1. P(x) = (x^2012+x^2011+x^2010+........+x+1)^2-x^2012    Q(x) = x^2011+x^2010+......+x+1The remainder when P(x) is divided by Q(x) is ?Ans: 0 

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2. In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water ?Ans: 22 

3. Directions for Q. 1 to Q. 5: Refer the data:J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.No two among them collected the same number.(i) 3 collected the same number as K and M together.(ii) L collected 3 more than the cube of an integer(iii) The no. Collected by J was the square of an integer.(iv) Total no. Collected by K was either the square or cube of an integer.1. The no. Collected by J was:(1) 27 (2) 49 (3) 36 (4) 642. The no. Collected by K was:(1) 16 (2) 27 (3) 25 (4) 363. The difference of numbers collected by L & M was:(1) 3 (2) 2 (3) 5 (4) 9Ans: L=12, N=11, J=27, M=14, K=36

4. A man can row 6 km/hr. in still water. If the speed of stream is 2km/hr., it takes him 3 hours to row to a place and back. How far is the place?Ans:  8 km 

5. F(n) is a function...where f(f(n))+f(n)=2n+3.F(n)=0; find f(2012) ? 

6. How many vehicle registration plate numbers can be formed with digits 1,2,3,4,5(no digits being repeated)if it is given that registration number can have 1 to 5 digits ?Options: 205 100 325 105Ans: 325  

7. A merchant buys 20kg of wheat at rs.30.00 per kg and 40kg wheat at rs.25.00 per kg.He mixes them and sell one third of the mixture at rs.26.00 per kg. The price at which the merchant should sell the remaining mixture so that he may earn a profit of 25% on his whole outlay is..?Ans: 37

 

8. Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friendwill get the chocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers on two dice equals that number, the concerned person will get the chocolate. Rahul's choice was7, Ravi's choice was 9, Rajesh's choice was 10 and Rohan's choice was 11. Who has the maximum probability of winning the amount?A) Rahul b) Ravi c) Rajesh d) RohanAns: Rahul

9. Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?A) 24 inches b) 8 inches c) 20 inches d) 32 inchesAns: 24 inches

10. In month of jan 4 thursday and 4 sunday then on 1st jan of that month which will be the day?1. Monday2. Friday3.saturday

4. WednesdayAns: MONDAY

11. There is a 12*6 grid...grid contains 1*1 squares. What is d total number of squares..(consider 1*1,2*2,3*3,4*4,5*5,6*6 size squares as well).Ans: 217   

12. 5, 9, 12, 18, 26, 36, 47, 72, _?Ans:  5, 9, 12, 18, 26, 36, 47, 72, 75, 144 

13. F(x)=f(f(x))=f(x^2)....how many such functions with degree >2 existAns: Don’t Exist  

14. The length and breadth of a field is 300x400ft, if there are 3 ants on average per square inch of field, find the approximate number of ants in field.Ans: 3*17280000 ants  

15. The diagonal of a square is twice the side of equilateral triangle the ratio of Area of the Triangle to the Area of Square is?A) 3:8 B) 2:5C) 3:6D) 2:4Ans:  sqrt3/8  

16. A, B COMMON TO ALL THREE. THEN ATLEAST 1 ELEMNT COMMON TO 2 IE X1,X2,X2,X3,X3,X1. FINDMINIMUM ELEMENTS IN EACH GROUP.or 

17. There are 3 groups A,B,C2 members belong to all the three3 members belong to A&B3 members belong to B&C3 members belong to C& A

minimum possible number of members in any three.Ans: 4   

18. What is the probability of throwing 3 dices to get a sum of 10?Ans: 27/216 

19. Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?A) 1/72B) 1/9C) 25/216D)1/8Ans: 27/216 == 1/8 

20. From 52 cards 3 cards drawn randomly prob of getting 1 spade , 1 red queen and 1 black king??Ans: 0.00235 

21. In how many ways can 3 postcards can be posted in 5 postboxes?Ans: 5^3 

22. In how many ways can 5 postboxes hold 3 post cards?Ans: 3^5  

23. The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?A) 41 b) 42 c) 40 d) 43Ans: 40 

24. Two cyclist begin training on oval racecourse at same time the professional cyclist complete each lap in 4 sec noves take 6 minute how many minute after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12Ans: 12

