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GATE2016-3-26
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
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GATE2015-1-29
The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is $425/432$ $19/144$ $13/144$ $125/432$
The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is$425/432$$19/144$$13/144$$125/432$
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GATE2015-1-3
Simpson’s $\dfrac{1}{3}$ rule is used to integrate the function $f(x)=\dfrac{3}{5}x^2+\dfrac{9}{5}$ between $x = 0$ and $x=1$ using the least number of equal sub-intervals. The value of the integral is ______________
Simpson’s $\dfrac{1}{3}$ rule is used to integrate the function $f(x)=\dfrac{3}{5}x^2+\dfrac{9}{5}$ between $x = 0$ and $x=1$ using the least number of equal sub-interv...
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GATE2016-2-27
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\Gamma$ is
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\G...
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GATE2015-3-41
The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
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GATE2015-1-28
Find the solution of $\dfrac{d^2y}{dx^2}=Y$ which passes through the origin and the point $\left(\ln 2,\dfrac{3}{4}\right)$ $y=\dfrac{1}{2}e^x-e^{-x} $ $y=\dfrac{1}{2}(e^x+e^{-x}) $ $y=\dfrac{1}{2}(e^x-e^{-x}) $ $y=\dfrac{1}{2}e^x+e^{-x} $
Find the solution of $\dfrac{d^2y}{dx^2}=Y$ which passes through the origin and the point $\left(\ln 2,\dfrac{3}{4}\right)$$y=\dfrac{1}{2}e^x-e^{-x} $$y=\dfrac{1}{2}(e^x+...
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GATE2016-2-2
The values of $x$ for which the function $f(x)=\dfrac{x^2-3x-4}{x^2+3x-4}$ is NOT continuous are $4$ and $−1$ $4$ and $1$ $-4$ and $1$ $−4$ and $−1$
The values of $x$ for which the function$$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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GATE2016-2-1
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$$k < −1/2$
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GATE2016-1-3
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as $-x^2 + y^2 + $ constant $x^2 – y^2 +$ constant $x^2 + y^2 +$ constant $-(x^2 + y^2) +$ constant
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{-1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as$-x^2 + y^2 + $ const...
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GATE2015-2-2
At $x$ = $0$, the function $f(x) = \mid x \mid $ has a minimum a maximum a point of inflexion neither a maximum nor minimum
At $x$ = $0$, the function $f(x) = \mid x \mid $ hasa minimuma maximuma point of inflexionneither a maximum nor minimum
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GATE2015-1-5
Given two complex numbers $z_1=5+(5\sqrt{3})i$ and $z_2=\dfrac{2}{\sqrt{3}}+2i$ , the argument of $\dfrac{z_1}{z_2}$ in degrees is $0$ $30$ $60$ $90$
Given two complex numbers $z_1=5+(5\sqrt{3})i$ and $z_2=\dfrac{2}{\sqrt{3}}+2i$ , the argument of $\dfrac{z_1}{z_2}$ in degrees is$0$$30$$60$$90$
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GATE2015-1-2
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? $I$ $II$ $III$ $IV$
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?$I$$II$$III$$IV$
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GATE2016-1-1
The solution to the system of equations $\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is $6,2$ $-6,2$ $-6,-2$ $6,-2$
The solution to the system of equations$\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is$6,2$$-6,2$$...
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GATE MOCK TEST(MADE EASY)
The area enclosed between the circles r=2a cos$\theta$ and r=a$\sqrt{2}$.
The area enclosed between the circles r=2a cos$\theta$ and r=a$\sqrt{2}$.
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GATE2016-3-5
The root of the function $f(x) = x^3+x-1$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $x_0=1$ is $0.682$ $0.686$ $0.750$ $1.000$
The root of the function $f(x) = x^3+x-1$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $x_0=1$ is$0.682$$0.686$$0.750$...
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GATE2016-2-4
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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