Recent questions and answers in Engineering Mathematics

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GATE2014-2-1
Which one of the following statements is true for all real symmetric matrices? All the eigenvalues are real. All the eigenvalues are positive. All the eigenvalues are distinct. Sum of all the eigenvalues is zero.

answered Oct 26, 2018 in Linear Algebra by Abhisek Tiwari 4 (140 points)

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GATE2014-2-2
Consider a dice with the property that the probability of a face with $n$ dots showing up is proportional to $n$. The probability of the face with three dots showing up is ________.

answered Nov 4, 2017 in Probability & Statistics by Avik10 (140 points)

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GATE2013-63
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is $(-\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$

asked Feb 12, 2017 in Numerical Methods by piyag476 (1.5k points)

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4

GATE2013-51
The state variable formulation of a system is given as $\begin{vmatrix} x^\cdot_1 \\ x^\cdot_2 \end{vmatrix}=\begin{vmatrix} -2 & 0\\ 0 & -1 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}+\begin{vmatrix} 1\\ 1 \end{vmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1-\frac{1}{2}e^{-2t}-\frac{1}{2}e^{-t}$ $e^{-2t}-e^{-t}$ $1-e^{-t}$

asked Feb 12, 2017 in Linear Algebra by piyag476 (1.5k points)

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GATE2013-50
The state variable formulation of a system is given as $\begin{vmatrix} x^\cdot_1 \\ x^\cdot_2 \end{vmatrix}=\begin{vmatrix} -2 & 0\\ 0 & -1 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}+\begin{vmatrix} 1\\ 1 \end{vmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ and $y=\begin{vmatrix} 1 & 0 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}$ The system is

asked Feb 12, 2017 in Calculus by piyag476 (1.5k points)

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GATE2013-46
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\frac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$

asked Feb 12, 2017 in Calculus by piyag476 (1.5k points)

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GATE2013-36
$\oint \frac{z^2-4}{z^2+4} dz$ evaluated anticlockwise around the circle $|z-i|=2$ , where $i=\sqrt{-1}$, is $-4\pi$ 0 $2+\pi$ $2+2i$

asked Feb 12, 2017 in Differential Equations by piyag476 (1.5k points)

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GATE2013-23
Square roots of $-i$,where $i=\sqrt{-1}$, are $i,-i$ $cos(-\frac{\pi }{4} )+isin(-\frac{\pi }{4})+cos(\frac{3\pi }{4})+isin(\frac{3\pi }{4})$ $cos(\frac{\pi }{4} )+isin(\frac{3\pi }{4})+cos(\frac{3\pi }{4})+isin(\frac{\pi }{4})$ $cos(\frac{3\pi }{4} )+isin(-\frac{3\pi }{4})+cos(-\frac{3\pi }{4})+isin(\frac{3\pi }{4})$

asked Feb 12, 2017 in Complex Variables by piyag476 (1.5k points)

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GATE2013-11
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}$, $0< x< \infty$. then P{X> $1$} $0.368$ $0.5$ $0.632$ $1.0$

asked Feb 12, 2017 in Probability & Statistics by piyag476 (1.5k points)

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GATE2014-3-26
Integration of the complex function $f(z)=\frac{z^2}{z^2-1}$ , in the counterclockwise direction, around $|z-1|$ = $1$, is $-\pi i$ 0 $\pi i$ 2$\pi i$

asked Feb 12, 2017 in Calculus by makhdoom ghaya (9.2k points)

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GATE2014-3-4
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of k is ________.

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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GATE2014-3-1
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$ ; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N$-$1$ $N$ $2N$

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.2k points)

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GATE2014-3-GA-9
The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students in $2011$ and $2012$ is equal, what is the ratio of male students in $2012$ to male students in $2011$? $1:1$ $2:1$ $1.5:1$ $2.5:1$

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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GATE2014-3-GA-5
The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. What is the average of the marks obtained by the class in the examination? $1.34$ $1.74$ $3.02$ $3.91$

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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GATE2014-3-GA-8
The Gross Domestic Product $(GDP)$ in Rupees grew at $7$% during $2012$-$2013$.For international comparison, the $GDP$ is compared in $US$ Dollars $(USD)$ after conversion based on the market exchange rate. During the period $2012$-$2013$ ... $USD$ during the period $2012$-$2013$ increased by $5 $% decreased by $13$% decreased by $20$% decreased by $11$%

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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GATE2014-2-28
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is $20$ $28$ $16$ $32$

asked Feb 12, 2017 in Calculus by makhdoom ghaya (9.2k points)

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GATE2014-2-27
Let $X$ be a random variable with probability density function $f(x)=\left\{\begin{matrix} 0.2,& for|x|\leq 1\\ 0.1,& for 1< |x|\leq 4\\ 0 & otherwise \end{matrix}\right.$ The probability $P(0.5<X<5)$ is ______.

