# EC GATE 2007 (Test 8)

Tag: ec gate 2007
Q.1
If E denotes expectation, the variance of a random variable X is given by
A. E X − E X
B. E X + E X
C. E X
D. E X
Explaination / Solution:

The variance of a random variable x is given by E X − E X

Workspace
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Q.2
The following plot shows a function which varies linearly with x . The value of the integral is A. 1.0
B. 2.5
C. 4.0
D. 5.0
Explaination / Solution:

The given plot is straight line whose equation is Workspace
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Q.3
For |x| << 1, coth (x) can be approximated as
A. x
B. x2
C. 1/x
D. 1/x2
Explaination / Solution: Workspace
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Q.4 A. 0.5
B. 1
C. 2
D. not defined
Explaination / Solution: Workspace
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Q.5
Which one of following functions is strictly bounded?
A. 1/X2
B. ex
C. x2
D. Explaination / Solution: Workspace
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Q.6
For the function ex , the linear approximation around x = 2 is
A. (3 - x)e-2
B. 1 − x
C. [3 + 3√2 - (1 - √2)x]e-2
D. e2
Explaination / Solution: Neglecting higher powers

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Q.7
Consider the function f (x) = x − x − . The maximum value of f (x) in the closed interval [− 4, 4] is
A. 18
B. 10
C. -225
D. indeterminate
Explaination / Solution:

We have
f (x) = x − x + Workspace
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Q.8
An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is
A. 0.5
B. 0.18
C. 0.12
D. 0.06
Explaination / Solution: Workspace
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Q.9
The solution of the differential equation under the boundary conditions
(i) y = y1 at x = 0 and
(ii) y = y2 at x = , where k, y1 and y2 are constants, is
A. B. C. D. Explaination / Solution:  Workspace
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Q.10
The equation x − x + x − = is to be solved using the Newton - Raphson method. If x = is taken as the initial approximation of the solution, then next approximation using this method will be
A. 2/3
B. 4/3
C. 1
D. 3/2 