1
GATE PI 2008
+1
-0.3
If $$\overrightarrow r$$ is the position vector of any point on a closed surface $$S$$ that encloses the volume $$V$$ then $$\,\,\int {\int\limits_s {\left( {\overrightarrow r \,.\,d\overrightarrow s } \right)\,\,} }$$ is equal to
A
$${1 \over 2}V$$
B
$$V$$
C
$$2V$$
D
$$3V$$
2
GATE PI 2008
+2
-0.6
In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Assuming that players $$X$$ starts the game the probability of player $$X$$ winning the game is
A
$$1/3$$
B
$$1/4$$
C
$$2/3$$
D
$$3/4$$
3
GATE PI 2008
+1
-0.3
For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean is $$\,\mu = 100\,\,.$$ If the probability is $$\,\,P = \alpha \,\,$$ for $$\,\,x \ge 110.\,\,\,$$ Then the probability of $$x$$ lying $$b/w$$ $$90$$ and $$110$$ i.e., $$\,P\left( {90 \le x \le 110} \right)\,\,$$ and equal to
A
$$\,1 - 2\alpha$$
B
$$\,1 - \alpha$$
C
$$1 - \alpha /2$$
D
$$2\,\alpha$$
4
GATE PI 2008
+1
-0.3
The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are
A
$${e^{ - \left( {1 + i} \right)x}},{e^{ - \left( {1 - i} \right)x}}$$
B
$${e^{\left( {1 + i} \right)x}},\,\,{e^{\left( {1 - i} \right)x}}$$
C
$${e^{ - \left( {1 + i} \right)x}},\,\,{e^{\left( {1 + i} \right)x}}$$
D
$${e^{\left( {1 + i} \right)x}},\,\,{e^{ - \left( {1 + i} \right)x}}$$
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