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1
GATE IN 2021 | Question: 1
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is $1$ $2$ $3$ $4$
Consider the row vectors $v=(1,0)$ and $w=(2,0)$. The rank of the matrix $M=2v^{T}v+3w^{T}w$, where the superscript $\text{T}$ denotes the transpose, is$1$$2$$3$$4$
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GATE IN 2021 | Question: 2
Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is $0$ $1$ $2$ $\infty$
Consider the sequence $x_{n}=0.5x_{n-1}+1,n=1,2, \dots \:\dots$ with $x_0=0$ . Then $\displaystyle \lim_{n\rightarrow \infty} x_n$ is$0$$1$$2$$\infty$
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GATE IN 2021 | Question: 23
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
Consider the function $f\left ( x \right )=-x^{2}+10x+100$. The minimum value of the function in interval $[5,10]$ is ___________.
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GATE IN 2021 | Question: 25
The determinant of the matrix $\text{M}$ shown below is _______________. $M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$
The determinant of the matrix $\text{M}$ shown below is _______________. $$M=\begin{bmatrix} 1 & 2 & 0 & 0\\ 3 & 4 & 0 & 0\\ 0 & 0 & 4 & 3\\ 0 & 0 & 2 & 1 \end{bmatrix}$$...
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GATE IN 2021 | Question: 38
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
Given $A=\begin{pmatrix} 2 & 5\\ 0 & 3 \end{pmatrix}$. The value of the determinant $\left | A^{4}-5A^{3}+6A^{2}+2I \right |=$ _______________.
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11
GATE2020 IN: 27
Consider the differential equation $\frac{dx}{dt}=\sin(x),$ with the initial condition $x(0)=0. $ The solution to this ordinary differential equation is __________ $x(t)=0$ $x(t)=\sin(t)$ $x(t)=\cos(t)$ $x(t)=\sin(t)-\cos(t)$
Consider the differential equation $\frac{dx}{dt}=\sin(x),$ with the initial condition $x(0)=0. $The solution to this ordinary differential equation is __________$x(t)=0$...
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GATE2020 IN: 28
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1. The equation that describes this line is __________. $\text{y=-0.5x+1}$ $\text{y=x-0.5}$ $\text{y=0.5x-1}$ $\text{y=2x+1}$
A straight line drawn on an x-y plane intercepts the x-axis at -0.5 and the y-axis at 1.The equation that describes this line is __________.$\text{y=-0.5x+1}$$\text{y=x-0...
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GATE2020 IN: 31
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
Consider the function $f(x,y)=x^2+y^2.$ The minimum value the function attains on the line $x+y=1$ (rounded off to one decimal place) is __________.
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18
GATE2020: 15
Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction is ____________ $0$ $2\pi i$ $-2\pi i$ $4\pi i$
Let $f(z)=\frac{1}{z+a},a>0.$ the value of the integral $\oint f(z)dz$ over a circle $C$ with center $(-a,0)$ and radius $R>0$ evaluated in the anti-clockwise direction i...
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GATE2020: 19
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
Consider the signal $x(t)=e^{-|t|}$. Let $X(j\omega)=\int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ be the Fourier transform of $x(t)$. The value of $X(j0) $is _________
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22
GATE2019 IN: 2
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightarrow{\bigtriangledown}$ x $\overrightarrow{A}$| is -1 0 1 $\infty$
The vector function $\overrightarrow{A}$ is given by $\overrightarrow{A}$ = $\overrightarrow{\bigtriangledown}$u , where u(x, y) is a scalar function. Then |$\overrightar...
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GATE2019 IN: 3
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is 4/15 7/16 ½ 8/15
A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and...
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GATE2019 IN: 16
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.
A 3 x 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is $\_\_\_\_$.
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25
GATE2019 IN: 26
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional to x$^{-1}$ x$^{2}$ x$^{3}$ x$^{4}$
The curve y = f(x) is such that the tangent to the curve at every point (x,y) has a y-axis intercept c, given by c = -y. Then,f(x) is proportional tox$^{-1}$x$^{2}$x$^{3}...
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34
GATE2018IN: 4
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
Consider two functions f(x) = (x – 2)$^2$ and g(x) = 2x – 1, where x is real. The smallest value of x for which f(x) = g(x) is $\_\_\_\_\_\_$
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35
GATE2018IN: 3
X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is 0 1 2 3
X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X – Y. The variance of Z is0123
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GATE2018IN: 1
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 0 0,0,1 0,1,1 1,1,1
Let N be a 3 by 3 matrix with real numbers entries. The matrix N is such that N$^2$ = 0. The eigen values of N are 0, 0, 00,0,10,1,11,1,1
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39
GATE2017: 35
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
The Laplace transform of a casual signal $y(t)$ is $Y(s)$ = $\frac{s+2}{s+6}$. The value of the signal $y(t)$ at $t $ = $0.1\:s$ is_____________ unit.
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40
GATE2017: 27
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
The angle between two vectors $X_1=\begin{bmatrix}2 & 6 & 14\end{bmatrix}^T$ and $X_2=\begin{bmatrix}-12 & 8 & 16\end{bmatrix}^T$ in radian is __________.
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