IIFT 2009 Question Paper

Total automobile production in the year 2004 = 800+500+475 = 1775

Total automobile production in the year 2005 = 700+550+450 = 1700

Total automobile production in the year 2006 = 1025+675+475 = 2175

Total automobile production in the year 2007 = 1200+650+475 = 2325

Total automobile production in the year 2008 = 1250+600+350 = 2200

We can see that production decreased only twice during the given period in the year 2005 and 2008.

Hence, the percentage decrease in the year 2005 over the year 2004 = $$\dfrac{1775-1700}{1775}\times 100$$ = 4.225 percent.

Similarly, the percentage decrease in the year 2008 over the year 2007 = $$\dfrac{2325-2200}{2325}\times 100$$ = 5.376 percent.

Therefore, we can say that option D is the correct answer. 

Total automobile production exported in the year 2004 = (800+500+475)-(700+450+300) = 325

Total automobile production exported in the year  2005 = (700+550+450)-(675+500+350) = 175

Total automobile production exported in the year  2006 = (1025+675+475)-(900+625+400) = 250

Total automobile production exported in the year  2007 = (1200+650+475)-(1050+600+375) = 300

Total automobile production exported in the year  2008 = (1250+600+350)-(975+550+350) = 325

From the data itself we can see that highest growth occurred in the year 2006. 

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

Total commercial vehicles sold from the year 2004 to 2008 = 450+500+625+600+550 = 2725

Total passenger vehicles sold from the year 2004 to 2008 = 700+675+900+1050+975 = 4300

Total three wheelers sold from the year 2004 to 2008 = 300+350+400+375+350 = 1775

Hence, the percent of earnings is contributed by commercial vehicle segment alone = $$\dfrac{5*2725}{5*2725+3*4300+2*1775}\times 100$$ = 45.30 % $$\approx$$ 45%.

Hence, option A is the correct answer. 

Total domestic sales of automobiles in the year 2004 = (700+450+300) = 1450

Total domestic sales of automobiles in the year  2005 = (675+500+350) = 1525

Total domestic sales of automobiles in the year  2006 = (900+625+400) = 1925

Total domestic sales of automobiles in the year  2007 = (1050+600+375) = 2025

Total domestic sales of automobiles in the year  2008 = (975+550+350) = 1875

Average domestic sales of automobiles for the given period = $$\dfrac{1450+1525+1925+2025+1875}{5}$$ = 1760.

Hence, we can say that the domestic sales in the year 2008 is the closest to the average domestic sales. Hence, option D is the correct answer.

Total domestic sales of automobiles in the year 2004 = (700+450+300) = 1450

Total domestic sales of automobiles in the year  2005 = (675+500+350) = 1525

Total domestic sales of automobiles in the year  2006 = (900+625+400) = 1925

Total domestic sales of automobiles in the year  2007 = (1050+600+375) = 2025

Total domestic sales of automobiles in the year  2008 = (975+550+350) = 1875

We can see that the automobiles sales rose by the highest amount in the year 2006 as compared to other years. Also, the base is relatively smaller for remaining year except 2004. But the absolute growth is much higher in the year 2006 as compared to the year 2005. Hence, option B is the correct answer. 

Total automobile production in the year 2004 = 800+500+475 = 1775

Total automobile production in the year 2005 = 700+550+450 = 1700

Total automobile production in the year 2006 = 1025+675+475 = 2175

Total automobile production in the year 2007 = 1200+650+475 = 2325

Total automobile production in the year 2008 = 1250+600+350 = 2200

Total domestic sales of automobiles in the year 2004 = (700+450+300) = 1450

Total domestic sales of automobiles in the year  2005 = (675+500+350) = 1525

Total domestic sales of automobiles in the year  2006 = (900+625+400) = 1925

Total domestic sales of automobiles in the year  2007 = (1050+600+375) = 2025

Total domestic sales of automobiles in the year  2008 = (975+550+350) = 1875

In the year 2005 and 2008 the production and sales respectively are not increasing absolutely. Hence, we will check only for the year 2006 and 2007. 

The ratio between absolute increase in domestic sales in the year 2006 over the year 2005 and absolute increase in production in the year 2006 over the year 2005 = $$\dfrac{1925-1525}{2175-1700}$$ = 0.84

Similarly, the required ratio for year 2007 = $$\dfrac{2025-1925}{2325-2175}$$ = 0.66

Hence, we can say that the ratio is the highest for the year 2006. Therefore, option B is the correct answer.

As the numbers are far apart we can approximate the money allocation data to the nearest multiple of 0.5. The money allocation data can be approximated as below. 

Let us assume that Rs. 100 is invested in each fund. 
Total return on investing Rs. 100 in fund Alpha =
1.5*1.05+3*1.12+7*.95+1.5*1.15+7.5*1.11+10*1.21
+9*1.08+26*1.06+14.5*1.25+6*1.18+4.5*1.10+5.5*.98+4*1.17 = Rs. 111.24.

Hence, net return per rupee in fund Alpha = $$\dfrac{111.24}{100}$$ = Rs. 1.1124.

Similarly, we can calculate total return on investing Rs. 100 in fund Beta and Gama.

Net return per rupee in fund Beta = $$\dfrac{107.225}{100}$$ = Rs. 1.07225.

Net return per rupee in fund Gama = $$\dfrac{109.48}{100}$$ = Rs. 1.0948. 

We can see that return per rupee is the highest for Alpha fund. Hence, option A is the correct answer. 

Let us tabulate the ranks of various sectors according to fund allocation.

Statement I : Automobile is ranked by both Alpha and Beta as same. This statement is incorrect. 

Statement II : Financial is most favoured by all three Mutual Funds. This statement is incorrect as Energy sector is most favored by fund Gama. 

Statement III : Services is ranked by all three Mutual Funds within top 9 ranks. We can see that this statement is correct. Hence, option D is the correct answer. 

As the numbers are far apart we can approximate the money allocation data to the nearest multiple of 0.5. The money allocation data can be approximated as below. 

Total return on investing Rs. 100 in fund Gama =
5*1.12+4*.95+6*1.15+9.5*1.11+20.5*1.21+15.5*1.08
+17*1.06+2*1.25+3*1.18+10*.92+4*1.1+3.5*.98 = Rs. 109.48.

Hence, total return of an investment of 10 lakhs in fund Gama after a year = $$\dfrac{109.48}{100}*10$$ = 10.948 lakhs $$\approx$$ 10.95 lakhs.
Hence, option B is the correct answer. 

Jowar's yield in the year 2007 = $$\dfrac{368}{673}$$ $$\approx$$ 0.55

Soyabean's yield in the year 2008 = $$\dfrac{799}{650}$$ $$\approx$$ 1.23

Hence, the required ratio = 0.55 : 1.23 = 0.445 : 1 or 0.89: 2.00

Therefore, option C is the correct answer.  

Caster Seed's yield in the year 2006 = $$\dfrac{135}{106}$$ = 1.273

Groundnut's yield in the year 2006 = $$\dfrac{491}{317}$$ = 1.55

Maize's yield in the year 2006 = $$\dfrac{1102}{1004}$$ = 1.097

Sunflower's yield in the year 2006 = $$\dfrac{880}{472}$$ = 1.864

Rice's yield in the year 2006 = $$\dfrac{153}{107}$$ = 1.429

Bazra's yield in the year 2006 = $$\dfrac{2172}{4992}$$ =0.435

Top 3 yields in 2006: Sunflower,Groundnut,Rice

Moth's yield in the year 2008 = $$\dfrac{250}{1199}$$ = 0.2083

Sesamum's yield in the year 2008 = $$\dfrac{70}{280}$$ = 0.25 

Millets's yield in the year 2008 = $$\dfrac{4}{15}$$ = 0.266

Moong's yield in the year 2008 = $$\dfrac{260}{725}$$ = 0.358

Arhar's yield in the year 2008 = $$\dfrac{9}{19}$$ = 0.474

Urd's yield in the year 2008 = $$\dfrac{35}{102}$$ = 0.343

Chaula's yield in the year 2008 = $$\dfrac{30}{101}$$ = 0.297

Bottom 3 yields in 2008: Moth, Sesamum, Millets

Productivity is defined as total production per hectare. 
Total productivity of pulses in the year 2006 = $$\frac{130+31+149+13+26+2}{799+124+1228+20+126+5}$$ = $$0.1524$$

Total productivity of pulses in the year 2007 = $$\frac{270+30+191+9+45+3}{751+101+1151+19+110+5}$$ = $$0.2564$$

Total productivity of pulses in the year 2008 = $$\frac{260+35+250+9+30+2}{725+102+1199+19+101+5}$$ = $$0.2724$$

We can see that clearly, Total productivity of pulses in the year 2008 > Total productivity of pulses in the year 2007 >Total productivity of pulses in the year 2006. Hence, statement I is incorrect. Hence, we can reject option A and B.

