Previous GATE Questions in Engineering Mathematics

+1 vote

1 answer

GATE2001-2.15 GATE1994-1.6
How many undirected graphs are possible with n vertices if graphs are not necessarily connected if they are necessarily connected

asked Oct 12 in Graph Theory by rishi71662data4 Active (1.2k points) | 45 views

+1 vote

1 answer

EC,GATE2007
An examination consists of two papers , paper1 and paper2 . the probability of failing in paper 1 is 0.3 and that in paper 2 is 0.2 . Given that a student has failed in paper2 , the probability of failing in paper1 is 0.6 .The ... creat sample space and then try to find probability, what's wrong here ? Someone verify pls ...M getting different ans ...

asked Sep 1 in Probability by sid1221 Active (2.1k points) | 91 views

0 votes

0 answers

ME , GATE2006
Assuming $i=\sqrt{-1}$ and t is real number , $\int_{0}^{\Pi /3} e^{it}dt$ given ans is $\sqrt{3}/2 + i/2 , and i am getting \sqrt{3}/2-i/2$ i solved first put $e^{it}= cost +isint$ then and integrate , but in solution they first integrate $e^{it}$ then put the value of it ... but ans different ... why is this happening .. am i missing something ??

asked Aug 29 in Calculus by sid1221 Active (2.1k points) | 32 views

0 votes

0 answers

http://ee.gateoverflow.in/212/gate2016-1-2

asked Aug 26 in Linear Algebra by sid1221 Active (2.1k points) | 56 views

+2 votes

0 answers

#Gate2003
Consider the following logic program P A(x) <- B(x, y), C(y) <- B(x,x) Which of the following first order sentences is equivalent to P? Can anyone explain how it can be solved ? [closed]

asked Jun 29 in Mathematical Logic by Syedarshadali (157 points) | 138 views

+9 votes

5 answers

GATE2017-1-02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ (A) $IV$ only (B) $I$ and $IV$ only (C) $II$ only (D) $II$ and $III$ only

asked Feb 14 in Mathematical Logic by khushtak Boss (7.6k points) | 1.6k views

+5 votes

6 answers

GATE2017-1-01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? I. $p \Rightarrow q$ II. $q \Rightarrow p$ III. $\left ( ¬q \right ) \vee p$ IV. $\left ( ¬p \right ) \vee q$ (A) I. only (B) I. and IV. only (C) II. only (D) II. and III. only

asked Feb 14 in Mathematical Logic by khushtak Boss (7.6k points) | 1.1k views

+5 votes

4 answers

GATE2017-2-52
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______

asked Feb 14 in Linear Algebra by Madhav Active (2k points) | 1.4k views

+8 votes

4 answers

GATE2017-2-23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .

asked Feb 14 in Graph Theory by Madhav Active (2k points) | 1.8k views

+10 votes

3 answers

GATE2017-2-48
If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X+2)2] equals ___.

asked Feb 14 in Probability by Kantikumar Loyal (4.4k points) | 1.4k views

+12 votes

3 answers

GATE2017-2-47
If the ordinary generating function of a sequence $\big \{a_n\big \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .

asked Feb 14 in Combinatory by Arjun Veteran (319k points) | 1.4k views

+4 votes

3 answers

GATE2017-2-31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For ... z)^N$. The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone

asked Feb 14 in Probability by Arjun Veteran (319k points) | 981 views

+6 votes

3 answers

GATE2017-2-26
P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P ... probability that P does not apply for the job given that Q does not apply for this job is 4/5 5/6 7/8 11/12

asked Feb 14 in Probability by Arjun Veteran (319k points) | 1.3k views

+5 votes

3 answers

GATE2017-2-22
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .

asked Feb 14 in Linear Algebra by Arjun Veteran (319k points) | 1.1k views

+2 votes

4 answers

GATE2017-1-47
The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ____________ .

asked Feb 14 in Set Theory & Algebra by Arjun Veteran (319k points) | 1.1k views

+8 votes

2 answers

GATE2017-1-31
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. (I) One eigenvalue must be in $\left [ -5,5 \right ]$ (II) The eigenvalue with the largest ... $A$ is/are necessarily CORRECT? (A) Both (I) and (II) (B) (I) only (C) (II) only (D) Neither (I) nor (II)

asked Feb 14 in Linear Algebra by Arjun Veteran (319k points) | 1.3k views

+5 votes

2 answers

GATE2017-1-30
Let $u$ and $v$ be two vectors in R2 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 $v$? (A) 2 (B) 1/2 (C) 1 (D) -1/2

asked Feb 14 in Linear Algebra by Arjun Veteran (319k points) | 1.7k views

+3 votes

4 answers

GATE2017-1-29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is (A) a tautology. (B) a contradiction. (C) always TRUE when $p$ is FALSE. (D) always TRUE when $q$ is TRUE.

