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National Champion Test -GATE 2018 EE: Engineering Mathematics
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Question 1
The maximum value of θ until which the approximation sin θ ≈ θ holds to within 10% error is
Question 2
A function 
is defined in the closed interval [–1, 1]. The value of x, in the open interval (–1, 1) for which the mean value theorem is satisfied, is
is defined in the closed interval [–1, 1]. The value of x, in the open interval (–1, 1) for which the mean value theorem is satisfied, isQuestion 3
A fair coin is tossed independently four times. The probability of the event “the number of time heads shown up is more than the number of times tails shown up” is
Question 4
Consider a closed surface S surrounding a Volume V. If 
is the position vector of a point inside S, with 
the unit normal on S, the value of the integral 
is
is the position vector of a point inside S, with the unit normal on S, the value of the integral isQuestion 5
Consider a 
square matrix
Where x is unknown. If the eigenvalues of the matrix A are
and 
the x is equal to
square matrix Where x is unknown. If the eigenvalues of the matrix A are and the x is equal toQuestion 6
Consider the following statements regarding the complex pointing vector 
for the power radiated by a point source in an infinite homogeneous and lossless medium. Re 
denotes the real part of 
, S denotes a spherical surface whose centre is at the point source, and 
denotes the unit surface normal on S. Which of the following statements is TRUE?
for the power radiated by a point source in an infinite homogeneous and lossless medium. Re denotes the real part of , S denotes a spherical surface whose centre is at the point source, and denotes the unit surface normal on S. Which of the following statements is TRUE?Question 7
Consider the first order initial value problem
with exact solution
For x = 0.1, the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size h = 0.1 is ____
with exact solution
For x = 0.1, the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size h = 0.1 is ____ Question 8
Given 
. If C is a counter clockwise path in the z-plane such that | z + 1| = 1, the value of 
is
. If C is a counter clockwise path in the z-plane such that | z + 1| = 1, the value of is Question 9
identify which of the following provides a general solution of the question
Where C is a constant
Where C is a constant
Question 10
If 
is the solution of the differential equation 
k is _________.
is the solution of the differential equation k is _________. Question 11
If 
then 
over the path shown in the figure is
then over the path shown in the figure is Question 12
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is _____.
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Oct 5ESE & GATE EE
