PREVIOUS YEAR SOLVED PAPERS MCQ - GATE 2017 Shift 2

6 “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent - namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms."
The author's belief that ideology is not as important as literature is revealed by the word:

It appears to be ‘B’, so the right option is ‘B’.

7 X is a 30 digit number starting with the digit 4 followed by the digit 7, then the number X³ will have

X = 4777....(7 29times)
It can be written as X = 4.7777... * 10²⁹
X³ = (4.777⋯∗10²⁹)³
= (4.777…)³ ∗ 10⁸⁷
Now, even if we round up 4.777... to 5, we could represent 5³ = 125 in 3 digits. So, can say (4.77...)³also has 3 digits before decimal point.
So, X³ requires 3 + 87 = 90 digits.

8 There are three boxes, one contains apples, another contains oranges and last one contains both apples and oranges. All three are known to be incorrectly labelled. You are permitted to open just one box and then pull out and inspect only one fruit. Which box would you open to determine the contents of all three boxes?

Here in given question there are three boxes incorrectly labeled:
.Box 3 – labeled as Apples and Oranges – Original Content can be Apple or Orange (This box will have only one fruit, so whichever we pick would be the correct label). Let’s say the picked item was Apple, therefore the box labeled Orange will have Apples and Oranges.)
.Box 2 – Oranges – This box will definitely not have orange (as its mislabeled) and it can not contain only apple (As it is in box 3) – So this will have Original Content- both oranges and Apples
.Box 1 – Apples – This is the leftover box and it can now have Original Content – Orange

9 An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

Region	Air pressure difference
P	0.95 - 0.90 = 0.05
Q	0.80 - 0.75 = 0.05
R	0.85 - 0.65 = 0.20
S	0.95 - 0.90 = 0.05

In general thunderstorms are occurred in a region where suddenly air pressure changes (i.e.,) sudden rise (or) sudden fall of air pressure. From the given contour map in ‘R’ region only more changes in air pressure. So, the possibility of a thunderstorms in this region.
So option C. is correct.

10 The number of roots of e^x + 0.5x² - 2 =0 in the range [-5,5] is ______.

The given function is a continuous function in range [-5, 5].
The Intermediate Value Theorem states if a continuous function has values of opposite sign inside an interval, then it has a root in that interval.
The function changes sign twice in range [-5, 5].
It becomes positive to negative in range [-5, 0] when ex + 0.5x² becomes less than 2.
It becomes positive to negative in range [0, 5] when ex + 0.5x² becomes more than 2.