1
GATE ME 2016 Set 2
Numerical
+2
-0
The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,}$$ using the trapezoidal rule with three intervals of equal length between $$0$$ and $$\pi$$ is _________.
2
GATE ME 2016 Set 1
Numerical
+2
-0
Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first iteration, up to second decimal, is _____________.
3
GATE ME 2016 Set 1
Numerical
+2
-0
Gauss-Seidel method is used to solve the following equations (as per the given order). $${x_1} + 2{x_2} + 3{x_3} = 5$$$$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$\,3{x_1} + 2{x_2} + {x_3} = 3$$\$
Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.
4
GATE ME 2015 Set 3
Numerical
+2
-0
Newton-Raphson method is used to find the roots of the equation, $${\,{x^3} + 2{x^2} + 3x - 1 = 0}$$ If the initial guess is $${x_0} = 1,$$ then the value of $$x$$ after $${2^{nd}}$$ iteration is ___________.
GATE ME Subjects
EXAM MAP
Medical
NEETAIIMS
The text passage contains multiple numerical problems from the GATE ME (Mechanical Engineering) exam, each with a specific question and a request for a numerical answer. None of the questions provide an answer within the text.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
1
GATE ME 2016 Set 2
Numerical
+2
-0
The error in numerically computing the integral $$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,}$$ using the trapezoidal rule with three intervals of equal length between $$0$$ and $$\pi$$ is _________.
2
GATE ME 2016 Set 1
Numerical
+2
-0
Solve the equation $$x = 10\,\cos \,\left( x \right)$$ using the Newton-Raphson method. The initial guess is $$x = {\pi \over 4}.$$ The value of the predicted root after the first iteration, up to second decimal, is _____________.
3
GATE ME 2016 Set 1
Numerical
+2
-0
Gauss-Seidel method is used to solve the following equations (as per the given order). $${x_1} + 2{x_2} + 3{x_3} = 5$$$$$2{x_1} + 3{x_2} + {x_3} = 1$$$ $$\,3{x_1} + 2{x_2} + {x_3} = 3$$\$
Assuming initial guess as $${x_1} = {x_2} = {x_3} = 0,$$ the value of $${x_3}$$ after the first iteration is __________.
4
GATE ME 2015 Set 3
Numerical
+2
-0
Newton-Raphson method is used to find the roots of the equation, $${\,{x^3} + 2{x^2} + 3x - 1 = 0}$$ If the initial guess is $${x_0} = 1,$$ then the value of $$x$$ after $${2^{nd}}$$ iteration is ___________.
GATE ME Subjects
EXAM MAP
Medical
NEETAIIMS
user
The text passage contains multiple numerical problems from the GATE ME (Mechanical Engineering) exam, each with a specific question and a request for a numerical answer. None of the questions provide an answer within the text.

TYPE: MULTIPLE_QUESTIONS