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Featured
Most answered questions in Engineering Mathematics
20
votes
8
answers
81
TIFR CSE 2015 | Part A | Question: 7
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \times 8$ chessboard? $64$ $65$ $204$ $144$ $256$
A $1 \times 1$ chessboard has one square, a $2 \times 2$ chessboard has five squares. Continuing along this fashion, what is the number of squares on the regular $8 \time...
makhdoom ghaya
3.1k
views
makhdoom ghaya
asked
Dec 5, 2015
Combinatory
tifr2015
combinatory
counting
+
–
74
votes
8
answers
82
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...
Ishrat Jahan
33.0k
views
Ishrat Jahan
asked
Nov 3, 2014
Probability
gateit-2005
probability
binomial-distribution
expectation
normal
+
–
37
votes
8
answers
83
GATE IT 2005 | Question: 31
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which of the following statements is always true for all such functions $f$ and $g$? ... is onto $h$ is onto $\implies$ $f$ is onto $h$ is onto $\implies$ $g$ is onto $h$ is onto $\implies$ $f$ and $g$ are onto
Let $f$ be a function from a set $A$ to a set $B$, $g$ a function from $B$ to $C$, and $h$ a function from $A$ to $C$, such that $h(a) = g(f(a))$ for all $a ∈ A.$ Which...
Ishrat Jahan
8.9k
views
Ishrat Jahan
asked
Nov 3, 2014
Set Theory & Algebra
gateit-2005
set-theory&algebra
functions
normal
+
–
29
votes
8
answers
84
GATE IT 2005 | Question: 3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}$ $-1$ $0$ $1$ $2$
The determinant of the matrix given below is$$\begin{bmatrix}0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1\end{bmatrix}$$$-1$$0$$1$$2$
Ishrat Jahan
23.3k
views
Ishrat Jahan
asked
Nov 3, 2014
Linear Algebra
gateit-2005
linear-algebra
normal
determinant
+
–
25
votes
8
answers
85
GATE IT 2004 | Question: 5
What is the maximum number of edges in an acyclic undirected graph with $n$ vertices? $n-1$ $n$ $n+1$ $2n-1$
What is the maximum number of edges in an acyclic undirected graph with $n$ vertices?$n-1$$n$$n+1$$2n-1$
Ishrat Jahan
7.0k
views
Ishrat Jahan
asked
Nov 1, 2014
Graph Theory
gateit-2004
graph-theory
graph-connectivity
normal
+
–
26
votes
8
answers
86
GATE IT 2006 | Question: 26
What are the eigenvalues of the matrix $P$ given below $P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$ $a, a -√2, a + √2$ $a, a, a$ $0, a, 2a$ $-a, 2a, 2a$
What are the eigenvalues of the matrix $P$ given below$$P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$$ $a, a -√2, a + √2...
Ishrat Jahan
7.5k
views
Ishrat Jahan
asked
Oct 31, 2014
Linear Algebra
gateit-2006
linear-algebra
eigen-value
normal
+
–
25
votes
8
answers
87
GATE IT 2007 | Question: 80
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy-$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line ... or the smallest $y$-coordinate among all the points The difference between $x$-coordinates $P_{a}$ and $P_{b}$ is minimum None of the above
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy-$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the...
Ishrat Jahan
5.3k
views
Ishrat Jahan
asked
Oct 30, 2014
Linear Algebra
gateit-2007
cartesian-coordinates
+
–
61
votes
8
answers
88
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvect...
Ishrat Jahan
16.3k
views
Ishrat Jahan
asked
Oct 29, 2014
Linear Algebra
gateit-2007
linear-algebra
eigen-value
normal
+
–
33
votes
8
answers
89
GATE IT 2008 | Question: 28
Consider the following Hasse diagrams. Which all of the above represent a lattice? (i) and (iv) only (ii) and (iii) only (iii) only (i), (ii) and (iv) only
Consider the following Hasse diagrams. Which all of the above represent a lattice?(i) and (iv) only(ii) and (iii) only(iii) only(i), (ii) and (iv) only
Ishrat Jahan
15.1k
views
Ishrat Jahan
asked
Oct 28, 2014
Set Theory & Algebra
gateit-2008
set-theory&algebra
lattice
normal
+
–
26
votes
8
answers
90
GATE CSE 1996 | Question: 1.1
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to $A \cup B$ $A^c \cup B^c$ $A \cap B$ $A^c \cap B^c$
Let $A$ and $B$ be sets and let $A^c$ and $B^c$ denote the complements of the sets $A$ and $B$. The set $(A-B) \cup (B-A) \cup (A \cap B)$ is equal to$A \cup B$$A^c \cup ...