Productivity of Maize in the year 2006 = $$\dfrac{1102}{1004}$$ = 1.097

Productivity of Maize in the year 2007 = $$\dfrac{1116}{1020}$$ = 1.094

Productivity of Maize in the year 2008 = $$\dfrac{1182}{1101}$$ = 1.073

We can see that productivity is approximately same during the given period for Maize. Hence, statement II is correct. Therefore, we can reject option D.

Thus, we can say that option C is the correct answer. 

Productivity is defined as total production per hectare. 
Total productivity of cereals in the year 2006 = $$\frac{153+173+2172+1102+5}{107+598+4992+1004+16}$$ = $$0.5366$$

Total productivity of cereals in the year 2008 = $$\frac{190+380+3350+1182+4}{110+720+4800+1101+15}$$ = $$0.756$$

We can see that clearly, Total productivity of cereals in the year 2008 > Total productivity of cereals in the year 2006. Hence, statement I is correct. 

Now let us check statement II. 

Total yield of oil seeds in the year 2006 = $$\frac{63+491+856+880+135}{422+317+744+472+106}$$ = $$1.1766$$

Total yield of oil seeds in the year 2008 = $$\frac{70+374+799+699+106}{280+298+650+325+80}$$ = $$1.254$$

We can see that yield of Oil seeds is not on decline. Hence, statement II is incorrect. 

Now let us check statement III. 

Area under Urd production in the year 2006 = 124

Area under Urd production in the year 2008 = 102

Total Urd production in the year 2006 = 31

Total Urd production in the year 2008 = 35

Urd's yield in the year 2006 = $$\frac{31}{124}$$ = 0.25

Urd's yield in the year 2008 = $$\frac{35}{102}$$ = 0.34

Hence, we can say that statement III is correct. Therefore, option A is the correct answer. 

Total Oil used in the year 1998 = 22+1012+1732+104 = 2870. 

Therefore, the percentage of total used that is used for House Hold = $$\frac{22}{2870}\times 100$$ = 0.766. 

Similarly we can calculate for remaining year. 

From the table we can see that, in the year 1999 the Oil used for House Hold as a percentage of total Oil Used is highest. Hence, option B is the correct answer.

Total oil produced in the year 1996 = 10+700+1794+104+650 = 3258.

Therefore, oil production loss as a percentage of total oil produced in the year = $$\dfrac{650}{3258}\times 100$$ = 19.95%.

Similarly, we can calculate for the remaining year. Tabulating the same data, 

From the table, we can see that the oil production loss as a percentage of total oil produced is the lowest for the year 2002. Hence, option A is the correct answer. 

Total oil used in the year 1996 = 10+700+1794+104 = 2608.

Therefore, Oil used by Suburban as a proportion of Total Oil Used = $$\dfrac{104}{2608}\times 100$$ = 3.99 percent. 

Similarly, we can calculate for the remaining years. 

From the table, we can see that oil used by suburban as a proportion of total oil used is the highest for the year 2008. Hence, option D is the correct answer. 

Total oil used in the year 1996 = 10+700+1794+104 = 2608.

Total oil produced in the year 1996 = 10+700+1794+104+650 = 3258.

Similarly, we can calculate for the remaining quantities for both the years. Tabulating the same data, 

Therefore, growth rate of total oil used in the year 1997 as compared to 1996 = $$\dfrac{2914-2608}{2608}\times 100$$ = 11.73%

Therefore, growth rate of total oil produced in the year 1997 as compared to 1996 = $$\dfrac{3646-3258}{3258}\times 100$$ = 11.91%

Similarly, we can calculate for the remaining year. Tabulating the same data, 

From the table we can see that, the growth rate in ‘Production of Oil’ is more than the growth rate in ‘Total Oil Used’ in eight years. 
{Year 1996, 1997, 1998, 2003, 2004, 2005, 2006, 2007}. Hence, option D is the correct answer.

Total oil used in the year 1996 = 10+700+1794+104 = 2608.

Total oil produced in the year 1996 = 10+700+1794+104+650 = 3258.

Similarly, we can calculate for the remaining quantities for both the years. Tabulating the same data, 

From the table, we can see that quantity of 'total oil Produced’ is increasing every year since 2003. Hence, option D is the correct answer. 

The first point  tells us that "Paul lives between Som and Krishna".
This gives us an initial thought that these three can occupy the houses 1, 2, 3 in the row with Paul occupying the 2nd house and Som and Krishna sharing houses 1 and 3 in no particular order. In this case Laxman has to occupy the 4th house, i.e. the Yellow house. OR they can occupy the houses 2,3,4 with Paul occupying the 3rd house and Som and Krishna sharing houses 2 and 4 in no particular order. In this case Laxman has to occupy the 1st house, i.e. the Blue house.
However, since we know from point (II) that Laxman does not stay in the Blue house we reject this possibility.
Consequently, we can fix the position of Paul and Laxman in the Green and Yellow houses respectively.

At this point if we use point (VIII), we see that since ԋrishna lives in between two houses he cannot be in the first house. Hence, Krishna takes the third house and Som takes the 1st one.

Thus, the grid converts to:

From this point we need to focus on fixing the values of the salaries of the 4 individuals.
The values of the four salaries can first be identified as 30000, 50000 (from point VIII), 80000 ( point ) and 110000 (point VI). We also know from Point VIII that Krishna lives between the people
earning 30000 and 50000 which means that 30000 and 50000 could be Laxman and Paul's salary.
Further, the salary difference between Laxman and Som being 30000, their salaries would have to be 50000 and 80000, with Laxman getting 50000 and Som getting 80000. Consequently Paul gets 30000 and Krishna would earn 110000. The solution grid would then look like below:

So Krishna lives in Red house 

The first point tells us that "Paul lives between Som and Krishna".
This gives us an initial thought that these three can occupy the houses 1, 2, 3 in the row with Paul occupying the 2nd house and Som and Krishna sharing houses 1 and 3 in no particular order. In this case Laxman has to occupy the 4th house, i.e. the Yellow house. OR they can occupy the houses 2,3,4 with Paul occupying the 3rd house and Som and Krishna sharing houses 2 and 4 in no particular order. In this case Laxman has to occupy the 1st house, i.e. the Blue house.
However, since we know from point (II) that Laxman does not stay in the Blue house we reject this possibility.
Consequently, we can fix the position of Paul and Laxman in the Green and Yellow houses respectively.

At this point if we use point (VIII), we see that since ԋrishna lives in between two houses he cannot be in the first house. Hence, Krishna takes the third house and Som takes the 1st one.

Thus, the grid converts to:

From this point we need to focus on fixing the values of the salaries of the 4 individuals.
The values of the four salaries can first be identified as 30000, 50000 (from point VIII), 80000 ( point ) and 110000 (point VI). We also know from Point VIII that Krishna lives between the people
earning 30000 and 50000 which means that 30000 and 50000 could be Laxman and Paul's salary.
Further, the salary difference between Laxman and Som being 30000, their salaries would have to be 50000 and 80000, with Laxman getting 50000 and Som getting 80000. Consequently Paul gets 30000 and Krishna would earn 110000. The solution grid would then look like below:

Red house is occupied by person earning highest salary

The first point tells us that "Paul lives between Som and Krishna".
This gives us an initial thought that these three can occupy the houses 1, 2, 3 in the row with Paul occupying the 2nd house and Som and Krishna sharing houses 1 and 3 in no particular order. In this case Laxman has to occupy the 4th house, i.e. the Yellow house. OR they can occupy the houses 2,3,4 with Paul occupying the 3rd house and Som and Krishna sharing houses 2 and 4 in no particular order. In this case Laxman has to occupy the 1st house, i.e. the Blue house.
However, since we know from point (II) that Laxman does not stay in the Blue house we reject this possibility.
Consequently, we can fix the position of Paul and Laxman in the Green and Yellow houses respectively.

