IIFT 2013 Question Paper

While going down the ball will first cover $$180$$m, then $$\frac{180*3}{5}$$, then $$\frac{180*3*3}{5*5}$$ and so on.
After rebouncing the ball will cover $$\frac{180*3}{5}$$, then $$\frac{180*3*3}{5*5}$$ and so on
Thus, there are 2 infinite G.Ps here one of $$180$$, $$\frac{180*3}{5}$$, $$\frac{180*3*3}{5*5}$$,......
and other $$\frac{180*3}{5}$$, $$\frac{180*3*3}{5*5}$$,.........
Total distance covered by the ball = Distance covered while going up + Distance covered while going down
= $$\frac{180}{1-\frac{3}{5}} + \frac{180*\frac{3}{5}}{1-\frac{3}{5}}$$ = $$720$$ m.
Hence, option C is the correct answer.

In match we have to select 2 men and 2 women such that there is no couple.
2 men can be selected in 9C2 way = 36
Now 2 women has to be selected such that they are these 2 men's wife and that can be done in 7C2 ways = 21
Thus, the total number of ways in which a match can be played = 36*21 = 756
2 teams can be formed and thus, the required answer is 756*2 = 1512.
Hence, option A is the correct answer.

Let 'A' and 'B' be the event of train reaching at the station respectively. 

P(A)$$_{\text{Late}}$$ = $$\dfrac{7}{9}$$, therefore, P(A)$$_{\text{On time}}$$ = $$\dfrac{2}{9}$$.

P(B)$$_{\text{Late}}$$ = $$\dfrac{11}{27}$$, therefore, P(B)$$_{\text{On time}}$$ = $$\dfrac{16}{27}$$.

The probability that train Q will be late, given that train P is late, is 8/9.

P$$(\dfrac{B_{\text{Late}}}{A_{\text{Late}}})$$=$$\dfrac{8}{9}$$

P(A$$_{\text{Late}} \cap$$ B$$_{\text{Late}})$$ = P(A)$$_{\text{Late}}$$*P($$\dfrac{B_{\text{Late}}}{A_{\text{Late}}})$$

P(A$$_{\text{Late}} \cap$$ B$$_{\text{Late}})$$ = $$\dfrac{7}{9}$$*$$\dfrac{8}{9} = \dfrac{56}{81}$$

Therefore, the probability that neither train is late = 1 - (P(A)$$_{\text{Late}}$$+P(B)$$_{\text{Late}}$$ - P(A$$_{\text{Late}} \cap$$ B$$_{\text{Late}})$$)

$$\Rightarrow$$ 1 - ($$\dfrac{7}{9}$$+$$\dfrac{11}{27}$$-$$\dfrac{56}{81}$$)

$$\Rightarrow$$ $$\dfrac{41}{81}$$

Hence, we can say that option B is the correct answer.

We are given that 80% MBA applicants are extremely good in logical reasoning. Also, some MBA applicants who are extremely good in logical reasoning can be also good in data interpretation, with conditional probability 0.15. 

Therefore, the probability of that an applicant is sound in data interpretation as well as logical reasoning = 0.80*0.15 = 0.12

We are given that the other 20 percent are extremely good in quantitative aptitude. Also, some MBA applicants who are extremely good in quantitative aptitude can be also good in data interpretation, with conditional probability 0.87. 

Therefore, the probability of that an applicant is sound in data interpretation as well as quantitative aptitude = 0.20*0.87 = 0.174

An applicant surveyed is found to be strong in data interpretation then probability that the applicant is also strong in quantitative aptitude is = 

$$\dfrac{0.174}{0.174+0.12} \approx$$ 0.60. Hence, option B is the correct answer.

A cone is formed when the 2 edges of the sector of a circle are joined. 

We have to find the central angle subtended to find out the area of the sheet required to make the cone. 
It has been given that the height of the cone is 26.5 cm and the base radius is 14 cm. 

The slant height of the cone will be equal to the radius of the sector of the circle. 