Kathleen
6.1k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
easy
set-theory
+
–
25
votes
8
answers
91
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 $...
Kathleen
4.6k
views
Kathleen
asked
Oct 4, 2014
Probability
gate1994
probability
normal
conditional-probability
fill-in-the-blanks
+
–
77
votes
8
answers
92
GATE CSE 2014 Set 2 | Question: 50
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum element in the symmetric difference of the two sets is in $U$. Consider the ... $S1$ is true and $S2$ is false $S2$ is true and $S1$ is false Neither $S1$ nor $S2$ is true
Consider the following relation on subsets of the set $S$ of integers between $1$ and $2014$. For two distinct subsets $U$ and $V$ of $S$ we say $U\:<\:V$ if the minimum ...
go_editor
15.9k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set2
set-theory&algebra
normal
set-theory
+
–
99
votes
8
answers
93
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...
go_editor
37.4k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
+
–
43
votes
8
answers
94
GATE CSE 2014 Set 2 | Question: 4
If the matrix $A$ is such that $A= \begin{bmatrix} 2\\ −4\\7\end{bmatrix}\begin{bmatrix}1& 9& 5\end{bmatrix}$ then the determinant of $A$ is equal to ______.
If the matrix $A$ is such that $$A= \begin{bmatrix} 2\\ −4\\7\end{bmatrix}\begin{bmatrix}1& 9& 5\end{bmatrix}$$ then the determinant of $A$ is equal to ______.
go_editor
12.9k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set2
linear-algebra
numerical-answers
easy
determinant
+
–
30
votes
8
answers
95
GATE CSE 1998 | Question: 1.1
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is $\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}$
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is$\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}...
Kathleen
8.5k
views
Kathleen
asked
Sep 25, 2014
Probability
gate1998
probability
easy
+
–
53
votes
8
answers
96
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
Arjun
14.2k
views
Arjun
asked
Sep 24, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
59
votes
8
answers
97
GATE CSE 2013 | Question: 26
The line graph $L(G)$ of a simple graph $G$ is defined as follows: There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$. For any two edges $e$ and $e'$ in $G$, $L(G)$ has an edge between $v(e)$ and $v(e')$, if and only if ... planar graph is planar. (S) The line graph of a tree is a tree. $P$ only $P$ and $R$ only $R$ only $P, Q$ and $S$ only
The line graph $L(G)$ of a simple graph $G$ is defined as follows:There is exactly one vertex $v(e)$ in $L(G)$ for each edge $e$ in $G$.For any two edges $e$ and $e'$ in ...
Arjun
19.1k
views
Arjun
asked
Sep 24, 2014
Graph Theory
gatecse-2013
graph-theory
normal
graph-connectivity
+
–
48
votes
8
answers
98
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...
Kathleen
12.6k
views
Kathleen
asked
Sep 21, 2014
Combinatory
gatecse-2007
combinatory
+
–
43
votes
8
answers
99
GATE CSE 2007 | Question: 22
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ ... $\forall x \, \Bigl ( \text{ Graph}(x) \implies \lnot \text{ Connected}(x) \Bigr )$
Let $\text{ Graph}(x)$ be a predicate which denotes that $x$ is a graph. Let $\text{ Connected}(x)$ be a predicate which denotes that $x$ is connected. Which of the follo...
Kathleen
8.9k
views
Kathleen
asked
Sep 21, 2014
Mathematical Logic
gatecse-2007
mathematical-logic
easy
first-order-logic
+
–
28
votes
8
answers
100
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$? $i$ $i+1$ $2i$ $2^i$
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$?$i$$i+1$$2i$$2^i$
gatecse
8.2k
views
gatecse
asked
Sep 21, 2014
Combinatory
gatecse-2005
normal
generating-functions
+
–
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