IIFT 2014 Question Paper

Total 8 digit number which can be made using all digits when repetition is allowed = $$9*10^7$$ = $$90000000$$

Total 8 digit number which can be made using all digits when repetition is not allowed = $$9*9*8*7*6*5*4*3$$ = $$1632960$$

Therefore, The total number of eight - digit landline telephone numbers that can be formed having at least one of their digits repeated =  $$90000000$$ - $$1632960$$ = $$88367040$$.  Hence the correct answer is None of the above (D).

On drawing the Venn diagram

It is given that TCS has a total of 42 business analysts covering at least one of the three locations: Singapore, New York and London.

Therefore, (12 - x) + (14 - x) + (12 - x) + 6 + 4 + 8 + x = 42

$$\Rightarrow$$ 56 - 2x = 42 i.e. x = 7. 

Therefore, the number of analysts covering New York alone = 14 - x = 14 - 7 = 7.

Eight years after completion of your MBA degree, you start a business of your own. You invest INR 30,00,000 in the business that is expected to give you a return of 6%, compounded annually. If the expected number of years by which your investment shall double is 72/r, where r is the percent interest rate, the approximate expected total value of investment (in INR) from your business 48 years later is:

It is given that the expected number of years by which your investment shall double is 72/r, where r is the percent interest rate.

We are given that r = 6%. Therefore, it will take 72/6 = 12 years for money to grow twice of initial investment. In every 12 years, the money will become 2 fold. Therefore, in 48 years money will grow to = $$2^{48/12}$$ = 16 times. 

Therefore, the approximate expected total value of investment (in INR) from your business 48 years later = 16*30,00,000 = 4,80,00,000.

It is given that the radius of cylinder = 6 cm. The rectangular solid with a square base is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall.

Therefore, the diagonal of square base = the diameter of circular base 

Hence, a$$\sqrt{2}$$ = 2*6 = 12 => a = $$6\sqrt{2}$$ cm.

The volume of water = Volume of the cylinder - Volume of the rectangular solid

$$\Rightarrow$$ $$\pi*6^2*24$$ - $$(6\sqrt{2})^2*20$$

$$\Rightarrow$$ $$864*\pi - 1440$$

$$\Rightarrow$$ $$288(3\pi - 5)$$

Let 'N' be the total effective student work day required to finish the sponsorship works.

N = 1+(1+2)+(1+2+3)+...+(1+2+3+ ... +20)

N = $$\sum_{n=1}^{n=20} \dfrac{(n)*(n+1)}{2}$$

N = $$\dfrac{1}{2}*[\dfrac{20*21*41}{6}+\dfrac{20*21}{2}]$$

N = 1540

We can say that 1540 engineering students can finish the sponsorship task in one day. It is given that each MBA student is twice as efficient as an engineering student. Hence, we can say that 770 MBA students will finish the sponsorship task in a day.

Therefore, time taken by 11 MBA students would take to do the same activity = $$\dfrac{770}{11}$$ = 70 days

It is given that a total of  6000 strips are manufactured out of which the company supplied 600 strips of free medicines to the doctors.

Hence, the number of strips which were sold = 6000 - 600 = 5400.

It is given that the company was able to sell 4/5th of the strips at 25 percent discount and the balance at the printed price of Rs. 250. 

Total revenue generated by the firm = $$(0.75*250)*(\dfrac{4}{5}*5400)+(250)*(\dfrac{1}{5}*5400)$$ = Rs. 1080000

Net revenue after vendor’s discount = 0.7*1080000 = Rs. 756000

We can see that the company invested Rs. 800000 for the drug creation. 

Hence, percentage loss incurred by the company = $$\dfrac{800000-756000}{800000}*100$$ = 5.5%

Therefore, option C is the correct answer. 

Total distance covered by the ball = $$32+(\dfrac{32}{2}+\dfrac{32}{2}+\dfrac{32}{2^2}+\dfrac{32}{2^2}+\dfrac{32}{2^3}+...)$$

=$$32+2(\dfrac{32}{2}+\dfrac{32}{2^2}+\dfrac{32}{2^3}+...)$$

$$\Rightarrow$$ $$32 + 64(\dfrac{1/2}{1-1/2}$$) = 96 m.

Mr. Raj is not to be included in the committee if Ms. Rani i.e. they both cannot be included together.
Let
i) Raj is selected and Rani is not.
Thus, the remaining 2 males can be selected $$^7C_{2}$$ ways and the remaining 4 females can be selected in $$^6C_{4}$$ ways.
Thus, the total number of ways = $$^7C_{2}$$*$$^6C_{4}$$ = $$315$$
ii) Raj is not selected and Rani is selected.

Thus, the remaining 3 males can be selected $$^6C_{3}$$ ways and the remaining 3 females can be selected in $$^6C_{3}$$ ways

Thus, the total number of ways = $$^7C_{3}$$*$$^6C_{3}$$ = $$700$$
iii) Both are not selected.

Thus, the remaining 3 males can be selected $$^7C_{3}$$ ways and the remaining 4 females can be selected in $$^6C_{4}$$ ways.
Thus, the total number of ways = $$^7C_{3}$$*$$^6C_{4}$$ = $$525$$
Thus, the total number of ways = $$315+700+525 = 1540$$
Hence, option C is the correct answer.