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Recent questions tagged gb2019gtmaths
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GATEBOOK2019 Grand Test Mathematics1
Let $x_n = \dfrac{n^n}{n!}; (n = 1, 2, 3, \ldots )$ $\displaystyle{\lim_{n \to \infty} \dfrac{x_{n+1}}{x_n} = ?}$ $\sqrt{e}$ $e^2$ $e$ $e^{1}$
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GATEBOOK2019 Grand Test Mathematics2
The inverse of the matrix $M = \begin{bmatrix} 2 & 1 & 3 \\ 0 & 1 & 2 \\ 4 & 3 & 1 \end{bmatrix}$ is the matrix $M^{1} = \dfrac{1}{6} \begin{bmatrix} 7 & 8 & a \\ 8 & 10 & 4 \\ 4 & b & 2 \end{bmatrix}$ where $a=5, b=2$ $a = 2, b = 3$ $a=3, b = 2$ $a= 5, b = 1$
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GATEBOOK2019 Grand Test Mathematics3
Let $G$ be the set of all $2 × 2$ real matrices, trace of which is $0$, and $+$ denotes the operation of matrix addition. Then the algebraic structure $(G, +)$ is A groupoid only A semi group only A monoid only A group
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Jan 7
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gb2019gtmaths
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GATEBOOK2019 Grand Test Mathematics4
A coin is tossed five times. Probability of getting at least $\text{2 heads}$ and $\text{1 tail}$ is $\left (\dfrac{25}{32} \right )$ $\left (\dfrac{27}{32} \right )$ $\left (\dfrac{5}{6} \right )$ $\left (\dfrac{11}{16} \right )$
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GATEBOOK2019 Grand Test Mathematics5
A die is rolled $10$ times. The probability that exactly $ 7$ odd numbers turn up among the $10$ outcomes is $\left (\dfrac{15}{128} \right )$ $\left (\dfrac{14}{128}\right )$ $\left (\dfrac{16}{128} \right )$ none of these
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GATEBOOK2019 Grand Test Mathematics6
Consider the adjacency matrix of undirected graph $G$ ... where chromatic partition is defined as the number of integer (positive) partitions possible for the chromatic number of $G$? $1$ $2$ $3$ $4$
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Jan 7
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Graph Theory
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GATEBOOK2019 Grand Test Mathematics7
Let $a_n = \left ( \dfrac{n+2}{n+1} \right ) ^{2n+3}$. Determine $\displaystyle{\lim_{n \to \infty } a_n}$ $1$ $e$ $e^2$ $e^3$
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Engineering Mathematics
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gb2019gtmaths
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GATEBOOK2019 Grand Test Mathematics8
The value of $\large\int\limits_{1}^{4} \mid y2 \mid dy$ is $3$ $\left (\dfrac{3}{2} \right )$ $\left (\dfrac{5}{2} \right )$ $\left (\dfrac{7}{2} \right )$
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Jan 7
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Calculus
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GATEBOOK2019 Grand Test Mathematics9
Let the matrix be $A = \begin{bmatrix} 2 & 4 \\ 1 & 2 \end{bmatrix}$ and consider the equation: $A^4 = nA$ For which value of $n$ the given equation gets satisfied? $2^3$ $2^4$ $2^5$ $2^6$
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Jan 7
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GATEBOOK2019 Grand Test Mathematics10
Consider the system of equation $2x+3y+5z = 30 \\ 4x+6y+10z =40 \\ x+y z = 2 $ The above system has No solution a unique solution More than one but finite solutions an infinite number of solutions
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Jan 7
in
Linear Algebra
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gb2019gtmaths
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1
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11
GATEBOOK2019 Grand Test Mathematics11
Find $k$ so that the matrix $A = \begin{bmatrix} k & 1 & 2 \\ 1 & 2 & k \\ 1& 2 & 3 \end{bmatrix}$ has eigenvalue $\lambda = 1$ $\dfrac{1}{2}$ $\dfrac{1}{2}$ $0$ $1$
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GATEBOOK2019 Grand Test Mathematics12
Consider the following systems of linear equations: $ 2x+y2z=1 \\ 4x+3y6z=5 \\ x+2y4z=7$ The given system has no solution infinite solution unique solution finite solutions
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Jan 7
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13
GATEBOOK2019 Grand Test Mathematics13
In a test there are $5$ questions (TrueFalse type) and the probability of correctly guessing a question by a student is $30\%$. What is the probability of getting more than $3$ correct answers? $0.031$ $0.023$ $0.056$ $0.05$
