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'

If the quadratic equation is of type $$Ax^+Bx+C=0$$ then the roots of the quadratic equation are given by

$$x = \dfrac{-B\pm\sqrt{B^2 - 4AC}}{2A}$$

Comparing $$Ax^+Bx+C=0$$ with $$bx^{2}-2ax+a=0$$, A = b,  B = -2a,  C = a

Hence, the roots = $$\dfrac{2a\pm\sqrt{4a^2 - 4ba}}{2b}$$

x = $$\dfrac{a\pm\sqrt{a^2 - ba}}{b}$$

Let $$x_{1}$$ = $$\dfrac{a-\sqrt{a^2 - ba}}{b}$$,  $$x_{2}$$ = $$\dfrac{a+\sqrt{a^2 - ba}}{b}$$

Rationalizing  $$x_{1}$$ = $$\dfrac{a-\sqrt{a^2 - ba}}{b}$$

$$\Rightarrow$$ $$x_{1}$$ = $$\dfrac{a-\sqrt{a^2 - ba}}{b}*\dfrac{a+\sqrt{a^2 - ba}}{a+\sqrt{a^2 - ba}}$$

$$\Rightarrow$$ $$x_{1}$$ = $$\dfrac{a^2-(a^2 - ba)}{b*(a+\sqrt{a^2 - ba})}$$

$$\Rightarrow$$ $$x_{1}$$ = $$\dfrac{ab}{b*(a+\sqrt{a^2 - ba})}$$

$$\Rightarrow$$ $$x_{1}$$ = $$\dfrac{a}{a+\sqrt{a^2 - ba}}$$

$$\Rightarrow$$ $$x_{1}$$ = $$\dfrac{a}{a+\sqrt{a}*\sqrt{a - b}}$$

$$\Rightarrow$$ $$x_{1}$$ = $$\dfrac{\sqrt{a}}{\sqrt{a}+\sqrt{a - b}}$$

Similarly, $$x_{2}$$ = $$\dfrac{\sqrt{a}}{\sqrt{a}-\sqrt{a - b}}$$

Therefore, x = $$\dfrac{\sqrt{a}}{\sqrt{a}\pm\sqrt{a - b}}$$. Hence, option C is the correct answer. 

let G be number of days in which Dr. gupta can complete the evaluation of answer sheet , let Sh be number of days in which Dr. Sharma can complete the evaluation of answer sheet , let Si be number of days in which Dr. Singh can complete the evaluation of answer sheet

Given Dr. Gupta is 40% more efficient than Dr. Sharma therefore number of days required by Dr. Sharma to complete the evaluation of answer sheet = 1.4*G

Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work i.e. 1.4G-G = 10 therefore G = 25 and hence Sh = 35

Also given that Dr. Sharma is 20% more efficient than Dr. Singh therefore number of days required by Dr. Singh to complete the evaluation of answer sheet = $$\frac{35}{1.2}$$ = 42 i.e. Si = 42

Dr. Gupta starts the evaluation work and works for 10 days therefore he completes $$\frac{10}{25}$$ of work then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days therefore he completes $$\frac{15}{35}$$ of work. Fraction of work left is 1 - $$\frac{10}{25}$$ - $$\frac{15}{35}$$ = $$\frac{6}{35}$$ now time required by Dr. Singh to complete this amount of work is $$\frac{6*42}{35}$$ = 7.2 days

Therefore our answer is option 'A'

$$[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+[\sqrt{4}]+....+[\sqrt{360}]$$ = 1 + 1 + 1 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3.. 7 times + 4 + 4 +......9 times +.........+ 18 + 18 + ......37 times

= 1*3 + 2*5 + 3*7 + 4*9+............+18*37 

= $$\sum_1^{18}$$ n(2n+1)

=  $$\sum_1^{18}$$ $$2n^2+n$$

= $$\frac{2n*(n+1)*(2n+1)}{6}$$ + $$\frac{n*(n+1)}{2}$$

= $$\frac{2*18*(19)*(37)}{6}$$ + $$\frac{18*19}{2}$$

= 4389

Therefore our answer is option 'A' 

$$\sqrt{\frac{a}{b}}$$, If $$\log_{4}\log_{4}4^{a-b}=2\log_{4}(\sqrt{a}-\sqrt{b})+\log_{4}{4}$$

i.e. $$\log_{4}\log_{4}4^{a-b}=\log_{4}((\sqrt{a}-\sqrt{b})^2)*4$$

i.e. $$\log_{4}4^{a-b}=((\sqrt{a}-\sqrt{b})^2)*4$$

i.e. (a-b)*$$\log_{4}4=((\sqrt{a}-\sqrt{b})^2)*4$$

i.e. a-b = 4a+4b-8$$\sqrt{ab}$$

i.e. 3a + 5b - 8$$\sqrt{ab}$$ = 0

i.e. $$3\sqrt\frac{a}{b}^2$$ - 8$$\sqrt\frac{a}{b}$$+5 = 0

put $$\sqrt\frac{a}{b}$$ = t

therefore 3$$t^2$$ - 8t + 5 = 0 

solving we get t = 1 or t = $$\frac{5}{3}$$

i.e. $$\sqrt\frac{a}{b}$$ = 1 or $$\frac{5}{3}$$

but if $$\sqrt\frac{a}{b}$$ = 1 then a=b then $$\log_{4}(\sqrt{a}-\sqrt{b})$$ will become indefinite

Therefore  $$\sqrt\frac{a}{b}$$ = $$\frac{5}{3}$$

Therefore our answer is option 'C' 

Let the capacity of the tank be 60 litres.
Capacity of the first pipe = 12 l/hr
Capacity of the second pipe = 6 l/hr
Capacity of the third pipe = 4 l/hr
In 2 hrs, first pipe fills (9 + 12) l = 21 l
In 2 hrs, second pipe fills (4.5 + 6) = 10.5 l
In 2 hrs, third pipe fills (16/3) l
In 2 hrs, tank filled = (21 + 10.5 + 5.33) l = 36.83 l
Tank left to be filled = (60 - 36.83) l = 23.17 l
Time required = (23.17/22) hr = 1.05 hrs
Total time = 3.05 hrs
Hence, option C is the correct answer.

Using AM $$\geq$$ GM, We can say that 

$$\dfrac{3^{sinx}+3^{cosx}}{2}$$ $$\geq$$ $$\sqrt{3^{sinx}*3^{cosx}}$$

$$\Rightarrow$$ $$3^{sinx}+3^{cosx}$$ $$\geq$$ $$2*3^\frac{sinx+cosx}{2}$$  ... (1)

We know that -$$\sqrt{A^2+B^2}$$ $$\leq$$ Asinx+Bcosx $$\leq$$ $$\sqrt{A^2+B^2}$$

Therefore,   -$$\sqrt{1^2+1^2}$$ $$\leq$$ sinx+cosx $$\leq$$ $$\sqrt{1^2+1^2}$$

$$\Rightarrow$$ -$$\sqrt{2}$$ $$\leq$$ sinx+cosx $$\leq$$ $$\sqrt{2}$$

Hence, we can say that the minimum value of sinx+cosx = -$$\sqrt{2}$$  ... (2)

From equation (1) and (2) we can say that,

$$\Rightarrow$$ $$3^{sinx}+3^{cosx}$$ $$\geq$$ $$2*3^\frac{-\sqrt{2}}{2}$$

$$\Rightarrow$$ $$3^{sinx}+3^{cosx}$$ $$\geq$$ $$2*3^\frac{-1}{\sqrt{2}}$$

Therefore, option B is the correct answer. 

