PGDBA 2019 Question Paper

Let's tabulate the information in the graph ,we get 

From the table, it is evident that there are 20 members who got at least 320

Hence C is the correct answer.

Let's tabulate the information in the graph ,we get 

 No. of labourers who receive a wage less than 250 will be at least 10 but not more than 40 in which case all the people in the range 200-240 will be receiving a wage less than 250.

So if all the people in the range  >= 240 - <280 are included then to a maximum there will be 40 labourers to whom the wage will be less than 250.

Hence B is the correct answer.

Let's tabulate the information in the graph ,we get 

The total number of labourer = 100

50% of the total labourers is 50 who will fall in the range >=280 - <320

$$\therefore$$ The maximum wage such that at least 50% of the labourers definitely earn more than that is 280

Hence B is the correct answer.

Let's solve the options one by one,

In 2017

Option A:The percentage increase of Foreign Tourists in FEB = 570-500/500 = 14% 

Option B:The percentage increase of Foreign Tourists in JUL = 660-600/600 = 10%

Option C:The percentage increase of Foreign Tourists in SEP = 875-700/700 = 25%

Option D:The percentage increase of Foreign Tourists in DEC = 1090-1000/1000 = 9%

From the above values it is clear that the percentage increase of Foreign Tourists in DEC is minimum.

Hence D is the correct answer

Let's solve the options one by one,

In 2017

Option A:The percentage increase of Foreign Tourists in MAR= 720-570/570 = 26.32% 

Option B:The percentage increase of Foreign Tourists in SEP= 875-696/696 = 25.72% 

Option C:The percentage increase of Foreign Tourists in OCT= 984-875/875 = 12.46% 

Option D:The percentage increase of Foreign Tourists in NOV= 1170-984/984 = 18.90% 

It is clear that the percentage increase of Foreign Tourists in MAR is maximum

Hence A is the correct answer.

Logarithmic function is defined only for positive values 

So $${\frac{2 - x}{9 - x^2}}$$ >0 and $$9-x^{2}$$ should not equal 0.

x $$\in$$ (-3,2)$$\cup$$ (3,$$\infty$$)

D is the correct answer.

Let's represent the system of linear equations
$$2x+ y+7z = a$$
$$6x-2y+11z = b$$
$$2x-y+3z = c$$ in the Matrix Equation form

$$\begin{bmatrix}2 & 1 &7 & a  \\6 & -2 & 11 & b &\\2 & -1 &3 & c \end{bmatrix}$$

Order of the matrix = 3

Now represent the matrix in echelon form 

$$\begin{bmatrix}2 & 1 &7 & a  \\0 & -5 & -10 & b-3a &\\0 & -2 &-4 & c-a \end{bmatrix}$$

$$\begin{bmatrix}2 & 1 &7 & a  \\6 & -2 & 11 & b &\\0 & 0 &0 & 5c-5a-2b+6a \end{bmatrix}$$

Rank of the matrix = No of Non-zero rows after transforming the matrix into echelon form

The system of linear equations will have infinite solutions only if Rank of the matrix is not equal to Order of the Matrix

$$\therefore$$ 5c-5a-2b+6a=0

a-2b+5c=0

D is the correct answer.

$$\frac{1}{\alpha\ +1}+\frac{1}{\beta\ +1}=\frac{\left(\alpha\ +\beta\ +2\right)}{\alpha\ \beta\ +\alpha\ +\beta\ +1}$$

Since $$\alpha\ ,\beta\ $$ are roots of the given equation:

$$\alpha+\beta\ =-3$$

$$\alpha\times\beta\ =-3$$

Then we have: $$\frac{\left(\alpha\ +\beta\ +2\right)}{\alpha\ \beta\ +\alpha\ +\beta\ +1}=\frac{\left(-3+2\right)}{-3-3+1}=\frac{1}{5}$$

Let $$e^x+e^{-x}=P$$

$$P^3+3P^2+3P-7 = 0$$

$$\left(P-1\right)(P^2+4P+7)=0$$

P = 1 and the other two roots are imaginary roots 

$$e^x + e^{-x} = 1$$ but the minimum value of $$e^x + e^{-x} is 2$$, as $$e^x$$ is a positive number and sum of a positive number and its reciprocal is at least 2.

