1
GATE ME 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3}$$ and $${1 \over 6}$$, respectively. Then mean value and the variance of the number of defective pieces produced by
A
$$1$$ and $$1/3$$
B
$$1/3$$ and $$1$$
C
$$1$$ and $$4/3$$
D
$$1/3$$ and $$4/3$$
2
GATE ME 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider two solutions $$\,x\left( t \right)\,\,\,\, = \,\,\,{x_1}\left( t \right)\,\,$$ and $$x\left( t \right)\,\,\,\, = \,\,\,{x_2}\left( t \right)\,\,$$ of the differential equation
$$\,\,{{{d^2}x\left( t \right)} \over {d{t^2}}} + x\left( t \right) = 0,t > 0,\,\,$$ such that
$$\,{x_1}\left( 0 \right) = 1,{\left. {{{d{x_1}\left( t \right)} \over {dt}}} \right|_{t = 0}} = 0,$$ $$\,\,\,\,{x_2}\left( 0 \right) = 0,{\left. {{{d{x_2}\left( t \right)} \over {dt}}} \right|_{t = 0}} = 1$$

The wronskian $$\,w\left( t \right) = \left| {{{\matrix{ {{x_1}\left( t \right)} \cr {d{x_1}\left( t \right)} \cr } } \over {dt}}} \right.\left. {{{\matrix{ {{x_2}\left( t \right)} \cr {d{x_2}\left( t \right)} \cr } } \over {dt}}} \right|$$ at $$\,\,t = \pi /2$$

A
$$1$$
B
$$-1$$
C
$$0$$
D
$$\pi /2$$
3
GATE ME 2014 Set 3
Numerical
+2
-0
The definite integral $$\,\int\limits_1^3 {{1 \over x}} dx\,\,$$ is evaluated using Trapezoidal rule with a step size of $$1.$$ The correct answer is
Your input ____
4
GATE ME 2014 Set 3
Numerical
+1
-0
The real root of the equation $$5x-2cosx=0$$ (up to two decimal accuracy) is
Your input ____
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