1
GATE IN 2007
MCQ (Single Correct Answer)
+1
-0.3
For real $$x,$$ the maximum value of $${{{e^{Sin\,x}}} \over {{e^{Cos\,x}}}}\,\,$$ is
A
$$1$$
B
$$e$$
C
$${e^{\sqrt 2 }}$$
D
$$ \propto $$
2
GATE IN 2007
MCQ (Single Correct Answer)
+1
-0.3
Assume that the duration in minutes of a telephone conversation follows the exponential distribution $$\,f\left( x \right) = {1 \over 5}{e^{ - x/5}},\,x \ge 0.\,\,\,$$ The probability that the conversation will exceed five minutes is
A
$${1 \over e}$$
B
$$1 - {1 \over e}$$
C
$${1 \over {{e^2}}}$$
D
$$1 - {1 \over {{e^2}}}$$
3
GATE IN 2007
MCQ (Single Correct Answer)
+1
-0.3
For the function $${{\sin z} \over {{z^3}}}$$ of a complex variable z, the point z = 0 is
A
a pole of order 3
B
a pole of order 2
C
a pole of order 1
D
not a singularity
4
GATE IN 2007
MCQ (Single Correct Answer)
+1
-0.3
The polynomial $$\,p\left( x \right) = {x^5} + x + 2\,\,$$ has
A
all real roots
B
$$3$$ real and $$2$$ complex roots
C
$$1$$ real and $$4$$ complex roots
D
all complex roots