1
GATE ME 2004
MCQ (Single Correct Answer)
+1
-0.3
The sum of the eigen values of the matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr } } \right]$$ is
A
$$5$$
B
$$7$$
C
$$9$$
D
$$18$$
2
GATE ME 2004
MCQ (Single Correct Answer)
+2
-0.6
The volume of an object expressed in spherical co-ordinates is given by
$$V = \int\limits_0^{2\pi } {\int\limits_0^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}} {\int\limits_0^1 {{r^2}} \,Sin\phi \,drd\phi \,d\theta .} } $$ The value of the integral
A
$${{\pi \over 3}}$$
B
$${{\pi \over 6}}$$
C
$${{{2\pi } \over 3}}$$
D
$${{\pi \over 4}}$$
3
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
$$Cot{\theta \over 2}$$
4
GATE ME 2004
MCQ (Single Correct Answer)
+2
-0.6
From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kings, if the card is NOT replaced?
A
$$1/26$$
B
$$1/52$$
C
$$1/169$$
D
$$1/221$$
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