1
GATE ECE 2017 Set 1
Numerical
+1
-0
Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _________.
Your input ____
2
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Consider the following statements about the linear dependence of the real valued functions $${y_1} = 1,\,\,{y_2} = x$$ and $${y_3} = {x^2}$$. Over the field of real numbers.

$${\rm I}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly independent on $$ - 1 \le x \le 0$$
$${\rm II}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly dependent on $$0 \le x \le 1$$
$${\rm III}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly independent on $$0 \le x \le 1$$
$${\rm IV}.\,\,\,\,\,$$ $${y_1},{y_2}$$ and $${y_3}$$ are linearly dependent on $$ - 1 \le x \le 0$$

Which one among the following is correct?

A
Both $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ are true
B
Both $${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ are true
C
Both $${\rm I}$$$${\rm I}$$ and $${\rm IV}$$ are true
D
Both $${\rm I}$$$${\rm I}$$$${\rm I}$$ and $${\rm IV}$$ are true
3
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?
A
$$y = 1 + x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant
B
$$y = 1 + x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant
C
$$y = 1 - x + {\tan ^{ - 1}}\left( {x + c} \right),$$ where $$c$$ is a constant
D
$$y = 1 - x + \tan \left( {x + c} \right),$$ where $$c$$ is a constant
4
GATE ECE 2017 Set 1
Numerical
+2
-0
Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's method (up to two decimal places) is ______________
Your input ____
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