Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

2 votes

2 answers

8441

probability
Three numbers are chosen at random without replacement from $\left\{1, 2, 3,....., 10 \right\}$. What is the probability that minimum of the chosen numbers is $3$ or their maximum is $7$? $\frac{11}{30}$ $\frac{11}{40}$ $\frac{1}{7}$ $\frac{1}{8}$

Three numbers are chosen at random without replacement from $\left\{1, 2, 3,....., 10 \right\}$. What is the probability that minimum of the chosen numbers is $3$ or thei...

Himanshu1

2.1k views

Himanshu1 asked Dec 26, 2015

3 votes

1 answer

8442

Eigen values
The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is A). $\pm i$ B), $(\pm i,\pm1)$ C). $\pm1$ D). $(0,\pm i)$

The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is A). $\pm i$B), $(\pm i,\pm1)$C). $\pm1$D). $(0,\pm i)$

Himanshu1

2.0k views

Himanshu1 asked Dec 26, 2015

2 votes

1 answer

8443

Graph theory
How many non isomorphic directed simple graph are there with n vertices?

How many non isomorphic directed simple graph are there with n vertices?

ManojK

1.4k views

ManojK asked Dec 26, 2015

0 votes

1 answer

8444

graph theory
How many non-isomorphic simple graph are there with 5 vertices and 3 edges?how to approach this qus....

How many non-isomorphic simple graph are there with 5 vertices and 3 edges?how to approach this qus....

ManojK

409 views

ManojK asked Dec 26, 2015

1 votes

1 answer

8445

Subject Topic- Probability
what is positively skewed ,symmetric and negatively skewed distribution?

what is positively skewed ,symmetric and negatively skewed distribution?

Amey

960 views

Amey asked Dec 25, 2015

4 votes

3 answers

8446

Propositional logic
which one is not tautology? 1.((p v q)^(r v s)) -> ((p^r) v q vs) 2. ((p v q)^(r v s)) -> (q v s) 3.((p v q)^(r v s)) -> (r v q v s) 4.((p v q)^(r v s)) -> (p v q v s) 5.((p v q)^(r v s)) -> (p v q) please tell how to approach this types of qs,this type of qs came many times in gate.I tried it by making table,but it is not doable..so,help me.

which one is not tautology?1.((p v q)^(r v s)) - ((p^r) v q vs)2. ((p v q)^(r v s)) - (q v s)3.((p v q)^(r v s)) - (r v q v s)4.((p v q)^(r v s)) - (p v q v s)5.((p v q)^...

resuscitate

2.1k views

resuscitate asked Dec 24, 2015

0 votes

1 answer

8447

Restriction of quantifiers
How is restriction of universal quantification same as the universal quantification of a conditional statement while restriction of existential quantification is same as the existential quantification of a conjunction ?

How is restriction of universal quantification same as the universal quantification of a conditionalstatement while restriction of existential quantification is same as t...

radha gogia

397 views

radha gogia asked Dec 24, 2015

5 votes

2 answers

8448

How to calculate This recurrence ?
. The finite automaton below: accepts no word of length zero, no word of length one, and only two words of length two (01 and 10). There is a fairly simple recurrence equation for the number N(k) of words of length k that this automaton accepts. Discover this recurrence and ... greater than 14. a) N(14) = 280 b) N(11) = 76 c) N(13) = 2730 d) N(11) = 32

. The finite automaton below:accepts no word of length zero, no word of length one, and only two words of length two (01 and 10). There is a fairly simple recurrence equ...

Akash Kanase

2.5k views

Akash Kanase asked Dec 23, 2015

2 votes

0 answers

8449

TIFR-2015-Maths-B-15
Let $d(x, y)$ be the usual Euclidean metric on $\mathbb{R}^{2}$. Which of the following metric spaces is complete? $\mathbb{Q}^{2}\subset\mathbb{R}^{2}$ with the metric $d(x, y)$. $[0, 1]\times [0, \infty)\subset \mathbb{R}^{2}$ ... $d''(x, y) = \min \left \{ 1, d(x, y) \right \}$.

Let $d(x, y)$ be the usual Euclidean metric on $\mathbb{R}^{2}$. Which of the following metric spaces is complete?$\mathbb{Q}^{2}\subset\mathbb{R}^{2}$ with the metric $d...

makhdoom ghaya

442 views

makhdoom ghaya asked Dec 21, 2015

3 votes

1 answer

8450

TIFR-2015-Maths-B-14
Let $G$ be a group. Suppose $|G|= p^{2}q$, where $p$ and $q$ are distinct prime numbers satisfying $q ≢ 1 \mod p$. Which of the following is always true? $G$ has more than one $p$-Sylow subgroup. $G$ has a normal $p$-Sylow subgroup. The number of $q$-Sylow subgroups of $G$ is divisible by $p$. $G$ has a unique $q$-Sylow subgroup.

Let $G$ be a group. Suppose $|G|= p^{2}q$, where $p$ and $q$ are distinct prime numbers satisfying $q ≢ 1 \mod p$. Which of the following is always true?$G$ has mor...

makhdoom ghaya

821 views

makhdoom ghaya asked Dec 21, 2015

2 votes

1 answer

8451

TIFR-2015-Maths-B-13
Let $X=\left\{(x, y) \in \mathbb{R}^{2}: 2x^{2}+3y^{2}= 1\right\}$. Endow $\mathbb{R}^{2}$ with the discrete topology, and $X$ with the subspace topology. Then. $X$ is a compact subset of $\mathbb{R}^{2}$ in this topology. $X$ is a connected subset of $\mathbb{R}^{2}$ in this topology. $X$ is an open subset of $\mathbb{R}^{2}$ in this topology. None of the above.