No. of real roots is 0.

Hence A is the correct answer.

$$e^k = \sum_{n = 0}^\infty \frac{k^n}{n!} = 1 + k + \frac{k^2}{2!} + \frac{k^3}{3!}+ ....$$

We are given,

 $$x = -\frac{1}{1!}\cdot\frac{3}{4} + \frac{1}{2!}\cdot(\frac{3}{4})^2 -\frac{1}{3!}\cdot(\frac{3}{4})^3 +....$$

This can be written as,

$$e^{-\frac{3}{4}}\ =\ 1\ -\ \frac{1}{1!}\left(\frac{3}{4}\right)\ +\ \frac{1}{2!}\left(\frac{3}{4}\right)^2-\frac{1}{3!}\left(\frac{3}{4}\right)^3....$$

$$x\ =\ -\ \frac{1}{1!}\left(\frac{3}{4}\right)\ +\ \frac{1}{2!}\left(\frac{3}{4}\right)^2-\frac{1}{3!}\left(\frac{3}{4}\right)^3....\ \ =\ e^{-\frac{3}{4}}\ -\ 1$$

We also know that,

$$\log\left(1\ +\ k\right)\ =\ k\ -\ \frac{k^2}{2}\ +\ \frac{k^3}{3}+\ ....$$

We can also write,

$$y=x-\frac{x^2}{2}+\frac{x^3}{3}-...\ =\ \log\left(1\ +\ x\right)$$

Substituting the value of x, we get,

$$y\ =\ \log\left(1\ +\ e^{-\frac{3}{4}}\ -\ 1\right)\ =\ \log\left(e^{-\frac{3}{4}}\right)\ =\ -\frac{3}{4}$$

Hence, A is the correct answer.

$$P^c \cap Q \subseteq R^c \cap Q$$

$$P^c \cap Q^c \subseteq R^c \cap Q^c$$

=> $$\left(P^c\cap Q\right)U\ \left(P^c\cap Q^c\right)\subseteq\left(R^c\cap Q\right)U\ \left(R^c\cap Q^c\right)$$

=> $$P^c\cap\left(Q\ U\ Q^c\right)\subseteq R^c\cap\left(Q\ U\ Q^c\right)$$

=> $$P^c\subseteq R^c$$

=>$$R\subseteq P$$

We have 4 cases 
1: Largest side = 12  then Sides of the triangle are 8,10,12
2: Largest side = 10  then Sides of the triangle are 10,8,6
3: Largest side = 8  then Sides of the triangle are 8,6,4
4: Largest side = 6  then Sides of the triangle are 6,4,2
According to the properties of the triangle,
Sum of any two sides of a triangle is greater than the third side and difference of any two sides of a triangle is lesser than the third side
All the above cases satisfy the properties of the triangle except case 4 
Hence C is the correct answer.

Let's find the point of intersection of the circle $$x^2 + y^2 = 9$$ and the parabola $$y^2 = 8x$$

$$x^2 + 8x= 9$$

On solving the equation we will get the values of x as 1,-9 

Since the angle between the tangents has to be found in the first Quadrant, value of x is 1

$$\therefore value of y = 2\sqrt{2}$$

Let's find the slope of the tangent to the circle and the parabola

On differentiating the equation of the circle ,we get 

$$2x+2y\frac{\text{d}y}{\text{d}x}=0$$

Slope of the tangent to the circle $$\ m_1= -1/ x$$

On differentiating the equation of the parabola ,we get 

$$2y\frac{\text{d}y}{\text{d}x}=8$$

Slope of the tangent to the parabola $$m_2= 4/ y$$

Angle between the tangents $$\tan \theta$$= $$\frac{m_1-m_2}{1+m_1m_2}$$

                                           =$$\frac{-1/2\sqrt{2}-4/2\sqrt{2}}{1+-1/2\sqrt{2}*4/2\sqrt{2}}$$

                                           =$$\tan^{-1} (\frac{5}{\sqrt{2}})$$

Hence C is the correct answer.

