Mechanical Engineering
GATE ME area:engineering-mathematics PYQs
Build your understanding with focused practice from past exam papers.
Questions 31–40 of 148. Imported answers require independent review unless marked reviewed.
Question 11
Open questionMEMCQ1 markNeeds review
A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are
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 12
Open questionMEMCQ1 markNeeds review
The figure shows the plot of a function over the interval
. Which one of the options given CORRECTLY identifies the function? 
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 31
Open questionMENAT1 markNeeds review
A vector field
is defined over a conical region having height h = 2, base radius r = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin.
If n denotes the unit outward normal to the curved surface S of the cone, the value of the integral
equals ________ . (Answer in integer)
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 32
Open questionMENAT1 markNeeds review
A linear transformation maps a point
in the plane to the point
according to the rule
Then, the disc
gets transformed to a region with an area equal to ________ . (Rounded off to two decimals)Use π = 3.14.
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 33
Open questionMENAT1 markNeeds review
The value of k that makes the complex-valued function
analytic, where
, is ________.(Answer in integer)
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 questionMEMCQ2 marksNeeds review
Which one of the options given is the inverse Laplace transform of
?
denotes the unit-step function.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 49
Open questionMENAT2 marksNeeds review
Consider the second-order linear ordinary differential equation
with the initial conditions
The value of
at
equals ________.(Answer in integer)
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 50
Open questionMENAT2 marksNeeds review
The initial value problem
is solved numerically using the forward Euler’s method with a constant and positive time step of
.Let
represent the numerical solution obtained after
steps. The condition
is satisfied if and only if
does not exceed ____________.(Answer in integer)
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 questionGAMCQ1 markNeeds review
If
, what is the area bounded by
for the interval
on the
-axis?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 11
Open questionMEMCQ1 markNeeds review
The limit
has a finite value for a real
. The value of
and the corresponding limit
areYour 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