Mechanical Engineering
GATE ME area:engineering-mathematics PYQs
Build your understanding with focused practice from past exam papers.
Questions 91–100 of 148. Imported answers require independent review unless marked reviewed.
Question 35
Open questionMENAT2 marksNeeds review
For the integral
, the absolute percentage error in numerical evaluation with the Trapezoid rule, using only the end points, is ______ (round off to one decimal place).Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 36
Open questionMENAT2 marksNeeds review
An analytic function of a complex variable z = x + iy (i = √−1) is defined as
where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z = (1 + i) is ______ (round off to 2 decimal places).
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 36
Open questionMENAT2 marksNeeds review
A fair coin is tossed 20 times. The probability that ‘head’ will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 1
Open questionMEMCQ1 markNeeds review
Consider the matrix
. The number of distinct eigenvalues of
isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 1
Open questionMEMCQ1 markNeeds review
In matrix equation
,
One of the eigenvalues of matrix
isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 2
Open questionMEMCQ1 markNeeds review
A parabola
with
is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360° around the x-axis is
Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 2
Open questionMEMCQ1 markNeeds review
The directional derivative of the function
along a line directed from
to
, evaluated at the point
isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 3
Open questionMEMCQ1 markNeeds review
For the equation
, if
, then the value of
isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 3
Open questionMEMCQ1 markNeeds review
The differential equation
is valid in the domain
with
. The solution of the differential equation isYour answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 4
Open questionMEMCQ1 markNeeds review
The lengths of a large stock of titanium rods follow a normal distribution with a mean (
) of 440 mm and a standard deviation (
) of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?Your answerChoose one option.
Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer