1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The transverse displacement $$y(x, t)$$ of a wave on a string is given by $$y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}.$$ This represents $$a:$$
A
wave moving in $$-x$$ direction with speed $$\sqrt {{b \over a}} $$
B
standing wave of frequency $$\sqrt b $$
C
standing wave of frequency $${1 \over {\sqrt b }}$$
D
wave moving in $$+x$$ direction speed $$\sqrt {{a \over b}} $$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
A mass $$M,$$ attached to a horizontal spring, executes $$S.H.M.$$ with amplitude $${A_1}.$$ When the mass $$M$$ passes through its mean position then a smaller mass $$m$$ is placed over it and both of them move together with amplitude $${A_2}.$$ The ratio of $$\left( {{{{A_1}} \over {{A_2}}}} \right)$$ is :
A
$${{M + m} \over M}$$
B
$${\left( {{M \over {M + m}}} \right)^{{1 \over 2}}}$$
C
$${\left( {{{M + m} \over M}} \right)^{{1 \over 2}}}$$
D
$${M \over {M + m}}$$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
$$100g$$ of water is heated from $${30^ \circ }C$$ to $${50^ \circ }C$$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $$4184$$ $$J/kg/K$$):
A
$$8.4$$ $$kJ$$
B
$$84$$ $$kJ$$
C
$$2.1$$ $$kJ$$
D
$$4.2$$ $$kJ$$
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
A thermally insulated vessel contains an ideal gas of molecular mass $$M$$ and ratio of specific heats $$\gamma .$$ It is moving with speed $$v$$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:
A
$${{\left( {\gamma - 1} \right)} \over {2\gamma R}}M{v^2}K$$
B
$${{\gamma {M^2}v} \over {2R}}K$$
C
$${{\left( {\gamma - 1} \right)} \over {2R}}M{v^2}K$$
D
$${{\left( {\gamma - 1} \right)} \over {2\left( {\gamma + 1} \right)R}}M{v^2}K$$
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