1
GATE ME 2005
MCQ (Single Correct Answer)
+1
-0.3
A lot had $$10$$% defective items. Ten items are chosen randomly from this lot. The probability that exactly $$2$$ of the chosen items are defective is
A
$$0.0036$$
B
$$0.1937$$
C
$$0.2234$$
D
$$0.3874$$
2
GATE ME 2005
MCQ (Single Correct Answer)
+1
-0.3
Stokes theorem connects
A
a line integral and a surface integral
B
a surface integral and a volume integral
C
a line integral and a volume integral
D
gradient of a function and its surface integral.
3
GATE ME 2005
MCQ (Single Correct Answer)
+2
-0.6
By a change of variables $$x(u, v) = uv,$$ $$\,\,y\left( {u,v} \right) = {v \over u}$$ in a double integral, the integral $$f(x, y)$$ changes to $$\,\,\,f\left( {uv,{\raise0.5ex\hbox{$\scriptstyle v$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle u$}}} \right).\,\,\,$$ Then $$\,\,\phi \left( {u,v} \right)\,\,\,$$ is ________.
A
$${{2v} \over u}$$
B
$$2$$ $$uv$$
C
$${{v^2}}$$
D
$$1$$
4
GATE ME 2005
MCQ (Single Correct Answer)
+1
-0.3
Changing the order of integration in the double integral
$${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{$\scriptstyle x$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}}^2 {f\left( {x,\,y} \right)dy\,dx} } $$ leads to $$\,{\rm I} = \int\limits_r^s {\int\limits_p^q {f\left( {x,\,y} \right)dy\,dx} } .$$ What is $$q$$?
A
$$4y$$
B
$${16{y^2}}$$
C
$$x$$
D
$$8$$
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