Let the number of professors, associate professors and assistant professors be x, y and z respectively and their average ages be a, b and c respectively.
xa + yb + zc = 2160   -------------------(1)

Average age =36

$$\therefore$$ x+y+z=60

xa + yb = 39 (x + y)
11(yb + zc) = 360(y + z)
3(xa + zc) = 110(x + z)
x(a + 1) + y(b + 6) + z(c + 7) = 2160 + 5*(60) -------(2)            [$$\because$$ Average increases by 5]

Eq 2- Eq 1

We get x+6y+7z=300

Lets solve the options one by one
Option A: x = 16 , y = 24, z = 20

16+6*24+7*20=300 which satisfies the equations.

So either A or C can be the answer.

Now check for the values of a, b, c

a=45, b=35, c=30

ax+by+cz = 45*16+35*24+30*20

=2160

Hence, option A is the correct answer.

Let $$\log_{5}{2}$$ = y

Let us assume  $$\log_{5}{2}$$ is a rational number.

$$\log_{5}{2}$$ = p/q, where p and q are co primes.

5^(p/q)=2 => 5^p=2^q.

5^p=5*5*5*5*5*5*5..................p times

2^p=2*2*2*2*2*2*2..................q times

No value of p and q can satisfy the equation. Hence y is an irrational number.

Let us assume that 'a' is the length of the side of equal sides of the isosceles triangle. 

We can see that $$a+\sqrt{2}*a+a=2$$

$$\Rightarrow$$ a = $$\dfrac{2}{2+\sqrt{2}}$$

Therefore, the perimeter of the regular octagon = $$8*a*\sqrt{2}$$

$$\Rightarrow$$ $$\dfrac{8\sqrt{2}*2}{2+\sqrt{2}}$$

$$\Rightarrow$$ $$\dfrac{16}{1+\sqrt{2}}$$ ... (1)

Area of regular octagon = $$2x^2(1+\sqrt{2})$$ where 'x' is the length of each side. 

Here, x = $$a\sqrt{2}$$ = $$\dfrac{2\sqrt{2}}{2+\sqrt{2}}$$ = $$\dfrac{2}{1+\sqrt{2}}$$

Therefore, area of the regular octagon = $$2*(\dfrac{2}{1+\sqrt{2}})^2(1+\sqrt{2})$$ = $$\dfrac{8}{1+\sqrt{2}}$$ =$$\dfrac{8}{1+\sqrt{2}}*\dfrac{1+\sqrt{2}}{1+\sqrt{2}}$$ = $$\dfrac{8*(1+\sqrt{2})}{3+2\sqrt{2}}$$

Hence, we can say that none of the given answer is correct. 

7! can be broken into prime factors.

7! = 1*2*3*4*5*6*7 = $$2^4*3^2*5*7$$

Hence, the smallest perfect square which is divisible by 7! will $$2^4*3^2*5^2*7^2$$ = 5040*5*7 =  176400

Let the number of people who watched exactly one movie be 'a', the number of people who watched exactly two movies be 'b' and the number of people who watched exactly three movies be 'c'
Then, a + b + c = 100 - 3 = 97 ...............(i)
also, a + 2b + 3c = 61 + 46 + 29 = 136.......................(ii)
On subtracting (i) from (ii), we get
b + 2c = 39
It is given that, b = 25
So, c = 7
Therefore, 7% people watched all the three movies.
Hence, option D is the correct answer.

Let AC = $$2^k$$
AC = 2 * AB
So, AB = $$2^{k - 1}$$
Only 256 and 512 satisfy this condition as the third side is 295 and we have to ensure that sum of the two sides of the triangle is greater than the third side.
Thus, the perimeter = (256 + 512 + 295) = 1063.
Hence, option C is the correct answer.

It is given that sum of the first $$(x - 1)$$ numbers is equal to sum of the numbers from $$(x + 1)$$ to 49
or, sum of $$(x - 1)$$ numbers = sum of first 49 numbers - sum of first $$x$$ numbers
$$\dfrac{x(x - 1)}{2} = \dfrac{49 * 50}{2} - \dfrac{x(x + 1)}{2}$$
On solving, we get $$x$$ = 35
Hence, option C is the correct answer.

Let the interest on the second part be $$r$$ %
Then, the rate on the first part = ($$r$$ + 10)%It is given that, 
$$30000(1 + \dfrac{r + 10}{100})^2 - 30000(1 + \dfrac{r}{100})^2 = 7500$$
On solving, we get $$r$$ = 20%
Let the first part be Rs. $$a$$
Then, the second part = Rs. (60000 - $$a$$)
$$a(1 + \dfrac{20 + 10}{100})^2 - (60000 - a)(1 + \dfrac{20}{100})^2$$ = 38800
On solving, we get $$a$$ = Rs. 40000

Hence, option C is the correct answer.

We can write $$(1 - x^{6})^{4}$$ = $$4C0(1)^4(x^6)^0$$ - $$4C1(1)^3(x^6)^1$$ + $$4C2(1)^2(x^6)^2$$ - $$4C3(1)^1(x^6)^3$$+ $$4C4(1)^0(x^6)^4$$

$$\Rightarrow$$ $$(1 - x^{6})^{4}= (1-4x^6+6x^{12}-4x^{18}+x^{24})$$

Therefore, we can say

$$(1 - x^{6})^{4}(1 - x)^{-4}=(1-4x^6+6x^{12}-4x^{18}+x^{24})*(1 - x)^{-4}$$

We have to find out coefficient of $$x^{12}$$, $$x^6$$, $$x^0$$ in $$(1 - x)^{-4}$$.

We can use binomial expansion for negative coefficients. Therefore, coefficient of $$x^{12}$$ in $$(1 - x)^{-4}$$

$$\Rightarrow$$ $$\dfrac{(-4)*(-4-1)*(-4-2)* ... *(-4-11)}{12!}$$

$$\Rightarrow$$ $$\dfrac{15!}{12!*3!}$$

$$\Rightarrow$$ $$\dfrac{15*14*13}{3*2*1}$$

$$\Rightarrow$$ $$455$$

Similarly, coefficient of $$x^6$$ in $$(1 - x)^{-4}$$

$$\Rightarrow$$ $$\dfrac{(-4)*(-4-1)*(-4-2)* ... *(-4-5)}{6!}$$

$$\Rightarrow$$ $$\dfrac{9!}{6!*3!}$$

$$\Rightarrow$$ $$\dfrac{7*8*9}{3*2*1}$$

$$\Rightarrow$$ $$84$$

Coefficient of $$x^0$$ in $$(1 - x)^{-4}$$ is 1. 

Therefore, we can say that the coefficient of $$x^{12}$$ in the expansion of $$(1 - x^{6})^{4}(1 - x)^{-4}$$ = 455+(-4*84)+(1*6) = 125. Hence, option C is the correct answer. 

Alternative Solution:

$$(1-x^6)^4 = (1-x)^4(1+x+x^2+x^3+x^4+x^5)^4$$

$$\Rightarrow (1-x^6)^4(1-x)^{-4} = (1+x+x^2+x^3+x^4+x^5)^4$$

Hence we need to find coeff of  $$x^{12}$$ in $$(1+x+x^2+x^3+x^4+x^5)^4$$

= $$(1+x+x^2+x^3+x^4+x^5)\times$$

$$(1+x+x^2+x^3+x^4+x^5)\times$$

$$(1+x+x^2+x^3+x^4+x^5)\times$$

$$(1+x+x^2+x^3+x^4+x^5)$$

This will be equal to number of integral solutions for a + b + c + d = 12, 0<=a,b,c,d<=4

a is the power of x from the first expression, b is the power of x 

Lets find the set of values for (a,b,c,d)

(5,5,2,0) => Number of ways of arranging = 4!/2! = 12

(5,5,1,1) => Number of ways of arranging = 4!/(2!*2!) = 6

(5,4,3,0) => Number of ways of arranging = 4! = 24

(5,4,2,1) => Number of ways of arranging = 4! = 24

(5,3,2,2) => Number of ways of arranging = 4!/2! = 12

(5,3,3,1) => Number of ways of arranging = 4!/2! = 12

(4,4,4,0) => Number of ways of arranging = 4!/3! = 4

(4,4,3,1) => Number of ways of arranging = 4!/2! = 12

(4,4,2,2) => Number of ways of arranging = 4!/(2!*2!) = 6

(4,3,3,2) => Number of ways of arranging = 4!/2! = 12

(3,3,3,3) => Number of ways of arranging = 4!/4! = 1

Hence the coeff of $$x^{12}$$ = 24*2 + 12*5 + 6*2 + 4 + 1 = 125

Let us assume that Mukesh and Suresh started on bike from Delhi to Mathura and Dinesh started walking at the same time. Mukesh drops Suresh in a mid-way such that Suresh will take same time to reach Mathura with Mukesh and Dinesh. In the same time Mukesh will turn back and will pick up Dinesh. 

