1
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
$$8$$
2
GATE ME 2004
MCQ (Single Correct Answer)
+1
-0.3
If $$\,\,\,x = a\left( {\theta + Sin\theta } \right)$$ and $$y = a\left( {1 - Cos\theta } \right)$$ then $$\,\,{{dy} \over {dx}} = \,\_\_\_\_\_.$$
A
$$Sin{\theta \over 2}$$
B
$$Cos{\theta \over 2}$$
C
$$Tan{\theta \over 2}$$
D
$$Cot{\theta \over 2}$$
3
GATE ME 1999
MCQ (Single Correct Answer)
+1
-0.3
Value of the function $$\mathop {Lim}\limits_{x \to a} \,{\left( {x - a} \right)^{x - a}}$$ is _______.
A
$$1$$
B
$$0$$
C
$$\infty $$
D
$$a$$
4
GATE ME 1997
MCQ (Single Correct Answer)
+1
-0.3
Area bounded by the curve $$y = {x^2}$$ and the lines $$x=4$$ and $$y=0$$ is given by
A
$$64$$
B
$${{64} \over 3}$$
C
$${{128} \over 3}$$
D
$${{128} \over 4}$$
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