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0
votes
31
Factor of determinant with identical row
How the following fact applies to determinants (I came across it while solving problems): Consider A is a n× n matrix, the elements of which are real (or complex) polynomials in x. If r rows of the determinant become identical when x ... is collapsing of rows of matrix (into one row) with order of its factors. Am I missing some stupid fact here?
How the following fact applies to determinants (I came across it while solving problems):Consider A is a n× n matrix, the elements of which are real (or complex) po...
1.9k
views
answered
Dec 6, 2014
Linear Algebra
matrix
linear-algebra
polynomials
+
–
11
votes
32
GATE IT 2004 | Question: 7
Which one of the following regular expressions is NOT equivalent to the regular expression $(a + b + c)^*$? $(a^* + b^* + c^*)^*$ $(a^*b^*c^*)^*$ $((ab)^* + c^*)^*$ $(a^*b^* + c^*)^*$
Which one of the following regular expressions is NOT equivalent to the regular expression $(a + b + c)^*$?$(a^* + b^* + c^*)^*$$(a^*b^*c^*)^*$$((ab)^* + c^*)^*$$(a^*b^* ...
8.8k
views
answered
Dec 2, 2014
Theory of Computation
gateit-2004
theory-of-computation
regular-expression
normal
+
–
6
votes
33
Max no of edges in disconnected graph
In a simple undirected graph with n vertices what is maximum no of edges that you can have keeping the graph disconnected? A) nC2 -1 B) nC2 C) n-1C2 D n-1C2 - 1 Ans is C) ....Please explain how?
In a simple undirected graph with n vertices what is maximum no of edges that you can have keeping the graph disconnected?A) nC2 -1B) nC2C) n-1C2D n-1C2 - 1Ans is C) .......
8.2k
views
answered
Dec 2, 2014
65
votes
34
GATE CSE 2004 | Question: 84
The recurrence equation $ T(1) = 1$ $T(n) = 2T(n-1) + n, n \geq 2$ evaluates to $2^{n+1} - n - 2$ $2^n - n$ $2^{n+1} - 2n - 2$ $2^n + n $
The recurrence equation$ T(1) = 1$$T(n) = 2T(n-1) + n, n \geq 2$evaluates to$2^{n+1} - n - 2$$2^n - n$$2^{n+1} - 2n - 2$$2^n + n $
17.3k
views
answered
Nov 30, 2014
Algorithms
gatecse-2004
algorithms
recurrence-relation
normal
+
–
40
votes
35
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...
15.5k
views
answered
Nov 21, 2014
Graph Theory
gatecse-2003
graph-theory
normal
degree-of-graph
+
–
28
votes
36
GATE CSE 1995 | Question: 24
Prove that in finite graph, the number of vertices of odd degree is always even.
Prove that in finite graph, the number of vertices of odd degree is always even.
5.7k
views
answered
Nov 21, 2014
Graph Theory
gate1995
graph-theory
degree-of-graph
proof
descriptive
+
–
39
votes
37
GATE IT 2004 | Question: 37
What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$? $10$ $11$ $18$ $19$
What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$?$10$$11$...
12.9k
views
answered
Nov 21, 2014
Graph Theory
gateit-2004
graph-theory
graph-connectivity
normal
+
–
4
votes
38
GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is$3...
30.4k
views
answered
Nov 21, 2014
Probability
gateit-2005
probability
binomial-distribution
expectation
normal
+
–
19
votes
39
GATE IT 2004 | Question: 6
What values of x, y and z satisfy the following system of linear equations? $\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}$ $x = 6$, $y = 3$, $z = 2$ $x = 12$, $y = 3$, $z = - 4$ $x = 6$, $y = 6$, $z = - 4$ $x = 12$, $y = - 3$, $z = 0$
What values of x, y and z satisfy the following system of linear equations?$$\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bm...