Let us assume that '4D' is the distance covered by by Mukesh and Suresh. Then Suresh must have covered remaining 300 - 4D kms by walking at 15 km/hr. When Mukesh dropped Suresh by that time Dinesh have already covered D kms and now Mukesh and Dinesh and would have 3D kms apart. Since Mukesh is 4 times faster than Dinesh, Mukesh would have covered (4/5) of 3D kms. 

In addition to this, Mukesh and Dinesh have to cover 2.4D+300-4D kms to reach Mathura at 60 km/hr.

By equating the time taken by Mukesh and Suresh to reach Mathura after the point when Mukesh dropped Suresh,

$$\dfrac{300-4D}{15}=\dfrac{2.4D+2.4D+300-4D}{60}$$

$$\Rightarrow$$ 16.8*D = 900

$$\Rightarrow$$ D = $$\dfrac{375}{7}$$ kms

Therefore, minimum time taken by them to finish the journey = $$\dfrac{4D}{60}+\dfrac{300-4D}{15}$$

$$\Rightarrow$$ $$20 - \dfrac{D}{5}$$

$$\Rightarrow$$ $$20 - \dfrac{375}{7*5}$$

$$\Rightarrow$$ $$20 - \dfrac{75}{7}$$

$$\Rightarrow$$ $$\dfrac{65}{7}$$ or $$9\dfrac{2}{7}$$ hours. Hence, option B is the correct answer. 

Let us draw an appropriate diagram. Let us assume that 'R' is the radius of the hole. 

$$\dfrac{1}{2}$$*(Total volume - Volume of the hole) = Volume of the hole

Volume of the hole = $$\dfrac{1}{3}*\text{Total volume of the rocket}$$

$$\pi*R^2*(8/3)x$$ = $$\dfrac{1}{3}*(\pi*8^2*5x+\dfrac{1}{3}*\pi*8^2*3x)$$

$$R^2*(8/3)$$ = $$\dfrac{1}{3}*(8^2*5+\dfrac{1}{3}*8^2*3)$$

$$R^2 = 48$$

$$R$$ = $$4\sqrt{3}$$ cm. Hence, option A is the correct answer.

Let the production cost be Rs. 100
The, Selling Price = Rs. 120
Price of component A = Rs. 10
Price of component B = Rs. 20
Price of other components = Rs. (100 - 10 - 20) = Rs. 70

After increase in prices,

Price of component A = Rs. 12
Price of component B = Rs. 28
Price of other components = Rs. 70
Total Cost of production = Rs. (12 + 28 + 70) = Rs. 110
Selling price = Rs. (1.15 * 120) = Rs. 138
Profit = Rs. 28
Profit % = 25.45%

Hence, option B is the correct answer.

Applying the cosine rule , we get $$c^{2} = a^{2} + b^{2} - 2ab cos θ$$

Hence, option A is the correct answer.

Total number of subsets that can be formed with the left of 11 elements = $$2^{11}$$ = 2048
The number of subsets which contain only odd numbers(1, 3, 5, 7, 9, 11} = $$2^{6}$$ = 64
Number of subsets which contain at least one even integer = Total number of subsets -  the number of subsets which contain only odd numbers
$$\Rightarrow$$ 2048 - 64 = 1984. Hence, option C is the correct answer. 

Let us draw a table consisting the day and competition. 

In statement 5, it is given that none of the competition was conducted on Thursday and Sunday. Also, Street Play competition was held on Monday. 

It is given that Group Song competition was conducted neither on Wednesday nor on Saturday. Hence, the Group Song competition can take place on either Tuesday or Friday. We are also given that there was gap of two days between Debate competition and Group Song competition. 

If the Group Song competition is on Friday, then Debate competition should take place in 24th Oct, Monday but that slot is already filled. Hence, this case is not possible. Therefore, we can say that Group Song competition was on Tuesday. Consecutively, we can say that the Debate competition was on Saturday. 

Rock band competition was not conducted on the closing day. Hence, we can say that Rock Band competition took place on either 19th Oct or 21st Oct.

It is also given that Fash-p was conducted on the day prior to debate competition. Hence, we can say that Fash-P was conducted on 21st Oct Friday. Consequently, we can say that Rock Band competition took place on 19th Oct Wednesday. 

Also, we can say that folk dance competition held on 26th Oct. 

From the table, we can see that the cultural week started with Rock Band. Hence, option D is the correct answer.

Let us draw a table consisting the day and competition. 

In statement 5, it is given that none of the competition was conducted on Thursday and Sunday. Also, Street Play competition was held on Monday. 

It is given that Group Song competition was conducted neither on Wednesday nor on Saturday. Hence, the Group Song competition can take place on either Tuesday or Friday. We are also given that there was gap of two days between Debate competition and Group Song competition. 

If the Group Song competition is on Friday, then Debate competition should take place in 24th Oct, Monday but that slot is already filled. Hence, this case is not possible. Therefore, we can say that Group Song competition was on Tuesday. Consecutively, we can say that the Debate competition was on Saturday. 

Rock band competition was not conducted on the closing day. Hence, we can say that Rock Band competition took place on either 19th Oct or 21st Oct.

It is also given that Fash-p was conducted on the day prior to debate competition. Hence, we can say that Fash-P was conducted on 21st Oct Friday. Consequently, we can say that Rock Band competition took place on 19th Oct Wednesday. 

Also, we can say that folk dance competition held on 26th Oct. 

From the table, we can see that there is a gap of 5 days between rock band competition and group song competition. Hence, option D is the correct answer.

Let us draw a table consisting the day and competition. 

In statement 5, it is given that none of the competition was conducted on Thursday and Sunday. Also, Street Play competition was held on Monday. 

It is given that Group Song competition was conducted neither on Wednesday nor on Saturday. Hence, the Group Song competition can take place on either Tuesday or Friday. We are also given that there was gap of two days between Debate competition and Group Song competition. 

If the Group Song competition is on Friday, then Debate competition should take place in 24th Oct, Monday but that slot is already filled. Hence, this case is not possible. Therefore, we can say that Group Song competition was on Tuesday. Consecutively, we can say that the Debate competition was on Saturday. 

Rock band competition was not conducted on the closing day. Hence, we can say that Rock Band competition took place on either 19th Oct or 21st Oct.

It is also given that Fash-p was conducted on the day prior to debate competition. Hence, we can say that Fash-P was conducted on 21st Oct Friday. Consequently, we can say that Rock Band competition took place on 19th Oct Wednesday. 

Also, we can say that folk dance competition held on 26th Oct. 

From the table, we can see that Rock Band and Folk Dance were conducted on Wednesdays.

Hence, option C is the correct answer.

Let us draw a table consisting the day and competition. 

In statement 5, it is given that none of the competition was conducted on Thursday and Sunday. Also, Street Play competition was held on Monday. 

It is given that Group Song competition was conducted neither on Wednesday nor on Saturday. Hence, the Group Song competition can take place on either Tuesday or Friday. We are also given that there was gap of two days between Debate competition and Group Song competition. 

If the Group Song competition is on Friday, then Debate competition should take place in 24th Oct, Monday but that slot is already filled. Hence, this case is not possible. Therefore, we can say that Group Song competition was on Tuesday. Consecutively, we can say that the Debate competition was on Saturday. 