Sum of the interior angles of a polygon is given by (2n-4)90

Smallest interior angle = 120

Let the number of sides of the convex-polygon be n 

$$\frac{n}{2}\left(2(120)+\left(n-1\right)\times\ 5\right)=(2n-4)90$$

n(240+5n-5)=360n-720

$$5n^2+235n=360n-720$$

$$5n^2-125n+720=0$$

$$n^2-25n+144=0$$

n=9,16

for a polygon to be convex, each interior angle should be less than 180

The interior angle when n=16 is 120+15*5=195 So n is not equal to 16

Interior angle when n =9 is 120+8*5 =160 

No of sides of the polygon =9

B is the correct answer.

Let $$\sqrt{32\sqrt{32\sqrt{32.......}}}$$ = x

$$\sqrt{32x}$$ = x

Squaring on both sides , we get 

32x=$$x^{2}$$

$$\therefore x$$ = 32

Hence B is the correct answer.

The number of elements in set A = 10

The number of elements in set B = 9

for the mapping to be onto there will be a element in set B which has 2 pre-images from set A

Two elements can be selected in $$^{10}C_2 $$ ways and the elements in set B can be arranged in 9! ways 

$$\therefore$$ No of onto functions = $$^{10}C_2 \times 9!$$

A is the correct answer

All the words starting with the letter A =3!

All the words starting with the letter E =3!

All the words starting with the letter R =3!

All the words starting with the letter WA =2!

All the words starting with the letter WEAR =1

$$\therefore$$ position of the word 'WEAR' in this list is at number 3!*3 + 2+1

=21

Hence B is the correct answer.

Multiples of 7 are {301,308 ................................1099}
Using the Ap formula, we can get that 301+ (n-1)7 = 1099
Giving n=115, that is there are 115 numbers that multiples of 7 in the given range. 

Multiples of 13 are {312,323,.................................1092} n = 61

Multiples of 91 are {364,455.................................1092} n= 9

Number of integers which are divisible by either 7 or 13 but not both is 115+61-2*9

=158

Hence B is the correct answer.

Let's rewrite the equation $$24x + 7y =168$$ in intercept form

$$\frac{x}{7}+\frac{y}{24}$$ = 1

$$\therefore$$ The co-ordinates of the triangle are (7,0),(0,0),(0,24)

Diameter of the circumcircle formed by the vertices is given by the hypotenuse, which is between (7,0) and (0,24).

Distance between the co-ordinates (7,0) and (0,24) =$$\sqrt{7^{2} +24^{2}}$$ =25.

Hence C is the correct answer.

An even function is symmetric about the y axis. Hence if there are 10 non-differential points, 5 of them lie towards the left side of the y-axis and 5 towards the right. Origin cannot be a non-differential point for an even function.

Hence $$f'\left(0\right)=0$$

$$f'\left(x\right)=2x-1\ \ ,\ x<1$$

$$f'\left(x\right)=\frac{2x}{3}\ \ ,\ x\ge\ 1$$

$$f'\left(1^+\right)=\frac{2}{3}\ \ \ and\ f'\left(1^-\right)=1$$ => Right hand Derivative is not equal to LHD. Hence is is not differentiable at x=1

Left hand limit = 0 and RHL = 0. Hence it is continuos at x=1

Let, $$h(x)=f(x)-g(x).$$

Then, $$h'(x)=f'(x)-g'(x)$$

Now according to question, $$f'(x)>g'\left(x\right)$$

So, $$f'(x)-g'\left(x\right)>0$$

So, $$h'(x)>0$$
So, h(x) is an increasing function.

Hence, there are two cases possible:-

Case 1:- The curve lies only in positive y axis. In this case it won't intersect x-axis. So, number of points of intersection is zero.

Case 2:- The curve is moving from negative y axis to positive y axis, since it is increasing. In this case it will intersect x-axis at 1 point. So, number of points of intersection is 1.

