+
–
30
votes
95
GATE CSE 1994 | Question: 1.15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is $n$ $n^2$ $\frac{n(n-1)}{2}$ $\frac{n(n+1)}{2}$
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is$n$$n^2$$\frac{n(n-1)}{2}$$\frac{n(n+1)}{2}$
9.9k
views
answered
Oct 11, 2014
Combinatory
gate1994
combinatory
counting
normal
+
–
3
votes
96
GATE CSE 1994 | Question: 25
An array $A$ contains $n$ integers in non-decreasing order, $A[1] \leq A[2] \leq \cdots \leq A[n]$. Describe, using Pascal like pseudo code, a linear time algorithm to find $i, j,$ such that $A[i]+A[j]=a$ given integer $M$, if such $i, j$ exist.
An array $A$ contains $n$ integers in non-decreasing order, $A \leq A \leq \cdots \leq A[n]$. Describe, using Pascal like pseudo code, a linear time algorithm to find $...
4.9k
views
answered
Oct 11, 2014
DS
gate1994
data-structures
array
normal
descriptive
+
–
33
votes
97
GATE CSE 1991 | Question: 03,vii
The following sequence of operations is performed on a stack: $PUSH (10), PUSH (20), POP, PUSH (10), PUSH (20), POP, POP, POP, PUSH (20), POP$ The sequence of values popped out is $20,10,20,10,20$ $20,20,10,10,20$ $10,20,20,10,20$ $20,20,10,20,10$
The following sequence of operations is performed on a stack:$PUSH (10), PUSH (20), POP, PUSH (10), PUSH (20), POP, POP, POP, PUSH (20), POP$The sequence of values poppe...
4.3k
views
answered
Oct 10, 2014
DS
gate1991
data-structures
stack
easy
+
–
5
votes
98
GATE CSE 2011 | Question: 34
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probabil...
18.0k
views
answered
Oct 10, 2014
Probability
gatecse-2011
probability
normal
+
–
4
votes
99
GATE CSE 1997 | Question: 1.1
The probability that it will rain today is $0.5$. The probability that it will rain tomorrow is $0.6$. The probability that it will rain either today or tomorrow is $0.7$. What is the probability that it will rain today and tomorrow? $0.3$ $0.25$ $0.35$ $0.4$
The probability that it will rain today is $0.5$. The probability that it will rain tomorrow is $0.6$. The probability that it will rain either today or tomorrow is $0.7$...
6.2k
views
answered
Oct 10, 2014
Probability
gate1997
probability
easy
+
–
–4
votes
100
GATE CSE 1994 | Question: 2.6
The probability of an event $B$ is $P_1$. The probability that events $A$ and $B$ occur together is $P_2$ while the probability that $A$ and $\bar{B}$ occur together is $P_3$. The probability of the event $A$ in terms of $P_1, P_2$ and $P_3$ is _____________
The probability of an event $B$ is $P_1$. The probability that events $A$ and $B$ occur together is $P_2$ while the probability that $A$ and $\bar{B}$ occur together is $...
4.5k
views
answered
Oct 10, 2014
Probability
gate1994
probability
normal
conditional-probability
fill-in-the-blanks
+
–
3
votes
101
GATE CSE 1994 | Question: 3.4
Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations
Match the following items(i) Newton-Raphson(a) Integration(ii) Runge-Kutta(b) Root finding(iii) Gauss-Seidel(c) Ordinary Differential Equations(iv) Simpson's Rule(d) Solu...
11.6k
views
answered
Oct 10, 2014
Numerical Methods
gate1994
numerical-methods
easy
out-of-gate-syllabus
+
–
39
votes
102
GATE CSE 1997 | Question: 6.5
Which one of the following is not decidable? Given a Turing machine $M$, a string $s$ and an integer $k$, $M$ accepts $s$ within $k$ steps Equivalence of two given Turing machines Language accepted by a given finite state machine is not empty Language generated by a context free grammar is non-empty
Which one of the following is not decidable?Given a Turing machine $M$, a string $s$ and an integer $k$, $M$ accepts $s$ within $k$ stepsEquivalence of two given Turing m...
10.0k
views
answered
Oct 7, 2014
Theory of Computation
gate1997
theory-of-computation
decidability
easy
+
–
89
votes
103
GATE CSE 1994 | Question: 1.11
In a compact single dimensional array representation for lower triangular matrices (i.e all the elements above the diagonal are zero) of size $n \times n$, non-zero elements, (i.e elements of lower triangle) of each row are stored one after another, starting from the first row, the index of the ... is: $i+j$ $i+j-1$ $(j-1)+\frac{i(i-1)}{2}$ $i+\frac{j(j-1)}{2}$
In a compact single dimensional array representation for lower triangular matrices (i.e all the elements above the diagonal are zero) of size $n \times n$, non-zero eleme...