Rock band competition was not conducted on the closing day. Hence, we can say that Rock Band competition took place on either 19th Oct or 21st Oct.

It is also given that Fash-p was conducted on the day prior to debate competition. Hence, we can say that Fash-P was conducted on 21st Oct Friday. Consequently, we can say that Rock Band competition took place on 19th Oct Wednesday. 

Also, we can say that folk dance competition held on 26th Oct. 

From the table, we can see that Debate competition precedes the street play competition. Hence, option C is the correct answer.

Let us draw a table consisting the day and competition. 

In statement 5, it is given that none of the competition was conducted on Thursday and Sunday. Also, Street Play competition was held on Monday. 

It is given that Group Song competition was conducted neither on Wednesday nor on Saturday. Hence, the Group Song competition can take place on either Tuesday or Friday. We are also given that there was gap of two days between Debate competition and Group Song competition. 

If the Group Song competition is on Friday, then Debate competition should take place in 24th Oct, Monday but that slot is already filled. Hence, this case is not possible. Therefore, we can say that Group Song competition was on Tuesday. Consecutively, we can say that the Debate competition was on Saturday. 

Rock band competition was not conducted on the closing day. Hence, we can say that Rock Band competition took place on either 19th Oct or 21st Oct.

It is also given that Fash-p was conducted on the day prior to debate competition. Hence, we can say that Fash-P was conducted on 21st Oct Friday. Consequently, we can say that Rock Band competition took place on 19th Oct Wednesday. 

Also, we can say that folk dance competition held on 26th Oct. 

From the table, we can see that Fash-p follows Rock Band. Hence, option C is the correct answer. 

It is given that Esteem is second to the right of i10. Punto, who is the neighbor of Alto is parked diagonally opposite to i10. We can draw the diagram as shown in the figure below. 

Swift is parked in front of Alto and SX4 is parked to the immediate right of Alto. 

We have arranged all six cars according to the conditions given in the question. 

Now we are asked to interchange SX4 and Esteem's positions mutually and then figure out the car(s) adjacent to Esteem. These cars should be same as SX4 in the original arrangement. From the diagram, we can see that only Alto will be adjacent to Esteem in new position. Therefore, option C is the correct answer. 

It is given that Esteem is second to the right of i10. Punto, who is the neighbor of Alto is parked diagonally opposite to i10. We can draw the diagram as shown in the figure below. 

Swift is parked in front of Alto and SX4 is parked to the immediate right of Alto. 

We have arranged all six cars according to the conditions given in the question. 

It is given that Alto changes position with i10 and Punto changes position with SX4 and Swift shifts one position to the right to accommodate Beatle. 

From, the arrangement we can see that Alto and Swift are neighbors of Beatle. Hence, option D is the correct answer. 

It is given that Esteem is second to the right of i10. Punto, who is the neighbor of Alto is parked diagonally opposite to i10. We can draw the diagram as shown in the figure below. 

Swift is parked in front of Alto and SX4 is parked to the immediate right of Alto. 

We have arranged all six cars according to the conditions given in the question. 

In the original parking scheme four new cars enter the parking lot such that Wagon-R is second to the right of i10 and Zen is second to the left of SX4. Jazz is parked second to the left to Wagon-R and Beat is parked to the right of Alto. Let us place 4 news cars - WagonR, Zen, Jazz and Beat. 

Hence, we can say that i10, Punto, SX4 and Esteem are moved out. Therefore, option D is the correct answer.

Let us draw the table first. 

 It is given that Anup is posted in Jamshedpur and Kabir is posted in Kolkata. Also, Rahul has an e-mail id with Rediffmail and works at Pune.

It is given that neither Alok nor Raghu work in Noida. Hence, we can say that Amit work in HCL-Noida. Also, the one having e-mail account with Sancharnet works in Noida. Hence we can say that Amit has Sancharnet's email address. 

Also, the one having an e-mail account with Indiatimes works for Tisco. Hence, we can say that Anup has Indiatimes's email account. 

Alok does not work for Mecon. Hence, we can say that Raghu works in Mecon-Ranchi. Consequently, we can say that Alok work in Wipro-Bangalore. 

Also, the one who works for Mecon has an e-mail id with Gmail.

The one who works for Wipro does not have an e-mail account with Yahoo. Hence, we can say that Kabeer has yahoo's email account and Alock has hotmail's email account. 

From the table, we can see that the man who works in Wipro has a e-mail account with hotmail. Hence, option D is the correct answer. 

Let us draw the table first. 

 It is given that Anup is posted in Jamshedpur and Kabir is posted in Kolkata. Also, Rahul has an e-mail id with Rediffmail and works at Pune.

It is given that neither Alok nor Raghu work in Noida. Hence, we can say that Amit work in HCL-Noida. Also, the one having e-mail account with Sancharnet works in Noida. Hence we can say that Amit has Sancharnet's email address. 

Also, the one having an e-mail account with Indiatimes works for Tisco. Hence, we can say that Anup has Indiatimes's email account. 

Alok does not work for Mecon. Hence, we can say that Raghu works in Mecon-Ranchi. Consequently, we can say that Alok work in Wipro-Bangalore. 

Also, the one who works for Mecon has an e-mail id with Gmail.

The one who works for Wipro does not have an e-mail account with Yahoo. Hence, we can say that Kabeer has yahoo's email account and Alock has hotmail's email account. 

From the table, we can see that Raghu-Ranchi-Gmail is a correct combination. Hence, option D is the correct answer. 

Let us draw the table first. 

 It is given that Anup is posted in Jamshedpur and Kabir is posted in Kolkata. Also, Rahul has an e-mail id with Rediffmail and works at Pune.

It is given that neither Alok nor Raghu work in Noida. Hence, we can say that Amit work in HCL-Noida. Also, the one having e-mail account with Sancharnet works in Noida. Hence we can say that Amit has Sancharnet's email address. 

Also, the one having an e-mail account with Indiatimes works for Tisco. Hence, we can say that Anup has Indiatimes's email account. 

Alok does not work for Mecon. Hence, we can say that Raghu works in Mecon-Ranchi. Consequently, we can say that Alok work in Wipro-Bangalore. 

Also, the one who works for Mecon has an e-mail id with Gmail.

The one who works for Wipro does not have an e-mail account with Yahoo. Hence, we can say that Kabeer has yahoo's email account and Alock has hotmail's email account. 

From the table, we can see that Kabeer has an e-mail id with Yahoo. Hence, option C is the correct answer. 

Let us draw the table first. 

 It is given that Anup is posted in Jamshedpur and Kabir is posted in Kolkata. Also, Rahul has an e-mail id with Rediffmail and works at Pune.

It is given that neither Alok nor Raghu work in Noida. Hence, we can say that Amit work in HCL-Noida. Also, the one having e-mail account with Sancharnet works in Noida. Hence we can say that Amit has Sancharnet's email address. 

Also, the one having an e-mail account with Indiatimes works for Tisco. Hence, we can say that Anup has Indiatimes's email account. 

Alok does not work for Mecon. Hence, we can say that Raghu works in Mecon-Ranchi. Consequently, we can say that Alok work in Wipro-Bangalore. 

Also, the one who works for Mecon has an e-mail id with Gmail.

The one who works for Wipro does not have an e-mail account with Yahoo. Hence, we can say that Kabeer has yahoo's email account and Alock has hotmail's email account. 

From the table, we can see that Alok, Kabeer, Anup, Rahul, Raghu, and Amit work in Bangalore, Kolkata, Jamshedpur, Pune, Ranchi and Noida in that order. None of the option represents the same sequence. Hence, option D is the correct answer. 

Let us draw the table first. 

 It is given that Anup is posted in Jamshedpur and Kabir is posted in Kolkata. Also, Rahul has an e-mail id with Rediffmail and works at Pune.

