1
GATE EE 2016 Set 2
+2
-0.6
Let $$P = \left[ {\matrix{ 3 & 1 \cr 1 & 3 \cr } } \right].$$ Consider the set $$S$$ of all vectors $$\left( {\matrix{ x \cr y \cr } } \right)$$ such that $${a^2} + {b^2} = 1$$ where $$\left( {\matrix{ a \cr b \cr } } \right) = P\left( {\matrix{ x \cr y \cr } } \right).$$ Then $$S$$ is
A
a circle of radius $$\sqrt {10}$$
B
a circle of radius $${1 \over {\sqrt {10} }}$$
C
an ellipse with major axis along $$\left( {\matrix{ 1 \cr 1 \cr } } \right)$$
D
an ellipse with minor axis along $$\left( {\matrix{ 1 \cr 1 \cr } } \right)$$
2
GATE EE 2016 Set 2
+2
-0.6
The value of the integral $$\,\,2\int_{ - \infty }^\infty {\left( {{{\sin \,2\pi t} \over {\pi t}}} \right)} dt\,\,$$ is equal to
A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$2$$
3
GATE EE 2016 Set 2
+1
-0.3
The value of line integral $$\,\,\int {\left( {2x{y^2}dx + 2{x^2}ydy + dz} \right)\,\,}$$ along a path joining the origin $$(0, 0, 0)$$ and the point $$(1, 1, 1)$$ is
A
$$0$$
B
$$2$$
C
$$4$$
D
$$6$$
4
GATE EE 2016 Set 2
Numerical
+2
-0
The line integral of the vector field $$\,\,F = 5xz\widehat i + \left( {3{x^2} + 2y} \right)\widehat j + {x^2}z\widehat k\,\,$$ along a path from $$(0, 0, 0)$$ to $$(1,1,1)$$ parameterized by $$\left( {t,{t^2},t} \right)$$ is _________.
GATE EE Papers
2023
2022
2021
2020
2019
2018
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
EXAM MAP
Medical
NEET