1
GATE EE 2010
+1
-0.3
Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r$$ is
A
$$3$$
B
$${1 \over r}$$
C
$$\widehat i + \widehat j + \widehat k$$
D
$$3\left( {\widehat i + \widehat j + \widehat k} \right)$$
2
GATE EE 2010
+1
-0.3
A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probability that the $$2$$nd removed ball is red is
A
$$1/3$$
B
$$3/7$$
C
$$1/2$$
D
$$4/7$$
3
GATE EE 2010
+2
-0.6
For the differential equation $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 8x = 0$$ with initial conditions $$x(0)=1$$ and $${\left( {{{dx} \over {dt}}} \right)_{t = 0}}$$ $$=0$$ the solution
A
$$x\left( t \right) = 2{e^{ - 6t}} - {e^{ - 2t}}$$
B
$$x\left( t \right) = 2{e^{ - 2t}} - {e^{ - 4t}}$$
C
$$x\left( t \right) = - {e^{ - 6t}} - 2{e^{ - 4t}}$$
D
$$x\left( t \right) = - {e^{ - 2t}} - 2{e^{ - 4t}}$$
4
GATE EE 2010
+1
-0.3
Given $$f\left( t \right) = {L^{ - 1}}\left[ {{{3s + 1} \over {{s^3} + 4{s^2} + \left( {k - 3} \right)}}} \right].$$
$$\mathop {Lt}\limits_{t \to \propto } \,\,f\left( t \right) = 1$$ then value of $$k$$ is
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
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