1
GATE ECE 2014 Set 3
Numerical
+2
-0
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ________.
2
GATE ECE 2014 Set 3
Numerical
+2
-0
Let $${X_1},{X_{2,}}$$ and $${X_{3,}}$$ be independent and identically distributed random variables with the uniform distribution on $$\left[ {0,1} \right].$$ The probability $$P\left\{ {{X_1} + {X_2} \le {X_3}} \right\}$$ is _______.
3
GATE ECE 2014 Set 3
+2
-0.6
Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independent and dependent variables respectively?
A
$${{dy} \over {dx}} + xy = {e^{ - x}}$$
B
$${{dy} \over {dx}} + xy = 0$$
C
$${{dy} \over {dx}} + xy = {e^{ - y}}$$
D
$${{dy} \over {dx}} + {e^{ - y}} = 0$$
4
GATE ECE 2014 Set 3
+2
-0.6
Match the application to appropriate numerical method

Applications
$$P1:$$ Numerical integration
$$P2:$$ Solution to a transcendental equation
$$P3:$$ Solution to a system of linear equations
$$P4:$$ Solution to a differential equation

Numerical Method
$$M1:$$ Newton-Raphson Method
$$M2:$$ Runge-Kutta Method
$$M3:$$ Simpson's $$1/3-$$rule
$$M4:$$ Gauss Elimination Method

A
$$P1 - M3,\,\,P2 - M2,\,\,P3 - M4,\,\,P4 - M1$$
B
$$P1 - M3,\,\,P2 - M1,\,\,P3 - M4,\,\,P4 - M2$$
C
$$P1 - M4,\,\,P2 - M1,\,\,P3 - M3,\,\,P4 - M2$$
D
$$P1 - M2,\,\,P2 - M1,\,\,P3 - M3,\,\,P4 - M4$$
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