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Previous GATE
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Previous GATE Questions in Engineering Mathematics
37
votes
8
answers
541
GATE CSE 2008 | Question: 27
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer ... what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
Kathleen
asked
in
Probability
Sep 11, 2014
by
Kathleen
7.6k
views
gatecse-2008
probability
normal
conditional-probability
36
votes
2
answers
542
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
Kathleen
asked
in
Calculus
Sep 11, 2014
by
Kathleen
8.4k
views
gatecse-2008
calculus
maxima-minima
easy
17
votes
8
answers
543
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Kathleen
asked
in
Combinatory
Sep 11, 2014
by
Kathleen
5.5k
views
gatecse-2008
combinatory
easy
summation
39
votes
7
answers
544
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 $\frac{n}{3}$
Kathleen
asked
in
Graph Theory
Sep 11, 2014
by
Kathleen
55.0k
views
gatecse-2008
graph-theory
normal
graph-planarity
29
votes
6
answers
545
GATE CSE 2008 | Question: 3
The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $-1$ any real number
Kathleen
asked
in
Linear Algebra
Sep 11, 2014
by
Kathleen
10.0k
views
gatecse-2008
easy
linear-algebra
system-of-equations
28
votes
8
answers
546
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
Kathleen
asked
in
Set Theory & Algebra
Sep 11, 2014
by
Kathleen
9.2k
views
gatecse-2008
normal
set-theory&algebra
set-theory
25
votes
9
answers
547
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
Kathleen
asked
in
Calculus
Sep 11, 2014
by
Kathleen
10.0k
views
gatecse-2008
calculus
limits
easy
1
vote
1
answer
548
GATE CSE 1993 | Question: 01.5
Fourier series of the periodic function (period 2π) defined by ... $\frac{{\pi }^2 }{4}$ $\frac{{\pi }^2 }{6}$ $\frac{{\pi }^2 }{8}$ $\frac{{\pi }^2 }{12}$
srinath
asked
in
Calculus
Sep 2, 2014
by
srinath
2.7k
views
gate1993
calculus
normal
out-of-gate-syllabus
multiple-selects
78
votes
6
answers
549
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Arjun
asked
in
Mathematical Logic
Sep 2, 2014
by
Arjun
16.4k
views
gate1992
mathematical-logic
normal
first-order-logic
79
votes
5
answers
550
GATE CSE 2007 | Question: 25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$
priya
asked
in
Linear Algebra
Sep 2, 2014
by
priya
16.6k
views
gatecse-2007
eigen-value
linear-algebra
difficult
45
votes
3
answers
551
GATE CSE 2013 | Question: 47
Which one of the following is NOT logically equivalent to $¬∃x(∀ y (α)∧∀z(β ))$ ? $∀ x(∃ z(¬β )→∀ y(α))$ $∀x(∀ z(β )→∃ y(¬α))$ $∀x(∀ y(α)→∃z(¬β ))$ $∀x(∃ y(¬α)→∃z(¬β ))$
gatecse
asked
in
Mathematical Logic
Aug 21, 2014
by
gatecse
11.8k
views
mathematical-logic
normal
marks-to-all
gatecse-2013
first-order-logic
31
votes
2
answers
552
GATE CSE 2013 | Question: 2
Suppose $p$ is the number of cars per minute passing through a certain road junction between $5$ PM and $6$ PM, and $p$ has a Poisson distribution with mean $3$. What is the probability of observing fewer than $3$ cars during any given minute in this interval? $\dfrac{8}{(2e^{3})}$ $\dfrac{9}{(2e^{3})}$ $\dfrac{17}{(2e^{3})}$ $\dfrac{26}{(2e^{3})}$
gatecse
asked
in
Probability
Aug 7, 2014
by
gatecse
8.9k
views
gatecse-2013
probability
poisson-distribution
normal
33
votes
3
answers
553
GATE CSE 2013 | Question: 1
A binary operation $\oplus$ on a set of integers is defined as $x \oplus y = x^{2}+y^{2}$. Which one of the following statements is TRUE about $\oplus$? Commutative but not associative Both commutative and associative Associative but not commutative Neither commutative nor associative
gatecse
asked
in
Set Theory & Algebra
Aug 7, 2014
by
gatecse
7.5k
views
gatecse-2013
set-theory&algebra
easy
binary-operation
26
votes
3
answers
554
GATE CSE 2012 | Question: 17
Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to $3$ $4$ $5$ $6$
gatecse
asked
in
Graph Theory
Aug 5, 2014
by
gatecse
10.0k
views
gatecse-2012
graph-theory
graph-planarity
normal
33
votes
4
answers
555
GATE CSE 2012 | Question: 13
What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” $\exists x (\text{real}(x) \lor \text{rational}(x))$ $\forall x (\text{real}(x) \to \text{rational}(x))$ $\exists x (\text{real}(x) \wedge \text{rational}(x))$ $\exists x (\text{rational}(x) \to \text{real}(x))$
gatecse
asked
in
Mathematical Logic
Aug 5, 2014
by
gatecse
8.6k
views
gatecse-2012
mathematical-logic
easy
first-order-logic
32
votes
5
answers
556
GATE CSE 2012 | Question: 11
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
gatecse
asked
in
Linear Algebra
Aug 5, 2014
by
gatecse
11.3k
views
gatecse-2012
linear-algebra
eigen-value
60
votes
4
answers
557
GATE CSE 2012 | Question: 9
Consider the function $f(x) = \sin(x)$ in the interval $x =\left[\frac{\pi}{4},\frac{7\pi}{4}\right]$. The number and location(s) of the local minima of this function are One, at $\dfrac{\pi}{2}$ One, at $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{2}$ and $\dfrac{3\pi}{2}$ Two, at $\dfrac{\pi}{4}$ and $\dfrac{3\pi}{2}$
gatecse
asked
in
Calculus
Aug 5, 2014
by
gatecse
13.9k
views
gatecse-2012
calculus
maxima-minima
normal
33
votes
5
answers
558
GATE CSE 2012 | Question: 1
Consider the following logical inferences. $I_{1}$: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. $I_{2}$: If it rains then the cricket match will not be played. It did not rain. Inference: ... $I_{2}$ is a correct inference Both $I_{1}$ and $I_{2}$ are not correct inferences
gatecse
asked
in
Mathematical Logic
Aug 5, 2014
by
gatecse
9.1k
views
gatecse-2012
mathematical-logic
easy
logical-reasoning
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