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Answers by suraj
4
votes
1
GATE CSE 1998 | Question: 9
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one ...
3.3k
views
answered
Jun 20, 2019
Linear Algebra
gate1998
linear-algebra
system-of-equations
descriptive
+
–
0
votes
2
GATE CSE 2018 | Question: 30
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ ... $\mid i-j \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements.No...
27.3k
views
answered
Feb 16, 2018
Algorithms
gatecse-2018
algorithms
graph-algorithms
graph-search
normal
2-marks
+
–
2
votes
3
Sorting
Two unsorted arrays of size m and n are to be sorted into a single array, what is best case time complexity?
Two unsorted arrays of size m and n are to be sorted into a single array, what is best case time complexity?
937
views
answered
Nov 20, 2017
Algorithms
algorithms
sorting
time-complexity
+
–
9
votes
4
Maths: Linear Algebra
Any shortcut?
Any shortcut?
637
views
answered
Nov 6, 2017
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
127
votes
5
GATE CSE 2017 Set 1 | Question: 51
Consider a $2$-way set associative cache with $256$ blocks and uses $\text{LRU}$ replacement. Initially the cache is empty. Conflict misses are those misses which occur due to the contention of multiple blocks for the same cache set. Compulsory ... $10$ times. The number of conflict misses experienced by the cache is _________ .
Consider a $2$-way set associative cache with $256$ blocks and uses $\text{LRU}$ replacement. Initially the cache is empty. Conflict misses are those misses which occur d...
38.6k
views
answered
Feb 17, 2017
CO and Architecture
gatecse-2017-set1
co-and-architecture
cache-memory
conflict-misses
normal
numerical-answers
+
–
50
votes
6
GATE CSE 2017 Set 1 | Question: 31
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements. One eigenvalue must be in $\left [ -5,5 \right ]$ The eigenvalue ... than $5$ Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements.One eigenvalu...
49.6k
views
answered
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
eigen-value
normal
+
–
25
votes
7
GATE CSE 2017 Set 1 | Question: 30
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $...
14.0k
views
answered
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
normal
vector-space
+
–
84
votes
8
GATE CSE 2017 Set 1 | Question: 3
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ ... has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$.Consider the set of linear equations$...
20.3k
views
answered
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
system-of-equations
normal
+
–
12
votes
9
GATE_2014 ME
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a ≠ b then x1y1 + x2y2 + x3y3 is a) a b) b c) ab d) 0
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne...
2.4k
views
answered
Mar 7, 2016
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
10
votes
10
GATE2013 EE: GA-2
In the summer of $2012$, in New Delhi, the mean temperature of Monday to Wednesday was $41°C$ and of Tuesday to Thursday was $43°C$. If the temperature on Thursday was $15\%$ higher than that of Monday, then the temperature in $°C$ on Thursday was $40$ $43$ $46$ $49$
In the summer of $2012$, in New Delhi, the mean temperature of Monday to Wednesday was $41°C$ and of Tuesday to Thursday was $43°C$. If the temperature on Thursday was ...
6.9k
views
answered
Feb 22, 2016
Quantitative Aptitude
gate2013-ee
quantitative-aptitude
percentage
+
–
0
votes
11
A is a 4-square matrix and A 5 = 0. Then
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 = a) I b) -I c) 0 d) A
A is a 4-square matrix and A_5 (a raised to the power of 5) = 0. Then A_4 =a) Ib) -Ic) 0d) A
4.5k
views
answered
Sep 1, 2015
Linear Algebra
matrix
linear-algebra
+
–
4
votes
12
prove that y=cos2x+6 is not a one one and onto function.
693
views
answered
Apr 23, 2015
0
votes
13
is there any short cut to find the determinant of the matrix
1 0 0 0 0 2 0 1 0 0 2 0 0 0 1 2 0 0 0 0 2 1 0 0 0 2 0 0 1 0 2 0 0 0 0 1
1 0 0 0 0 20 1 0 0 2 00 0 1 2 0 00 0 2 1 0 00 2 0 0 1 02 0 0 0 0 1
941
views
answered
Apr 23, 2015
39
votes
14
GATE CSE 1999 | Question: 1.1
Suppose that the expectation of a random variable $X$ is $5$. Which of the following statements is true? There is a sample point at which $X$ has the value $5$. There is a sample point at which $X$ has value greater than $5$. There is a sample point at which $X$ has a value greater than equal to $5$. None of the above.