So option B.

$$\int_{-\frac{1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}} (\frac{x^2 - \tan x}{1 + x^2})dx$$

=$$\int_{-1/\sqrt{3}}^{1/\sqrt{3}} \frac{x^2+1-1 - \tan x}{1 + x^2}dx$$

=$$\int_{-1/\sqrt{3}}^{1/\sqrt{3}} \frac{x^2+1-1 - \tan x}{1 + x^2}dx$$

=$$\int_{-1/\sqrt{3}}^{1/\sqrt{3}}1-\int_{-1/\sqrt{3}}^{1/\sqrt{3}}\frac{1}{1+x^{2}}+\int_{-1/\sqrt{3}}^{1/\sqrt{3}}\frac{\tan x}{1+x^{2}}$$

=x-$$\tan^{-1}x$$+0     [$$\because$$ 

$$\frac{\tan x}{1+x^2}\ is\ an\ odd\ function,\ and\ will\ become\ zero$$

=$$\frac{1}{\sqrt{3}}-\frac{\pi}{6}$$ - $$\frac{-1}{\sqrt{3}}-\frac{\pi}{6}$$

=$$2(\frac{1}{\sqrt{3}} - \frac{\pi}{6})$$

Hence A is the correct answer.

$$y^2 = 16(1 + x )$$ and $$y^2 = 16(1 - x)$$

Equating the parabolas ,we will get the point of intersection of both 

16(1+x) = 16(1-x)

x=0

Substitute the value of x in the parabola $$y^2 = 16(1 + x )$$

y = $$\pm$$ 4

Point of intersection = (0,4),(0,-4)

=$$2(\int_{-4}^{4} (\frac{y^{2}-16}{16})-(\frac{16-y^{2}}{16}))$$ dy

= $$2(\int_{0}^{4} (\frac{y^{2}-16}{16})-(\frac{16-y^{2}}{16}))$$ dy                      [$$\because$$ $$\int_{0}^{2a} F(x)dx$$=2$$(\int_{0}^{a} F(x)dx)$$]

=$$2(\int_{0}^{4} (\frac{y^{2}}{16})-1-1+(\frac{y^{2}}{16}))$$

=$$2(\int_{0}^{4} (\frac{y^{2}}{8})-2))$$

=2$$(\frac{y^{3}}{3*8}-2y))$$ y varies from 0-4 

=2(8/3 - 8)

=2(16/3)   ($$\because$$ Area cant be negative)

=32/3

Hence C is the correct answer

=$$\int_{0}^{1} 0 e^{x}dx+ \int_{1}^{\sqrt{2}} 1 e^{x} dx$$

=0 +  $$e^{\sqrt{\ 2}}-e^1$$

=$$e^{\sqrt{2}} - e^{1}$$

Hence C is the correct answer.

$$f(x) = ax^2 + bx + c$$ < x

$$ax^2+x\left(b-1\right)+c\ <0$$

Here, $$x^2$$ is the significant term that influences the value of the expression. So, if the coefficient of this term is positive, irrespective of the other terms, the expression will be greater than x when the value of x goes higher.  

But if the value of a is negative, then this curve will be an inverted U-curve. So, $$a\le\ 0$$ is a correct condition.

Let the point P be $$\left(\alpha\ ,B\right)$$

Let OS =a, OR=b and RS = c and $$\angle\ OSR=\theta\ $$ , PS = z

=> a=ccos$$\theta\ $$ and b = c sin$$\theta\ $$

$$\alpha\ =a\ -\ z\ \cos\theta\ $$ and $$\beta\ \ =z\ \sin\theta\ $$

$$\alpha\ \ =\ c\ \cos\theta\ \ -z\ \cos\theta\ $$

=> $$\cos\ \theta\ \ =\ \frac{\alpha}{c-z}$$ and $$\sin\theta\ \ \ =\ \frac{\beta\ }{z}$$

$$\ \frac{\alpha\ ^2}{\left(c-z\right)^2}+\ \frac{\beta\ ^2}{z^2}=1$$ which is an ellipse.

