## Monday, 13 February 2012

### GATE-2012 Solutions (General Aptitude)(CE/CS/ME/PI)

Q1) The cost of function for a product in a firm is 5q2, where q is the amount of production. The firm can sell the product at a market price of Rs 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
(A)      5           (B)      10         (C)      15         (D)     25                             (1 Mark)
Solution:
Cost = 5q2
Price per unit = 50 => Price of q units = 50q
Profit = P(q) = Selling price – Cost price = 50q - 5q2
To find the value of q at which the profit is maximum, we follow differentiation method.
P’(q) = 50 – 10q
P’’(q) = -10 < 0 => P(q) is maximum at q where P’(q) = 0
=> 50-10q = 0 => q = 5

Q2) choose the most appropriate alternative from the options given below to complete the following sentence:                                                                                     (1 Mark)
Despite several ___ the mission succeeded in its attempt to resolve the conflict.
(A)      attempts         (B)      setbacks          (C)      meetings         (D)     delegations
Solution:
As “Despite” invokes a negative meaning, setbacks is the correct option here. All other options are suitable for the situation where the conflict is not resolved.

Q3) which one of the options is the closest in meaning to the word given below?
Mitigate                                                                                                         (1 Mark)
(A)      Diminish          (B)      Divulge             (C)      Dedicate          (D)     Denote
Solution:
Meaning of “Mitigate” is “to lessen”
“Diminish” is closest one

Q4) A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x-0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is:
(A)      8 meters          (B)      10 meters                    (C)      12 meters        (D)     14 meters
(2Marks)
Solution:
y = 2x-0.1x2
Here we need to find the max possible height ‘y’. As y is a function of x, we can go for the differentiation approach again.
y = f(x) = 2x-0.1x2
f’(x) = 2 – 0.1(2x) = 2 – 0.2x
f’’(x) = -0.2 < 0 => f(x) is max at x where f’(x) = 0
=>  2 – 0.2x = 0 => x = 10
=> ymax = f(10) = 2(10)-0.1(10)2 = 20 – 10 = 10

Q5) given the sequence of terms, AD CG FK JP, the next term is:
(A)      OV        (B)      OW                   (C)      PV         (D)     PW                                    (2Marks)
Solution:
Observe the first letters: A,C,F,J => The difference between each consecutive letters is incrementing by one letter. Or if we number the letters, the sequence is 1,3,6,10 and the difference of the consecutive numbers in order is 2,3,4. Hence the next difference is 5 and so the next number is 10+5 = 15 ie letter ‘O’.
Observe the second letters: D,G,K,P => If we number these letters, they are: 4,7,11,16
and the difference of the consecutive numbers in order is 3,4,5. Hence the next difference is 6 and so the next number is 16+6 = 22 ie letter ‘V’.
Hence the next term is ‘OV’

Q6) which of the following assertions are correct?
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
(A)      P,Q       (B)      Q,R                   (C)      P,R        (D)     R,S                               (2Marks)
Solution:
If A is the mean of n values x1,x2,…xn, then
A = (x1+x2+x3+…+xn)/n
If we add 7 to each entry in a list, then the new mean,
Anew = (x1+7 + x2+7 + x3+7…+xn+7)/n
= (x1+x2+x3+…+xn+7n)/n
=   (x1+x2+x3+…+xn)/n + (7n/n) = A+7
=> the mean of the list is also incremented by 7
If we double each entry, then the new mean, Anew = (2x1+2x2+2x3+…+2xn)/n = 2A
=> the mean of the list is also doubled
As the options P and R are found to be correct the answer-option (C) can be selected without checking the other options Q and S

Q7) Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economical data. Requirements: High-school pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.
Which one of the following is the best inference from the above advertisement?
(A)     Gender-discriminatory
(B)      Xenophobic
(C)     Not designed to make the post attractive
(D)     Not Gender-discriminatory                                                                         (2Marks)
Solution:
Observe the words Temporary, Part-time and also observe that the salary part is no where mentioned. “The travel and other expenses will be reimbursed” is only mentioned and those are the expenses of the employee and there is no mention about attractive salary emoluments etc., This makes us to go for the option (C). Options (A) and (D) can be easily eliminated as there is no concern about Gender. Option (B) can also be eliminated as it is not at all related to “fear of new things/places”.

Q8) An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is:
(A)     0.288    (B)      0.334   (C)     0.667    (D)     0.720                               (2Marks)
Solution:
This one is based on “conditional probability”.
P(“made by Y” given “found to be reliable”) is to be found out.
P(A/B) = P(A and B)/ P(B)
P(A and B) = P(made by Y  and found to be reliable) = (0.4)(0.72)
P(B) = P(found to be reliable) = (0.6)(0.96)+(0.4)(0.72)
=> P(A/B) = (0.4)(0.72) / {(0.6)(0.96)+(0.4)(0.72)} = 1/3 = 0.333..

Q9) Choose the most appropriate alternative from the options given below to complete the following:
Suresh’s dog is the one ________ was hurt in the stampede
(A)  that          (B)    which     (C)   who         (D)   whom                                    (1Mark)

Q10) Choose the grametically incorrect sentence:
(A)  They gave us the money back less the service charges of Three Hundred rupees.
(B)   This country’s expenditure is not less than that of Bangladesh.
(C)  The committee initially asked for a funding of Fifty Lakh rupees, but  latter settled for a lesser sum.
(D)  This country’s expenditure on educational reforms is very less.              (1Mark)

1. Consider the following sentences. Both are acceptable, but their meanings are subtly different:

The books, which have red covers, are new.
The books that have red covers are new.

In the first sentence, the words "which have red covers" are addinginformation about the books. That is, they're telling you more about the books than you'd otherwise have known. (They're red, not some other colour.) All of the books are new.
In the second sentence, the words "that have red covers" are limitingwhich books we're talking about. We're no longer talking about all the books; we're only talking about the ones with red covers. So this time, only the red books are new.
Now, here's our rule of thumb: Use which (surrounded by commas) if a group of words adds information. Use that if it limits the set of things you're talking about.
Here are two more examples just to make that clear:

Classes that are held on Wednesdays are in building 206.
Leap years, which have 366 days, contain an extra day in February.

In the first sentence, the words "that are held on Wednesdays" arelimiting the type of classes that we're talking about. (We're not talking about all the classes, only the ones held on Wednesdays.) We thus usethat.
In the second sentence, the words "which have 366 days" are addinginformation. We thus use which surrounded by commas.

2. Anonymous, It is a very good reasoning.But in my view, the contexts here is a different one.

Suresh's dog is the one ____ was hurt in the stampede.

See, the stress part here is -"is the one".
Here we can have two contexts.
In the fist context,the information already on hand is - a dog was hurt in the stampede. And afterwards, we came to know that it is Suresh's. That's why, "which" is more appropriate here. I think this context suits the given scenario.
In the other context in which we are not knowing that a dog was hurt in the stampede, we can straight away say that "Suresh's dog was hurt in the stampede".

3. "Temporary ,part time " dosnt makes it unattractive, it will depend on perception of the seeker. one wanting a job desperately will not consider it as "not attractive" for him anything is cool.
for D may be right, because from the seeker side it is not giving any impression of discriminating between gender, for confirmation one may ask his/her female/male friend