## HCU PHD CS 2018 June

 Question 1
Random sampling is helpful as it is
 A Reasonably accurate B Flee from personal biases C An economical method of data collection D All the above
Question 1 Explanation:
A method of selecting a sample (random sample) from a statistical population in such a way that every possible sample that could be selected has a predetermined probability of being selected.
 Question 2
Type I Error occurs if
 A The null hypothesis is rejected even though it is true B The null hypothesis is accepted even though it is false C Both the null hypothesis as well as alternative hypotheses are rejected D None of the above
Question 2 Explanation:
Rejecting the null hypothesis when it is in fact true is called a Type I error.
 Question 3
The F-test:
 A is essentially a two tailed test B is essentially a one tailed test C can be one tailed as well as two tailed depending on the hypothesis D can never be a one tailed test
Question 3 Explanation:
An F-test is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test.
The two-tailed version tests against the alternative that the variances are not equal.
The one-tailed version only tests in one direction, that is the variance from the first population is either greater than or less than (but not both) the second population variance. The choice is determined by the problem.
 Question 4
When two or more successive footnotes refer to the same work which one of the are the following expressions used?
 A et al. B op. cit C loc. cit D ibid
Question 4 Explanation:
Ibid meaning "in the same place", commonly used in an endnote, footnote, bibliography citation, or scholarly reference to refer to the source cited in the preceding note or list item. This is similar to īdem, literally meaning "the same", abbreviated id., which is commonly used in legal citation.
“Et al.” is a scholarly abbreviation of the Latin phrase et alia, which means “and others.” It is commonly used when you don't want to name all the people or things in a list, and works in roughly the same way as “etc.”
 Question 5
Suppose a random sample of 100 objects was considered and their widths were measured. The mean width of the sample was 64 inches and the standard deviation of the sample was 5 inches. Assume that the widths of the objects are normally distributed. Which interval below includes approximately 95% of the widths of the objects?
 A 63 to 65 inches B 59 to 69 inches C 54 to 74inches D Cannot be determined from the information given
 Question 6
A random sample of 1000 measurements was taken. Assume that the 99% confidence interval for the population mean was 68 to 73 (in arbitrary units). Now, if a 95% confidence interval is to be calculated, then
 A The 95% confidence interval will be wider than the 99% B The 95% confidence interval will be narrower than the 99% C 95% and 99% confidence interval will be the same D One cannot make a general statement about whether the 95% confidence interval would be narrower, wider or the same as the 99%
Question 6 Explanation:
For a given sample, the 99% confidence interval would be wider than the 95% confidence interval, because it allows one to be more confident that the unknown population parameter is contained within the interval.
 Question 7

Having two sets of data, we wish to compare then:;catering.

Which of the following statement/s is/are TRUE?