At this point if we use point (VIII), we see that since ԋrishna lives in between two houses he cannot be in the first house. Hence, Krishna takes the third house and Som takes the 1st one.

Thus, the grid converts to:

From this point we need to focus on fixing the values of the salaries of the 4 individuals.
The values of the four salaries can first be identified as 30000, 50000 (from point VIII), 80000 ( point ) and 110000 (point VI). We also know from Point VIII that Krishna lives between the people
earning 30000 and 50000 which means that 30000 and 50000 could be Laxman and Paul's salary.
Further, the salary difference between Laxman and Som being 30000, their salaries would have to be 50000 and 80000, with Laxman getting 50000 and Som getting 80000. Consequently Paul gets 30000 and Krishna would earn 110000. The solution grid would then look like below:

Rs. 30,000 is earned by person living in green house .

We can draw a direction diagram according to the problem statement. 

Net displacement in the east direction = 26 + 19 - 40 = 5 km. 

Net displacement in the north direction = 30 - 8 - 10 = 12 km. 

Hence, net distance from the starting point = $$\sqrt{12^2+5^2}$$ = 13 km.

Therefore, option C is the correct answer. 

In the first car - Raju's father, grandmother, mother and maternal grandfather - 4 members
In the second car - Raju's brother, sister-in-law, and brother-in-law - 3 members
In the third car - Raju, Raju's wife, sister-in-law, brother-in-law, daughter-in-law, grandson - 6 members

Total = (4 + 3 + 6) = 13

Members not present - Raju's sister, sister-in-law's husband, brother-in-law's wife, son - 4 members.

Hence, option A is the correct answer.

Let 'a' be the number of cards with B. If A gives five cards to ‘B’ then ‘B’ will have as many cards as ‘D’. 

Hence, the number of cards with D = 'a+5'.

B has four cards more than what C has. Hence, the number of cards with c = 'a-4'.

Let us assume that number of cards with A = 'x'. It is given that if ‘B’ gives 'A' five cards the A will have as many cards as ‘E’ has.

Hence, the number of cards with 'E' = x+5.

It is also given that A and B together has 20 cards more than what D and E have together.

Hence, (a+x) - (a+5+x+5) = 20.

Data given in the question contradicts with th information. Hence, this question can't be answer. Therefore, option D is the correct answer. 

According to the given information we can classify the working of instructors as :-

Music Instructor works from 12-4 pm on - Monday, Thursday and Sunday.

Dance Instructor works from 10 am-2 pm on - Tuesday, Wednesday, Thursday and Sunday

Painting Instructor works from -9 am - 12 noon on - Tuesday,  Thursday and Friday

                                               2 - 4 pm on - Wednesday, Saturday and Sunday

After this classification it is clear that Tuesday and Thursday are the days of the week the dance and painting sessions are simultaneously held.

Abhijit's revised minimum pay will be Rs. $$37400$$ and his grade pay will be Rs. $$10000$$. 

Abhijit already had 2 increments and by 2009 will have 3 more. Thus, a total of 5 increments.

Thus his salary in 2009 = $$(37400+10000)\times (1.03)^5=54949.6\approx 54950$$

Hence, the answer is option C.

The new basic pay would have been = $$(15600+5400)(1.03)^4=23636$$

Due to the error, the pay is = $$15600+5400=21000$$

DA + HRA = $$28\% + 30\% = 58\%$$ of the basic pay

Thus, total loss in pay = $$1.58\times (23636-21000)=4164$$

Hence, the answer is option C.

Divide the whole sequence into group of words of 4, 2 and 4 so in the input the-

First group will be- Smile Nile Style Mile 

Second group will be - Shine Wine

Third group will be - Mine Swine Bovine Feline

In step 1 the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e.  Mine Swine are exchanging their position with Bovine Feline respectively with everything else constant

therefore step 1 is- Smile Nile  Style   Mile   Shine Wine  Bovine Feline  Mine    Swine

In step 2 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Smile Nile are exchanging their position with Style Mile respectively with everything else constant

therefore step 2 is- Style  Mile  Smile Nile    Shine Wine  Bovine Feline  Mine   Swine

In step 3 the 1 and 2 of Second group are exchanging their position i.e.  Shine is exchanging it's position with Wine with everything else constant

therefore step 3 is- Style Mile Smile Nile Wine Shine Bovine Feline Mine Swine

In step 4 the 1 and 2 of First group are exchanging their position i.e.  Style is exchanging it's position with Mile , 3 and 4 of First group are exchanging their position i.e.  Smile is exchanging it's position with Nile and Similarly the 1 and 2 of Third group are exchanging their position i.e.  Bovine is exchanging it's position with Feline , 3 and 4 of Third group are exchanging their position i.e. Mine is exchanging it's position with Swine with the positions of Shine and Wine remaining same

therefor step 4 is- Mile Style Nile Smile Wine Shine Feline Bovine Swine  Mine

In step 5 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Mile Style are exchanging their position with Nile Smile respectively and the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e. Feline Bovine are exchanging their position with Swine Mine respectively with everything else constant

therefor step 5 is- Nile Smile Mile Style Wine Shine Swine Mine Feline Bovine

In step 6 the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e. Swine Mine are exchanging their position with Feline Bovine respectively with everything else constant

therefor step 6 is- Nile Smile Mile Style Wine Shine Feline Bovine Swine  Mine

In step 7 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Nile Smile are exchanging their position with Mile Style respectively with everything else constant

therefor step 7 is- Mile  Style  Nile    Smile Wine  Shine Feline  Bovine Swine  Mine

As can be observed the pattern is repeating

therefore step 8 will be Mile  Style  Nile    Smile Shine Wine Feline  Bovine Swine  Mine

step 9- Style Mile Smile Nile Shine Wine Bovine Feline Mine Swine

step 10- Smile Nile Style Mile Shine Wine Mine Swine Bovine Feline

step 11- Smile Nile Style Mile Shine Wine Bovine Feline Mine Swine

step 12- Style Mile Smile Nile Shine Wine Bovine Feline Mine Swine

step 13- Style Mile Smile Nile Wine Shine Bovine Feline Mine Swine

step 14- Mile Style Nile Smile Wine Shine Feline Bovine Swine Mine

Therefore the answer is option 'C'

Divide the whole sequence into group of words of 4, 2 and 4 so in the input the-

First group will be- Smile Nile Style Mile 

Second group will be - Shine Wine

Third group will be - Mine Swine Bovine Feline

In step 1 the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e.  Mine Swine are exchanging their position with Bovine Feline respectively with everything else constant

therefore step 1 is- Smile Nile  Style   Mile   Shine Wine  Bovine Feline  Mine    Swine

In step 2 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Smile Nile are exchanging their position with Style Mile respectively with everything else constant

therefore step 2 is- Style  Mile  Smile Nile    Shine Wine  Bovine Feline  Mine   Swine

