IIFT 2009 Question Paper

4 is the starting statement as it introduces the topic of discussion. (Asia being less exposed to the crisis)

2 will follow as it puts forth a counterpoint.

1 will follow 2 as it mentions a possible solution for the situation in 2.

3 explains the solution mentioned in 1.

Hence, the sequence is 4213 and the answer is option A.

4-3 will form a logical pair as the "individual rights" and "social consensus" mentioned in 4 are referred to in 3 as the "former" and the "latter".

Only option C has the above-mentioned pair. Thus, it will be the answer.

4 will be the starting sentence as it introduces Allopathy and Ayurveda.

1 will follow as it talks about Allopathy by using the pronoun "first".

2 will follow 1 as it mentions the significance of Ayurveda.

3 is the perfect concluding statement as it talks about the synergy between the two types of medicine.

Hence, the required sequence is 4123 and the answer is option B.

4 will start the topic as it introduces Julian and talks about the beginning of the journey.

3 mentions Julian's first thought after beginning the journey of hiring a Sherpa but deciding otherwise. Thus, it will follow 4.

2 mentions what he did instead of hiring a Sherpa. Thus, it will come directly after 3.

1 will be the concluding statement as it mentions the final start of the climb.

Hence, the required sequence is 4321 and the answer is option D.

SUV  consumes diesel at the rate of $$\frac{1}{400}{(\frac{100}{x}+x})$$ liters per km 

Cost of 1 liter diesel is Rs. 35

Total distance to be covered is 800 kms

Therefore total cost of diesel consumption by SUV is $$\frac{1}{400}{(\frac{100}{x}+x})$$*35*800

Per hour Chargers of Driver is Rs. 125 and total time is $$\frac{800}{x}$$

Therefore total cost of driver is $$\frac{100000}{x}$$

Total Cost = $$\frac{100000}{x}$$ + $$\frac{1}{400}{(\frac{100}{x}+x})$$*35*800

               = $$\frac{107000}{x}$$ + 70x

We need total cost to be minimum so differentiating total cost w.r.t x and equating to 0 we get

0 = -$$\frac{107000}{x^2}$$ + 70

i.e. $$x^2$$ = $$\frac{107000}{70}$$

x = 39 approximately

Therefore option 'A' is the answer

The ratio of initial speeds of Anil and Sunil is 2:1 (Since speed is inversely proportional to time )

So in the time Sunil covers 'x' distance, Anil will cover '2x' distance.

Thus, at the start of the second round, they will meet for the first time time(Since Anil will complete 2 rounds while Sunil will complete his round).

Now, since the speed of Sunil is halved, the ratio will become 4:1.

At the starting point of the third round, they will meet for $$1+3=4^{th}$$ time(Since Anil will complete 4 rounds while Sunil will complete his round).

Now we can observe a pattern that at the starting point of every $$n^{th}$$ round, they are meeting at the $$\Sigma\ \left(2^k-1\right)^{th}time$$, where k ranges from 1 to (n-1).

Thus, at the start of the 7^th round, they will meet for the 120^th time, and at the starting point of the 9^th round, they will meet for the 502^th time.

The $$n^{th}$$ time they will meet between the 6^th and 9^th rounds (excluding the 6^th and 9^th rounds) are $$120^{st}$$, $$122^{nd}$$, $$123^{rd}$$....... $$501^{st}$$, $$502^{nd}$$.

So, the total meeting points will be 383 points.

Since the starting point of the $$7^{th}$$ round is excluded,

Total meets = 383 - 1 (Starting of 7^thround) = 382 meets


Alternate explanation:

Since Time = $$\frac{Distance}{Speed}$$ therefore as Sunil halves his speed the time required to complete the round will double therefore time required for Round 1 = 2 mins

Round 2 = 4 mins

Round 3 = 8 mins

Round 4 = 16 mins

Round 5 = 32 mins

Round 6 = 64 mins

Round 7 = 128 mins

Round 8 = 256 mins

Round 9 = 512 mins

The time required by Anil for Round 1 to Round 9 = 1 mins each

Thus, in the first two minutes, Sunil finished his 1st round, at the same time Anil finished 2 rounds.

