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GATE Chemical 2013 | Question: 3
Which of the following statements are TRUE?P.The eigenvalues of a symmetric matrix are realQ.The value of the determinant of an orthogonal matrix can only be +1R.The tr...
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GATE Chemical 2020 | Question: 54
Given $\dfrac{dy}{dx}=y-20$, and $y \mid_{x=0}=40$, the value of $y$ at $x=2$ is _________ (round off to nearest integer)
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GATE Chemical 2012 | Question: 5
Consider the following $(2\times2)$ matrix $\left( \begin{array}{c} 4 & 0 \\ 0 & 4 \end{array} \right)$Whi...
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GATE Chemical 2017 | Question: 26
For the initial value problem$$\frac{dx}{dt}=\sin\left ( t \right ),\:\:\:\:x\left ( 0 \right )=0$$the value of $x$ at $t=\pi /3$ , is _____________.
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GATE Chemical 2016 | Question: 30
Values of $f\left ( x \right )$ in the interval $\left [ 0,4 \right ]$ are given below.$\begin{array}{|cl|cI|cI|cI|cI|cI|}\hline&{x} & \text{0} & \text{1} & \text{2} & \t...
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GATE Chemical 2018 | Question: 2
The fourth order Runge-Kutta ($RK4$) method to solve an ordinary differential equation $\frac{dy}{dx}=f\left ( x,y \right )$ is given as $$y\left ( x+h \right )=y\left ( ...
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GATE Chemical 2015 | Question: 11
The following set of the three vectors$$\begin{pmatrix} 1\\2\\1 \end{pmatrix}, \begin{pmatrix} x\\6\\x \end{pmatrix}\:and \:\begin{pmatrix} 3\\4 \\2 \end{pmatrix},$$is li...
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GATE Chemical 2013 | Question: 2
For two rolls of a fair die, the probability of getting a 4 in the first roll and a number less than 4 in the second roll, up to 3 digits after the decimal point, is ____...
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GATE CH 2021 | Question: 16
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ ... $x=0$ $f(x)$ is differentiable at $x=0$
For the function $f(x) = \begin{cases} -x, & x<0 \\ x^2, & x \geq 0 \end{cases}$ the $\text{CORRECT}$ statement(s) is/are$f(x)$ is continuous at $x=1$$f(x) $ is different...
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GATE Chemical 2016 | Question: 3
What are the modulus $\left ( r \right )$ and argument $\left ( \theta \right )$ of the complex number $3+4i$ ?$r=\sqrt{7}, \theta =tan^{-1}\left ( \frac{4}{3} \right )$$...
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GATE Chemical 2015 | Question: 14
A complex-valued function, $f(z)$, given below is analytic in domain $D$:$$f\left ( z \right )=u\left ( x,y\right )+i\nu \left ( x,y\right )\:\:\:\:\:\:\:z=x+iy$$Which of...
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GATE Chemical 2014 | Question: 26
Consider the following differential equation$\frac{dy}{dx}=x+In\:\left ( y \right ); y=2 \: at \: x=0$The solution of this equation at $x=0.4$ using Euler method with a s...
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GATE Chemical 2016 | Question: 1
Which one of the following is an iterative technique for solving a system of simultaneous linear algebraic equations?Gauss eliminationGauss-JordanGauss-Seidel$LU$ decompo...
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GATE Chemical 2013 | Question: 29
The value of the integral${\scriptstyle \int^{0.5} _{0.1}}$ e$^{-x^3}$dxevaluated by Simpson’s rule using 4 subintervals (up to 3 digits after the decimal point) is $\_...
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GATE Chemical 2012 | Question: 2
If $a$ and $b$ are arbitrary constants, then the solutions to the ordinary differential equation $\dfrac{d^...
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GATE Chemical 2012 | Question: 3
For the function $f(t) = e^{-t}/\tau$,the Taylor series approximation for $t\ll$$\tau$ is$1+\frac{t}{\tau}$$1-\frac{t}{\tau}$$1-\frac{t^2}{2\tau^2}$$1+t$
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GATE CH 2021 | Question: 20
$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$ ... is __________
$\textbf{A, B, C}$ and $\textbf{D}$ are vectors of length $4$. $$\textbf{A} = \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \end{bmatrix} \\ \textbf{B} = \begin{bmatrix}b_1 & b_2...
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GATE Chemical 2016 | Question: 27
What is the solution for the second order differential equation $\frac{\mathrm{d} ^{2}y}{\mathrm{d} x}^{2}+y=0$, with the initial conditions $y\left | _{x-0}=5\:and\:\fra...
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GATE Chemical 2015 | Question: 13
Consider a linear ordinary differential equation: $\frac{dy}{dx}+p\left ( x \right )y=r\left ( x \right )$. Functions $p\left ( x \right )$ and $r\left ( x \right )$ are...
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GATE Chemical 2014 | Question: 9
Integral of the time-weighted absolute error $(ITAE)$ is expressed as$\int _{0}^{\infty }\frac{\left | \varepsilon \left ( t \right ) \right |}{t^{2}}dt$$\int _{0}^{\inft...
