Recent questions and answers in Engineering Mathematics

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asked Jun 15, 2018 in Calculus by rajutsrk (110 points)

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GATE2012-64
An automobile plant contracted to buy shock absorbers from two suppliers $X$ and $Y.$ $X$ supplies $60\%$ and $Y$ supplies $40\%$ ... chosen shock absorber, which is found to be reliable, is made by $Y$ is $0.288$ $0.334$ $0.667$ $0.720$

asked Mar 20, 2018 in Probability and Statistics by Andrijana3306 (1.5k points)

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GATE2018-2-24
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _____ (correct to two decimal places)

answered Feb 22, 2018 in Probability and Statistics by Balaji Jegan (2.9k points)

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GATE2018-2-27
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean 1/6 exponentially distributed with mean 2 normally distributed with mean 3/4 normally distributed with mean 1/6

answered Feb 22, 2018 in Probability and Statistics by Balaji Jegan (2.9k points)

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GATE2018-2-GA-10
An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head ans T stands for tail, the following are the observations from the four trials. HTHTHT TTHHHT HTTHHT HHHT_ _ Which ... of being correct? Two T will occur One H and one T will occur Two H will occur One H wll be followed by one T

answered Feb 22, 2018 in Probability and Statistics by Balaji Jegan (2.9k points)

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GATE2018-2-19
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).

answered Feb 22, 2018 in Linear Algebra by Balaji Jegan (2.9k points)

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GATE2018-2-GA-5
The value of the expression $\frac{1}{1+ \log_u \: vw} + \frac{1}{1+ \log_v \: wu} + \frac{1}{1+\log_w uv}$ is _______ -1 0 1 3

answered Feb 21, 2018 in Linear Algebra by Balaji Jegan (2.9k points)

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GATE2018-2-35
The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ has no solution one solution two solutions more than two solutions

asked Feb 17, 2018 in Numerical Methods by Arjun (21.5k points)

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GATE2018-2-36
Given the ordinary differential equation $\frac{d^2y}{dx^2}+\frac{dy}{dx}-6y=0$ with $y(0)=0$ and $\frac{dy}{dx}(0)=1$, the value of $y(1)$ is _____ (correct to two decimal places).

asked Feb 17, 2018 in Differential Equations by Arjun (21.5k points)

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GATE2018-2-28
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, ... $\frac{\overrightarrow{r}}{\overrightarrow{r} \bullet \overrightarrow{r} } $ $\frac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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GATE2018-2-26
Let $z$ be a complex variable. FOr a counter-clockwise integration around a unit circle $C$, centered at origin, $\oint \frac{1}{5z-4} dz=A \pi i$, the value of $A$is 2/5 1/2 2 4/5

asked Feb 17, 2018 in Numerical Methods by Arjun (21.5k points)

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GATE2018-2-4
If $y$ is the solution of the differential equation $y^3 \frac{dy}{dx}+x^3 = 0, \: y(0)=1,$ the value of $y(-1)$ is -2 -1 0 1

asked Feb 17, 2018 in Differential Equations by Arjun (21.5k points)

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GATE2018-2-2
The divergence of the vector field $\overrightarrow{u}=e^x(\cos \: y\hat{i}+\sin \: y \hat{j})$ is $0$ $e^x \cos y + e^x \sin y$ $2e^x \cos y$ $2e^x \sin y$

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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GATE2018-2-3
Consider a function $u$ which depends on position $x$ and time $t$. The partial differential equation $\frac{\partial u}{\partial t} = \frac{\partial^2 u }{\partial x^2}$ is known as the Wave equation Heat equation Laplace's equation Elasticity equation

asked Feb 17, 2018 in Differential Equations by Arjun (21.5k points)

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GATE2018-2-1
The Fourier cosine series for an even function $f(x)$ is given by $ f(x)=a_0 + \Sigma_{n=1}^\infty a_n \cos (nx).$ The value of the coefficient $a_2$ for the function $f(x)=\cos ^2 (x)$ in $[0, \pi]$ is -0.05 0.0 0.5 1.0

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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GATE2018-1-GA-9
Which of the following functions describe the graph shown in the below figure? $y=\mid \mid x \mid + 1 \mid -2$ $y=\mid \mid x \mid - 1 \mid -1$ $y=\mid \mid x \mid + 1 \mid -1$ $y=\mid \mid x \mid - 1 \mid -1$

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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GATE2018-1-GA-6
For integers, $a$, $b$ and $c$, what would be the minimum and maximum values respectively of $a+b+c$ if $\log \mid a \mid + \log \mid b \mid + \log \mid c \mid =0$? -3 and 3 -1 and 1 -1 and 3 1 and 3

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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GATE2018-1-51
The minimum value of $3x+5y$ such that $3x+5y \leq 15$ $4x+9y \leq 18$ $13x+2y \leq 2$ $x \geq 0, \: y \geq 0$ is ______

asked Feb 17, 2018 in Numerical Methods by Arjun (21.5k points)

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GATE2018-1-1
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is 1/72 1/55 1/36 1/27

asked Feb 17, 2018 in Probability and Statistics by Arjun (21.5k points)

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GATE2018-1-2
The rank of the matrix $\begin{bmatrix} -4 & 1 & -1 \\ -1 & -1 & -1 \\ 7 & -3 & 1 \end{bmatrix}$ is 1 2 3 4

asked Feb 17, 2018 in Linear Algebra by Arjun (21.5k points)

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GATE2018-1-3
According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_a^b f(x) dx = $ $f(\xi)(b-a)$ $f(b)(\xi-a)$ $f(a)(b-\xi)$ $0$

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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GATE2018-1-4
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations? 0 1 -1 y

asked Feb 17, 2018 in Calculus by Arjun (21.5k points)

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