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Previous GATE
Featured
Previous GATE Questions in Engineering Mathematics
24
votes
3
answers
481
GATE CSE 2009 | Question: 25
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $ $0$ $1$ $\ln 2$ $1/2 \ln 2$
$\int^{\pi/4}_0 (1-\tan x)/(1+\tan x)\,dx $$0$$1$ $\ln 2$$1/2 \ln 2$
gatecse
5.8k
views
gatecse
asked
Sep 15, 2014
Calculus
gatecse-2009
calculus
integration
normal
+
–
34
votes
8
answers
482
GATE CSE 2009 | Question: 24
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
The binary operation $\Box$ is defined as follows$$\begin{array}{|c|c|c|} \hline \textbf{P} & \textbf{Q} & \textbf{P} \Box \textbf{Q}\\\hline \text{T} & \text{T}& \text{T...
gatecse
8.6k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
propositional-logic
+
–
40
votes
8
answers
483
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
Which one of the following is the most appropriate logical formula to represent the statement?"Gold and silver ornaments are precious".The following notations are used: ...
gatecse
8.5k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2009
mathematical-logic
easy
first-order-logic
+
–
40
votes
9
answers
484
GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
For the composition table of a cyclic group shown below:$$\begin{array}{|c|c|c|c|c|} \hline \textbf{*} & \textbf{a}& \textbf{b} &\textbf{c} & \textbf{d}\\\hline \textbf{a...
gatecse
8.9k
views
gatecse
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2009
set-theory&algebra
normal
group-theory
+
–
78
votes
11
answers
485
GATE CSE 2009 | Question: 21
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the ... following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is ev...
gatecse
16.5k
views
gatecse
asked
Sep 15, 2014
Probability
gatecse-2009
probability
normal
conditional-probability
+
–
25
votes
3
answers
486
GATE CSE 2009 | Question: 4
Consider the binary relation $R = \left\{(x,y), (x,z), (z,x), (z,y)\right\}$ on the set $\{x,y,z\}$. Which one of the following is TRUE? $R$ is symmetric but NOT antisymmetric $R$ is NOT symmetric but antisymmetric $R$ is both symmetric and antisymmetric $R$ is neither symmetric nor antisymmetric
Consider the binary relation $R = \left\{(x,y), (x,z), (z,x), (z,y)\right\}$ on the set $\{x,y,z\}$. Which one of the following is TRUE?$R$ is symmetric but NOT antisymme...
gatecse
5.1k
views
gatecse
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2009
set-theory&algebra
easy
relations
+
–
49
votes
11
answers
487
GATE CSE 2009 | Question: 2
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n > 2$. $2$ $3$ $n-1$ $n$
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n 2$.$2$$3$$n-1$ $n$
gatecse
13.2k
views
gatecse
asked
Sep 15, 2014
Graph Theory
gatecse-2009
graph-theory
graph-coloring
normal
+
–
27
votes
4
answers
488
GATE CSE 2009 | Question: 1
Which one of the following is NOT necessarily a property of a Group? Commutativity Associativity Existence of inverse for every element Existence of identity
Which one of the following is NOT necessarily a property of a Group?CommutativityAssociativity Existence of inverse for every element Existence of identity
gatecse
8.2k
views
gatecse
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2009
set-theory&algebra
easy
group-theory
+
–
14
votes
5
answers
489
GATE CSE 1995 | Question: 1.18
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$ $\left(\dfrac{9}{10}\right)^{3}$ $\dfrac{27}{75}$ $\dfrac{18}{25}$
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$$\left(\dfrac{9}{10}\right)^...
gatecse
11.1k
views
gatecse
asked
Sep 15, 2014
Probability
gate1995
probability
normal
+
–
37
votes
6
answers
490
GATE CSE 2014 Set 1 | Question: 1
Consider the statement "Not all that glitters is gold Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ ... $\exists x: \text{glitters}(x)\wedge \neg \text{gold}(x)$
Consider the statement "Not all that glitters is gold”Predicate glitters$(x)$ is true if $x$ glitters and predicate gold$(x)$ is true if $x$ is gold. Which one of the ...
gatecse
6.6k
views
gatecse
asked
Sep 15, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
first-order-logic
+
–
15
votes
4
answers
491
GATE CSE 2001 | Question: 4
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b - 1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers. Prove that the function $h$ is an injection (one-one). Prove that it is also a Surjection (onto)
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b - 1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers.Prove that the function $...