Suppose that the expectation of a random variable $X$ is $5$. Which of the following statements is true?There is a sample point at which $X$ has the value $5$.There is a ...
10.1k
views
answered
Apr 13, 2015
Probability
gate1999
probability
expectation
easy
+
–
4
votes
15
Value of a^2+b^2 ?
500
views
answered
Mar 31, 2015
Linear Algebra
complex-number
+
–
4
votes
16
GATE CSE 2015 Set 3 | Question: GA-7
The head of newly formed government desires to appoint five of the six selected members $P, Q, R, S, T$ and $U$ to portfolios of Home, Power, Defense, Telecom, and Finance. U does not want any portfolio if $S$ gets one of the five. $R$ wants either Home ... -Power, $T$-Defense, $S$-Telecom, $U$-Finance $Q$-Home, $U$-Power, $T$-Defense, $R$-Telecom, $P$-Finance
The head of newly formed government desires to appoint five of the six selected members $P, Q, R, S, T$ and $U$ to portfolios of Home, Power, Defense, Telecom, and Financ...
4.3k
views
answered
Feb 13, 2015
Analytical Aptitude
gatecse-2015-set3
analytical-aptitude
normal
logical-reasoning
+
–
70
votes
17
GATE CSE 2005 | Question: 11
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is: $12$ $8$ less than $8$ more than $12$
Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of G is $8$. Then, the size of the maximum independent set of $G$ is:$1...
11.7k
views
answered
Feb 6, 2015
Graph Theory
gatecse-2005
graph-theory
normal
graph-connectivity
+
–
2
votes
18
GATE CSE 2007 | Question: 37, ISRO2009-37
Consider a pipelined processor with the following four stages: IF: Instruction Fetch ID: Instruction Decode and Operand Fetch EX: Execute WB: Write Back The IF, ID and WB stages take one clock cycle each to complete the operation. The number of clock cycles for the EX ... $ R5$-$R4} \\ \end{array}$ $7$ $8$ $10$ $14$
Consider a pipelined processor with the following four stages:IF: Instruction FetchID: Instruction Decode and Operand FetchEX: ExecuteWB: Write BackThe IF, ID and WB stag...
16.0k
views
answered
Feb 5, 2015
CO and Architecture
gatecse-2007
co-and-architecture
pipelining
normal
isro2009
+
–
15
votes
19
TIFR CSE 2010 | Part A | Question: 18
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ? $2^{n+1}$ $2^{2n}$ $3^{n}$ $2^{n} + 1$ $3^{n + 1}$
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ?$2^{n+1}$$2^{2n}$$3^{n}$$2^{n} + 1$$3^{n + 1}...
4.7k
views
answered
Feb 2, 2015
Set Theory & Algebra
tifr2010
set-theory
+
–
2
votes
20
dgital
Which of the following multiplier pattern of boothe algo gives better performance and how: 1..01111111110 2..1111100011111 3..011111011111 4..111111111000
Which of the following multiplier pattern of boothe algo gives better performance and how:1..011111111102..11111000111113..0111110111114..111111111000
899
views
answered
Feb 2, 2015
69
votes
21
GATE CSE 2009 | Question: 28
Consider a $4$ stage pipeline processor. The number of cycles needed by the four instructions $I1, I2, I3, I4$ in stages $S1, S2, S3, S4$ ... the number of cycles needed to execute the following loop? For (i=1 to 2) {I1; I2; I3; I4;} $16$ $23$ $28$ $30$
Consider a $4$ stage pipeline processor. The number of cycles needed by the four instructions $I1, I2, I3, I4$ in stages $S1, S2, S3, S4$ is shown below:$$\begin{array}{|...
34.4k
views
answered
Jan 30, 2015
CO and Architecture
gatecse-2009
co-and-architecture
pipelining
normal
+
–
5
votes
22
Suppose the probability that x is the ith element in a list of n distinct integers is i/[n(n + 1)].