In step 3 the 1 and 2 of Second group are exchanging their position i.e.  Shine is exchanging it's position with Wine with everything else constant

therefore step 3 is- Style Mile Smile Nile Wine Shine Bovine Feline Mine Swine

In step 4 the 1 and 2 of First group are exchanging their position i.e.  Style is exchanging it's position with Mile , 3 and 4 of First group are exchanging their position i.e.  Smile is exchanging it's position with Nile and Similarly the 1 and 2 of Third group are exchanging their position i.e.  Bovine is exchanging it's position with Feline , 3 and 4 of Third group are exchanging their position i.e. Mine is exchanging it's position with Swine with the positions of Shine and Wine remaining same

therefor step 4 is- Mile Style Nile Smile Wine Shine Feline Bovine Swine  Mine

In step 5 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Mile Style are exchanging their position with Nile Smile respectively and the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e. Feline Bovine are exchanging their position with Swine Mine respectively with everything else constant

therefor step 5 is- Nile Smile Mile Style Wine Shine Swine Mine Feline Bovine

In step 6 the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e. Swine Mine are exchanging their position with Feline Bovine respectively with everything else constant

therefor step 6 is- Nile Smile Mile Style Wine Shine Feline Bovine Swine  Mine

In step 7 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Nile Smile are exchanging their position with Mile Style respectively with everything else constant

therefor step 7 is- Mile  Style  Nile    Smile Wine  Shine Feline  Bovine Swine  Mine

As can be observed the pattern is repeating

therefore step 8 will be Mile  Style  Nile    Smile Shine Wine Feline  Bovine Swine  Mine

step 9- Style Mile Smile Nile Shine Wine Bovine Feline Mine Swine

step 10- Smile Nile Style Mile Shine Wine Mine Swine Bovine Feline

step 11- Smile Nile Style Mile Shine Wine Bovine Feline Mine Swine

step 12- Style Mile Smile Nile Shine Wine Bovine Feline Mine Swine

step 13- Style Mile Smile Nile Wine Shine Bovine Feline Mine Swine

step 14- Mile Style Nile Smile Wine Shine Feline Bovine Swine Mine

As can be observed from steps 12-14 option D is not present 

Therefore the answer is option 'D'

Divide the whole sequence into group of words of 4, 2 and 4 so in the input the-

First group will be- Smile Nile Style Mile 

Second group will be - Shine Wine

Third group will be - Mine Swine Bovine Feline

In step 1 the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e.  Mine Swine are exchanging their position with Bovine Feline respectively with everything else constant

therefore step 1 is- Smile Nile  Style   Mile   Shine Wine  Bovine Feline  Mine    Swine

In step 2 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Smile Nile are exchanging their position with Style Mile respectively with everything else constant

therefore step 2 is- Style  Mile  Smile Nile    Shine Wine  Bovine Feline  Mine   Swine

In step 3 the 1 and 2 of Second group are exchanging their position i.e.  Shine is exchanging it's position with Wine with everything else constant

therefore step 3 is- Style Mile Smile Nile Wine Shine Bovine Feline Mine Swine

In step 4 the 1 and 2 of First group are exchanging their position i.e.  Style is exchanging it's position with Mile , 3 and 4 of First group are exchanging their position i.e.  Smile is exchanging it's position with Nile and Similarly the 1 and 2 of Third group are exchanging their position i.e.  Bovine is exchanging it's position with Feline , 3 and 4 of Third group are exchanging their position i.e. Mine is exchanging it's position with Swine with the positions of Shine and Wine remaining same

therefor step 4 is- Mile Style Nile Smile Wine Shine Feline Bovine Swine  Mine

In step 5 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Mile Style are exchanging their position with Nile Smile respectively and the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e. Feline Bovine are exchanging their position with Swine Mine respectively with everything else constant

therefor step 5 is- Nile Smile Mile Style Wine Shine Swine Mine Feline Bovine

In step 6 the 1 and 2 of Third group are exchanging their position with the 3 and 4 respectively i.e. Swine Mine are exchanging their position with Feline Bovine respectively with everything else constant

therefor step 6 is- Nile Smile Mile Style Wine Shine Feline Bovine Swine  Mine

In step 7 the 1 and 2 of First group are exchanging their position with the 3 and 4 respectively i.e. Nile Smile are exchanging their position with Mile Style respectively with everything else constant

therefor step 7 is- Mile  Style  Nile    Smile Wine  Shine Feline  Bovine Swine  Mine

As can be observed the pattern is repeating

therefore step 8 will be Mile  Style  Nile    Smile Shine Wine Feline  Bovine Swine  Mine

step 9- Style Mile Smile Nile Shine Wine Bovine Feline Mine Swine

step 10- Smile Nile Style Mile Shine Wine Mine Swine Bovine Feline

step 11- Smile Nile Style Mile Shine Wine Bovine Feline Mine Swine

step 12- Style Mile Smile Nile Shine Wine Bovine Feline Mine Swine

step 13- Style Mile Smile Nile Wine Shine Bovine Feline Mine Swine

step 14- Mile Style Nile Smile Wine Shine Feline Bovine Swine Mine

As can be seen the answer cannot be step 9/11/14 therefore by eliminating the options we get the answer as step 20

Therefore the answer is option 'C'

Option A:- C1, C2, C5, C6

therefore according to the given conditions if C1 is selected and since he hates river rafting then at least one of the C2, C5, C6 must like river rafting but C2 likes sightseeing and squash, C5 likes squash and C6 likes travelling i.e. none of C2, C5, C6 likes river rafting, therefore conditions are not getting satisfied therefore option A cannot be the answer

Option B:-C3, C4, C5, C6

therefore according to the given conditions if C3 is selected and since he hates sightseeing then at least one of the C4, C5, C6 must like sightseeingbut C4 likes trekking, C5 likes squash and C6 likes travelling i.e. none of C4, C5, C6 likes sightseeing, therefore conditions are not getting satisfied therefore option B cannot be the answer

Option C:-C1, C2, C4, C7 

Here C1 hates river rafting and C7 likes river rafting also C1 likes sightseeing and so does C2 therefore C1 can be on the team, C2 hates travelling and C1 likes travelling also C2 likes sightseeing and so does C1 therefore C2 can be on the team, C4 hates squash and C2 likes squash also C4 likes trekking and so does C7 therefore C4 can be on the team and finally C7 hates travelling and C1 likes travelling also C7 likes trekking and so does C4 therefore C7 can be on the team.

Since all the conditions are getting satisfied option 'C' is the answer. 

Arcelor was created in February 2002 through the merger of Arbed (Luxembourg) founded in 1911, Aceralia (Spain) and Usinor (France).
Hence, option C is the correct answer.

Imagining India is written by Nandan Nilekani.
Remaking India is written by Arun Maira.
A Better India A Better World is written by Narayan Murthy.
A Vision for the New Millennium is written by A P J Abdul Kalam.

Hence, option A is the correct answer.

There is a mistake in the question. Arun Maira is replaced by Ratan Tata.

The company Fem Care Pharma Limited, the manufacturer of Fem Bleach, was acquired by Dabur India Limited.
Hence, option D is the correct answer.

HANG SENG is the Stock Index of Hong Kong.
NASDAQ is the Stock index of USA.
FTSE is the Stock index of United Kingdom.
KOSPI is the Stock index of South Korea.

Hence, option B is the correct answer.

Companies Act 1956 is related to the formation and regulation of companies.
Competition Act 2002 is related to prohibition of anti-competitive agreements.
SEBI Act 1992 was enacted to protect the interests of the investors. 
FEMA Act 1999 was enacted to facilitate external trade and payments. 

Therefore, option A is the right answer.

Nicolas Sarkozy is from France.
Dmitry Medvedev is from Russia.
Yoweri Museveni if from Uganda.
Horst Kohler is from Germany.

Hence, option C is the correct answer. 

UNCTAD : United Nations Conference on Trade and Development
UNCED : United Nations Conference on Environment and Development
PFRDA : Pension Fund Regulatory and Development Authority
ASSOCHAM : Associated Chambers of Commerce and Industry of India.
There is no such acronym as TAFTA.

Hence, option A is the correct answer.

T N Manoharan, Suryakant Balakrishnan Mainak, Kiran Karnik  were nominated by the Government of India on the board of Satyam Computers Services.
Hence, option B is the correct answer.

CDS stands for Credit Default Swap.
Hence, option C is the correct answer.

Land Rover is of TATA, Jetta is of Volkswagen, Lexus is of Toyota and Xylo is of Mahindra.
Hence, option C is the correct answer.

HP's slogan is Technology you can trust.
Philips' slogan is Let's make things better.
Microsoft's slogan is You potential our passion.
Intel's slogan is Sponsors of tomorrow.

