IIFT 2010 Question Paper

$$\frac{2}{1!}+\frac{3}{2!}+\frac{6}{3!}+\frac{11}{4!}+\frac{18}{5!}+...$$ = 2 + 1.5 + 1 + 0.5 + 0.15 + smaller insignificant values $$\approx$$ 5.2

Option 'A' = 3e - 1 = 3*2.718-1 = 7.15 therefore cannot be our answer

Option 'B' = 3(e - 1) = 3*(2.718-1) = 5.154 therefore can be our answer

Option 'C' = 3(e + 1) = 3*(2.718+1) = 11.15 therefore cannot be our answer

Option 'D' = 3e + 1 = 9.15 therefore cannot be our answer

Therefore option 'B' is our answer

We are given exactly 7 digits - 3, 4, 4, 5, 6, 6, 7. The millions digit can be either 6 or 7. 

Case 1: When the millions digit is 6. 

6 _ _ _ _ _ _ We are left with six digits {3, 4, 4, 5, 6, 7}. 

These six digits can be arranged in six places in $$\dfrac{6!}{2!}$$ ways.

Case 1: When the millions digit is 7. 

7 _ _ _ _ _ _ We are left with six digits {3, 4, 4, 5, 6, 6}. 

These six digits can be arranged in six places in $$\dfrac{6!}{2!*2!}$$ ways.

Therefore, total number of numbers 'n' = $$\dfrac{6!}{2!}$$ + $$\dfrac{6!}{2!*2!}$$ = 360 + 180 = 540. Hence, option C is the correct answer.

Manufacturing cost (MC) of 14 machines = Rs. 42000
Output of 14 machines = Rs. 70000
Establishment cost (EC) = Rs. 12000
Profit = Rs.(70000 - 42000 - 12000) = Rs. 16000
Shareholder's profit = 12.5% of Rs. 16000 = Rs. 2000
It is given that 7.14% of the machines were non functional which means only 13 machines were functional.
MC of 13 machines = Rs. (42000 * $$\frac{13}{14}$$) = Rs. 39000 [As it is directly proportional to the number of functional machines]
Output of 13 machines = Rs. (70000 * $$\frac{13}{14}$$) = Rs. 65000 [As it is directly proportional to the number of functional machines]
EC of 13 machines = Rs. 12000 [As it does not depend on the number of functional machines]
Profit = Rs.(65000 - 39000 - 12000) = Rs. 14000
Shareholder's profit = 12.5% of Rs. 14000 = Rs. 1750
Reduction in Shareholder's profit = Rs.(2000 - 1750) = Rs. 250
Reduction % = $$\frac{250}{2000}$$*100% = 12.5%
Hence, option B is the correct answer.

If there are 10000 policy holders then 5000 are of standard, 3000 are of preferred and 2000 are of ultra-preferred

0.01 of standard policy holders may die next year i.e. 50 of standard policy holder may die next year

0.008 of preferred policy holders may die next year i.e. 24 of preferred policy holders may die next year

0.007 of ultra-preferred policy holders may die next year i.e. 14 of ultra-preferred policy holders may die next year

Total number of people that may die next year = 50+24+14 = 88

Probability that the person died is a preferred policy holder is $$\frac{24}{88}$$ = 0.2727

Therefore our answer is option 'B' 

It is given that the fare charged (in RS.) is defined by the function $$f=(54-\dfrac{x}{32})^{2}$$ where ‘x’ is the number of the people per trip.

Let 'x' be the number of people per trip that will make the marginal revenue equal to zero.

