# Engineering-Mathematics |Gate-2011| Previous Year Questions| Set-10 Engineering-Mathematics |Gate-2011|

1. If the difference between the expectation of the square of a random variable (E[X2]) and the square of the expectation of the random variable (E[X])2 is denoted by R, then : [GATE – 2011]

a. R=0
b. R<0
c. R>0
d. R>=0

1. Consider the matrix as given below. Which one of the following provides the CORRECT values of eigenvalues of the matrix? [GATE – 2011]

a. 1, 4, 3
b. 3, 7, 3
c. 7, 3, 2
d. 1, 2, 3

1. Which one of the following options is CORRECT given three positive integers x,y and z, and a predicate [GATE – 2011]

a. P(x) being true means that x is a prime number
b. P(x) being true means that x is a number other than 1
c. P(x) is always true irrespective of the value of x
d. P(x) being true means that x has exactly two factors other than 1 and x

1. Consider a finite sequence of random values X = [x1, x2, …, xn]. Let μx be the mean and σx be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as yi = a * xi + b, where a and b are positive constants, Let μy be the mean and σy be the standard deviation of this sequence. Which one of the following statements is INCORRECT? [GATE – 2011]

a. Index position of mode of X in X is the same as the index position of mode of Y in Y.
b. Index position of median of X in X is the same as the index position of median of Y in Y.
c. μy = aμx + b
d. σy = aσx + b

1. A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second. [GATE – 2011]

a. 1/5
b. 4/25
c. 1/4
d. 2/5