Hence, option C is the correct answer.

In the financial year 2008-09, the top three investing countries in terms of FDI inflows were Mauritius, Singapore, USA.
Hence, option B is the correct answer.

Negative inflation is also called deflation.

Deflation is when consumer and asset prices decrease over time, and purchasing power increases. Essentially, you can buy more goods or services tomorrow with the same amount of money you have today.

Hence, option B is the correct answer.

The co-founders of Google are Sergey Brin & Larry Page.
Hence, option C is the correct answer.

Except option D, all other statements are related to carbon credits.
Hence, option D is correct answer.

India signed the Kyoto Protocol on 26 August 2002.
Hence, option C is the correct answer.

C. K Prahlad wrote the book Core Competence of the Corporation.
Paul Krugman wrote International Trade and New Economic Geography.
Al gore is related to Climate Change and Global Warming.
Amartya Sen is related to Capability and Equality.

Hence, option B is the correct answer.

Ms Sikha Sharma is the CEO of Axis Bank.
Ms. Naina Lal Kidwaiekani was the CEO of HSBC.
Ms Indra Nooyi is the CEO of PepsiCo.
Ms. kiran Mazumdar Shaw is the CEO of Biocon India.

Hence, option C is the correct answer.

Section III

Statement (I) can be inferred from the first paragraph: "directors are chosen based of friendship and, sadly, pliability"

Statement (II) can directly be inferred from the third paragraph: "For this, independent directors should be trained in their in their in roles and responsibilities."

Statement (IV) can be inferred from the second paragraph: "The need of the hour is to strengthen the independence of the board. We have to put in place stringent standards for the independence of directors."

Statement (III) is incorrect.

Hence, the answer is option D.

The author says, "Ideally, the compensation committee should decide on the compensation of each independent director based on such a performance appraisal.", i.e., the compensation should depend upon the performance of independent directors and not the other way round.

Hence, the answer is option B.

Statement I can be inferred from the eleventh paragraph 
Internal auditors have not been mentioned in the passage. Statement II is incorrect. 
Statement III can be inferred from the last paragraph.
It is given in the passage that the body should comprise a "majority of non- practicing accountants to ensure independent oversight. Statement IV is wrong.

Hence, option C is the correct answer.

Option A :  Consider the sentence:- The assessment should focus on issues like competence, preparation, participation and contribution. Ideally, this evaluation should be performed by a third party.  This option surely improves accountability. Hence it is incorrect

Option B : The lead audit partner and the audit partner responsible for reviewing a company’s audit must be rotated at least once every three to five years. This option is also incorrect

Option D : The audit committee should establish procedures for the treatment of complaints received through anonymous submission by employees and whistle-blowers. This option also improves the accountability of the management to the shareholders. Hence this option is also incorrect.

Option C is not mentioned anywhere in the passage. Hence it is the most suitable option.

 Option A : Consider the sentence "As part of the board meeting agenda, the independent directors should have a meeting among themselves without the management being present." The author definitely advocates increased activism by the independent directors. 

 Option B : Consider the sentence "Hence, an independent body should be constituted to oversee the functioning of auditors for Independence, the quality of audit and professional competence." The author calls for measures to improve the independence of auditors. 

Option C :  Consider the sentence "Accounting standards do not always keep pace with changes in the business environment. Hence, the accounting standards-setting body should include members drawn from the industry, the profession and regulatory bodies." The author says that the accounting standards should be modified based on the changing business conditions.

Hence all these options are advocated by the author.

The author does not advocate option D. Hence option D is the correct answer.

From the second paragraph, we can infer that the cycle can be reversed. So, option B is factually wrong.

Hence, option B is the correct answer.

We have seen above that the marginal efficiency of capital depends, not only on the existing abundance or scarcity of capital-goods and the current cost of production of capital- goods, but also on current expectations as to the future yield of capital-goods - From these lines, options A, B and C can be inferred.

Availability of capital is nowhere mentioned as a factor on which marginal efficiency depends.

Hence, option D is the correct answer.

In the 1st paragraph it is mentioned that "the phenomenon of the ‘crisis’ the fact that the substitution of a downward for an upward tendency often takes place suddenly", from this option III can be concluded.

In the 2nd paragraph it is mentioned that "explanation of the crisis is, not primarily a rise in the rate of interest, but a sudden collapse in the marginal efficiency of capital. The later stages of the boom are characterized by optimistic expectations as to the future yield of capital goods sufficiently strong to offset their growing abundance and their rising costs of production and, probably, a rise in the rate of interest also.

From this option I and II can be concluded.
Thus, option B is the correct answer.

Statement (I) talks about eliminating greenhouse gases, but this sentiment is not expressed by the author in the passage. In fact, in the last paragraph, the author says that the natural greenhouse effect is beneficial for us. The additional greenhouse gases released by human activities are what's making it worse. Thus, this statement can be ruled out.

Statement (II) can be clearly ruled out as the author says that methane is far more dangerous than CO2.

Statement (III) is the main theme of the passage as thus, can be inferred.

Statement (IV) can be inferred from paragraph 7.

Hence, the answer is option D.

Option A can be inferred from the last paragraph where the author says that a natural level of global warming is beneficial for us as it keeps the planet habitable. Thus, it is true.

Option B can be inferred from the 7th paragraph, where the author states that deforestation causes more damage than all the vehicular emissions combined. Thus, this statement is also true.

Option C is mentioned in the last paragraph of the passage and is thus, true.

Option D is incorrect as the author has given the example of the Northern Hemisphere to indicate the historical changes in climate in that region.

Hence, the answer is option D.

The author mentions in the second paragraph that as mechanisation increased, the use of fossil fuels also increased to power those machines which gave rise to greenhouse emissions. Thus, statement (II) is one of the reasons.

The author says in the first paragraph that the process of global warming began with the Industrial Revolution. Thus, statement (III) is true.

Statement (IV) is given as the main reason for greenhouse emissions and global warming throughout the passage. Thus, statement (IV) is true.

Statement (I) is contrary to what the author has said. The author says in the first paragraph that manual intervention decreased with the emergence of machines and that led to global warming. Thus, statement (I) is false.

Hence, the answer is option D.

Talking about the fuels from heaven, the author says, "These all come from above ground, are endlessly renewable, and produce no harmful emissions."

Hence, the answer is option D.

Options A, B and C are mentioned in the last paragraph.
Option D is not a necessary condition as per the passage.
Hence, option D is the correct answer.

"It can be planted from seed, but this method takes much time and patience; the usual way is to plant it from cuttings, or slips. The first growth from these cuttings is called plant cane; after these are taken off the roots send out ratoons or shoots from which the crop of one or two years, and sometimes longer, is taken. If the soil is not rich and moist replanting is more frequently necessary and in places like Louisiana, where there is annual frost, planting must be done each year. When the cane is ripe it is cut and brought from the field to a central sugar mill, where heavy iron rollers crush from it all the juice. This liquid drips through into troughs from which it is carried to evaporators where the water portion of the sap is eliminated and the juice left; you would be surprised if you were to see this liquid.

Sugar isn't very attractive during its process of preparation," agreed Mr. Hennessey. "The sweet liquid left after the water has been extracted is then poured into vacuum pans to be boiled until the crystals form in it, after which it is put into whirling machines, called centrifugal machines that separate the dry sugar from the syrup with which it is mixed.

From these lines, we can infer that option A depicts the appropriate sequence of processes in sugar preparation.

Hence, option A is the correct answer.

"Largely from the plantations of Cuba and Porto Rico. Toward the end of the year we also get raw sugar from Java, and by the time this is refined and ready for the market the new crop from the West Indies comes along. In addition to this we get consignments from the Philippine Islands, the Hawaiian Islands, South America, Formosa, and Egypt. - From these lines, we can infer that cane plantation and sugar production process is not equally spread across the countries.

Hence, option D is the correct answer.

Options B, C and D suggest that the data was stubbornly suggesting something, which would not be logically coherent. 
Leaving us with option A fit for replacing the underlined portion in the text. 
This would suggest that they (the company) were being stubborn in shipping. 