6.4k
views
answered
Nov 21, 2014
Linear Algebra
gateit-2004
linear-algebra
system-of-equations
easy
+
–
12
votes
40
GATE IT 2004 | Question: 8
What is the minimum number of $\text{NAND}$ gates required to implement a $2\text{-input EXCLUSIVE-OR}$ function without using any other logic gate? $2$ $4$ $5$ $6$
What is the minimum number of $\text{NAND}$ gates required to implement a $2\text{-input EXCLUSIVE-OR}$ function without using any other logic gate?$2$$4$$5$$6$
11.2k
views
answered
Nov 21, 2014
Digital Logic
gateit-2004
digital-logic
min-no-gates
normal
+
–
54
votes
41
GATE IT 2004 | Question: 13
Let $P$ be a singly linked list. Let $Q$ be the pointer to an intermediate node $x$ in the list. What is the worst-case time complexity of the best-known algorithm to delete the node $x$ from the list ? $O(n)$ $O(\log^2 n)$ $O(\log n)$ $O(1)$
Let $P$ be a singly linked list. Let $Q$ be the pointer to an intermediate node $x$ in the list. What is the worst-case time complexity of the best-known algorithm to del...
24.6k
views
answered
Nov 21, 2014
DS
gateit-2004
data-structures
linked-list
normal
ambiguous
+
–
19
votes
42
GATE CSE 1997 | Question: 1.9
The conditional expansion facility of macro processor is provided to test a condition during the execution of the expanded program to expand certain model statements depending upon the value of a condition during the execution of the expanded ... recursion to expand certain model statements depending upon the value of a condition during the process of macro expansion
The conditional expansion facility of macro processor is provided totest a condition during the execution of the expanded programto expand certain model statements depend...
5.1k
views
answered
Nov 21, 2014
Compiler Design
gate1997
compiler-design
macros
easy
+
–
14
votes
43
GATE CSE 2010 | Question: 37
The program below uses six temporary variables $a, b, c, d, e, f$. a = 1 b = 10 c = 20 d = a + b e = c + d f = c + e b = c + e e = b + f d = 5 + e return d + f Assuming that all operations take their operands from registers, what is the minimum number of registers needed to execute this program without spilling? $2$ $3$ $4$ $6$
The program below uses six temporary variables $a, b, c, d, e, f$.a = 1 b = 10 c = 20 d = a + b e = c + d f = c + e b = c + e e = b + f d = 5 + e return d + fAssuming tha...
21.5k
views
answered
Nov 21, 2014
Compiler Design
gatecse-2010
compiler-design
target-code-generation
register-allocation
normal
+
–
11
votes
44
GATE CSE 1996 | Question: 2.16
Which of the following macros can put a macro assembler into an infinite loop? .MACRO M1, X .IF EQ, X ;if X=0 then M1 X + 1 .ENDC .IF NE, X ;if X ≠ O then .WORD X ;address (X) is stored here .ENDC .ENDM .MACRO M2, X .IF EQ, X M2 X .ENDC .IF NE, X .WORD X + 1 .ENDC .ENDM (ii) only (i) only both (i) and (ii) None of the above
Which of the following macros can put a macro assembler into an infinite loop?.MACRO M1, X .IF EQ, X ;if X=0 then M1 X + 1 .ENDC .IF NE, X ;if X ≠ O then .WORD X ;addre...
3.7k
views
answered
Nov 21, 2014
Compiler Design
gate1996
compiler-design
macros
normal
+
–
14
votes
45
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...
34.6k
views
answered
Sep 12, 2014
Graph Theory
gatecse-2012
graph-theory
normal
marks-to-all
counting
+
–
3
votes
46
GATE CSE 2008 | Question: 22
The Newton-Raphson iteration $x_{n+1} = \frac{1}{2}\left(x_n+\frac{R}{x_n}\right)$ can be used to compute the square of R reciprocal of R square root of R logarithm of R
The Newton-Raphson iteration $x_{n+1} = \frac{1}{2}\left(x_n+\frac{R}{x_n}\right)$ can be used to compute thesquare of R reciprocal of R square root of R l...
5.2k
views
answered
Sep 12, 2014
Numerical Methods
gatecse-2008
newton-raphson
normal
numerical-methods
out-of-syllabus-now
+
–
12
votes
47
GATE CSE 2008 | Question: 23
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$
Which of the following statements is true for every planar graph on $n$ vertices?The graph is connectedThe graph is EulerianThe graph has a vertex-cover of size at most $...
57.2k
views
answered
Sep 12, 2014
Graph Theory
gatecse-2008
graph-theory
normal
graph-planarity
+
–
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