Suppose the probability that x is the ith element in a list of n distinct integers is i/[n(n + 1)]. Find the average number of comparisons used by the linear search algorithm to find x or to determine that it is not in the list.
Suppose the probability that x is the ith element in a list of n distinct integers is i/[n(n + 1)]. Find the average number of comparisons used by the linear search algor...
2.3k
views
answered
Jan 29, 2015
Probability
probability
+
–
2
votes
23
do we need register to allocate to all a,b,c initially.....if following is program sequence
494
views
answered
Jan 29, 2015
Compiler Design
register-allocation
+
–
6
votes
24
Self Doubt: Permutations & Combinations
How many solutions are there to the equation $x+y+z=17$ in positive integers? $120$ $171$ $180$ $121$
How many solutions are there to the equation $x+y+z=17$ in positive integers?$120$$171$$180$$121$
3.4k
views
answered
Jan 29, 2015
Combinatory
self-doubt
combinatory
+
–
98
votes
25
GATE CSE 2014 Set 1 | Question: 47
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ ... the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$
A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true?There exis...
21.0k
views
answered
Jan 16, 2015
Calculus
gatecse-2014-set1
calculus
continuity
normal
+
–
32
votes
26
GATE IT 2008 | Question: 45
For the undirected, weighted graph given below, which of the following sequences of edges represents a correct execution of Prim's algorithm to construct a Minimum Spanning Tree? $\text{(a, b), (d, f), (f, c), (g, i), (d, a), (g, h), (c, e), (f, h)}$ ... $\text{(h, g), (g, i), (h, f), (f, c), (f, d), (d, a), (a, b), (c, e)}$
For the undirected, weighted graph given below, which of the following sequences of edges represents a correct execution of Prim's algorithm to construct a Minimum Span...
13.4k
views
answered
Jan 7, 2015
Algorithms
gateit-2008
algorithms
graph-algorithms
spanning-tree
normal
prims-algorithm
+
–
104
votes
27
GATE CSE 2014 Set 1 | Question: 42
Consider the following pseudo code. What is the total number of multiplications to be performed? D = 2 for i = 1 to n do for j = i to n do for k = j + 1 to n do D = D * 3 Half of the product of the $3$ consecutive integers. One-third of the product of the $3$ consecutive integers. One-sixth of the product of the $3$ consecutive integers. None of the above.
Consider the following pseudo code. What is the total number of multiplications to be performed?D = 2 for i = 1 to n do for j = i to n do for k = j + 1 to n do D = D * 3H...
34.6k
views
answered
Jan 4, 2015
Algorithms
gatecse-2014-set1
algorithms
time-complexity
normal
+
–
1
votes
28
What is the complexity of finding 50th smallest element in an already constructed binary min-heap?
What is the complexity of finding $50^{th}$ smallest element in an already constructed binary min-heap? $\Theta(1)$ $\Theta (\log n)$ $\Theta (n)$ $\Theta (n \log n)$
What is the complexity of finding $50^{th}$ smallest element in an already constructed binary min-heap?$\Theta(1)$$\Theta (\log n)$$\Theta (n)$$\Theta (n \log n)$
3.7k
views
answered
Dec 28, 2014
DS
data-structures
binary-heap
time-complexity
+
–
3
votes
29
Prove that maximam number of edges in a planer graph with n vertices is 3n-6
630
views
answered
Dec 17, 2014
48
votes
30
GATE CSE 2001 | Question: 9
A CPU has $32-bit$ memory address and a $256 \ KB$ cache memory. The cache is organized as a $4-way$ set associative cache with cache block size of $16$ bytes. What is the number of sets in the cache? What is the size (in bits) of ... are required to find the byte offset within a cache block? What is the total amount of extra memory (in bytes) required for the tag bits?
A CPU has $32-bit$ memory address and a $256 \ KB$ cache memory. The cache is organized as a $4-way$ set associative cache with cache block size of $16$ bytes.What is the...
13.1k
views
answered
Dec 15, 2014
CO and Architecture
gatecse-2001
co-and-architecture
cache-memory
normal
descriptive
+
–
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