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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GATE2014-2-26
To evaluate the double integral $\int_{0}^{8}(\int_{(y/2)}^{y/2+1}(\frac{2x-y}{2})dx)dy$ , we make the substitution $u=(\frac{2x-y}{2})$ and $v=\frac{y}{2}$ The integral will reduce $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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GATE2014-2-18
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$

asked Feb 12, 2017 in Calculus by makhdoom ghaya (9.2k points)

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20

GATE2014-2-5
Consider the differential equation $x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0$ . Which of the following is a solution to this differential equation for$x>0$? $e^x$ $x^2$ $1/x$ $lnx$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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21

GATE2014-2-3
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at x equal to $-\infty$ 0 1 $\infty$

asked Feb 12, 2017 in Numerical Methods by makhdoom ghaya (9.2k points)

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22

GATE2014-2-4
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ are purely imaginary. real and non-negative on the unit circle. equal in real and imaginary parts.

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.2k points)

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23

GATE2014-2-GA-9
The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in $2009$, by what percent did the number of male students increase in $2009?$

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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24

GATE2014-2-GA-8
If x is real and $|x^2 − 2x + 3|$ = $11$, then possible values of $| -x^3 + x^2 − x|$ include $2,4$ $2,14$ $4,52$ $14,52$

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.2k points)

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25

GATE2014-2-GA-6
The old city of Koenigsberg, which had a German majority population before World War $2$, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the ... Kaliningrad, as that was its original Russian name Poland and Lithuania are on the route from Kaliningrad to the rest of Russia

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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26

GATE2014-1-46
A system matrix is given as follows. $A=\begin{bmatrix} 0 & 1 & -1\\ -6 & 11 &-6 \\ -6& 11& 5 \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.2k points)

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27

GATE2014-1-27
A fair coin is tossed n times. The probability that the difference between the number of heads and tails is $(n-3)$ is $2^{-n}$ $0$ $n_{C_{n-3}}2^{-n}$ $2^{-n+3}$

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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28

GATE2014-1-28
The line integral of function $F$ = $yzi$, in the counterclockwise direction, along the circle $x^2$+$y^2$ = $1$ at $z$ = $1$ is $-2\pi$ $-\pi$ $\pi$ $2\pi$

asked Feb 12, 2017 in Calculus by makhdoom ghaya (9.2k points)

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29

GATE2014-1-17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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30

GATE2014-1-2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval ($0,\infty$) is $e^{-1}$ $e$ $1$-$e^{-1}$ $1$+$e^{-1}$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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31

GATE2014-1-1
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its solutions The system has a unique solution for any given $b_1$ and $b_2$ The system will have infinitely many solutions for any given $b_1$ and $b_2$ Whether ... a solution exists depends on the given $b_1$ and $b_2$ The system would have no solution for any values of $b_1$ and $b_2$

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.2k points)

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32

GATE2014-1-3
The solution for the differential equation $\frac{d^2x}{dt^2}=-9x$ with initial conditions $x(0)=1$ and $\frac{dx}{dt}|_{t=0}=1$ , is $t^2+t+1$ $sin3t+\frac{1}{3}cos3t+\frac{2}{3}$ $\frac{1}{3}sin3t+cos3t$ $cos3t$+$t$

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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33

GATE2014-1-5
Let $S$ be the set of points in the complex plane corresponding to the unit circle. (That is, $S$={$z$ : $|z|$=$1$}). Consider the function $f(z)=zz^*$ where $z^*$ denotes the complex conjugate of $z$. The $f(z)$ maps $s$ to which one of the following in the complex plane unit circle horizontal axis line segment from origin to $(1, 0)$ the point $(1, 0)$ the entire horizontal axis

asked Feb 12, 2017 in Complex Variables by makhdoom ghaya (9.2k points)

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34

GATE2014-1-GA-4
If $(z+1/z)^2$ = $98$, compute $(z^2+1/z^2)$

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.2k points)

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35

GATE2014-1-GA-9
In a survey, $300$ respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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36

GATE2014-1-GA-5
The roots of $ax^2+bx+c=0$ are real and positive. $a$, $b$ and $c$ are real. Then $ax^2+b|x|+c=0$ has no roots $2$ real roots $3$ real roots $4$ real roots

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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37

GATE2015-2-28
A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.

asked Feb 12, 2017 in Differential Equations by makhdoom ghaya (9.2k points)

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38

GATE2015-2-27
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the following is TRUE? The coin tosses are independent. R is fair, S is not. S is fair, R is not. The coin tosses are dependent.

asked Feb 12, 2017 in Probability & Statistics by makhdoom ghaya (9.2k points)

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39

GATE2015-2-26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.

asked Feb 12, 2017 in Calculus by makhdoom ghaya (9.2k points)

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40

GATE2015-2-3
Match the following. P. Stokes’s Theorem 1. $∯ D.ds = Q$ Q. Gauss’s Theorem 2. $\oint f(z) dz =0$ R. Divergence Theorem 3. $\int \int \int (\triangledown. A) dv = ∯ A. ds$ S. Cauchy’s Integral Theorem 4. $\int \int (\triangledown \times A).ds = \oint A. dl$ (A) P-2 Q-1 R-4 S-3 (B) P-4 Q-1 R-3 S-2 (C) P-4 Q-3 R-1 S-2 (D) P-3 Q-4 R-2 S-1

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.2k points)