Therefore, Option A is the correct answer. 

The main point presented by the underlined sentence is that the companies are looking at the emerging markets in Asia and Latin America. The reason for this is given as, to maintain their growth rates and margins, which is the subordinate clause.

This structure is correctly represented in option D.

The answer is option D.

"Wherever they are" and "Whatever they do" is given as additional information about the people mentioned. Thus, it has to be separated from the primary sentence using a hyphen or a comma.

Hence, the answer is option B.

A "sonnet" is a short poem. Thus, it has to be paired with poets.

"Symphonies" are composed by composers, and "contemplation about God" is done by philosophers.

All these are properly paired in option B.

Thus, the answer is option B.

The main idea is that car sales have increased due to two factors: the introduction of new models and the decrease in borrowing costs, both of which have contributed to bringing new buyers back to the market. Option A effectively represents this sequence, maintaining clear connections between the causes (new models and falling borrowing costs) and the result (new buyers returning).

Thus, the correct answer is indeed option A, as it presents the idea in a grammatically sound and logically coherent manner.

In the context of the sentence, "pedantic" means difficult to understand.

"Esoteric" means something that is understood by very few people. Thus, they are both synonymous in this context.

Hence, the answer is option C.

"Chagrin" means to be annoyed or distressed.

Option A: Intense happiness or excitement, often overwhelming. 

Option B:   The act of calming or soothing someone, often to reduce anger.

Option C: Joyful delight or amusement, often with a sense of mischief.

Option D: Deep embarrassment or stress, often due to humiliation.

Of the given options, Mortification works best as a synonym for chagrin. 

Hence, the answer is option D.

"Genuflect" means to bow or bend the knee to somebody.

"Grovel" also refers to kneeling in front of someone. Thus, both these words can be used in the same context.

Hence, the answer is option A.

"Stentorian" refers to something loud.

Among the options, only "blaring" can be used to refer to loud noises.

Hence, the answer is option C.

The word "bemused" means confused or puzzled. Among the given options, Option B) bewildered,  is the closest synonym, as it also means being perplexed or confused. The other options have different meanings:

Amused: entertained, finding something funny

Enlightened: having a deeper understanding or awareness

Enthused: excited or enthusiastic

"Specious" refers to something that seems right but is actually wrong.

"Unfeigned" means "genuine". Thus, it is an antonym of the given word.

Hence, the answer is option B.

"Exacting" means very demanding.

"Insouciant" means showing a casual lack of concern. Thus, it is an antonym of the given word.

Hence, the answer is option A.

"Levitating" means floating or rising in the air.

"Gravitating" means to move toward something [land in this case].

Hence, the answer is option A.

"Ensnared" means to get trapped in.

"Released" means to set free. Thus, it is an antonym of the given word.

Hence, the answer is option D.

Quagmire means an awkward, complex, or hazardous situation.
Tranquility means the quality or state of being calm.
So, tranquility and quagmire are antonyms.
Hence, option C is the correct answer.

A. "Serendipity" refers to something happening by chance, and "faux pas" refers to a mistake. These do not fit the sentence.

B. "Predilection" means "preference", and "Despair" means "loss of hope". These do not fit the sentence either.

C. "Intensity" means "force of feelings", and "success" means to accomplish something. These go well with the overall sentence.

D. "Oddity" means strangeness, and "conformity" means compliance. These do not fit the sentence.

Hence, the answer is option C.

The "but" indicates that the second part is a negative/undesirable effect.

Only option B conforms with the given situation. 

Hence, the answer is option B.

Since the sentence is talking about diversity in a positive way, "alleviate"[make less severe], "annihilate"[destroy], and exasperate[frustrate] are inappropriate for the second blank.

Option A: "stupefying" [astonishing/amazing] and "negotiate" [to reach acceptance] make the sentence meaningful.

Hence, the answer is option A.

Since the sentence is in a positive tone, "repudiated" and "decimated" are inappropriate for the first blank. Thus, options B and D are ruled out.

"Exacerbate" means to make something worse. Since the discomfort was removed, it is the wrong choice for the second blank.

Hence, the answer is option A.

Statement 2 talks about talented employees being poached, while, statement 1 suggests a retention strategy to this problem..
Statement 4 has the word "Further", suggesting that the 4 is an extended solution to the existing risk or problem(poaching)
Therefore 214 becomes a logical block.

3 will be the starting statement as it introduces the topic of discussion. (by calling humans a transmission tower)

4 will continue the thought about the transmissions.

2 will be the next sentence as it talks about the reach of the frequencies transferred by us.

1 will be the concluding statement as it continues the idea in statement 2.

Hence, the required sequence is 3421 and the answer is option C.

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.

Let’s consider the content of each sentence. Sentence IV introduces the "principle of separation of powers" and its purpose—creating a tension between individual rights and social consensus. This is a foundational concept, making it a strong starting point as it sets the stage for discussing how democracy functions within this framework. 

Sentence III follows logically, explaining the judiciary’s role in protecting individual rights (the "former" from IV) from excesses in legislative and governmental actions (which relate to social consensus, the "latter" from IV). It directly ties to IV by detailing how this separation is implemented. 

Next, sentence I warns about the "dangers of conflicting irrational majoritarianism with enlightened consensus," introducing a specific challenge within this system—majoritarianism versus a balanced consensus—which connects to the tension mentioned in IV and the judiciary’s protective role in III.

Finally, sentence II defines "real democracy" as mediating popular will through institutions and law, providing a broader conclusion that ties together the roles of governance, judiciary, and the balance of rights and consensus discussed earlier.

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. 

We can see that we will get a regular octagon as shown in the figure below. 

Let 'a' be the length of the side of the regular octagon. 

Hence, we can say that, $$\dfrac{a}{\sqrt{2}}+a+\dfrac{a}{\sqrt{2}} = 2$$

$$\Rightarrow$$ $$a = \dfrac{2}{\sqrt{2}+1}$$. 

Area of a regular octagon = $$2*(1+\sqrt{2})*a^2$$

$$\Rightarrow$$ $$2*(1+\sqrt{2})*(\dfrac{2}{\sqrt{2}+1})^2$$ 

$$\Rightarrow$$ $$\dfrac{8}{(\sqrt{2}+1)}$$.

Therefore, option D is the correct answer. 

first month he will have deficiency of 2000, second month he will have deficiency of 2500, Third month he will have deficiency of 3000, and so on

He won't borrow until all of his savings (60000) gets exhausted i.e. until 60000 - (2000 + 2500 + 3000 + ........ up to nth month ) becomes negative

i.e $$60000<\frac{n}{2}*(4000+(n-1)500)$$

I.e. 1200<n*(35+5n)

i.e 240<n*(7+n)

This condition first becomes true for n=13 therefore Rashid will have to borrow from 13th month

Therefor the answer is option 'D' 

All the terms of the expansion $$(X + Y + Z + W)^{30}$$ are of the form $$k*X^a*Y^b*Z^c*W^d$$ where a,b,c,d are all positive integers and a+b+c+d=30

We need to find number of solutions of above equation and that will be the number of distinct terms in the expansion

number of solutions of equation a+b+c+d=30 is given by $$(n+r-1)C_{r-1}$$ here n = 30 and r = 4 

therefore number of solutions = $$(33)C_{3}$$ = 5456 

Therefore our answer is Option 'B'

For X:-

Probability that the card drawn is a black card = $$\frac{26}{52}$$

Probability that the card drawn is a king = $$\frac{4}{52}$$

Probability that the card drawn is a black king = $$\frac{2}{52}$$

Therefore probability The card drawn is black or a king. = $$\frac{26}{52}$$ + $$\frac{4}{52}$$ - $$\frac{2}{52}$$ = $$\frac{28}{52}$$

For Y:-

Probability that the card drawn is a club card  = $$\frac{13}{52}$$

Probability that the card drawn is a heart card = $$\frac{13}{52}$$

Probability that the card drawn is a jack = $$\frac{4}{52}$$ 

Probability that the card drawn is a jack of club or a jack of heart = $$\frac{2}{52}$$

Therefore probability The card drawn is a club or a heart or a jack  = $$\frac{13}{52}$$ + $$\frac{13}{52}$$ + $$\frac{4}{52}$$ - $$\frac{2}{52}$$ = $$\frac{28}{52}$$

For Z:- 

Probability that the card drawn is a diamond card  = $$\frac{13}{52}$$

Probability that the card drawn is an ace card = $$\frac{4}{52}$$ 

Probability that the card drawn is a queen card = $$\frac{4}{52}$$

Probability that the card drawn is a diamond card of ace or queen = $$\frac{2}{52}$$

Therefore the probability The card drawn is an ace or a diamond or a queen. = $$\frac{13}{52}$$ + $$\frac{4}{52}$$ + $$\frac{4}{52}$$ - $$\frac{2}{52}$$ =  $$\frac{19}{52}$$ 

Therefore, $$P(X) = P(Y) > P(Z)$$ 

Therefore option C is the correct answer.

