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#3101
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#icegate #test #maths #probability
If the marks obtained by the students in a competitive exam follows normal distribution with mean value 50 and variance 10. If the passing marks is 40 then percentage of failed students is ____%
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#3102
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gate 2008
lim x->infinity (x-sinx/x+cosx)
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#3103
372
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1 answers
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Functions
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#3104
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Propositional logic self doubt
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#3105
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1 answers
1 votes
Stuck on this combinatorics question
A florist sells roses of five different colors. How many bunches of a half-dozen roses can be formed? a 196210236300Please help me understand this question with ... explanation. I got the answer but looking for the logical reasoning to it.
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#3106
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GATE previous years with little Modification
The Minimum number of possible edges in an undirected graph with n vertices and k components is ______
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#3107
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ME TEST
How is g(x) is many one ?
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#3108
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Binomial distribution
Is there any relation between MEAN, VARIANCE and MODE for binomial distribution?Let, Mean = 8, variance = 6 for any binomial distribution.np = 8 and npq = 6 => q=$3/4$, p=$1/4$Now is there any relation to find value of MODE ?
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#3109
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1 answers
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How to solve such question
... problem as I am looking for a procedure and want to learn this topic from this question possibly.
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#3110
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6 answers
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TIFR CSE 2019 | Part A | Question: 1
Let $X$ be a set with $n$ elements. How many subsets of $X$ have odd cardinality?$n$ $2^n$2^{n/2}$2^{n-1}$Can not be determined without knowing whether $n$ is odd or even
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#3111
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2 answers
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TIFR CSE 2019 | Part A | Question: 3
$A$ is $n \times n$ square matrix for which the entries in every row sum to $1$. Consider the following statements:The column vector $[1,1,\ldots,1]^T$ ... $Only $(i)$ and $(iii)$(i),(ii) \text{ and }(iii)$
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#3112
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1 answers
7 votes
TIFR CSE 2019 | Part A | Question: 4
What is the probability that a point $P=(\alpha,\beta)$ picked uniformly at random from the disk $x^2 +y^2 \leq 1$ satisfies $\alpha + \beta \leq 1$?$\frac{1}{\pi}$\frac{3}{ ... $\frac{3}{4}+ \frac{1}{4} \cdot \frac{2}{\pi}$1$\frac{2}{\pi}$
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#3113
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1 answers
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TIFR CSE 2019 | Part A | Question: 6
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is said to be $\textit{convex}$ if for all $x,y \in \mathbb{R}$ and $\lambda$ such that $0 \leq \lambda \leq1,$ ... must be convex?Only $p$Only $q$Only $r$Only $p$ and $r$Only $q$ and $r$
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#3114
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TIFR CSE 2019 | Part A | Question: 12
Let $f$ be a function with both input and output in the set $\{0,1,2, \dots ,9\}$, and let the function $g$ be defined as $g(x) = f(9-x)$. The function $f$ ... $\text{(i)}$ and $\text{(ii)}$ Only $\text{(iii)}$ None of themAll of them
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#3115
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2 answers
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TIFR CSE 2019 | Part A | Question: 13
Consider the integral$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$What is the value of this integral correct up to two decimal places?$0.00$0.02$0.10$0.33$1.00$
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#3116
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1 answers
8 votes
TIFR CSE 2019 | Part A | Question: 14
A drawer contains $9$ pens, of which $3$ are red, $3$ are blue, and $3$ are green. The nine pens are drawn from the drawer one at at time (without replacement) such ... are drawn in succession ?$7/12$1/6$1/12$1/81$\text{None of the above}$
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#3117
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5 answers
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TIFR CSE 2019 | Part A | Question: 15
Consider the matrix$A = \begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$What ... 1}{2} & \frac{1}{2}\end{bmatrix}$\text{The limit exists, but it is none of the above}$
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#3118
1.7k
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1 answers
5 votes
TIFR CSE 2019 | Part B | Question: 3
A graph is $d$ - regular if every vertex has degree $d$. For a $d$ - regular graph on $n$ vertices, which of the following must be TRUE?$d$ divides $n$Both $d$ and ... oddAt least one of $d$ and $n$ is oddAt least one of $d$ and $n$ is even
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#3119
1.5k
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2 answers
7 votes
TIFR CSE 2019 | Part B | Question: 4
Let $\varphi$ be a propositional formula on a set of variables $A$ and $\psi$ be a propositional formula on a set of variables $B$ , such that $\varphi \Rightarrow \psi$ ... $ ?$q$\varphi$ itself$q \vee s$q \vee r$\neg q \wedge s$
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#3120
2.5k
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1 answers
6 votes
TIFR CSE 2019 | Part B | Question: 12
Let $G=(V,E)$ be a directed graph with $n(\geq 2)$ vertices, including a special vertex $r$. Each edge $e \in E$ has a strictly positive ... the minimum weight directed Hamiltonian cycle in $G$, when $G$ has a directed Hamiltonian cycle
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