Since the expression $$\lim_{x\rightarrow0}\frac{ae^x - be^{-x}}{x + \sin x}$$ is in 0/0 form, as RHS is a finite number, and denominator is zero, hence, the numerator must also be zero to get a finite number. Hence, a-b=0 when x tends to 0.

L'Hospitals rule can be applied 

$$\lim_{x \rightarrow 0}\frac{ae^x + be^{-x}}{1 + \cos x}$$ = 1

$$\frac{a+b}{2}$$ = 1 which is valid only when a = b = 1

$$\therefore$$ ab=1

Hence D is the correct answer.

|a|>a holds only if a is negative.

Similarly, $$\mid \frac{x + 1}{x - 1} \mid$$ will be greater than  $$\frac{x + 1}{x - 1}$$ only if  $$\frac{x + 1}{x - 1}$$ < 0

The above inequality is true if x lies in the range $$\in$$ (-1,1)

Hence, B is the correct answer.

If the row sums are all odd, then the total number of 1s is the sum of these 6 odd numbers, hence even. If the column sums are all odd, then the total number of 1s is the sum of these 7 odd numbers, hence odd. A contradiction; hence the number of such matrices is 0

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases

1: T owns 2 handsets
2: T owns 1 handset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one handset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

It is clear from the table that T owns 1 handset.

Hence option A is the correct answer.

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases
1: T owns 2 handsets
2: T owns 1 handset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one handset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

Hence option A is the correct answer.

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases

1: T owns 2 headsets
2: T owns 1 headset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one headset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

Since R must own a handset in common with T and it owns only a single handset and a handset brand can be owned by a maximum of 2 people .

R and T must own Samsung brand handset

Hence B is the correct answer.

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases

1: T owns 2 headsets
2: T owns 1 headset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one headset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

Let's consider the options one by one,

Option A: If R owns handsets of Samsung and One Plus then T can own Samsung ,Q can own Motorola ,Iphone ,One Plus , S can own Iphone brand handsets. So this combination is possible.

Option B: If R owns handsets of Samsung and Iphone then T can own Samsung ,Q can own Motorola ,Iphone ,One Plus , S can own One Plus brand handsets. So this combination is possible.

Option C: If R owns handsets of One Plus and Motorola then T can own One Plus.We are left with only two brands but Q has handsets of 3 different brands. So this combination is not possible.

Hence C is the correct answer.

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases

1: T owns 2 headsets
2: T owns 1 headset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one headset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

Since we have to maximise the number of handsets with Q and S together ,R and T owns 1 handset each i.e Samsung .

S owns 2 handsets of either Iphone or One plus ,Q owns 4 handsets

So maximum number of handsets that Q and S together can own is 7 

Hence C is the correct answer

Let's have a look at the meanings of each of the words
Peak : The pointed top of a mountain or the point of highest activity, quality, or achievement.
Peek: Look quickly or furtively.
Peak traffic hours means rush hours. Hence this is used correctly in the given context
Ensure : Make sure that (something) will occur or be the case
Insure: Arrange for compensation in the event of damage to or loss of (property)
Insure means arrange for compensation in the event of theft. Hence this is used correctly in the given context
Illicit: Forbidden by law, rules, or custom
Elicit: Evoke or draw out (a reaction, answer, or fact) from someone.
Elicit means draw out or to take opinion from someone. Hence this is used correctly in the given context
Principal: First in order of importance; main.
Principle: A rule or belief governing one's behaviour
Principal means main or important is misused in the given context.

Hence D is the correct answer.

Let's have a look at the meanings of each of the words.
Complemented: A thing that contributes extra features to something else in such a way as to improve or emphasize its quality.
Complimented: A polite expression of praise or admiration
A compliment which means a polite expression of praise is used correctly in the sentence.
Beneficent:(of a person) generous or doing good.
Beneficial: Resulting in good; favourable or advantageous
A rule can be beneficent. Hence beneficial was misused in the sentence.
Oversight: An unintentional failure to notice or do something.
Oversite: A layer of concrete used to seal the earth under the ground floor of a house
An oversight which means failure to notice is used correctly in the sentence
Break: Fail to continue with 
Brake: A device for slowing or stopping a moving vehicle
A break which means failure to continue is used correctly in the sentence.

