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GATE Electrical 2021 | Question: 38
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is ___________________.
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is _________________...
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GATE Electrical 2020 | Question: 42
The number of purely real elements in a lower triangular representation of the given $3\times 3$ ... $5$ $6$ $8$ $9$
The number of purely real elements in a lower triangular representation of the given $3\times 3$ matrix, obtained through the given decomposition is ______________.$$\beg...
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GATE Electrical 2021 | Question: 1
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are $1$ and $1$ $1$ and $-1$ $j$ and $-j$ $pq$ and $-pq$
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are$1$ and $1$$1$ and $-1$$j$ and $...
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GATE Electrical 2021 | Question: 2
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ ... $p\left ( z \right )=0$ come in conjugate pairs All the roots cannot be real
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ is a complex number.Which one of the following is true?$\text{conjugate}\:\lef...
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GATE Electrical 2021 | Question: 13
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Then $u+v=$ _______________.
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Th...
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GATE Electrical 2021 | Question: 26
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ has two real roots one real root three real roots no real roots
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ hastwo real rootsone real rootthree real rootsno real roots
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GATE Electrical 2017 Set 2 | Question: 20
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
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GATE Electrical 2017 Set 2 | Question: 19
Let $x$ and $y$ be integers satisfying the following equations $2x^{2}+y^{2}=34$ $x+2y=11$ The value of $(x+y)$ is _______.
Let $x$ and $y$ be integers satisfying the following equations$2x^{2}+y^{2}=34$$x+2y=11$The value of $(x+y)$ is _______.
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GATE Electrical 2020 | Question: 2
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ ...
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ as applicable?...
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GATE Electrical 2020 | Question: 26
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively, ______. $7$ and $1/4$ $7$ and $1$ $-2$ and $-1/2$ $1$ and $1/4$
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively...
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GATE Electrical 2020 | Question: 5
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is: $\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is:$$\int _{C}\frac{z^{2}+1}{z...
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GATE Electrical 2019 | Question: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$ $3te^{-t}+e^{-t}$ $3e^{-t}$ $2te^{-t}+e^{-t}$ $4te^{-t}+e^{-t}$
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$$3te^{-t}+e^{-t}$$3e^{-t}$$2te^{-t}+e^{-t}$$4te^{-t}+e^{-t}$
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GATE Electrical 2019 | Question: 2
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are $4$ and $9$ $2$ and $3$ $-2$ and $-3$ $16$ and $81$
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are$4$ and $9$$2$ and $3$$-2$ and $-3$$16$ and $81$
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GATE Electrical 2019 | Question: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}-1}{z} \\ $ $\frac{z^{2}-1}{z+2} \\ $ $\frac{z^{2}-1}{z-0.5} \\ $ $\frac{z^{2}-1}{z+j0.5} $
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ?$\frac{z^{2}-1}{z} \\ $$\frac{z^{2}-1}{z+2} \\ $$\frac{z^{2}-1}{z-0.5} \\ $$\frac{z^...
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GATE Electrical 2019 | Question: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-3,2)\rightarrow(2,6,2) \rightarrow(2,6,-1) $ is___________.
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-...
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GATE Electrical 2019 | Question: 24
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
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GATE Electrical 2019 | Question: 27
The closed-loop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counter-clockwise, is $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$
The closed-loop line integral $$\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$$evaluated Counter-clockwise, is $+8 j \pi$$-8 j \pi$$-4 j \pi$$+4 j \pi$
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GATE Electrical 2019 | Question: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
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GATE Electrical 2018 | Question: 44
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$...
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GATE Electrical 2018 | Question: 43
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
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GATE Electrical 2018 | Question: 42
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$...
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GATE Electrical 2018 | Question: 35
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is $1$ $0$ $-1$ $-2$
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is$1$$0$$-1$$-2$
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GATE Electrical 2018 | Question: 34
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is$3$$4$$5$$6$
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GATE Electrical 2018 | Question: 18
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0...
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GATE Electrical 2018 | Question: 13
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is $\frac{\pi i}{2} \\ $ $2 \pi i\\$ $ – \frac{\pi i}{2}\\$ $-2 \pi i$
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is$\frac{\pi i}...
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GATE Electrical 2018 | Question: 12
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2 \textbf{j} + 2 \textbf{k}$ is $1$ $0.95$ $0.93$ $0.9$
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2...
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