text: 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
explanation: The document contains multiple numerical problems from the GATE ME (Mechanical Engineering) exam. Each problem is a math question that requires a numerical answer. There are no provided answers to these questions in the text.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains multiple numerical problems from the GATE ME (Mechanical Engineering) exam. Each problem is a math question that requires a numerical answer. There are no provided answers to these questions in the text.
  
  Label: multiple-question