Hence B is the correct answer.

After going through the sentence, we can understand that the paragraph talks about setting up data centres in China.

Sentence 4 which talks about setting up data centres in poorer remote areas sets up the context Hence this can be the opening sentence.
Sentence 1 which refutes the sentence 4 can be its continuation.
Sentence 1 and 3 are pairs as they talk about the data centres in main cities.
Sentence 2 talks about the number of data centres in China concludes the paragraph.
Hence the correct sequence is 4132.

A is the correct answer.

After going through the sentences, we can understand that the paragraph talks about life on the planet Mars.
Sentence 3 introduces the topic as it talks about Mars and its qualities.
3 and 1 are pairs as sentence 1 further talks about Mars and how it has been among friendlier places to live.
Sentence 4 which furthers the discussion by stating the difficulty in tracing the past evidence.
Sentence 2 concludes talking about how 2020 rover will attempt to do.
The sequence is 3142.

D is the correct answer.

After going through the sentences, we can understand that the paragraph talks about the financial crisis in Germany.
Sentence 3 introduces the topic by stating a 0.2 per cent fall in GDP.
Sentence 1 will follow it as it explains the reasons for the downfall.
Sentence 2 refutes the explanation in sentence 1.
Sentence 4 furthers the discussion by indicators of business sentiment which slowed the growth across the eurozone.
3124 is the correct sequence.

B is the correct answer.

Option A can be inferred from the fifth paragraph, where the author has mentioned that Italy allocates only 1 per cent of its gross domestic product to social protection benefits — half the European average. One child out of three here is at risk of relative poverty

Option C can be inferred from the fourth paragraph, where the author mentions the birth rates of Italy and France as 1.37 and 2, respectively.

Option D can be inferred from the penultimate paragraph, where Prime Minister Matteo Renzi, whose own health minister started the campaign, distanced himself from the ads in a radio interview. Under Mr Renzi, Italy's government has paid families with a so-called baby bonus of 80 to 160 euros, or about $90 to $180, for low- and middle-income households. and it has approved labour laws giving more flexibility on parental leave

Option B cannot be inferred, as the ad campaign was launched with a series of online advertisements and a hashtag on Twitter. Therefore, B is the correct answer.

In the fourth paragraph, the author emphasized a family-oriented system provides a far more generous social safety net that includes daycare and subsidies for families to have children which were existing in France where the fertility rate is 2 whereas it lacks in Italy's economy which has the lowest fertility rate of 1.37.Hence the absence of a support system for families with children is the key reason for Italy's low fertility rate.
C is the correct answer.

Disassociation which means to separate or to detach. In the penultimate paragraph, the author has mentioned Prime Minister Matteo Renzi distanced himself from the ads in a radio interview. Hence, disassociation which means the state of being disconnected would be the Prime Minister Matteo Renzi's reaction to the fertility campaign.

Belligerence which means hostile and aggressive.Prime Minister Matteo Renzi was nowhere offensive to the fertility campaign.

Indifference which means lack of concern. We can infer that Prime Minister Matteo Renzi was not indifferent as during his rule Italy's government has paid families with a so-called baby bonus of 80 to 160 euros, or about $90 to $180, for low- and middle-income households. And it has approved labour laws giving more flexibility on parental leave.

Solidarity which means mutual support within a group.No wherein the passage the author has mentioned support among the group.

Hence A is the correct answer.

Option A: In the third paragraph, the author has mentioned "Many companies do not offer flexible hours for working mothers" as one of the reasons why Italy has the lowest birthrate. So if all private companies allow flexible working hours to pregnant women and new moms, this will have a meaningful impact on Italy's fertility rate.

Option B: In the fourth paragraph, the author emphasised the role of a family-oriented system, which provides a far more generous social safety net that includes daycare and subsidies for families to have children. Hence, this will have a meaningful impact on Italy's fertility rate.

Option C: In the third paragraph, the author mentions, "Many working women, without an extended family to care for a child, face a dilemma, as private childcare is expensive. Some also worry that their job security may be undermined by missing workdays because of childcare issues. " Therefore, this will have a significant impact on Italy's fertility rate.