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GATEBOOK2019 Grand Test Mathematics14
The number of stationary points of the following function is $f(t) = 4t^3 +15t^2 18t + 6$ is $0$ $1$ $2$ $3$
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Jan 7
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GATEBOOK2019 Grand Test Mathematics15
How many integral solutions are there for $x_1 + x_2 + x_3 +x_4 +x_5 = 30$, where $x_i > i \: for \: i = 1,2,3,4,5$ ? $C(19 ,15)$ $C(14, 10)$ $C(34, 10)$ None of the these
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16
GATEBOOK2019 Grand Test Mathematics16
If $ A = \begin{pmatrix} 3 & 1 \\ 1 & 1 \end{pmatrix} \: and \: I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} $ , which of the following matrix polynomial vanishes? $A^2 – 2A 4I$ $A^2 – 2A+ 4I$ $A^2 + A+ 2I$ $A^2 – 2A 2I$
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GATEBOOK2019 Grand Test Mathematics17
A random variable $X$ follows normal distribution i.e., $x$ follows $N(\mu, \sigma^2)$ and $p(9.6 \leq x \leq 13.8) = 0.7008$ and $p(x>9.6) = 0.8159$ Given $\sigma =2, \: \phi(0.9) = 0.8159$ and $\phi(1.2) = 0.8849$. Find the value of $\mu$. $2$ $4$ $11.4$ $13.2$
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gb2019gtmaths
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18
GATEBOOK2019 Grand Test Mathematics18
Let $p(\lambda)$ be the characteristic polynomial for an $(n \times n)$ matrix $A$. if $\lambda = 0$ is a root of $p(\lambda)$ then which of the following statement(s) is/are always FALSE? I. $A$ has $n$ linearly independent eigenvectors. II. $det[p(A)] = 0$ III. A is invertible. I only II only III only I and III only
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19
GATEBOOK2019 Grand Test Mathematics19
Let $A = \begin{pmatrix} 2 & 1 \\ 1 & t \end{pmatrix}$. For how many value(s) of $t$ does $A$ posses a repeated eigenvalue? $1$ $2$ $3$ $infinite$
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Jan 7
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20
GATEBOOK2019 Grand Test Mathematics20
Consider the binomial distribution, with probability distribution function of happening of $r$ events is given by $P(r) = ^nC_r p^r q^{nr}$ Considering $n \to \infty$ and $p \to 0$ such that $np$ is finite Then the above distribution is modified to Uniform Normal Poisson None of the above
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gb2019gtmaths
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21
GATEBOOK2019 Grand Test Mathematics21
Box $P$ has $6$ red balls & $12$ blue balls and box $Q$ has $7$ blue & $5$ red balls.A ball is selected by first selecting a box and then choosing a ball from the selected box. The probability of selecting box $P$ is $\dfrac{3}{4}$ whereas box $Q$ is ... $\left ( \dfrac{17}{48} \right ) $ $\left ( \dfrac{3}{4} \right ) $
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Jan 7
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Probability
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gb2019gtmaths
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22
GATEBOOK2019 Grand Test Mathematics22
Box $P$ has $6$ red balls & $12$ blue balls and box $Q$ has $7$ blue & $5$ red balls.A ball is selected by first selecting a box and then choosing a ball from the selected box. The probability of selecting box $P$ is $\dfrac{3}{4}$ whereas box $Q$ is ... $\left ( \dfrac{1}{4} \right ) $ $\left ( \dfrac{24}{31} \right ) $
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Jan 7
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23
GATEBOOK2019 Grand Test Mathematics23
A fair coin is tossed $2n$ times to form the string of length $2n$. If it is head, it is $0$, otherwise $1$. What is the probability of bitwise anding of two strings consisting of all $1$? $\left ( \dfrac{1}{2^{n}} \right ) $ $\left ( \dfrac{1}{n} \right ) $ $\left ( \dfrac{1}{4^{n}} \right ) $ $\left ( \dfrac{2}{(4)^{n}} \right ) $
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Jan 7
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24
GATEBOOK2019 Grand Test Mathematics24
If $\mathrm{e}^y = x^x$, then $y$ has a Maximum at $ x =\mathrm{e}$ Minimum at $ x = \mathrm{e}$ Maximum at $ x = \mathrm{e}^{1}$ Minimum at $ x = \mathrm{e}^{1}$
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Jan 7
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gb2019gtmaths
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