 

25. Two points r there two person from A running to same direction with speed 20 km/hr. & 15/hr. respectively and from other end another person running to opposite direction with 30 km/hr.? Distance between them 100 km??At what time they will meet?Ans: 2.857 

26. Tim and Elan are 90km away from each other .they are starting to move towards each other simultaneously, Tim at speed 10kmph and Elan at 5kmph ,,if every hr. they double the speed ,what is distance that Tim will pass until he meets Elan?Ans: 60 

27. There are 10 stepping stones numbered 1 to 10. A fly jumps from 1st stone as follows: every minute it jumps to the 4th stone from where it started -that is from 1st it would go to 5th, from 5th it would go to 9th, from 9th it would go to 3rd, etc .where would the fly be at 60th minute if it starts at 1?Ans: 1

28. Given the following information who is youngest?C is younger than a; a is taller than b;C is younger than d;C is older than b;B is taller than c;A is older than d(1)d (2)b (3)a (4)cAns: B 

29. 1!+2!+3!...+50! Divided by 5! Remainder will be ? (0 or 33)Ans: 33  

30. If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?Ans: 3600 

31. An article manufactured by a company consists of two parts X and Y.

In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?a)0.6485  b)0.6565  c)0.8645 d)none of theseAns=c (0.8645)  

 32. There are six multiple choice questions in the examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and last two have 5 choices each?Ans: 3600 

33. The ratio of perimeter of an equilateral triangle having an altitude equal to the radius of the circle, to the perimeter of an equilateral triangle inscribed in that circle is ?Ans: 2:3  

34. Arun was all bent on building a new house. He carefully got the blue print of his house designed by his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?27*48/2*3=216  

35. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? A.2 b.5/2 c.3/2 d.1Ans: 2  

36. Roy is now 4 year older than Erik and half of that amount than Lewis. If in two years Roy will be twice as old as Erick, then in two year what would be Roy age multiplied by Lewis age??Ans: 48  

37. My name is PREET. But my son accidentally types the by interchanging a pair of letters in my name. What is the probability that despite this interchange, the name remains unchanged? A.5% b.10%

c.25% d.12.5%Ans: 10%  

38. In how many ways can 20 identical pencils be distributed among three girls soThat each gets at least 1 pencil?Ans: 171 

39. A sequence {An}is defined A(1)=0&A(n+1)=A(n)+2(n)WHAT IS VALUE OF A(100) (A)9902 (B)9900 (C)10100 (D)9904Ans: 9900  

40. The sequence {A (n)} is defined by A (1) =2 and A (n+1) =A (n) +2n. What is the value of a (100)Ans: 9902 

41. In a sequence of integers, A(n)=A(n-1)-A(n-2),where A(n) is the nth term in the sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S (1000), where S (1000) is the sum of first 1000 terms.Ans: 1 

42. In base 7, number is written only using digit0, 1, 6.a number 135in base 7 is 1*7^2+3*7+5=75in base10.what is sum of base7 numbers1234&6543in base 7? (A) 11101(B) 11110(C) 10111(D) 11011Ans: b) 11110 

43. Which of following true: A occur only B or C occur B occur D&E occur if C not occur g occur if A and F occur option A occur whenever F occur2) F never occur3) G not occur if D not occur  4) none of theseAns: G not occur if D not occur  

44. House1 is older than H2, H3 is taller than H4, and H4 is older than H1... (I)H1 is older than H3 (ii) H2 is taller than H4 (a) only 1 (b) both (c) neither (d) only2Ans: neither is true  

45. Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is

11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is:A) 3.50 b) 10.53 c) 1.17 d) 2.8Ans: 3.62 

46. The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?A) ARBSEUB) ARBESUC) ARBSUED) ARBEUSAns: B   

47. The milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk and half water ?Ans: 7:5 

48. Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki beach resort.They stand for group photograph if Mr smith never stand next to Mrs smith then how many way group arrange in row(A) 20!(B) 19! +18!(C) 18*19!(D) 2*19!Ans: C  

49. A father purchases dress for his three daughters. The dresses are of same colour but of different size .the dressis kept in dark room .What is the probability that all the three will not choose their own dress.Ans: 1/3  