27.9k
views
answered
Oct 7, 2014
DS
gate1994
data-structures
array
normal
+
–
0
votes
104
FSM
Suppose we have an encoding of a fsm ... 1.is it regular? 2.does the fsm accepts its own encoding ?
Suppose we have an encoding of a fsm ... 1.is it regular? 2.does the fsm accepts its own encoding ?
639
views
answered
Sep 27, 2014
30
votes
105
GATE CSE 1998 | Question: 1.14
A multiplexer with a $4-bit$ data select input is a $4:1$ multiplexer $2:1$ multiplexer $16:1$ multiplexer $8:1$ multiplexer
A multiplexer with a $4-bit$ data select input is a$4:1$ multiplexer$2:1$ multiplexer$16:1$ multiplexer$8:1$ multiplexer
9.0k
views
answered
Sep 27, 2014
Digital Logic
gate1998
digital-logic
multiplexer
easy
+
–
29
votes
106
GATE CSE 1998 | Question: 1.22
Give the correct matching for the following pairs: ... $\text{A-R B-P C-S D-Q}$ $\text{A-P B-R C-S D-Q}$ $\text{A-P B-S C-R D-Q}$
Give the correct matching for the following pairs: $$\begin{array}{ll|ll}\hline \text{(A)} & \text{$O (\log n)$} & \text{(P)} & \text{Selection} \\\hline \text{(B)} & \t...
7.7k
views
answered
Sep 27, 2014
Algorithms
gate1998
algorithms
sorting
easy
match-the-following
+
–
22
votes
107
GATE CSE 1998 | Question: 2.8
Which of the following operations is commutative but not associative? AND OR NAND EXOR
Which of the following operations is commutative but not associative?ANDORNANDEXOR
9.1k
views
answered
Sep 27, 2014
Digital Logic
gate1998
digital-logic
easy
boolean-algebra
+
–
56
votes
108
GATE CSE 2014 Set 1 | Question: 10
Consider the following program in C language: #include <stdio.h> main() { int i; int*pi = &i; scanf("%d",pi); printf("%d\n", i+5); } Which one of the following statements is TRUE? Compilation fails. Execution ... $5$ more than the address of variable $i$. On execution, the value printed is $5$ more than the integer value entered.
Consider the following program in C language:#include <stdio.h main() { int i; int*pi = &i; scanf("%d",pi); printf("%d\n", i+5); }Which one of the following statements is...
17.3k
views
answered
Sep 27, 2014
Programming in C
gatecse-2014-set1
programming
programming-in-c
easy
pointers
+
–
49
votes
109
GATE CSE 2006 | Question: 52
The median of $n$ elements can be found in $O(n)$ time. Which one of the following is correct about the complexity of quick sort, in which median is selected as pivot? $\Theta (n)$ $\Theta (n \log n)$ $\Theta (n^{2})$ $\Theta (n^{3})$
The median of $n$ elements can be found in $O(n)$ time. Which one of the following is correct about the complexity of quick sort, in which median is selected as pivot?$\T...
53.3k
views
answered
Sep 27, 2014
Algorithms
gatecse-2006
algorithms
sorting
easy
+
–
11
votes
110
GATE CSE 2012 | Question: 35
Suppose a circular queue of capacity $(n −1)$ elements is implemented with an array of $n$ elements. Assume that the insertion and deletion operations are carried out using REAR and FRONT as array index variables, respectively. Initially, $REAR = FRONT = 0$. The conditions to detect ... : $(REAR+1) \mod n == FRONT$ full: $(FRONT+1) \mod n == REAR$ empty: $REAR == FRONT$
Suppose a circular queue of capacity $(n −1)$ elements is implemented with an array of $n$ elements. Assume that the insertion and deletion operations are carried out u...
24.0k
views
answered
Sep 27, 2014
DS
gatecse-2012
data-structures
queue
normal
+
–
12
votes
111
GATE CSE 2012 | Question: 33
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of val...
21.8k
views
answered
Sep 27, 2014
Probability
gatecse-2012
probability
conditional-probability
normal
+
–
24
votes
112
GATE CSE 2012 | Question: 37
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set? $ 2^{n}$ $2^{n} – 1$ $2^{n} – 2$ $2(2^{n} – 2)$
How many onto (or surjective) functions are there from an $n$-element $(n ≥ 2)$ set to a $2$-element set?$ 2^{n}$$2^{n} – 1$$2^{n} – 2$$2(2^{n} – 2)$
9.3k
views
answered
Sep 27, 2014
Set Theory & Algebra
gatecse-2012
set-theory&algebra
functions
normal
+
–
104
votes
113
GATE CSE 2012 | Question: 39
A list of $n$ strings, each of length $n$, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation is $O (n \log n) $ $ O(n^{2} \log n) $ $ O(n^{2} + \log n) $ $ O(n^{2}) $
A list of $n$ strings, each of length $n$, is sorted into lexicographic order using the merge-sort algorithm. The worst case running time of this computation is$O (n \log...