Let $X=\left\{(x, y) \in \mathbb{R}^{2}: 2x^{2}+3y^{2}= 1\right\}$. Endow $\mathbb{R}^{2}$ with the discrete topology, and $X$ with the subspace topology. Then.$X$ is a c...

makhdoom ghaya

361 views

makhdoom ghaya asked Dec 21, 2015

2 votes

1 answer

8452

TIFR-2015-Maths-B-12
Let $X \subset \mathbb{R}$ and let $f,g : X \rightarrow X$ be a continuous functions such that $f(X)\cap g(X)=\emptyset$ and $f(X)\cup g(X)= X$. Which one of the following sets cannot be equal to $X$? $[0, 1]$ $(0, 1)$ $[0, 1)$ $\mathbb{R}$

Let $X \subset \mathbb{R}$ and let $f,g : X \rightarrow X$ be a continuous functions such that $f(X)\cap g(X)=\emptyset$ and $f(X)\cup g(X)= X$. Which one of the followin...

makhdoom ghaya

503 views

makhdoom ghaya asked Dec 21, 2015

1 votes

0 answers

8453

TIFR-2015-Maths-B-11
Let $(X, d)$ be a path connected metric space with at least two elements, and let $S=\left\{d(x, y):x, y \in X\right\}$. Which of the following statements is not necessarily true ? $S$ is infinite. $S$ contains a non-zero rational number. $S$ is connected. $S$ is a closed subset of $\mathbb{R}$

Let $(X, d)$ be a path connected metric space with at least two elements, and let $S=\left\{d(x, y):x, y \in X\right\}$. Which of the following statements is not necessar...

makhdoom ghaya

348 views

makhdoom ghaya asked Dec 21, 2015

2 votes

0 answers

8454

TIFR-2015-Maths-B-9
Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by $A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarrow \infty} f(x_{n}), \text {for some sequence} x_{n} \rightarrow +\infty\right\}$ Then the set A is necessarily. $A$ connected set $A$ compact set $A$ singleton set None of the above

Let $f: \mathbb{R}\rightarrow\mathbb{R}$ be a continuous function and $A \subset \mathbb{R}$ be defined by$A=\left\{ y \in \mathbb{R}:y = \displaystyle \lim_{n \rightarro...

makhdoom ghaya

342 views

makhdoom ghaya asked Dec 21, 2015

4 votes

2 answers

8455

TIFR-2015-Maths-B-8
For a group $G$, let $F(G)$ denote the collection of all subgroups of $G$. Which one of the following situations can occur ? $G$ is finite but $F(G)$ is infinite. $G$ is infinite but $F(G)$ is finite. $G$ is countable but $F(G)$ is uncountable. $G$ is uncountable but $F(G)$ is countable.

For a group $G$, let $F(G)$ denote the collection of all subgroups of $G$. Which one of the following situations can occur ?$G$ is finite but $F(G)$ is infinite.$G$ is in...

makhdoom ghaya

1.2k views

makhdoom ghaya asked Dec 21, 2015

2 votes

0 answers

8456

TIFR-2015-Maths-B-7
A complex number $\alpha \in \mathbb{C}$ is called algebraic if there is a non-zero polynomial $P(x) \in \mathbb{Q}\left[x\right]$ with rational coefficients such that $P(\alpha)=0$. Which of the following statements is true? There are only finitely many algebraic ... All complex numbers are algebraic $\sin (\frac{\pi}{3})+ \cos (\frac{\pi}{4}$) is algebraic None of the above

A complex number $\alpha \in \mathbb{C}$ is called algebraic if there is a non-zero polynomial $P(x) \in \mathbb{Q}\left[x\right]$ with rational coefficients such that $P...

makhdoom ghaya

338 views

makhdoom ghaya asked Dec 21, 2015

5 votes

2 answers

8457

52 cards are equally given to 4 players Find probability that one of them has 3 spades out of remaining 5.

52 cards are equally given to 4 players a,b,c,d. a and b have together total 8 spades among them. Find probability that c has 3 spades out of remaining 5.In this ques , s...

radha gogia

745 views

radha gogia asked Dec 21, 2015

4 votes

1 answer

8458

TIFR-2015-Maths-B-6
Let $f: [0, 1]\rightarrow \mathbb{R}$ be a fixed continuous function such that $f$ is differentiable on $(0, 1)$ and $f(0) = f(1) = 0$. Then the equation $f(x) = f' (x)$ admits. No solution $x \in (0, 1)$ More than one solution $x \in (0, 1)$ Exactly one solution $x \in (0, 1)$ At least one solution $x \in (0, 1)$

Let $f: [0, 1]\rightarrow \mathbb{R}$ be a fixed continuous function such that $f$ is differentiable on $(0, 1)$ and $f(0) = f(1) = 0$. Then the equation $f(x) = f' (x)$ ...

makhdoom ghaya

477 views

makhdoom ghaya asked Dec 21, 2015

2 votes

2 answers

8459

Solve
At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has (A) a minimum (B) a discontinuity (C) a point of inflection (D) a maximum

At $t=0$, the function $f(t)=\frac{\sin t}{t}$ has(A) a minimum(B) a discontinuity (C) a point of inflection(D) a maximum

Riya Roy(Arayana)

2.8k views

Riya Roy(Arayana) asked Dec 21, 2015

2 votes

2 answers

8460

Solve : calculate the limit
Calculate the limit $\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$ (A) $1$ (B) $0$ (C) $2$ (D) Does not exist

Calculate the limit $$\lim_{x\rightarrow 1^- } \sqrt[3]{x+1}\: ln(x+1)$$(A) $1$(B) $0$(C) $2$(D) Does not exist

Riya Roy(Arayana)

749 views

Riya Roy(Arayana) asked Dec 21, 2015

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