asked Feb 14 in Mathematical Logic by Arjun Veteran (319k points) | 901 views

+5 votes

4 answers

GATE2017-1-28
The value of $\lim_{x\rightarrow 1} \frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}$ (A) is 0 (B) is -1 (C) is 1 (D) does not exist

asked Feb 14 in Calculus by Arjun Veteran (319k points) | 831 views

+7 votes

3 answers

GATE2017-1-19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $max\left ( X,0 \right )$ where $max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .

asked Feb 14 in Probability by Arjun Veteran (319k points) | 1.2k views

+3 votes

2 answers

GATE2017-1-3
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 $Ax = b$ where $A=\left [ a_{1}.....a_{n} ... $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. (B) no solution (C) infinitely many solutions (D) finitely many solutions

asked Feb 14 in Linear Algebra by Arjun Veteran (319k points) | 1k views

+2 votes

2 answers

GATE2017-2-21
Consider the set $X=\{a, b, c, d, e\}$ under partial ordering $R=\{(a,a), (a, b), (a, c), (a, d), (a, e), (b, b), (b, c), (b, e), (c, c), (c, e), (d, d), (d, e), (e, e) \}$. The Hasse diagram ... Hasse diagram of the partial order $(X, R)$ is shown below. The minimum number of ordered pairs that need to be added to $R$ to make $(X, R)$ a lattice is ______

asked Feb 14 in Set Theory & Algebra by khushtak Boss (7.6k points) | 1.2k views

+3 votes

2 answers

GATE2017-2-10
If $f(x) = R \: \sin ( \frac{\pi x}{2}) + S. f’(\frac{1}{2}) = \sqrt{2}$ and $\int_0^1 f(x) dx = \frac{2R}{\pi}$, then the constants $R$ and $S$ are $\frac{2}{\pi}$ and $\frac{16}{\pi}$ $\frac{2}{\pi}$ and 0 $\frac{4}{\pi}$ and 0 $\frac{4}{\pi}$ and $\frac{16}{\pi}$

asked Feb 14 in Calculus by Madhav Active (2k points) | 871 views

+3 votes

3 answers

GATE2017-2-24
Consider the quadratic equation $x^2-13x+36=0$ with coefficients in a base $b$. The solutions of this equation in the same base $b$ are $x=5$ and $x=6$. Then $b$= _____

asked Feb 14 in Set Theory & Algebra by khushtak Boss (7.6k points) | 1.3k views

+6 votes

6 answers

GATE2017-2-11
Let $p, q, r$ denote the statements It is raining , It is cold , and It is pleasant , respectively. Then the statement It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold is represented by $(\neg p \wedge ... r) \vee ((p \wedge q) \rightarrow \neg r)$ $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$

asked Feb 14 in Mathematical Logic by khushtak Boss (7.6k points) | 1.3k views

+1 vote

0 answers

VirtualGATE2017-1

asked Jan 18 in Calculus by ManojK Veteran (39k points) | 157 views

0 votes

0 answers

http://gateoverflow.in/1177/gate2005-52

asked Dec 29, 2016 in Probability by Adiaspirant Junior (775 points) | 60 views

0 votes

0 answers

GATE1988-16ii-iii
If $x \| \underline{x} \| \infty = 1< i^{max} < n \: \: max \: \: ( \mid x1 \mid ) $ for the vector $\underline{x} = (x1, x2 \dots x_n)$ and $\| A \| \infty = x^{Sup} \frac{\| A ... property of this norm. Although this norm is very easy to calculate for any matrix, explain why the condition number is difficult (i.e. expensive) to calculate.

asked Dec 20, 2016 in Linear Algebra by jothee Veteran (92.6k points) | 80 views

0 votes

0 answers

GATE1988-16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to 1, $U$ is upper-triangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 ... \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.

asked Dec 20, 2016 in Linear Algebra by jothee Veteran (92.6k points) | 112 views

0 votes

0 answers

GATE1988-14ii
Consider the following well-formed formula: $\exists x \forall y [ \neg \exists z [ p (y, z) \wedge p (z, y) ] \equiv p(y)$ Show using resolution principle that the well-formed formula, given above, cannot be satisfied for any interpretation.

asked Dec 20, 2016 in Mathematical Logic by jothee Veteran (92.6k points) | 71 views

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