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GATE Chemical 2014 | Question: 3
If $f*(x)$ is the complex conjugate of $f(x)=\cos(x) + i\: \sin(x)$, then for real $a$ and $b$, $\int _{a}^{b}f*\left ( x \right )f\left ( x \right )$ is $ALWAYS$positive...
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GATE Chemical 2020 | Question: 3
Consider the following continuously differentiable function $$\textbf{v}(x,y,z)=3x^2y \textbf{ i} + 8y^2z \textbf{ j} + 5xyz \textbf{ k}$$ where $\textbf{i, j,}$ and $\te...
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GATE Chemical 2015 | Question: 39
For complex variable $z$, the value of the contour integral $\frac{1}{2\pi i} \underset{C}{\int }\frac{e^{-2z}}{z(z-3)}dz$ along the clockwise contour $C:\left | z \right...
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GATE Chemical 2014 | Question: 2
For the time domain function $f(t)=t^{2}$, which $ONE$ of the following is the Laplace transform of $\int _{0}^{t}f\left ( t \right )dt$?$\frac{3}{s^{4}}$$\frac{1}{4s^{2}...
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GATE Chemical 2014 | Question: 1
Gradient of a scalar variable is alwaysa vectora scalara dot productzero
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GATE Chemical 2013 | Question: 1
The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15,respectively.what are the median and the mode for these data?18 and 11, respectively13 an...
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GATE Chemical 2018 | Question: 4
The figure which represents for $y=\frac{sin \:x}{x}$ for $x>0$ ($x$ in radians) is
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GATE Chemical 2016 | Question: 28
The model $y=mx^{2}$ is to be fit to the data given below.$$\begin{array}{|cl|cI|}\hline&{x} & {1} & {\sqrt{2}} & {\sqrt{3}} \\ \hline &{y} & {2} & {5} & {8} \\ \hline \e...
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GATE Chemical 2013 | Question: 7
An equation of state is explicit in pressure $p$ and cubic in the specific volume $v$. At the critical point $‘c’$ , the isotherm passing through $‘c’$ satisfies$...
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GATE CH 2021 | Question: 34
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ ... order of convergence for this iterative scheme near the solution is ________
To solve an algebraic equation $f(x)=0$, an iterative scehme of the type $x_{n+1} = g(x_n)$ is proposed, where $g(x)=x-\dfrac{f(x)}{f’(x)}$.At the solution $x=s,\: g’...
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GATE Chemical 2014 | Question: 27
The integrating factor for the differential equation$\frac{dy}{dx}-\frac{y}{1+x}=\left ( 1+x \right )$ is$\frac{1}{1+x}$$(1+x)$$x(1+x)$$\frac{x}{1+x}$
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GATE Chemical 2014 | Question: 28
The differential equation $\frac{d^{2}y}{dx^{2}}+x^{2}\frac{dy}{dx}+x^{3}y=e^{x}$ is a non-linear differential equation of first degreelinear differential equation of fir...
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GATE Chemical 2015 | Question: 38
The solution of the non-linear equation$$x^{3}-x=0$$is to be obtained using Newton-Raphson method. If the initial guess is $x=0.5$, the method converges to which one of t...
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GATE CH 2021 | Question: 35
The probability distribution function of a random variable $X$ is shown in the following figure. From this distribution, ... is _______ (round off to $3$ decimal places)
The probability distribution function of a random variable $X$ is shown in the following figure.From this distribution, random samples with sample size $n=68$ are taken. ...
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GATE Chemical 2013 | Question: 26
For the functionf(z) = $\frac{1}{(2-z)(z+2)}$the residue at z = 2 is $\_\_\_\_\_$
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GATE Chemical 2016 | Question: 26
A set of simultaneous linear algebraic equations is represented in a matrix form as shown below.$\begin{bmatrix} 0 &0 &0 &4 &13 \\ 2& 5& 5& 2& 10\\ 0&0 &2 &5 &3 \\ 0&0 &0...
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GATE Chemical 2015 | Question: 37
A vector $u=-2y\hat{i}+2x\hat{j}$, where $\hat{i}$ and $\hat{j}$ are unit vectors in $x$ and $y$ directions, respectively. Evaluate the line integral$$I=\oint _{C}u.dr$$w...
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GATE Chemical 2013 | Question: 28
The solution of the differential equation$\frac{d^2y}{dx^2}$ – $\frac{dy}{dx}$ + 0.25y = 0, given y = 0 at x = 0 and $\frac{dy}{dx}$ = 1 at x = 0 isxe$^{0.5x}$ – xe$...
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GATE Chemical 2013 | Question: 27
The solution of the differential equation$\frac{dy}{dx}$ – y$^{2}$ = 0, given y=1 at x=0 is$\frac{1}{1+x}$$\frac{1}{1-x}$$\frac{1}{(1-x)^2}$$\frac{x^3}{3}$+1
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GATE CH 2021 | Question: 36
For the ordinary differential equation $\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$ with ... $3$ decimal places).
For the ordinary differential equation $$\dfrac{d^3y}{dt^3}+6 \dfrac{d^2y}{dt^2}+11 \dfrac{dy}{dt}+6y=1$$ with initial conditions $y(0)=y’(0) = y’’(0)=y’’’(0)...
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