When Sunil finished his 6th round, at the same time Anil finished his =2+4+8+16+32+64 rounds

.

Now for the 7th round of Sunil, he will take 128 mins.

Thus Anil will run 128 rounds.

Thus both of them will meet 128-1 =127 times

.

Now for the 8th round of Sunil, he will take 256 mins.

Thus Anil will run 256 rounds.

Thus both of them will meet 256-1 =255 times

= 255 + 127

= 382

Therefore answer is option 'C' 

$$\frac{1}{1.2.3}+\frac{1}{3.4.5}+\frac{1}{5.6.7}+...$$ = 0.166..+0.0166..+0.00476..+..... which is always <0.2 but a positive number.

Option A = $$e^2$$ - 1 = 7.34 - 1 = 6.34 therefore this cannot be the Answer

Option B = $$\log_{e}{2}-1$$ = $$\frac{log_{10}{2}}{log_{10}{e}}$$ - 1 = $$\frac{log_{10}{2}}{log_{10}{2.72}}$$ - 1

We know that the value of $$\frac{log_{10}{2}}{log_{10}{2.72}}$$ < 1 and therefore value of $$\frac{log_{10}{2}}{log_{10}{2.72}}$$ - 1 < 0

therefore this cannot be the Answer

Option C = $$2\log_{10}{2}-1$$ = $$\log_{10}{4}-1$$

We know that the value of $$\log_{10}{4}$$ < 1 and therefore value of $$\log_{10}{4}-1$$ < 0

therefore this cannot be the Answer

Therefore the Answer is option 'D' 

$$\log_{2}{x}.\log_{\frac{x}{64}}{2}=\log_{\frac{x}{16}}{2}$$

i.e. $$\frac{log{x}}{log{2}} * \frac{log_{2}}{log{x}-log{64}} = \frac{log{2}}{log{x}-log{16}}$$

i.e. $$\frac{log{x} * (log{x}-log{16})}{log{x}-log{64}}$$ = $$\log{2}$$

let t = log x

Therefore,  $$\frac{t * (t-log{16})}{t-log{64}}$$ = $$\log{2}$$

$$t^2-4*log 2*t = t*log 2-6*(log 2)^2$$

I.e. $$t^2-5*log 2*t-6*(log 2)^2$$ = 0 

I.e. $$t^2-3*log 2*t-2*log 2*t-6*(log 2)^2$$ = 0 

i.e. $$t*(t-3*log 2)-2*log 2*(t-3*log 2)$$ = 0

i.e $$t=2*log 2$$ or $$t=3*log 2$$

i.e $$log x=log 4$$ or $$log x=log 8$$

therefore $$x=4$$ or $$8$$ 

therefore our answer is option 'B'

Top face will look like the figure shown below. 

Curved surface area of the cylinder = $$2*\pi*r*h$$

To calculate height of the cylinder in terms of 'r', we can see that $$\triangle$$ADC is similar to $$\triangle$$EFC. 

Therefore, 

$$\dfrac{AD}{DC}=\dfrac{EF}{FC}$$

$$\Rightarrow$$ $$\dfrac{10}{4} = \dfrac{h}{4-r}$$

$$\Rightarrow$$ $$h = \dfrac{5}{2}(4-r)$$

Therefore, the curved surface area of the cylinder = $$2*\pi*r*\dfrac{5}{2}(4-r)$$ = $$5πr(4 - r)$$.

Hence, option B is the correct answer.   

It is given that radius, R = 30 cm. 

Curved surface area, S= $$4\pi*R^2$$

$$\dfrac{dS}{dt}$$ = $$4\pi*(2R)*\dfrac{dR}{dt}$$

It is given that $$\dfrac{dR}{dt}$$ = 2. 

Hence, $$\dfrac{dS}{dt}$$ = $$4\pi*(2*30)*2$$ = $$480\pi$$. Hence, option B is the correct answer.