Option D: In the third paragraph, the author mentions, "It is not a lack of desire to have children , but the lack of significant support provided by the government and many employers in a country where the family remains the primary source of child care is the reasons why Italy has the lowest birthrate." Therefore, spending money on advertisements that encourage Italians to have more children will not have a meaningful impact on Italy's fertility rate, even if the government works hard to implement them. Thus, Option D is the correct answer.

In paragraph three,  the author has mentioned that the problem is not a lack of desire to have children, critics of the campaign say, but rather the lack of meaningful support provided by the government and many employers in a country where the family remains the primary source of child care. Many working women, without an extended family to care for a child, face a dilemma, as private child care is expensive. Some also worry that their job security may be undermined by missing workdays because of child care issues. Many companies do not offer flexible hours for working mothers. These are some of the reasons why Italy's fertility is low which the government failed to address. This is aptly captured in option C. 

The other options are not relevant from the passage's perspective. 

Hence C is the correct answer.

It is mentioned in the second paragraph, 'A truly self-driving car, after all, will have to be given ethical instructions of some sort by its human programmers ' Hence the equivalent of the person pulling the lever in the 'trolley problem' will be human programmers who give ethical instructions.

Though the excitement of self -driving cars led to the miniature boom of professional ethicists , It is because of the human programmers who gave ethical instructions of some sort to the self-driving cars which have led to the trolley problem.
CEOs of multinational car manufacturing firms and driverless-car owners who use their cars to travel abroad are nowhere mentioned in the passage.

Hence D is the correct answer.

It is mentioned in the last paragraph that since the preferences to save differed among nations and the researchers found that the world's countries clustered into three broad categories, which they dubbed "western" covering North America and the Christian cultural countries of Europe, "Eastern", including the Middle East, India and China and "Southern" Latin America and many of France's Former colonial possessions. 

Option A: It is not about being acceptable in different countries, but a comment on how different countries have different values. 

Option B: This option is close, but is a literal interpretation of the text, with no implication in place. Furthermore, it is not that countries do not have regulations for self-driving cars, but rather thatthey would have those. 

Option C: This is what the sentence implies. With the segregation of preferences for lives, different places have different ideas on who should be prioritized. And if we were to introduce self-driving cars, we would have to modify them according to the preferences of that culture. 

Option D: Training local software programmers is beyond the scope of the argument and can be eliminated as an option. 

Therefore, Option C is the correct answer. 

It is evident from the lines in the fourth paragraph that 'The strongest preferences, expressed by respondents from all over the world, were for saving human lives over animal ones, preferring to save many rather than few and prioritising children over the old. There were weaker preferences for saving women over men, pedestrians over passengers in the car and for taking action rather than doing nothing. Criminals were seen as literally sub-human ranking below dogs in the public's priority list, above cats.'

Option B is the clearest culmination of these, pitting babies and women with animals against an equal number of criminals (who traditionally were given a lower preference). 

Making Option B the best choice. 

In the Southern countries, it is given that there is a weaker preference while choosing between humans and animals. Moreover, it is given that this particular nation has high levels of gender inequality, so there would hardly be any preference between either gender. 
So for the software to face the most uncertainty in this region, the two potential victims should be a human and an animal respectively and both of opposite genders.
The option that best describes such a situation is Option B.

Option A: An international agreement to develop a separate signalling system for driverless cars would not solve the dilemma because preferences differed among nations.Hence A is not the correct answer.
Option B: A solution to the 'trolley problem' and an international agreement that cars should run on rails instead of roads will not solve the dilemma because Trolley problem will have different preferences to save in different countries and whether cars should run on rail or roads is beyond the scope of the passage.
Option C: As explained in option B, formation of an international panel of professional ethicists to solve the 'trolley problem' will not solve the dilemma 
Option D: An international agreement on guidelines for development of navigation software for self-driving cars will solve the dilemma because preference to save differed among Nations.Having an international agreement on guidelines will help the self-driving cars.
Hence D is the correct answer.