Kathleen
3.2k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
functions
set-theory&algebra
normal
descriptive
+
–
11
votes
2
answers
492
GATE CSE 2001 | Question: 3
Prove that powerset $(A \cap B) = \text{powerset}(A) \cap \text{powerset}(B)$ Let $\text{sum} (n) = 0 + 1 + 2 + ..... + n$ for all natural numbers n. Give an induction proof to show that the following equation is true for all natural numbers $m$ and $n$: $\text{sum}(m+n) = \text{sum}(m) + \text{sum}(n) + mn$
Prove that powerset $(A \cap B) = \text{powerset}(A) \cap \text{powerset}(B)$Let $\text{sum} (n) = 0 + 1 + 2 + ..... + n$ for all natural numbers n. Give an induction pro...
Kathleen
2.2k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
normal
set-theory
descriptive
+
–
53
votes
6
answers
493
GATE CSE 2001 | Question: 2.15
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices? $\frac{n(n-1)} {2}$ $2^n$ $n!$ $2^\frac{n(n-1)} {2} $
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?$\frac{n(n-1)} {2}$$2^n$$n!$$2^\f...
Kathleen
14.1k
views
Kathleen
asked
Sep 14, 2014
Graph Theory
gatecse-2001
graph-theory
normal
counting
+
–
38
votes
4
answers
494
GATE CSE 2001 | Question: 2.4
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day? $\dfrac{1}{7^7}\\$ $\dfrac{1}{7^6}\\$ $\dfrac{1}{2^7}\\$ $\dfrac{7}{2^7}\\$
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?$\dfrac{1}{7^7}\\$$\dfrac{1}{7^6}\\$$\dfrac{1}{2^7}\\$$\...
Kathleen
19.8k
views
Kathleen
asked
Sep 14, 2014
Probability
gatecse-2001
probability
normal
+
–
49
votes
5
answers
495
GATE CSE 2001 | Question: 2.3
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images.$S_1: f(E \cup F) = f(E) \cup f(F)$$S_2: f(E \cap F...
Kathleen
11.2k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
functions
normal
+
–
54
votes
5
answers
496
GATE CSE 2001 | Question: 2.2
Consider the following statements: $S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite. $S_2:$ There exists two irrational numbers $x$ and y such that $(x+y)$ ... $S_2$? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Consider the following statements:$S_1:$ There exists infinite sets $A$, $B$, $C$ such that $A \cap (B \cup C)$ is finite.$S_2:$ There exists two irrational numbers $x$ a...
Kathleen
8.9k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
normal
set-theory
+
–
38
votes
9
answers
497
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$
Kathleen
12.7k
views
Kathleen
asked
Sep 14, 2014
Combinatory
gatecse-2001
combinatory
normal
+
–
31
votes
5
answers
498
GATE CSE 2001 | Question: 1.3
Consider two well-formed formulas in propositional logic $F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$ Which one of the following statements is correct? $F_1$ is satisfiable, $F_2$ is valid $F_1$ unsatisfiable, $F_2$ is satisfiable $F_1$ is unsatisfiable, $F_2$ is valid $F_1$ and $F_2$ are both satisfiable
Consider two well-formed formulas in propositional logic$F_1: P \Rightarrow \neg P$ $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$Which one of the fo...
Kathleen
9.1k
views
Kathleen
asked
Sep 14, 2014
Mathematical Logic
gatecse-2001
mathematical-logic
easy
propositional-logic
+
–
24
votes
4
answers
499
GATE CSE 2001 | Question: 1.2
Consider the following relations: $R_1\:(a,b)$ iff $(a+b)$ is even over the set of integers $R_2 \:(a,b)$ iff $(a+b)$ is odd over the set of integers $R_3 \:(a,b)$ iff $a.b > 0$ ... $R_4$ are not $R_1$ and $R_4$ are equivalence relations, $R_2$ and $R_3$ are not $R_1, R_2, R_3$ and $R_4$ all are equivalence relations
Consider the following relations:$R_1\:(a,b)$ iff $(a+b)$ is even over the set of integers$R_2 \:(a,b)$ iff $(a+b)$ is odd over the set of integers$R_3 \:(a,b)$ iff $a.b ...
Kathleen
6.2k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
normal
relations
+
–
23
votes
6
answers
500
GATE CSE 2001 | Question: 1.1
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be non-singular S2: The sum of two $n \times n$ non-singular matrices may be singular Which one of the following statements is correct? $S1$ and $S2$ both are true $S1$ is true, $S2$ is false $S1$ is false, $S2$ is true $S1$ and $S2$ both are false
Consider the following statements:S1: The sum of two singular $n \times n$ matrices may be non-singularS2: The sum of two $n \times n$ non-singular matrices may be singul...
Kathleen
8.5k
views
Kathleen
asked
Sep 14, 2014
Linear Algebra
gatecse-2001
linear-algebra
normal
matrix
+
–
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