It is given that neither Alok nor Raghu work in Noida. Hence, we can say that Amit work in HCL-Noida. Also, the one having e-mail account with Sancharnet works in Noida. Hence we can say that Amit has Sancharnet's email address. 

Also, the one having an e-mail account with Indiatimes works for Tisco. Hence, we can say that Anup has Indiatimes's email account. 

Alok does not work for Mecon. Hence, we can say that Raghu works in Mecon-Ranchi. Consequently, we can say that Alok work in Wipro-Bangalore. 

Also, the one who works for Mecon has an e-mail id with Gmail.

The one who works for Wipro does not have an e-mail account with Yahoo. Hence, we can say that Kabeer has yahoo's email account and Alock has hotmail's email account. 

From the table, we can see that people who have e-mail account with Indiatimes, Sancharnet and Yahoo work Tisco, HCL and Usha Martin in that order. Hence, option D is the correct answer. 

We can see that only one zero present in the number such that it is immediately preceded by a nine but not immediately followed by seven. It is shown in round braces. 4th from the left. 
709(0)070890702030045703907

Therefore, option A is the correct answer. 

Let us draw the network diagram according to the given info.

The shortest route for the truck would be DC-R3-R1-R6-R7.
Thus, the total distance traveled would be 14 + 11 + 23 + 15 = 63 km. Hence, option C is the correct answer.

Let us check the option one by one. 

(A) For Westside, the decline in cost per square feet in the year 2005 = $$2411-1724$$ = 687

(B) For Pantaloon, the decline in cost per square feet in the year 2008 = $$2044-1656$$ = 388

(C) For S. Stop, the decline in cost per square feet in the year 2009 = $$2419-2197$$ = 222

(D) For Vishal, the decline in cost per square feet in the year 2010 = $$1659-1064$$ = 595

We can see that the sharpest decline is for Westside stores in the year 2005. Hence, option A is the correct answer. 

Let us check the option one by one. 

(A) For S. Stop, the increase in cost per square feet in the year 2006 = $$2135-1889$$ = 246

(B) For S. Stop, the increase in cost per square feet in the year 2007 = $$2464-2135$$ = 329

(C) For Pantaloon, the increase in cost per square feet in the year 2006 = $$1996-1729$$ = 267

(D) For Vishal, the increase in cost per square feet in the year 2006 = $$1802-1832$$ = -30

We can see that the maximum increase in its cost per square feet is for S.stop stores in the year 2007. Hence, option B is the correct answer. 

The cost per square feet of the retail sector, in the year 2007 = 2044+2464+1751+1525 = 7784

The cost per square feet of the retail sector, in the year 2010E = 1396+2230+1064+1051 = 5741

Therefore, What is the average rate of change in the cost per square feet of the retail sector for the given period = $$\dfrac{\dfrac{5741-7784}{7784}\times 100}{3}$$ = $$-8.74$$ percent. Hence, option D is the correct answer.

The percentage change in number of subscribers in March 10 as compared to Dec 09 in U.P. (E) = $$\dfrac{45.53-39.68}{39.68}$$ = 14.74 percent

The percentage change in number of subscribers in March 10 as compared to Dec 09 in Bihar = $$\dfrac{38.36-33.17}{33.17}$$ = 15.64 percent

The percentage change in number of subscribers in March 10 as compared to Dec 09 in Orissa = $$\dfrac{15.89-13.57}{13.57}$$ = 17.09 percent

The percentage change in number of subscribers in March 10 as compared to Dec 09 in Haryana = $$\dfrac{14.96-13.59}{13.59}$$ = 10.08 percent

We can see that Orissa observed maximum rate of change from Dec 2009 to March 2010. Hence, option C is the correct answer. 

It is given that R-com has 28% subscribers in the east and Vodafone has 72% subscribers in the east, these two are the only operators in the east.
Similarly, Idea and Airtel are the only players in the south whose shares are 48% and 52% respectively.
We are not given that name of the states which need to be considered under southern part of the country. But the number of subscribers should be in the same ratio of shares.

Checking with the options

Option (A): R-Com's share = $$\dfrac{28.03}{28.03+73.22}\times 100$$ = 27.68 percent. We are given that Rcom has 28% shares. Hence, this option is incorrect. 

Option (B): R-Com's share = $$\dfrac{30.03}{30.03+72.82}\times 100$$ = 29.19 percent. We are given that Rcom has 28% shares. Hence, this option is incorrect.

Option (C): R-Com's share = $$\dfrac{28.03}{28.03+76.24}\times 100$$ = 26.88 percent. We are given that Rcom has 28% shares. Hence, this option is incorrect.

Option (D): R-Com's share = $$\dfrac{30.03}{30.03+77.22}\times 100$$ = 28 percent. We are given that Rcom has 28% shares. Hence, this option is the correct.  

This question does not state explicitly that data from the previous question can be used, the percentage break up given in the previous question
cannot be assumed in this question. Hence, the given data is insufficient to solve the given problem. Therefore, option D is the correct answer. 

The number of subscribers in Dec 2009 = 562.18 millions. 

The number of subscribers in March 2010 = 621.30 millions. 

Therefore, the required percentage = $$\dfrac{621.30-562.18}{562.18}\times 100$$ = 10.51 percent. Hence, option B is the correct answer. 

In brand building points earned by Maheshwari & Co:

Points earned for having signage board = 10
Points earned for exterior walls of the store = 20
Points earned for Company X painting in the interior of the store = 2.5
Points earned for POP display of company X = 5
Points earned for stacking of company X goods in the shelves = 0

Hence, total brand building points earned by Maheshwari & Co. = 10+20+2.5+5 = 37.50

Also, Maheshwari & Co achieved a tageter more than 100%. Therefore, the sales target points earned by Maheshwari & Co = 15 + (56241-50000)*0.25 =  1575.25.

Therefore, total redeemable points acquired by Maheshwari & Co in Jul-Sep quarter = 1575.25+37.50 = 1612.75.

A tupperware set can be availed by redeeming 600 points. Hence, we can say that Maheshwari & Co can avail 2 Tupperware set by the end of the quarter. 

Hence, option A is the correct answer. 

In brand building points earned by Bhowmik Brothers: 

Bhowmik Brothers has only other brands signage in the front of the store, and company X painting on the side wall in the exterior of the store, Company X painting on the side wall in the interior of the store, no POP display of any Company and the goods of Company X is stacked in the front row with other brands. What is the total point Bhowmik Brothers need to accumulate to make them eligible for minimum redemption?

Points earned for having signage board of company X = -20
Points earned for painting on the side wall in the exterior of the store = 2.5
Points earned for painting on the side wall in the interior of the store = 2.5 
Points earned for POP display of company X = 0
Points earned for stacking of company X goods in the front row with other brands = 10

Hence, total brand building points earned by Bhowmik Brothers = -20+2.5+2.5+10 = -5

Also, Bhowmik Brothers achieved a target in 75% to 99% range. Therefore, the sales target points earned by Bhowmik Brothers = 12

Therefore, total redeemable points acquired by Bhowmik Brothers in Jul-Sep quarter = -5 + 12 = 7.

For minimum redemption they should have at least 40 points. Hence, we can say that Bhowmik Brothers need to accumulate 33 points to make them eligible for minimum redemption. Therefore, option D is the correct answer.

Total redeemable points earned by Saha H/W in this quarter = 85 + 15 + (24512-24000)*0.25 = 228. 

Points earned by Saha H/W through brand building and completing 100% sales target = 85+15 = 100. 

For a Kanjivaram Saree, Saha H/W needs 4000 points. Rest of the points should be earned by selling extra units. Each extra units will garner 0.25 points for Mr. Saha. 

Therefore, the number of extra units that Mr. Saha must sell in order to collect points for Kanjivaram Saree = $$\dfrac{4000-228-100}{0.25}$$ = 14688.

Hence, option A is the correct answer.

