GATE-CS-2014-(Set-2) - GeeksforGeeks

11 Oct, 2021
India is a post-colonial country because
   Column 1          Column 2
1) eradicate       P) misrepresent
2) distort         Q) soak completely
3) saturate        R) use
4) utilize         S) destroy utterly 
From 2 to 198 there are 19 multiples of 10.

These are 10,20,30.....180,190.

This is an A.P series, whose sum is (n/2{a1 + aN}), 
where a1 and aN are the 1st and last terms respectively.

Putting in the formula,

a1 = 10, aN = 190.

Sum = Sn = (19/2{10 + 190 }) = 1900

Average = Sum / Total number = 1900 / 19 = 100. 
let x = the given expression.
Now squaring both sides.

(x)^2 = 12 + x
(x)^2 - x - 12 = 0

Now solve this quadratic equation for finding the 
roots(value of x, or this expression).
(x-4)(x+3) = 0

hence x = 4.

A is incorrect because First line says that Kaliningrad (Koenigsberg before war) had a majority of the German population before the war. So, it was historically German and not Russian.
B is correct as although Kaliningrad is not contiguous with the rest of Russia (being surrounded by countries of Poland in the south and west, Lithuania in the east and Baltic sea on the north), it has a predominantly Russian population.
C cannot be inferred from the passage as it is nowhere in the passage what the original Russian name of Koenigsberg was.
D is also not true because no data about the route is mentioned in the passage.
A contradicts the conclusion of the municipal authorities. So, A is not the correct choice.
B is an incorrect choice because there is no data in the passage relating the reporting of cases and the efficiency of the administrative capabilities of the municipal authorities.
C is also incorrect as it contradicts the conclusion of the municipal authorities.
D is the correct choice as both malarial fever and dengue fever are caused by mosquito bite. If dengue fever had increased because of some other reason other than that concluded by the municipal authorities, then there would not have been increase in the people with malarial fever. This statement supports the conclusion of the municipal authorities.
Here we use the modulus property, which says:

|x| = x when x >= 0

|x| = -x when x < 0

i.e. range of a modulus function is always positive.

Now, given that |x^2 – 2x + 3| = 11, we can say that

x^2 – 2x + 3 = +11 ----------------(1)

and

x2 – 2x + 3 = -11------------------(2)

Solving 1st equation, we get real roots as 4 and -2.

Solving 2nd eq, we get imaginary roots, hence we ignore them.

Now, for eq |- x^3 + x^2 – x|, we put 4 and -2 in place of x.

putting x = 4, we get |-4^3 + 4^2-4| = |-64+16-4| =  52

putting x = -2 we get |-(-2)^3 + (-2)^2 - (-2)| = 14

so |- x^3 + x^2 – x| has possible values as 52 and 14 
Let x represent the males and y represent the females.

In 2008.
x / y = 2.5 -----------(1)

In 2009.
M / 2y = 3-------------(2)

where M is the total number of males in 2009.

Now x = 2.5y (from (1))
and M = 6y ( from (2))

hence increased number of males in 2009 are 
M - x = 6y - 2.5y = 3.5y

Now the increase in % of males =

(change in no of males / initial number)*100

= (3.5y / x )*100 = (3.5 / 2.5)*100 = 140 
                                 (given x/y = 2.5)

Hence, B is the right option.
Speed of the Hour hand = ( 360 degree ) / ( 12 * 60 minutes ) 
                       = 0.5 degree / minute.
Speed of the minute hand = ( 360 degree ) / ( 60 minutes ) 
                         = 6 degree / minute.

(180 - 6t) + 0.5t, when the minute hand is 
                   behind the hour hand or,

6t - (180 + 0.5t), when the minute hand is 
                    ahead of hour hand,

Now the the question asks for angle of 60 degree.

Hence, 
(180 - 6t) + 0.5t = 60 , we get t = 21.8 minute
and
6t - ( 180 + 0.5t ) = 60, we get t = 48 minutess
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