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Gate 2019: Engineering Mathematics National Champion Test (App update required to attempt this test)
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Question 1
If X and Y are random variables with variance 2 and 3, what will be the variance of 3X+4Y?
Question 2
An experiment succeeds twice as often as it fails. Find the chance that in the next four trials, there shall be at least one success.
Question 3
The Taylor series expansion of 
is
isQuestion 4
In how many ways can we distribute 5 distinct balls, B1, B2, ...., B5 in 5 distinct cells, C1, C2, ..., C5 such that ball Bi is not in cell Ci, 
and each cell contains exactly one ball?
and each cell contains exactly one ball? Question 5
Given that: A=
and I=
the value of A3 is
and I= the value of A3 is Question 6
Consider the following equations
3x – y – z + 2w = 0
3x + y – z – 2w = 0
12x + 3y – 4z – 6w = 0
The system of equations will be
3x – y – z + 2w = 0
3x + y – z – 2w = 0
12x + 3y – 4z – 6w = 0
The system of equations will be
Question 7
The value of 
where C is the contour 
is
where C is the contour is Question 8
For the function f(x) = x2e-x, the maximum occurs when x is equal to:
Question 9
If 
then a + b = _____.
then a + b = _____. Question 10
A problem in statistics is given to four students A, B, C and D and their chances of solving it are 
respectively. The probability that the problem will be solved is _________.
respectively. The probability that the problem will be solved is _________. Question 11
Let X be a random variable with probability density function
f(x)=x+1, if -1<x<0
=1-x, if 0
x<1
= 0, otherwise
If E(X) is expectation of X, find E(X2). (Round upto two decimal places)
f(x)=x+1, if -1<x<0
=1-x, if 0
x<1 = 0, otherwise
If E(X) is expectation of X, find E(X2). (Round upto two decimal places)
Question 12
Consider the following function. f(x)=x3-6x2 + 11x - 4
Find x2 using Newton-Raphson method with an initial guess of x0 = 0.3. (Round the answer upto two decimal places).
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Sep 21ESE & GATE EC