Total point earned by Malling Enterprise through sells alone = 15+(24000-23000)*0.25 = 265. 

Points required to avail three Nike Caps and an Umbrella = 3*100+40 = 340. 

Hence, Malling Enterprise must have earned through brand building activities =  340 - 265 = 75. 

Total point earned by Srikrishna Trader through sells alone = 15+(42000-40000)*0.25 = 515. 

Total point earned by Srikrishna Trader through brand building activities = 80. 

Therefore, total redeemable points with Srikrishna Trader = 515+80 = 595.

The tupperware set alone costs 600 points. Hence, option A, B and C can be ruled out. Therefore, option D is the correct answer.

$$CO_2$$ emission by the US after 2 years = $${(1-\dfrac{12.5}{100})}^2\times 1200$$ = 918.75 million tons. 

The per capita income in US after 2 years = $${(1+\dfrac{2}{100})}^2\times 300$$ = 312.12

Similarly, we can calculate the $$CO_2$$ emission and per capita income for remaining countries after two years from now.  

$$CO_2$$ emission by the China after 2 years = 903.44 million tons. 

The per capita income in China after 2 years = $${(1+\dfrac{4}{100})}^2\times 270$$ = 292.032

$$CO_2$$ emission by the Japan after 2 years = 861.33 million tons. 

The per capita income in Japan after 2 years = $${(1+\dfrac{3}{100})}^2\times 240$$ = 254.616

Hence, the required ratio = $$\dfrac{918.75}{312.12}$$, $$\dfrac{903.44}{292.032}$$, $$\dfrac{861.33}{254.616}$$, = 2.9, 3.1, 3.4. 

Therefore, we can say option C is the correct answer. 

CO2 emission required for USA = 225 million tonnes
CO2 emission required for China = 202.5 million tonnes
Required reduction for USA = 975 million tonnes
Required reduction for China = 977.5

O.5 million tone of CO2 ----> 1.25 carbon credits

In one year, a country can purchase 65 carbon credit

In one year, 26 million tonnes of CO2is compensated.
Required time =  977.5 / 26 = 37.59 years

Hence, option B is the correct answer.

Total emission in three years combined = 2000 million tonnes.
Thus, total credit = 5000 credits (approx)

Hence, option C is the correct answer.

India stands at 6th position if 200 million ton CO2 emission is deducted from the given CO2 emission figures of each country and 50 is added to the given per capita income of each country.

Hence, option D is the correct answer.

The number of units produced in Bihar exceed the number of units produced in Madhya Pradesh = $$\dfrac{45 - 32.4}{360}\times 72000$$ = 2520.

Therefore, option B is the correct answer. 

We know that, female population = Total population - Male population.

Therefore, the percentage increase in Female population in 1996 = $$\dfrac{(650-320) - (600-300)}{(600-300)}\times 100$$ = 10%

The percentage increase in Female population in 1999 = $$\dfrac{(750-400) - (700-380)}{(700-380)}\times 100$$ = 9.37%

The percentage increase in Female population in 2004 = $$\dfrac{(845-475) - (800-450)}{(800-450)}\times 100$$ = 5.71%

The percentage increase in Female population in 2005 = $$\dfrac{(900-480) - (845-475)}{(845-475)}\times 100$$ = 13.51%

Hence, option D is the correct answer. 

Number of female in the year 2002 = 790 - 440 = 350 million. 

Number of educated females in the year 2002 = $$\dfrac{4}{9}\times 545$$ $$\approx$$ 242 millions

Hence, total number of uneducated females in the year 2002 = 350 - 242 = 108 millions ... (1) 

Number of educated males in the year 2002 = $$\dfrac{5}{9}\times 545$$ $$\approx$$ 303 millions.

Therefore, the number of educated males in the year 2003 = 1.25*303 = 378.75 millions. 

Hence, the number of educated females in the year 2003 = Total educated population - the number of educated males = 560 - 378.75 $$\approx$$ 181.25 millions.

Total number of uneducated females in the year 2003 = Total number of females - the number of educated females = (800-450) - 181 =  169 millions. ... (2)

From equation (2) and (1), we can say that the percentage change in number of uneducated females in 2003 = $$\dfrac{169-108}{108}\times 100$$ $$\approx$$ 56 percent. Hence, we can say that option D is the correct answer.

In year 2005 total population living in urban area is equal to sixty eight percent of educated population. The ratio of number of people living in urban area to people living in rural area is 43:12 in 2010. What is the ratio of the rural population in 2005 to that in 2010?. 

Total population living in urban area in the year 2005 = 0.68*600 = 408 millions. 

Therefore, the population living in rural area in the year 2005 = 900 - 408 = 492 millions. 

It is given the the ratio of number of people living in urban area to people living in rural area is 43:12 in 2010. 

Hence, the number of people living in rural area in the year 2010 = $$\dfrac{12}{55}\times 1100$$ = 240 millions.

Therefore, the required ratio = 492/240 = 2.05. 

Throughout the passage, the author's ideas revolve around the fact that Kodak did not embrace new technology which led to its downfall.
Hence, option D is the correct answer.

From the first paragraph, we can infer that statements I and IV are true.
Hence, option B is the correct answer.

"Fisher also tried to move Kodak’s traditional retail photo-processing systems into digital world and in this regard installed tens of thousands of image magic kiosks. These kiosks came just as numerous companies introduced inexpensive, high-quality photo printers that people could use at home, which, in fact, is where customers preferred to view their images and fiddle with them." - from these lines, statement III can be inferred.

"ln 1997 Philippe Kahn lead the advent of cell phone camera. With the cell phone camera market growth Kodak didn't just lose out on more prints. The whole industry lost out on sales of digital cameras, because they became just a feature that was given away free on cell phones. Soon cameras became a free feature on many personal computers, too. What had been so profitable for Kodak for so long- capturing images and displaying them- was going to become essentially free" - from these lines, statement IV can be inferred.

Hence, option D is the correct answer.

Statement II - para 1
Statement IV - para 2
Statement I - para 3
Statement III - para 3

Hence, option C is the correct answer. 

1 ------> 'd' - "Prices plunged because the cameras generally followed Moore's Law, the famous prediction by Intel co-founder Gordon Moore in the l960s that the cost of a unit of computing power would fall by 50 percent every eighteen to twenty-four months."

2 ------> 'a' -  "Fisher’s solution was to hold on to the filmbusiness as long as possible, while adding atechnological veneer to it. For instance, he introducedthe Advantix Preview camera, a hybrid of digital andfilm technology. Users took pictures the way theyalways had, and the images were captured on film.Kodak spent more than $500 million developing Advantix, which flopped."

3 ------> 'b' - "Fisher also formed a partnership with AOL called "You've Got Pictures." Customers would have their film developed and posted online, where friends and family could view them. Customers would pay AOL $7 for this privilege, on top of the $9 paid for photo processing. However sites like Snapfish were allowing pictures to be posted online free."

4 ------> 'c' - "Agfa temporized on digital technology, then sold its film and paper business to private-equity investors in 2004. The business went into bankruptcy proceedings the following year, but that wasn't Agfa's problem. lt had cashed out at a halfway reasonable price."

Hence, option A is the correct answer.

Statements I and III capture the true essence of the passage. Statements II and IV are the supporting ideas to strengthen the main idea.

Government economic release in the passage is not the main point which author makes in the passage.

" irrational overreaction to key regulators" is used to elaborate the idea but is not the main point of the author.
Hence, option C is the correct answer.

The passage blames 'law of small numbers' as the culprit behind the poor decision making of the investors. Statements II and IV describe the same.
Hence, option C is the correct answer.

"Amos Tversky and Daniel Kahneman call this one the "law of small numbers.". The statistically valid "law of large numbers" states that large samples will usually be highly representative of the population from which they are drawn; for example, public opinion polls are fairly accurate because they draw on large and representative groups. The smaller the sample used, however (or the shorter the record), the more likely the findings are chance rather than meaningful. Yet the Tversky and Kahneman study showed that typical psychological or educational experimenters gamble their research theories on samples so small that the results have a very high probability of being chance." Statement I is what the author is talking about.
Hence, option B is the correct answer.