Total revenue generated per trip, g(x) = $$x*(54-\dfrac{x}{32})^{2}$$

When total revenue is maximum, then the marginal revenue will be zero. Therefore, we have to find out the value of 'x' for which g'(x) = 0

$$\Rightarrow$$ $$(54-\dfrac{x}{32})^{2}-\dfrac{2x}{32}*(54-\dfrac{x}{32})=0$$

$$\Rightarrow$$ $$(54-\dfrac{x}{32})^{2}-\dfrac{2x}{32}*(54-\dfrac{x}{32})=0$$

$$\Rightarrow$$ $$(54-\dfrac{x}{32})*(54-\dfrac{3x}{32})=0$$

$$\Rightarrow$$ $$x = 1728, 576$$

It is given that the train has a capacity of 900 only. Hence, x $$\neq$$ 1728 i.e. $$x = 576$$. Therefore, option B is the correct answer.

if $$Sin(\alpha+\beta-\gamma)=\frac{1}{\sqrt{2}} $$then $$\alpha+\beta-\gamma$$ = 45°  ...(1)

if $$Cosec(\beta+\gamma-\alpha)=\frac{2}{\sqrt{3}}$$ then $$\beta+\gamma-\alpha$$ = 60°   ...(2)

if $$tan(\gamma+\alpha-\beta)=\frac{1}{\sqrt{3}}$$ then $$\gamma+\alpha-\beta$$ = 30°  ...(3)

Adding we get $$\alpha+\beta+\gamma$$ = 135°  ...(4)

from 1,2,3 and 4 we get $$\alpha$$ = 37.5° therefore answer is option 'A'

Let the total profit be P. Shyam will get 0.2P for managing the business rest 0.8 P will be divided in the ratio of 2:4:3

i.e. shyam will get 0.2P+0.8P*$$\frac{2}{9}$$ and Gopal and Madhur will together get 0.8P*$$\frac{7}{9}$$

Given that 0.8P*$$\frac{7}{9}$$ - (0.2P+0.8P*$$\frac{2}{9}$$) = 2200

Solving we get P = 9000 therefore profit madhur will get is $$0.8*9000*\frac{1}{3}$$ = 2400 

Therefore our answer is option 'B'

We can see that letters are S, S, E, E, I, R.

Case 1: When all 4 letters are different. There is only one way where we select one each S, E, I, R.

Total number of 4 letter words which can be formed using these letters = $$4!$$ = 24.

Case 2: When all 2 letters are of 1 type and 2 letters are different.

Total number of ways in which 4 letter can be chosen = 2C1*3C2 = 6

Total number of 4 letter words which can be formed using these letters = $$6*\dfrac{4!}{2!}$$ = 72

Case 3: When all 2 letters are of 1 type and remaining 2 letters are of different another same type. There is only one way when we select S, S, E, E.

Total number of 4 letter words which can be formed using these letters = $$\dfrac{4!}{2!*2!}$$ = 6

We have considered all possible cases. Hence, total number of four letters of the word can be made = 24 + 72 + 6 = 102. Hence, option D is the correct answer.

Let us assume that X co-ordinate of the 3rd vertex is a. Then y = a + 5. So the co-ordinates of the vertex = (a, a+5) 

Ttherefore, 6 =   $$\dfrac{1}{2}\times \begin{vmatrix}1 & 1 & 1\\4 & -1 & 1\\a & a+5 & 1 \end{vmatrix}$$

$$\Rightarrow$$ $$\pm12$$ = 1(-1-a-5) -1(4 - a) + 1(4a+20+a)
$$\Rightarrow$$ $$\pm12$$ = 5a + 10
$$\Rightarrow$$ a = $$\dfrac{2}{5}$$, $$\dfrac{-22}{5}$$

Hence, the third vertex can be out of the two values ($$\dfrac{2}{5}$$, $$\dfrac{27}{5}$$) or ($$\dfrac{-22}{5}$$, $$\dfrac{3}{5}$$).

Therefore, option A is the correct answer. 

Given that cost of a type of pastry is equal to the quantity bought

if x,y,z are the no. of pastries bought of each type then $$x^2+y^2+z^2$$ = 211 and x+y+z = 23

Using options,

option A = 10,9,4 i.e. 100+81+16 = 197 therefore cannot be the answer

option B= 11, 9, 3 i.e. 121+81+9 = 211 Therefore is our answer

option C = 10, 8 , 5 i.e. 100+64+25 = 189 therefore cannot be the answer

option D = 11, 8, 4 i.e. 121+64+16 = 201 therefore cannot be the answer

Therefore our answer is option 'B'