1
GATE PI 2011
+2
-0.6
The line integral $$\int\limits_{{P_1}}^{{P_2}} {\left( {ydx + xdy} \right)}$$ from $${P_1}\left( {{x_1},{y_1}} \right)$$ to $${P_2}\left( {{x_2},{y_2}} \right)$$ along the semi-circle $${P_1}$$ $${P_2}$$ shown in the figure is
A
$${x_2}{y_2} - {x_1}{y_1}$$
B
$$\left( {y_2^2 - y_1^2} \right) + \left( {x_2^2 - x_1^2} \right)$$
C
$$\left( {{x_2} - {x_1}} \right)\left( {{y_2} - {y_1}} \right)$$
D
$${\left( {{y_2} - {y_1}} \right)^2} + {\left( {{x_2} - {x_1}} \right)^2}$$
2
GATE PI 2011
+1
-0.3
If $$A$$ $$(0,4,3),$$ $$B(0,0,0)$$ and $$C(3,0,4)$$ are there points defined in $$x, y, z$$ coordinate system, then which one of the following vectors is perpendicular to both the vectors $$\overrightarrow {AB}$$ and $$\overrightarrow {BC}$$.
A
$$16\widehat i + 9\widehat j - 12\widehat k$$
B
$$16\widehat i - 9\widehat j + 12\widehat k$$
C
$$16\widehat i - 9\widehat j - 12\widehat k$$
D
$$16\widehat i + 9\widehat j + 12\widehat k$$
3
GATE PI 2011
+2
-0.6
If $$T(x, y, z)$$ $$= {x^2} + {y^2} + 2{z^2}$$ defines the temperature at any location $$(x, y, z)$$ then the magnitude of the temperature gradient at point $$P(1,1,1)$$ is _________.
A
$$2$$$$\sqrt 6$$
B
$$4$$
C
$$24$$
D
$$\sqrt 6$$
4
GATE PI 2011
+2
-0.6
It is estimated that the average number of events during a year is three. What is the probability of occurrence of not more than two events over a two-year duration? Assume that the number of events follow a poisson distribution.
A
$$0.052$$
B
$$0.062$$
C
$$0.072$$
D
$$0.082$$
GATE PI Papers
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
1995
1994
1993
1992
1991
1990
1989
EXAM MAP
Medical
NEET