28.6k
views
answered
Sep 27, 2014
Algorithms
gatecse-2012
algorithms
sorting
normal
+
–
7
votes
114
GATE CSE 2013 | Question: 58
What will be the maximum sum of $44, 42, 40, \dots$ ? $502$ $504$ $506$ $500$
What will be the maximum sum of $44, 42, 40, \dots$ ?$502$$504$$506$$500$
5.6k
views
answered
Sep 26, 2014
Quantitative Aptitude
gatecse-2013
quantitative-aptitude
easy
arithmetic-series
+
–
43
votes
115
GATE CSE 2013 | Question: 61
Find the sum of the expression $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+............+\frac{1}{\sqrt{80}+\sqrt{81}}$ $7$ $8$ $9$ $10$
Find the sum of the expression$\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+............+\frac{1}{\sqrt{80}+\sqrt{81}}$$7$$8$$9$$10...
7.5k
views
answered
Sep 26, 2014
Quantitative Aptitude
gatecse-2013
quantitative-aptitude
normal
number-series
+
–
24
votes
116
GATE CSE 2013 | Question: 62
Out of all the $2$-digit integers between $1$ and $100,$ a $2$-digit number has to be selected at random. What is the probability that the selected number is not divisible by $7$ ? $\left(\dfrac{13}{90}\right)$ $\left(\dfrac{12}{90}\right)$ $\left(\dfrac{78}{90}\right)$ $\left(\dfrac{77}{90}\right)$
Out of all the $2$-digit integers between $1$ and $100,$ a $2$-digit number has to be selected at random. What is the probability that the selected number is not divisibl...
3.8k
views
answered
Sep 26, 2014
Quantitative Aptitude
gatecse-2013
quantitative-aptitude
easy
probability
factors
+
–
18
votes
117
GATE CSE 2013 | Question: 64
A tourist covers half of his journey by train at $60\;\text{km/h}$, half of the remainder by bus at $30\;\text{km/h}$ and the rest by cycle at $10\;\text{km/h}$. The average speed of the tourist in $\text{km/h}$ during his entire journey is $36$ $30$ $24$ $18$
A tourist covers half of his journey by train at $60\;\text{km/h}$, half of the remainder by bus at $30\;\text{km/h}$ and the rest by cycle at $10\;\text{km/h}$. The aver...
5.1k
views
answered
Sep 26, 2014
Quantitative Aptitude
gatecse-2013
quantitative-aptitude
easy
speed-time-distance
+
–
–5
votes
118
GATE CSE 2014 Set 1 | Question: 14
Let $P$ be quicksort program to sort numbers in ascending order using the first element as the pivot. Let $t_1$ and $t_2$ be the number of comparisons made by P for the inputs $[1 \ 2 \ 3 \ 4 \ 5]$ and $[4 \ 1 \ 5 \ 3 \ 2]$ respectively. Which one of the following holds? $t_1 = 5$ $t_1 < t_2$ $t_1>t_2$ $t_1 = t_2$
Let $P$ be quicksort program to sort numbers in ascending order using the first element as the pivot. Let $t_1$ and $t_2$ be the number of comparisons made by P for the i...
19.1k
views
answered
Sep 26, 2014
Algorithms
gatecse-2014-set1
algorithms
sorting
easy
+
–
11
votes
119
GATE CSE 2014 Set 1 | Question: 16
Consider the finite automaton in the following figure: What is the set of reachable states for the input string $0011$? $\{q_0,q_1,q_2\}$ $\{q_0,q_1\}$ $\{q_0,q_1,q_2,q_3\}$ $\{q_3\}$
Consider the finite automaton in the following figure: What is the set of reachable states for the input string $0011$?$\{q_0,q_1,q_2\}$$\{q_0,q_1\}$$\{q_0,q_1,q_2,q_3\}$...
14.8k
views
answered
Sep 26, 2014
Theory of Computation
gatecse-2014-set1
theory-of-computation
finite-automata
easy
+
–
2
votes
120
GATE CSE 1998 | Question: 1.12
The string $1101$ does not belong to the set represented by $110^*(0 + 1)$ $1(0 + 1)^*101$ $(10)^*(01)^*(00 + 11)^*$ $(00 + (11)^*0)^*$
The string $1101$ does not belong to the set represented by$110^*(0 + 1)$$1(0 + 1)^*101$$(10)^*(01)^*(00 + 11)^*$$(00 + (11)^*0)^*$
22.9k
views
answered
Sep 26, 2014
Theory of Computation
gate1998
theory-of-computation
regular-expression
easy
multiple-selects
+
–
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