"The truth is, market-letter writers have been wrong in their judgments far more often than they would like to remember...Those in the public eye usually gain large numbers of new subscribers for being right by random luck."

Since statement I reflects the idea given in the above excerpt of the second paragraph, it is not the correct choice.

"The psychologists and educators are far too confident in the significance of results based on a few observations or a short period of
time, even though they are trained in statistical techniques and are aware of the dangers."

Since statement II reflects the idea given in the above excerpt, it is not the correct choice.

"...public opinion polls are fairly accurate because they draw on large and representative groups."

Since 'diminutive' is the opposite of large, statement III is the farthest in explaining the meaning of the passage.

Thus, the correct option is B.

First, the instrumental prediction is that because people are mainly concerned with receiving desired outcomes from their encounters with organizations, changes in their level of commitment will depend primarily on the favorability of the encounter. Option B is the most relevant.

Option C is wrong because the second paragraph mentions cases where experiences influenced post experience loyalty both positively and negatively.

Option A is incorrect as the passage clearly states that the post experience loyalty depends upon the fairness of the experience. 

Hence, Option B is the correct answer.

 First, the instrumental prediction is that because people are mainly concerned with receiving desired outcomes from their encounters with organizations, changes in their level of commitment will depend primarily on the favorability of the encounter. - a matches with 1.

 According to the instrumental viewpoint, people are primarily concerned with the more material or tangible resources received from the relationship. - a matches with 4.

Hence, option A is the correct answer.

The passage does not explicitly talk about legal authorities. Thus, option A can be ruled out.

Option B can be ruled out because an individual's prior commitments to an institution are not based on the perceived fairness of decisions, according to the passage.

Option D does not represent everything mentioned in the passage.

Option C is the only one that completely captures the main idea of the passage and is thus, the answer.

Saddle shoes in the passage refers to profligacy. Deneir cri means latest fashion. Therefore, I and V are relevant.
Hence, option A is the correct answer.

Buffett was born during depression. Eisenhower years were in 1950s and Microsoft became famous during 1990s.
Morgan was senior to Buffett and Bill Gates junior to Buffett.
Hence, option A is the correct answer.

From the line "Buffett’s one concession........ privet " we can infer that Warren Buffet is old fashioned. Also he lives in a ordinary house which shows that he is a simple man. When he visited Paris, he had no interest in sight-seeing. On the beauty of sunset, he remarked that he had not focused on it. He rarely showed any feeling. All these inferences show that Warren is a deadpan. However from  the passage, we cannot conclude that he was against planned economy. Similarly, nothing can be said about his spiritual life. Hence D is the answer.

It can be understood from the above line that the first blank describes the issues which can be disrupted with a 'knee jerk reaction'(impulsive reaction). The most appropriate options among the four are 'Nuanced' and 'Ambiguous'. Since 'loss of plutocracy' is an extraneous phrase, the correct option is C.

The first half of the sentence describes a high growth and hence can only be filled by 'Relatively' or 'Sustainedly'. 'Intractable' refers to something which is hard to control. Since the author is commending the growth in the economic crisis period, 'Intractable' will not be a right fit in the second blank.

Thus, the correct answer is D.

The sentence is describing a dastardly act and urging everyone to condemn it. The aptest fit for the blanks are options A and C, but since 'concertedly' does not collocate with 'condemned' properly, the correct option is C.

In the second half of the sentence, the author describes a gallery filled with the family’s favourite snacks and beverages. The aptest word from the options to fill the second blank will be stocked, a synonym for filled.

Thus, the correct option is A.

The author in the above lines criticises Carin for bringing an inexperienced outsider to the oil field. Since only option D suitably matches the author's tone and intention, the correct option is D.

Since the sentence is talking about the economy being derailed by something, the first blank has to represent a negative idea. Thus, options A and B can be eliminated.

The use of "or" as a conjunction represents that the second blank is complimentary to the idea in the first one. Thus, "reduced" makes the most sense here.

Hence, the answer is option C.

Option A is a distorted statement rephrasing as it has removed the comparison between large and experienced firms with large and inexperienced firms. Option D can be ruled as each clause needs a subject and a verb. Since D is missing the model verb 'are', it is not grammatically correct.

Between B and C, since B is grammatically accurate and has more consistency than C,

the correct option is B.

Option A can be ruled out because of the wrong usage of the expression "doubled that of". Options B and C can be ruled out because a line beginning after 'supporting the expectations' should start with 'that'.

Since option D is the aptest substitution for the underlined phrase,

The correct option is D.

Option B can be ruled out as 'but also' should follow 'dangerous'. On the same ground, option D can be eliminated.

Since the usage of 'instruments' is inconsistent with 'itself', option C can be eliminated.

As there are no flaws with statement A,

The correct answer is A.

The question asks for a word pair unrelated to the given pair.

Impuissance refers to something powerless, while Desecrate means to destroy something.

Option A: Decrepit means physically worn out, and Desolate means barren, or abandoned. Both words are formal and negative, aligning with the tone of "impuissance" and "desecrate."

Option B: Effete means a state of weakness and sacrilege means weakness in a sense similar to impuissance. These are again similar to the given words. 

Option C: Ornery means Bad-tempered, and Contort means to distort something.

Option D: Bedraggled means dirty and disheveled, while profanity means blasphemous language. This too is somewhat close to the given words.   

Of the given options, only Option C is not related to the given words and hence would be the correct answer.  

'Insouciant' refers to someone showing a lack of concern, and 'Gossamer' refers to a fine, filmy substance consisting of cobwebs spun by small spiders, seen especially in autumn.

'Nymph' is a mythological spirit of nature imagined as a beautiful maiden inhabiting rivers, woods, or other locations, while 'Gehenna' is a place or state of misery.

Since this word pair does not share any relationship with the input pair, the correct option is A.

Both the words in option C are incorrectly spelt.

Correct spelling for 1st word is 'Dilettante' which means a person who cultivates an area of interest, such as the arts, without real commitment or knowledge.
Correct spelling for 2nd word is 'Reminiscence' which means a story told about a past event remembered by the narrator.

Both the words in option D are incorrectly spelt.

Correct spelling for 1st word is 'Munificent' which means generous.
Correct spelling for 2nd word is 'Pusillanimous' which means timid or showing a lack of courage or determination.

The given passage talks about the diagram called Stack and how it is organised.

Statement II introduces Stack.

Statement IV gives a basic overview of Stack.

Statement III goes on to expand on statement IV. Hence Statements II, IV, and III forms a mandatory pair.

Statement I say that on paper, Stack seems easy; however, in real life, the implementation of Stack is difficult. The premise that Stack seems easy could be reached only after explaining the basics of Stack. So Statement I is the last statement.

The correct order is II, IV, III, and I.

Statement II will follow statement I as it extends the idea presented in the latter. Statement V is a continuation of IV; hence, IV-V is a valid pair. Now III gives the reason stated in V and VI is completing III. Thus, IV-V-III-VI is a valid pattern. Since IV explains the thinking described in II, the correct pattern will be I-II-IV-V-III-VI.

Thus, the correct answer is D.

Among the given statements, I can be the opening statement followed by V which says knowledge even when it is exact doesn't lead to the appropriate actions. III is the continuation of V. Statement IV is the continuation of III. II states the reason which is followed by VI. The order will be I, V, III, IV, II, VI. The answer is option B.

III is the opening statement. V carries forward the idea as it talks about what statisticians do. V is followed by I. IV and II states what statisticians do leaving their brains in the class. The correct order is III, V, I, IV, II.
The answer is option A.

