1
GATE CE 1999
MCQ (Single Correct Answer)
+1
-0.3
The function $$f\left( x \right) = {e^x}$$ is _________.
A
Even
B
odd
C
Neither even nor odd
D
None
2
GATE CE 1999
MCQ (Single Correct Answer)
+1
-0.3
For the function $$\phi = a{x^2}y - {y^3}$$ to represent the velocity potential of an ideal fluid, $${\nabla ^2}\,\,\phi $$ should be equal to zero. In that case, the value of $$'a'$$ has to be
A
$$-1$$
B
$$1$$
C
$$-3$$
D
$$3$$
3
GATE CE 1999
MCQ (Single Correct Answer)
+1
-0.3
If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is
A
$$y=sin(x+c)$$
B
$$y=cos(x+c)$$
C
$$y=tan(x+c)$$
D
$$y = {e^x} + c$$
4
GATE CE 1999
MCQ (Single Correct Answer)
+1
-0.3
The Laplace transform of the function
$$\eqalign{ & f\left( t \right) = k,\,0 < t < c \cr & \,\,\,\,\,\,\,\,\, = 0,\,c < t < \infty ,\,\, \cr} $$
is
A
$$\left( {k/s} \right){e^{ - sc}}$$
B
$$\left( {k/s} \right){e^{sc}}$$
C
$$k\,{e^{ - sc}}$$
D
$$\left( {k/s} \right)\left( {1 - {e^{ - sc}}} \right)$$
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