Is the condition for n = 2 and this will go on for higher values of n

as can be seen the area between square 1 and circle 1 is finite ,   square 2 and circle 2 is finite and so on

sum of all these areas for a higher value of n will become infinite

Therefore our answer is option 'C' 

Let x be the probability of investigation.
Let us indicate the event of the investigation happening to be I.
=>Event of investigation not happening = I'
Similarly, let us indicate the event of importing the technology to be T.
=> The event of technology not getting imported before the deadline = T'
The probability of Alpha getting the contract, P(A) = P(A|I&T)P(I&T)+P(A|I'&T)P(I'&T)+P(A|I&T')P(I&T')+P(A|I'&T')P(I'&T')

Alpha's chances of getting a contract:-

1. If Gamma is able to import the technology and there is no investigation by the Government, P(A|I'&T)P(I'&T) = 0.8*0.67*(1-x)

2. If there is investigation and Gamma Ltd is unable to import the technology in time, P(A|I&T')P(I&T') = 0.72*0.2*x

3. If both events occur, P(A|I&T)P(I&T) = 0.8*0.58*x

4. If none events occur,P(A|I'&T')P(I'&T') = 0.85*0.2*(1-x)

The probability of the contract being awarded to Alpha Ltd is = 0.8*0.67*(1-x) + 0.72*0.2*x + 0.8*0.58*x + 0.85*0.2*(1-x)$$\geq$$0.65

0.536 - 0.536x + 0.144x + 0.464x + 0.17 - 0.17x$$\geq$$0.65

i.e. 0.056 $$\geq$$ 0.098x

i.e. 0.057 $$\geq$$ x

Therefore, option B is the right answer.

Amount of work done by A in one week = $$\frac{1}{6}$$

Amount of work done by V in one week = $$\frac{1}{9}$$

Amount of work done by Y in one week = $$\frac{1}{12}$$

Therefore Amount of work done by A, V and Y in one week = $$\frac{1}{6}$$ + $$\frac{1}{9}$$ + $$\frac{1}{12}$$ = $$\frac{13}{36}$$

They work together for 2 weeks therefore work done in these 2 weeks is = $$\frac{26}{36}$$

Amount of work remaining is = 1 - $$\frac{26}{36}$$ = $$\frac{10}{36}$$

Amount of work done by V and Y in one week = $$\frac{1}{9}$$ + $$\frac{1}{12}$$ = $$\frac{7}{36}$$

If total number of weeks required to complete the work is n then only V and Y work together for (n-3) weeks

Therefore work done in these (n-3) weeks is = $$\frac{7*(n-3)}{36}$$

Remaining $$\frac{10}{36}$$ - $$\frac{7*(n-3)}{36}$$ is completed by Y in one week

Therefore $$\frac{10}{36}$$ - $$\frac{7*(n-3)}{36}$$ = $$\frac{1}{12}$$

Solving we get n = 4

Therefore The job would be completed in 4 weeks 

Therefore our answer is option 'A'

Bonus share received in 2007 = 650 * (3/13) = 150
Bonus share received in 2008 = 800 * (1/2) = 400
So, has has (150 + 400) = 550 extra shares
Dividend of the share is always issued on face value irrespective of market value
Dividend = (Total value of shares) * (Percentage of dividend)
Dividend he will get $$= \dfrac{1200 * 10 * \frac{12.5}{100}}{650 * 10} = \dfrac{1200}{650} * \dfrac{1}{8} = \dfrac{3}{13} = 23$$%
Hence, option D is the correct answer.

Let the initial position of the warship be A and initial and final positions of the submarine be P and Q respectively.

$$AP = 50 km$$

In $$\triangle$$ APN

=> $$sin 30 = \frac{AN}{AP}$$

=> $$\frac{1}{2} = \frac{AN}{50}$$

=> $$AN = \frac{50}{2} = 25 km$$

=> $$BM = AN = 50 km$$

$$\therefore$$ In $$\triangle$$ BMQ

=> $$sin 60 = \frac{BM}{BQ}$$

=> $$\frac{\sqrt{3}}{2} = \frac{25}{BQ}$$

=> $$BQ = \frac{50}{\sqrt{3}} km$$

Let the initial position of the warship be A and initial and final positions of the submarine be P and Q respectively.

$$AP = 50 km$$

Ratio of speed of warship to submarine = $$2 : 1$$

=> $$AB = 2 PQ$$ ---------------Eqn(I)

In $$\triangle$$ APN

=> $$sin 30 = \frac{AN}{AP}$$

=> $$\frac{1}{2} = \frac{AN}{50}$$

=> $$AN = \frac{50}{2} = 25 km$$

=> $$BM = AN = 25 km$$

Similarly, $$PN = 25\sqrt{3} = AR$$

$$\therefore$$ In $$\triangle$$ BMQ

=> $$sin 60 = \frac{BM}{BQ}$$

=> $$\frac{\sqrt{3}}{2} = \frac{25}{BQ}$$

=> $$BQ = \frac{50}{\sqrt{3}} km$$

Similarly,  $$MQ = \frac{25}{\sqrt{3}}$$

Let $$RB = PM = x$$ and using Eqn (I), we get :

=> $$(AR + RB) = 2 (PM + MQ)$$

=> $$(25\sqrt{3} + x) = 2 (x + \frac{25}{\sqrt{3}}$$

=> $$(25\sqrt{3} + x) = 2x + \frac{50}{\sqrt{3}}$$

=> $$2x - x = 25\sqrt{3} - \frac{50}{\sqrt{3}}$$

=> $$x = \frac{25}{\sqrt{3}}$$

$$\therefore AB = 25\sqrt{3} + \frac{25}{\sqrt{3}}$$

=> $$AB = \frac{100}{\sqrt{3}}$$

$$\therefore$$ Speed of warship = $$2 \times \frac{100}{\sqrt{3}} = \frac{200}{\sqrt{3}} km/h$$

Let the number of 1 rupee , 2 rupee and 5 rupee coins be x, y and z respectively

At the grocery store he gives half of his 5 Rupee coins and in return receives the same number of 1 Rupee coins i.e z now become 0.5z and x now becomes x+0.5z

At the dairy store he gives all 2 Rupee coins and in return gets thirty 5 Rupee coins which increases the number of 5 Rupee coins to 75% more than the original number i.e now y = 0 and 0.5z = 0.5z+30

Also given 0.5z+30 = 1.75z

i.e. z=24

Also given that number of 1 Rupee coins now is 50 i.e. x+0.5z = 50 

i.e. x = 38

Therefore the number of 1 Rupee and 5 Rupee coins originally were 38 and 24 respectively. 