II is the opening sentence followed by I. IV is the continuation of I and III follows IV as it explains how the author is trying to be humble by setting a wide range. VI is the continuation of III. Statement V concludes the paragraph by saying how the underestimation happens at the core of author's professional activities. The  correct order is II, I, IV, III, VI, V. The answer is option D.

II must be the opening statement followed by IV. I contrasts with what stated in II and IV. IV is followed by I. III states what excited people do. So I should be followed by III. VI and V concludes the paragraph. The correct order is II, IV, I, III, VI, V. The answer is option C.

OMNISCIENT means knowing everything or "a third-person omniscient narrator". Hence, we can say that omniscient and knowledge are synonymous.

In similar manner, Boundless is related to expanse. Boundless means unlimited and expanse means a wide continuous area of something.

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

'Disquietude' refers to a state of 'anxiety'.

In the options, only 'Nonplus', which refers to a state of being surprised or confused, share the same relationship with 'Perplexed'(baffled, confused).

Cupidity refers to a Strong desire for money, whereas bellicose refers to a demonstration of aggression. 
Embellishment refers to making something more attractive; this is not related to "overstated". 
Magnitude refers to the size of a quantity, whereas unbridged means uncut. 

Thus, the correct option is A.

'Deviate' and 'Lecture' have opposite connotations as lecture requires good concentration.

Among the options, only 'Meander(to wander)' and 'Drive' share the same relationship and hence,

The correct option is A.

'Nebulous' refers to a vague or ill-defined 'form'.

Since 'insipid' refers to something lacking flavour or 'taste', option C will have a similar relationship with Nebulous: form.

Thus, the correct option is C.

In statement A, blunder mistake is an example of redundancy. It should be either 'He made a blunder' or "He made a mistake". 

In statement B, it should be "I have learnt this lesson word for word".

In statement C, it should be "She does not know how to swim".

Only statement D doesn't have any error. Hence, option D is the correct answer.

In statement A, "they" in second part is incorrect. It should be in accordance to the singular object present in first part of the sentence.

In statement B, it should be "The people in my country are smarter than those in other countries.".

In statement C, it should be "The number of failures of product in the final quality inspection are increasing every year.".

Only statement D doesn't have any error. Hence, option D is the correct answer.

The president of South Korea Lee Myung - Bak attended the Indian Republic Day Parade in 2010 as the chief guest.
Hence, option C is the correct answer.

R-Com, Airtel and Aircel won the maximum number of circles in the 3G spectrum auction.
Hence, option D is the correct answer.

Canara Bank, HSBC, Oriental Bank of Commerce Limited  formed a joint venture in Life Insurance Sector?.

Hence, option A is the correct answer.

NATO's headquarter is in Brussels, Belgium.
WWF's headquarter is in Gland, Switzerland.
OPEC's headquarter is in Vienna, Austria.
Interpol's headquarter is in Lyon, France.

Hence, option B is the correct answer.

Carol Bartz was the CEO of Yahoo based in California.
Ellen J Kullman was the CEO of Dupont based in Delaware.
Ursula Burns was the CEO of Xerox Corporation based in Connecticut.
Christina A Gold is the CEO of Western Union based in Colorado.

Hence, option C is the correct answer.

United Breweries acquired Shaw Wallace.
Mahindra and Mahindra acquired Schoneweiss.
Price Water Cooper acquired RSM Ambit.
Holcim acquired Ambuja Cement.

Hence, option D is the correct answer.

Toyota's tagline is 'Touch the perfection'.
BSNL's tagline is 'Connecting India'.
Airtel's tagline is 'Express yourself'.
MTNL's tagline is 'The easy way to stay in touch'.

Hence, option C is the correct answer.

The brand ambassador of Canara Bank is Venkatesh prasad.
The brand ambassador of Dena Bank is Juhi Chawla.
The brand ambassador of Bank of Rajasthan is Hema Malini.
The brand ambassador of Bank of Baroda is Rahul Dravid.

Hence, option D is the correct answer.

Tamil Nadu has the maximum number of major sea ports.
Hence, option D is the correct answer.

This question is based on the old numbering of National Highways in India.

NH6 runs through Gujarat, Maharashtra, Chhattisgarh, Odisha, Jharkhand and West Bengal state in India.
National Highway 7 or NH 7, is major North-South National Highway in India that runs through the states of Uttar Pradesh, Madhya Pradesh, Maharashtra, Telangana, Andhra Pradesh, Karnataka, and Tamil Nadu. 
National Highway 8 is the busiest highway in the subcontinent, as it connects the national capital Delhi to the financial capital Mumbai, as well as important cities Gurgaon, Jaipur, Ajmer, Udaipur, Ahmedabad, Vadodara and Surat. 
NH 15 runs through Pathankot - Amritsar - Tarn Taran Sahib - Bhatinda - Ganganagar - Bikaner - Jaisalmer - Barmer - Samakhiali (Punjab, Rajasthan and Gujarat)

Hence, option C is the correct answer.

Ethiopia was known as Abyssinia.

Zambia was known as Northern Rhodesia.

Namibia was known as South West Africa.

Zimbabwe was known as Rhodesia.

Hence, option B is the correct answer.

Warsaw is the capital of Poland.
Lisbon is the capital of portugal.
Chittagong is in Bangladesh.
Dresden is in Germany.
Hence, option D is the correct answer.

Budapest is known as Twin City.
Chicago is known as Windy City.
Philadelphia is known as Quaker City.
Belgrade is known as White City.

Hence, option C is the correct answer.

The State Bank of India was known as Imperial Bank of India in 1921, which was an amalgamation of Bank of Bengal, Bank of Bombay and Bank of Madras.
hence, option A is the correct answer.

India has borrowed the concept of 'Emergency Provision' from Germany.
Hence, option A is the correct answer.

Madhav National Park, Madhya Pradesh was established in 1958.
Khangchendzonga National Park, Sikkim was established in 1977.
Corbett National Park, Uttaranchal was established in 1936.
Tadoba National Park, Maharashtra was established in 1955.

Hence, option B is the correct answer.

Shiela Dixit won prestigious Dara Shikoh award by Indo-Iran Society for contributing towards nurturing the value of peace, harmony and brotherhood in 2010.
Hence, option C is the correct answer.

Puducherry is the Indian Union Territory is having the legislative assembly as of 2010.
Hence, option C is the correct answer.

The capital of Dadra and Nagar Haveli is Silvassa.
The capital of Andaman & Nicobar Island is Port Blair.
The capital of Puducherry is Puducherry.
The capital of Lakshadweep is Karavatti.

Hence, option D is the correct answer.

Jantar Mantar was included in UNESCO's world's cultural heritage list in 2010.
Hence, option B is the correct answer.

Pradeep Vasant Naik is the Chief of Air Staff.
Vijay Kumar Singh is the Chief of Army Staff.
Nirmal Verma is the Chief of Naval Staff.
Suresh Chand Mukul is the Chief of Integrated Defense Staff.

Hence, option B is the correct answer.

Santoor is the brand of Wipro.
Margo is the brand of Henkel.
Camay is the brand of Proctor & Gamble.
Hamam is the brand of HUL.

Hence, option B is the correct answer. 

The currency of Sweden is Krona.
The currency of Japan is Yen.
The currency Poland is Zloty.
The currency of Israel is New Shekkel.

Hence, option B is the correct answer.

Tejaswini Sawant was not an ambassador of Commonwealth Games, 2010.
Hence, option D is the correct answer.

SAIL is a Maharatna company.
GAIL is a Navratna company.
BSNL is a Mini Ratna category-I company.
HMT is a Mini Ratna Category-II company.

Hence, option B is the correct answer.

Netherlands has the maximum share in FDI equity inflow as in June 2010.
Hence, option D is the correct answer.

CNBC is owned by Raghav Bahal.
Times Now is owned by Bennett, Coleman and Co. Ltd.
Star News is owned by Anand Bazar Publication.
Aaj Tak is owned by India Today group.

Hence, option B is the correct answer.