1
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
If $$\overrightarrow A = xy\,\widehat a{}_x + {x^2}\widehat a{}_y\,\,$$ then $$\,\,\oint {\overrightarrow A .d\overrightarrow r \,\,} $$ over the path shown in the figure is GATE ECE 2010 Engineering Mathematics - Vector Calculus Question 12 English
A
$$0$$
B
$${2 \over {\sqrt 3 }}$$
C
$$1$$
D
$$2\sqrt 3 $$
2
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
A fair coin is tossed independently four times. The probability of the event ''The number of times heads show up is more than the number of times tails show up'' is
A
$$1/16$$
B
$$1/8$$
C
$$1/4$$
D
$$5/16$$
3
GATE ECE 2010
MCQ (Single Correct Answer)
+2
-0.6
A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right)} \over {{L^2}}} = 0$$ where $$L$$ is a constant. The boundary conditions are $$n(0)=k$$ and $$n\left( \propto \right) = 0.$$ The solution to this equation is
A
$$n\left( x \right) = k\,\exp \left( {{{ - x} \over L}} \right)$$
B
$$n\left( x \right) = k\,\exp \left( {{{ - x} \over {\sqrt L }}} \right)$$
C
$$n\left( x \right) = {k^2}\,\exp \left( {{{ - x} \over L}} \right)$$
D
$$n\left( x \right) = {k^2}\,\exp \left( {{{ - x} \over {\sqrt L }}} \right)$$
4
GATE ECE 2010
MCQ (Single Correct Answer)
+1
-0.3
Consider a differential equation $${{dy\left( x \right)} \over {dx}} - y\left( x \right) = x\,\,$$ with initial condition $$y(0)=0.$$ Using Euler's first order method with a step size of $$0.1$$ then the value of $$y$$ $$(0.3)$$ is
A
$$0.01$$
B
$$0.031$$
C
$$0.0631$$
D
$$0.1$$
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