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Most answered questions in Engineering Mathematics

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GATE2016-3-2
$\displaystyle{}\lim_{x\rightarrow 0}\dfrac{\log_e(1+4x)}{e^{3x}-1}$ is equal to $0 \\$ $\dfrac{1}{12} \\$ $\dfrac{4}{3} \\$ $1$
$\displaystyle{}\lim_{x\rightarrow 0}\dfrac{\log_e(1+4x)}{e^{3x}-1}$ is equal to$0 \\$$\dfrac{1}{12} \\$$\dfrac{4}{3} \\$$1$
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GATE2016-3-3
Solutions of Laplace’s equation having continuous second-order partial derivatives are called biharmonic functions harmonic functions conjugate harmonic functions error functions
Solutions of Laplace’s equation having continuous second-order partial derivatives are calledbiharmonic functionsharmonic functionsconjugate harmonic functionserror fun...
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GATE2016-3-4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
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GATE2016-3-5
The root of the function $f(x) = x^3+x-1$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $x_0=1$ is $0.682$ $0.686$ $0.750$ $1.000$
The root of the function $f(x) = x^3+x-1$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $x_0=1$ is$0.682$$0.686$$0.750$...
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GATE2016-2-27
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\Gamma$ is
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\G...
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GATE2016-2-29
The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ is ___________
The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ i...
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GATE2016-2-2
The values of $x$ for which the function $f(x)=\dfrac{x^2-3x-4}{x^2+3x-4}$ is NOT continuous are $4$ and $−1$ $4$ and $1$ $-4$ and $1$ $−4$ and $−1$
The values of $x$ for which the function$$f(x)=\dfrac{x^2-3x-4}{x^2+3x-4}$$is NOT continuous are$4$ and $−1$$4$ and $1$$-4$ and $1$$−4$ and $−1$
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GATE2016-2-3
Laplace transform of $\cos( \omega t)$ is $\dfrac{s}{s^2+\omega ^2} \\$ $\dfrac{\omega }{s^2+\omega ^2} \\$ $\dfrac{s}{s^2-\omega ^2} \\$ $\dfrac{\omega }{s^2-\omega ^2}$
Laplace transform of $\cos( \omega t)$ is$\dfrac{s}{s^2+\omega ^2} \\$$\dfrac{\omega }{s^2+\omega ^2} \\$$\dfrac{s}{s^2-\omega ^2} \\$$\dfrac{\omega }{s^2-\omega ^2}$
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GATE2016-2-4
A function of the complex variable $z= x+iy$, is given as $f(x,y) =u(x,y) +iv(x,y)$ , where $u(x,y) = 2kxy$ and $ v(x,y) =x^2 −y^2$. The value of $k$, for which the function is analytic, is _____
A function of the complex variable $z= x+iy$, is given as $f(x,y) =u(x,y) +iv(x,y)$ , where $u(x,y) = 2kxy$ and $ v(x,y) =x^2 −y^2$. The value of $k$, for which the fun...
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GATE2016-2-5
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is linear parabolic logarithmic hyperbolic
Numerical integration using trapezoidal rule gives the best result for a single variable function, which islinearparaboliclogarithmichyperbolic
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GATE2016-2-1
The condition for which the eigenvalues of the matrix $A=\begin{bmatrix} 2 & 1\\ 1 & k \end{bmatrix}$ are positive, is $k > 1/2$ $k > −2$ $k > 0$ $k < −1/2$
The condition for which the eigenvalues of the matrix$A=\begin{bmatrix} 2 & 1\\ 1 & k \end{bmatrix}$are positive, is$k 1/2$$k −2$$k 0$$k < −1/2$
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GATE2016-1-26
Consider the function $f(x)=2x^3-3x^2$ in the domain $[-1,2]$ The global minimum of $f(x)$ is ____________
Consider the function $f(x)=2x^3-3x^2$ in the domain $[-1,2]$ The global minimum of $f(x)$ is ____________
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GATE2016-1-27
If $y=f(x)$ satisfies the boundary value problem ${y}''+9y=0$ , $y(0)=0$ , $y(\pi /2)=\sqrt{2}$, then $y(\pi /4)$ is ________
If $y=f(x)$ satisfies the boundary value problem ${y}''+9y=0$ , $y(0)=0$ , $y(\pi /2)=\sqrt{2}$, then $y(\pi /4)$ is ________
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GATE2016-1-29
Gauss-Seidel method is used to solve the following equations (as per the given order): $x_1+2x_2+3x_3=5$ $2x_1+3x_2+x_3=1$ $3x_1+2x_2+x_3=3$ Assuming initial guess as $x_1=x_2=x_3=0$ , the value of $x_3$ after the first iteration is __________
Gauss-Seidel method is used to solve the following equations (as per the given order):$x_1+2x_2+3x_3=5$$2x_1+3x_2+x_3=1$$3x_1+2x_2+x_3=3$Assuming initial guess as $x_1=x_...
