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Previous GATE Questions in Engineering Mathematics

26 votes
7 answers
511
GATE CSE 2000 | Question: 1.3
The determinant of the matrix $\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$ $4$ $0$ $15$ $20$
The determinant of the matrix $$\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$$$4$$0$$15$$20$
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39 votes
6 answers
512
GATE CSE 2000 | Question: 1.1
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is $3$ $8$ $9$ $12$
The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is$3$$8$$9$$12$
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0 votes
0 answers
513
GATE CSE 1993 | Question: 02.10
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0 votes
1 answer
514
GATE CSE 1993 | Question: 02.9
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0 votes
0 answers
515
GATE CSE 1993 | Question: 02.8
Given $\vec v= x\cos ^2y \hat i + x^2e^z\hat j+ z\sin^2y\hat k$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes, the value of integral $\int^1 \int_s \vec V. \hat n dS$ is __________.
Given $\vec v= x\cos ^2y \hat i + x^2e^z\hat j+ z\sin^2y\hat k$ and $S$ the surface of a unit cube with one corner at the origin and edges parallel to the coordinate axes...
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24 votes
2 answers
516
GATE CSE 1993 | Question: 02.7
If $A = \begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i \end{pmatrix}$ the matrix $A^4$, calculated by the use of Cayley-Hamilton theorem or otherwise, is _______
If $A = \begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & -1 & 0 & -1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & -i \end{pmatrix}$ the matrix $A^4$, calculated by the use of Cayley-Hamilton theo...
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4 votes
2 answers
517
GATE CSE 1993 | Question: 02.6
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
The value of the double integral $\int^{1}_{0} \int_{0}^{\frac{1}{x}} \frac {x}{1+y^2} dxdy$ is_________.
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1 votes
1 answer
518
GATE CSE 1993 | Question: 02.3
If the linear velocity $\vec V$ is given by $\vec V = x^2y\,\hat i + xyz\,\hat j – yz^2\,\hat k$ The angular velocity $\vec \omega$ at the point $(1, 1, -1)$ is ________
If the linear velocity $\vec V$ is given by $$\vec V = x^2y\,\hat i + xyz\,\hat j – yz^2\,\hat k$$The angular velocity $\vec \omega$ at the point $(1, 1, -1)$ is ______...
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1 votes
0 answers
519
GATE CSE 1993 | Question: 02.2
The radius of convergence of the power series$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$ is: _____________
The radius of convergence of the power series$$\sum_{}^{\infty} \frac{(3m)!}{(m!)^3}x^{3m}$$ is: _____________
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15 votes
3 answers
520
GATE CSE 1993 | Question: 02.1
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
$\displaystyle \lim_{x \to 0} \frac{x(e^x - 1) + 2(\cos x -1)}{x(1 - \cos x)}$ is __________
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1 votes
1 answer
521
GATE CSE 1993 | Question: 01.7
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ has no local extremum one local minimum but no local maximum one local maximum but no local minimum one local minimum and one local maximum
The function $f\left(x,y\right) = x^2y - 3xy + 2y +x$ hasno local extremumone local minimum but no local maximumone local maximum but no local minimumone local minimum an...
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49 votes
7 answers
524
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
The eigen vector $(s)$ of the matrix $$\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$$ is (are)$(0,0,\alpha)$$(\alpha,0,0)$$(0,0,1)$$(0,\al...
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40 votes
4 answers
526
GATE CSE 1992 | Question: 14a
If $G$ is a group of even order, then show that there exists an element $a≠e$, the identity in $G$, such that $a^2 = e$.
If $G$ is a group of even order, then show that there exists an element $a≠e$, the identity in $G$, such that $a^2 = e$.
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33 votes
3 answers
527
GATE CSE 1992 | Question: 03,iii
How many edges can there be in a forest with $p$ components having $n$ vertices in all?
How many edges can there be in a forest with $p$ components having $n$ vertices in all?
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24 votes
4 answers
528
GATE CSE 1992 | Question: 02,xvi
Which of the following is/are a tautology? $a \vee b \to b \wedge c$ $a \wedge b \to b \vee c$ $a \vee b \to \left(b \to c \right)$ $a \to b \to \left(b \to c \right)$
Which of the following is/are a tautology?$a \vee b \to b \wedge c$$a \wedge b \to b \vee c$$a \vee b \to \left(b \to c \right)$$a \to b \to \left(b \to c \right)$
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9 votes
4 answers
529
GATE CSE 1992 | Question: 02,viii
A non-planar graph with minimum number of vertices has $9$ edges, $6$ vertices $6$ edges, $4$ vertices $10$ edges, $5$ vertices $9$ edges, $5$ vertices
A non-planar graph with minimum number of vertices has$9$ edges, $6$ vertices$6$ edges, $4$ vertices$10$ edges, $5$ vertices$9$ edges, $5$ vertices
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10 votes
1 answer
530
GATE CSE 1992 | Question: 01,x
Maximum number of edges in a planar graph with $n$ vertices is _____
Maximum number of edges in a planar graph with $n$ vertices is _____
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