Slant height = $$\sqrt{26.5^2+14^2}$$ = $$\sqrt{898.25}$$
$$\sqrt{898.25}$$ is very close in value to $$\sqrt{900}$$

Let us use $$\sqrt{900}$$ for the ease of calculation.
$$\sqrt{900}$$ = $$30$$ cm.
Area of sheet required to make 1 cap = Curve surface area of the cone = $$(\pi)rl$$ = (22/7)*14*30 =1320

Area of sheet required to make 7 cap = 7*1320 = 9240 sq cm

The given situation is as shown below:-

The area of the walking corridor = 4*34+4*21-4*4 = 204 m$$^2$$
The are of the garden = 34*21 = 714 m$$^2$$
Thus, the area of the garden = 714-204 = 510 m$$^2$$
Hence, option C is the correct answer.

Given that,
$$70-\dfrac{70x}{100} = 60+\dfrac{60x}{100}$$
Thus, $$7000-70x = 6000+60x$$
=> $$1000 = 130x$$
Thus, $$x\approx 7.7$$
Thus, $$7.7\% of 50 = $$dfrac{7.7*50}{100} \approx 3.84$$
Hence, option A is the correct answer.

The rod is cut into 3 equal parts thus the length of the rod will be a multiple of 3.
Each part is then cut into $$12 = 2^2*3$$
$$18 = 2*3^2$$ and $$32 = 2^5$$ parts and thus, each part of rod has to be a multiple of $$2^5*3^2 = 288$$
Thus, the rod will be a multiple of $$288*3 = 864$$
Thus, the minimum length of the rod is 864 units.
Hence, option B is the correct answer.

$$\log_{10} x - \log_{10} \sqrt[3]{x} = 6\log_{x}10$$
Thus, $$\dfrac{\log {x}}{\log {10}}$$ - $$\dfrac{1}{3}*\dfrac{\log {x}}{\log {10}}$$ = $$6*\dfrac{\log{10}}{\log{x}}$$
=> $$\dfrac{2}{3}*\dfrac{\log {x}}{\log {10}}$$ = $$6*\dfrac{\log{10}}{\log{x}}$$
Thus, => $$\dfrac{1}{9}*(\log{x})^2 = (\log{10})^2=1$$
Thus, $$(\log{x})^2 = 9$$  
Thus $$\log x = 3$$ or $$-3$$
Thus, $$ x = 1000$$ or $$\dfrac{1}{1000}$$
From amongst the given options, 1000 is the correct answer. 
Hence, option D is the correct answer.

Let the time taken by the Younger son to make the whole biryani be $$y$$ hours and the time taken by the Elder son to make the whole biryani be $$e$$ hours.
Thus, the time taken by the mother to make the biryani = $$e-1$$
Now we are given that, the biryani will be made in 4 hours if the elder son works for 1 hour and the younger son works for 4 hours.
Thus, in 1 hour the elder son will complete $$\dfrac{1}{e}$$ of the biryani and in 4 hours the younger son will complete $$\dfrac{4}{y}$$ of the biryani.
Thus, $$\dfrac{1}{e}$$+$$\dfrac{4}{y}$$ = $$1$$
=> $$y+4e = ey$$
=> $$e = \dfrac{y}{y-4}$$
Thus, the time taken by the mother = $$\dfrac{y}{y-4} - 1$$ = $$\dfrac{4}{y-4}$$
We are given that, It takes 30 minutes for all three of them cooking together to complete 50 percent of the task.
Thus, in 1 hour they'll complete the task.
Thus, $$\dfrac{1}{y}+\dfrac{y-4}{y}+\dfrac{y-4}{y} = 1$$
=> $$\dfrac{y-3}{y} + \dfrac{y-4}{4} = 1$$
=> $$4(y-3)+y(y-4) = 4y$$
=> $$4y-12+y^2-4y = 4y$$
=> $$y^2 - 4y - 12 = 0$$
Solving we get, $$y=6$$ hours and thus, $$e = \dfrac{6}{6-4} = 3$$ hours and thus, the time taken by the mother = $$2$$ hours
Thus, the mother will complete 50% of the biryani in 1 hour.
Hence, option B is the correct answer.