Therefore our answer is Option 'D'

Sukriti covers a distance of 1 km in 5 minutes and 50 seconds therefore will cover 5 kms in 25 mins 250 secs = 29.16 mins

Saloni covers the 1 km in 6 minutes and 4 seconds therefore her speed is $$\frac{1}{6.06}$$ kms per minute

Therefore Distance Covered by Saloni in 29.16 mins is 29.16 mins*$$\frac{1}{6.06}$$ $$\approx$$ 4.8 kms 

Therefore the distance with which Sukriti will win a 5 km mini marathon is $$\approx$$ 200 meters

therefore our answer is option 'B'

Area of a equilateral triangle is $$\frac{\sqrt3}{4}$$*$$a^2$$

Area of a regular pentagon is $$\frac{5}{4}$$*$$\sqrt{1+\frac{2}{\sqrt{5}}}$$*$$a^2$$

Therefore ratio of shaded area to unshaded area = $$\frac{\frac{5}{4}*\sqrt{1+\frac{2}{\sqrt{5}}}}{\frac{5*\sqrt3}{4}}$$.

i.e. $$\frac{\sqrt{1+\frac{2}{\sqrt{5}}}}{{\sqrt3}}$$

therefore our answer is Option 'D'.

P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours therefore when Both the pumps are opened simultaneously they can fill $$\frac{1}{8}$$ + $$\frac{1}{12}$$ = $$\frac{5}{24}$$ this much of tank in an hour.Therefore Time required by P1 and P2 to fill full tank is $$\frac{24}{}$$ Hence they can fill half the tank in $$\frac{12}{5}$$ = 2.4 hours. After all the 3 pipes are opened the tank will be filled at the rate of $$\frac{1}{8}$$ + $$\frac{1}{12}$$ - $$\frac{1}{8}$$ = $$\frac{1}{12}$$ therefore for filling the remaining tank we will need 6 more hours. If supervisor was planning to come exactly when the tank is fully filled then he must come after 8.4 hours

 Time required by P1 and P2 to fill 1/3rd of the tank is $$\frac{24}{5*3}$$ = $$\frac{8}{5}$$ = 1.6 hours therefore supervisor will come after = 8.4 - 1.6 = 6.8 hours 

In 6.8 hours all the three pipe will fill $$\frac{6.8}{12}$$ = 0.56 of the capacity of tank

therefore remaining tank to be filled when the supervisor comes = 1- 0.56 - 0.33 $$\approx$$ 0.1 i.e. 10%

Therefore option 'C' is our answer

When the ball is dropped from 45m height it will cover a distance of 45m while going down after rebound it'll cover a distance of $$45*\frac{3}{5}$$ while going up and a distance of $$45*\frac{3}{5}$$ while going down again. after 2nd rebound it'll cover a distance of $$45*\frac{3}{5}*\frac{3}{5}$$ while going up and a distance of $$45*\frac{3}{5}*\frac{3}{5}$$ while going down again and so on 

i.e. total distance traveled by the ball is 45 + $$45*\frac{3}{5}$$ + $$45*\frac{3}{5}$$ + $$45*\frac{3}{5}*\frac{3}{5}$$ + $$45*\frac{3}{5}*\frac{3}{5}$$ +...........

this form 2 infinite GPs as 45 + $$45*\frac{3}{5}$$ + $$45*\frac{3}{5}*\frac{3}{5}$$+....... and $$45*\frac{3}{5}$$+$$45*\frac{3}{5}*\frac{3}{5}$$+....

For 1st GP a=45 and r=$$\frac{3}{5}$$ therefore sum of this infinite GP is $$\frac{45}{1-\frac{3}{5}}$$ = $$\frac{225}{2}$$

For 2nd GP a=45*$$\frac{3}{5}$$  and r=$$\frac{3}{5}$$ therefore sum of this infinite GP is  $$\frac{45*\frac{3}{5}}{1-\frac{3}{5}}$$ = $$\frac{135}{2}$$

Therefore our answer = $$\frac{225}{2}+\frac{135}{2}$$ = 180 m i.e. option 'B'

From 2nd customer for each customer the purity of oil becomes 0.9 of it's previous value i.e. 2nd customer will get only 40*0.9=36 liters of pure petrol 3rd customer will get 36*0.9= 32.4 liters of pure petrol and so on. Therefore the 7th customer will get $$40*(0.9)^6$$= 21.25 liters of pure petrol

Therefore our answer is option 'B'.

Given that probability of getting a heart attack before any drug = 0.80

Drug D1 reduces the probability of a heart attack by 35 %. Therefore, the probability of a patient getting heart attack after he has taken D1 = (1-0.35)*0.80 = 0.52

Drug D2 reduces the probability of a heart attack by 20 %. Therefore, the probability of a patient getting heart attack after he has taken D2 = (1-0.20)*0.80 = 0.64

It is given that both D1 and D2 work independently. Therefore, the probability of a patient getting heart attack after he has taken both D1 and D2 = (1-0.35)*(1-0.20)*0.80 = 0.416

A total of 100 patients have taken both the drugs whereas only 50-50 patients took drug D1 and D2.

Hence, the probability that the selected patient was given both the drug is = $$\dfrac{0.416}{0.416+0.5*0.52+0.5*0.64}$$ = 0.417 $$\approx$$ 0.42

Therefore, we can say that option A is the correct answer.

zone 1 will grow to become 193.8*1.0725= 207.85

zone 2 will grow to become 79.3*1.082=85.8

zone 3 will grow to become 57.5*1.0715=61.61

Total sales this year = 355.26

Total sales last year = 330.6

Growth = $$\frac{355}{330}$$ = 1.0746 i.e. growth of 7.46%

decrease in purchase price for first month was $$\frac{3000-2750}{3000}$$ = 0.083

decrease in purchase price for second month was $$\frac{2750-2500}{2750}$$ = 0.0909

decrease in purchase price for the third month was $$\frac{2500-2400}{2500}$$ = 0.04

decrease in purchase price for the fourth month was $$\frac{2400-2250}{2400}$$ = 0.0625

Average decrease = $$\frac{0.083+0.0909+0.04+0.0625}{4}$$ = 0.069 i.e 6.9%

Therefore our answer is option'C'

We need to find the coefficient of $$x^7$$ in the expansion $$(1-x^{2}+x^{3})(1 + x)^{10}$$ 

Now, $$(1 + x)^{10}$$ will have all the powers of x from 0 to 10. Multiplying these powers by 1, $$x^2$$ and $$x^3$$ will yield different results but we are interested in finding only the coefficient of $$x^7$$. When we multiply $$x^7$$ of $$(1 + x)^{10}$$ by 1, $$x^5$$ of $$(1 + x)^{10}$$ by $$x^2$$ and  $$x^4$$ of $$(1 + x)^{10}$$ by $$x^3$$ we will get $$x^7$$. coefficient of $$x^7$$ in $$(1 + x)^{10}$$ is $$10C_7$$ = 120, coefficient of $$x^5$$ in $$(1 + x)^{10}$$ is $$10C_5$$ = 252, coefficient of $$x^4$$ in $$(1 + x)^{10}$$ is $$10C_4$$ = 210 adding 120 and 210 and subtracting(since $$x^2$$ has a negative sign) 252 we get coefficient of $$x^7$$ as 78

Therefore our answer is option 'B'

We know length of an arc is = angle subtended in radians * radius of the circle 

Therefore in our case Length of the arc = x*r

Also, area of sector = $$\frac{\textrm{angle subtended in radians}}{2}$$ * $$radius^2$$

Therefore in our case area of sector = $$\frac{x}{2}$$ * $$r^2$$

Also given that  area of sector = length of an arc^2

Therefore $$x^2*r^2$$ = $$\frac{x}{2}$$ * $$r^2$$

Solving we get x= 0.5

Therefore our answer is Option "A"

Let $$a, b, c$$ and $$d$$ be the sides of the cyclic quadrilateral.
Thus, $$s = \frac{(a+b+c+d)}{2}$$
$$Area = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$
Thus, after a threefold increase in the sides the sides will become $$4a, 4b, 4c$$ and $$4d$$.
Thus new $$s = s_{new} = (4a+4b+4c+4d)/2 = 4s$$
Thus, $$Area_{new} = \sqrt{(4s-4a)(4s-4b)(4s-4c)(4s-4d)}$$
= $$\sqrt{4*4*4*4*(s-a)(s-b)(s-c)(s-d)}$$  = $$16*Area$$
Thus, there is 1500% increase in the area.
Hence, option D is the correct answer.