I. For approximately equal average values, the one with a higher standard deviation is more scattered

II. For approximately equal standard deviation values, the one with a higher average is more scattered

III. For approximately equal standard deviation values, the one with a lower average is more scattered
 A I only B II only C Both I and II D Both I and III
Question 7 Explanation:
For approximately equal average values, the one with a higher standard deviation is more scattered
For approximately equal standard deviation values, the one with a lower average is more scattered
If both the averages and standard deviations differ much between the series, we can compare scattering using the coefficient of variation
 Question 8
The result of a statistical test, denoted p, shall be interpreted as follows:
 A the null hypothesis HO is rejected if p < 0.05 B the null hypothesis HO is rejected if p > 0.05 C the alternate hypothesis HI is rejected if p > 0.05 D the null hypothesis HO is accepted if p < 0.05
Question 8 Explanation:
For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is rejected when p < .05 and not rejected when p > .05. The p-value does not, in itself, support reasoning about the probabilities of hypotheses but is only a tool for deciding whether to reject the null hypothesis.
 Question 9
The Confidence Interval for the mean, calculated for a series of values, has the interpretation:
 A The true mean, the one that approximates the populations mean, is almost certainly inside the confidence interval B The true variance is almost certainly ~inside the confidence interval C The true median is almost certainly inside the confidence interval D None of the Above
 Question 10
When searching for the best fit line for data using linear regression, which of the following approaches commonly used?
 A Logarithmic Loss B ANOVA C Parametric Estimation D Least Square Error
Question 10 Explanation:
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals made in the results of every single equation
 Question 11
The probability of getting Five Mondays in a 31 day Month is:
 A 1/7 B 2/7 C 3/7 D None of these
Engineering-Mathematics       Probability-and-statistics
Question 11 Explanation:
There are a total 7 possibilities,because a month can start with any of the 7 days of the week .But there are only 3 possibilities of getting monday 5 times , if the month either starts with saturday or sunday or monday. So the required probability is 3/7.
 Question 12
A married couple has two children. One of the children is a girl: given that having either girl or boy is equiprobable then the probability that the other child is also a girl is:
 A 1/3 B 1/4 C 1/8 D None of these
Engineering-Mathematics       Probability-and-statistics
Question 12 Explanation:
Given that out of two children one is definitely girl.So the total possibilities are , {girl,boy} ,{girl,girl}
So the probability that another child is also a girl is =½.
 Question 13
How many 0's are at the end of 20! when represented in octal?
 A 4 B 5 C 6 D 7
Engineering-Mathematics       Combinatorics
Question 13 Explanation:
Count up the number of factors of 5 and the number of factors of 2 in 20!. Since we get a zero for every pair of factors 5x2, then the minimum of these will answer your question. More simply, 5 happens less often as a factor (since it's bigger than 2), so we need only count up the number of 5's. In particular, there's one each in 5,10,15,20, so there are 4 zeroes at the end.
 Question 14
A mineral collection contains 12 samples of Calomel, 7 samples of Magnesite, and N samples of Siderite. Suppose choosing at least 15 samples from the collection guarantees that you have 6 samples of the same type of mineral. What is N?
 A 6 B 2 C 3 D 4
Question 14 Explanation:
If the value of N is 4 then choosing at least 15 samples from the collection guarantees that u have 6 samples of the same type of mineral, because in worst case choose 4 from each collection then we have 4 samples of the same type of mineral and now siderite is finished and we have to select from remaining two samples .Now select 2 from 1 sample and 1 from other in worst case. Now we have selected 15 items out of which 6 are definitely from the same type of mineral.
 Question 15
You are told that n = 110179 is the product of two primes p and q. The number of positive integers . less than n that are relatively prime to n (i.e. those m such that gcd(m, n) = 1) is 109480. What is the value of p + q.
 A 700 B 750 C 600 D 650
Computer-Networks       Network-Security
Question 15 Explanation:
We use the concept of Euler to find function. It is used to give the no. of numbers which are less than and relatively prime to n and is represented as, Q(n).
So, ATQ,
n = p = q = 110179 ---(1)
and Q(n) = (p-1)(q-1) = 109480 ---(2)
Now let’s solve (2),
pq - p - q + 1 = 109480
Let put value of pq from (1),
110179 - p - q + 1 = 109480
110180 - 109480 = p + q
Therefore p+q = 700
 Question 16
The format for car number plates in a country is two digits followed by three vowels, e.g. 04 IOU. A license plate is called "confusing" if the digit 0 (zero) and the vowel o are both present on it. For example 04 IOU is confusing but 20 AEI is not. How are many distinct number plates possible that are not confusing?
 A 12500 B 6400 C 11341 D None of these
Engineering-Mathematics       Combinatorics
Question 16 Explanation:
102 × 43 plates without vowel O + 92 × (53 − 43 ) plates with vowel O but without 0. This gives 6400 + 4941 = 11341.
 Question 17
If the letters of the word "PROTECTION" which are at odd numbered position in English alphabet is picked up and arranged in alphabetical order from the left. If they are now substituted by Z, Y, X and so on beginning from left, which letter gets substituted by X?
 A E B 0 C T D I
Aptitude       Numerical
Question 17 Explanation:
Consider the position of the alphabets A is 1, B is 2, C is 3 and so on then
PROJECTION word gets the following numbers
P is 16, R is 18, O is15, T is 20, E is 5, C is 3, T is 20, I is 9, O is 15, N is 14
The letters O,E,C,I,O are in the odd positions 15,5,3 and 15 respectively
After arranging that letter alphabetical order ,C,E,I,O,O
Now substitute the above letters by Z,Y,X and so on then X will come in place of I.
 Question 18
Shankar ranks 7th from the top in a class of 35 students. What is the rank of Gopal from bottom who is four ranks below Shankar from top?
 A 25 B 26 C 27 D 28
Aptitude       Numerical
Question 18 Explanation:
According to the question rank of gopal from top is 7+4=11. Hence rank of gopal from bottom is 35-11+1 =25.
 Question 19

Questions 19 and 20 are based on the following information: P and Q are brothers of R. Q is son of Sand T. S is daughter of U. A is father-in-law of T. B is son of U.

What is the relation of P to B?
 A Nephew B Paternal uncle C Niece D Paternal aunt
Aptitude       Numerical
Question 19 Explanation:
P and Q are brothers. Q is son of S and T. S is daughter of U and B is son of U,means B is brother of S.Hence son of S will be nephew of B.Hence P is nephew of B.
There are 19 questions to complete.

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