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GATE 2019: Engineering Mathematics Champion Test 1
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Question 1
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 2
The Taylor series expansion of 
is
isQuestion 3
If X and Y are random variables with variance 2 and 3, what will be the variance of 3X+4Y?
Question 4
For 0≤t<∞ the maximum value of the function f(t)= e-t-2e-2t occurs at
Question 5
The series 
converges to
converges to Question 6
If x is real, the maximum value of 
is ____________.
is ____________. Question 7
The area of the region bounded by the curves 
and the x-axis is __________.
and the x-axis is __________. Question 8
Let 
be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability 
is ________.
be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability is ________. Question 9
In (0,π) If a constant ‘c’ is expanded as a half range sine series, then the coefficient of sin2x is
Question 10
What is directional derivative of ∅ =xy2 + yz3 at P(2,-1,1) in the direction of a normal to the surface x log z - y2 = -4 at A(-1, 2, 1) ?
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Jan 18ESE & GATE EE