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GATE2016-1-1
The solution to the system of equations $\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is $6,2$ $-6,2$ $-6,-2$ $6,-2$
The solution to the system of equations$\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is$6,2$$-6,2$$...
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GATE2016-1-2
If $f(t)$ is a function defined for all $t \geq 0$, its Laplace transform $F(s)$ is defined as $\int_{0}^{\infty }e^{st}f(t)dt \\$ $\int_{0}^{\infty }e^{-st}f(t)dt \\$ $\int_{0}^{\infty }e^{ist}f(t)dt \\$ $\int_{0}^{\infty }e^{-ist}f(t)dt$
If $f(t)$ is a function defined for all $t \geq 0$, its Laplace transform $F(s)$ is defined as$\int_{0}^{\infty }e^{st}f(t)dt \\$$\int_{0}^{\infty }e^{-st}f(t)dt \\$$\int...
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GATE2016-1-3
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as $-x^2 + y^2 + $ constant $x^2 – y^2 +$ constant $x^2 + y^2 +$ constant $-(x^2 + y^2) +$ constant
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as$-x^2 + y^2 + $ const...
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GATE2016-1-4
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $μ$. The standard deviation for this distribution is given by $\sqrt{\mu }$ $\mu ^2$ $\mu$ $1/\mu$
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $μ$. The standard deviation for this distribution is given by$\sqrt{\...
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GATE2016-1-5
Solve the equation $x=10\cos(x)$ using the Newton-Raphson method. The initial guess is $x=\pi /4$. The value of the predicted root after the first iteration, up to second decimal, is ________
Solve the equation $x=10\cos(x)$ using the Newton-Raphson method. The initial guess is $x=\pi /4$. The value of the predicted root after the first iteration, up to second...
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GATE2015-3-43
Newton-Raphson method is used to find the roots of the equation, $x^3+3x^2+3x-1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ________
Newton-Raphson method is used to find the roots of the equation, $x^3+3x^2+3x-1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ___...
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GATE2015-3-41
The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
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GATE2015-3-16
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
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GATE2015-3-13
Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________
Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________
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GATE2015-3-15
The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________
The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________
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GATE2015-2-27
The surface integral $\displaystyle{} \int \int_{s}^{ }\dfrac{1}{\pi }(9xi-3yj)\cdot nds$ over the sphere given by $x^2+y^2+z^2=9$ is
The surface integral $\displaystyle{} \int \int_{s}^{ }\dfrac{1}{\pi }(9xi-3yj)\cdot nds$ over the sphere given by $x^2+y^2+z^2=9$ is
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GATE2015-2-28
Consider the following differential equation: $\dfrac{dy}{dt}=-5y$; initial condition: $y=2$ at $t=0$. The value of $y$ at $t=3$ is $-5e^{-10}$ $2e^{-10}$ $2e^{-15}$ $-15e^{2}$
Consider the following differential equation:$\dfrac{dy}{dt}=-5y$; initial condition: $y=2$ at $t=0$. The value of $y$ at $t=3$ is$-5e^{-10}$$2e^{-10}$$2e^{-15}$$-15e^...
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GATE2015-2-1
At least one eigenvalue of a singular matrix is positive zero negative imaginary
At least one eigenvalue of a singular matrix ispositivezeronegativeimaginary
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GATE2015-2-2
At $x$ = $0$, the function $f(x) = \mid x \mid $ has a minimum a maximum a point of inflexion neither a maximum nor minimum
At $x$ = $0$, the function $f(x) = \mid x \mid $ hasa minimuma maximuma point of inflexionneither a maximum nor minimum
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