1
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptstyle {{x^2}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}}}} \,\,dx\,\,\,$$ is ________.
A
$$1$$
B
$${\pi }$$
C
$$2$$
D
$${2\pi }$$
2
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
$$\nabla \times \left( {\nabla \times P} \right)\,\,$$ where $$P$$ is a vector is equal to
A
$$P \times \nabla \times P \to {\nabla ^2}P$$
B
$${\nabla ^2}P + \nabla \left( {\nabla .P} \right)\,$$
C
$${\nabla ^2}P + \left( {\nabla \times P} \right)\,\,$$
D
$$\nabla \left( {\nabla .P} \right) \to {\nabla ^2}P$$
3
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
A fair dice is rolled twice. The probability that an odd number will follow an even number is
A
$${1 \over 2}$$
B
$${1 \over 6}$$
C
$${1 \over 3}$$
D
$${1 \over 4}$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
A solution of the differential equation $${{{d^2}y} \over {d{x^2}}} - 5{{dy} \over {dx}} + 6y = 0\,$$ is given by
A
$$y = {e^{2x}} + {e^{ - 3x}}$$
B
$$y = {e^{2x}} + {e^{3x}}$$
C
$$y = {e^{ - 2x}} + {e^{3x}}$$
D
$$y = {e^{ - 2x}} + {e^{ - 3x}}$$
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