50. An empty tank is filled with an inlet pipe 'A' in 42 minutes. After 12 minutes an outlet pipe 'B' is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe 'C' opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the

time taken to fill the tank?Ans: 58.5   

51. 16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?A) 41 b) 42 c) 40 d) 43Ans: 40  

52. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?A) 1 b) 6 c) 9 d) 5Ans: 5  

53. N! Have 13 zeros than what is the highest and lowest value of n?Ans: Highest value of N = 59 &        Lowest value of N = 55  

54. N is an integers and N>2 at most how many integers among N+2,N+4,N+5,N+6 and N+7 are prime integers?A) 1, b) 3, c) 2, d) 4Ans: 2

TCS PATTERN-54 SOLUTIONS1.Just put x=1 in both the equationsAnd now divide both the equations you will get remainder = 0   

2.Let the speed of the motorboat in still water be x kmph. Then, speed downstream = (x + 2) kmph. 

Speed upstream = (x - 2) kmph.:. 6/(x + 2) + 6/(x - 2) = 33/60 0r 11X2 – 240x – 44=011X2 – 242X + 2X –44 =0 or 11x(x – 22) + 2(x – 22) = 0or (x-22)(11x+2)=0 or x=22.:. Speed of motorboat in still water = 22 kmph. 

3. Follow this linkhttp://www.m4maths.com/11100-Directions-for-Q-1-to-Q-5-Refer-the-data-J-K-L-M-and-N-collected-stamps-They-collected.html 

4.speed in down stream=6+2=8km/hrspeed in up stream=6-2=4km/hrspeed=distance/timelet Xkm be the required distance(x/8)+(x/4)=3this gives x=8kms 

5.wrong question here f(0)=1then it will form a series f(0)=1f(1)=2;f(2)=3f(3)=4similary f(2012)=2013  

6.As we can form registration no. of 5 digit or 4 or 3 or 2 or 1 sofor 5 digit->5*4*3*2*1 for 4 digit-> 5*4*3*2 for 3 digit-> 5*4*3 for 2 digit->5*4 for 1 digit-> 5=120 + 120 + 60 + 20 +5=> 325 

7.Total cp = 20 * 30 + 40*25= 1600Sp = 125/100 * 1600= 2000Sp for 20kg mix = 26*20 =520

Rem sp = 2000-520 = 1480As this sp is for 40 kg = 1480 / 40 = Rs37 

8.Rahul has chosen 7, similarly Ravi-9,Rajesh-10,Rohan-11(1,1)(1,2)(1,3)(1,4)(1,5)(1,6) Sum of the digits are= 2,3,4,5,6,7(2,1)(2,2)(2,3)(2,4)(2,5)(2,6) Sum of the digits are= 3,4,5,6,7,8(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)Sum of the digits are= 4,5,6,7,8,9(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)Sum of the digits are= 5,6,7,8,9,10(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)Sum of the digits are= 6,7,8,9,10,11(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)Sum of the digits are= 7,8,9,10,11,12Among these 7 comes 6 times, 9 comes 4times, 10 comes 3times,11 comes only 2 times.So the maximum probability goes to Rahul 

9.Area of a rectangle= Area of the TriangleSo, l*b=1/2(b*h)or, 24*8=1/2(16*8)therefore 24 inches will be the answer 

10.Ans. mondayif we start the month on monday then only we are getting the 4 thursday and 4 sunday otherwise not getting. 

11.1*1 squares = 12*6 = 722*2 squares = 11*5 = 553*3 squares = 10*4 = 404*4 squares = 9*3 = 275*5 squares = 8*2 = 16 6*6 squares = 7*1 = 7Total squares = 217Or use formula - è [n*(n+1)*(3m-n+1)]/6 

12.5, 9, 12, 18, 26, 36, 47, 72, _?it is 5 ...... 12....... 26......... 47 12= 5+726= 12+2×747=26+3×7Next is 47+4×7=75 

and 9, 18, 36, 72 hence next 144Therefore 5, 9, 12, 18, 26, 36, 47, 72, 75, 144 

13.Does not exist as in question maximum power of x is 2.So, greater than 2 will not exist. 

14.As 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=172800001 sqr inch need 3 ant hence 17280000 sqr inch need  3*17280000 ants 

15.Let side of square is athen diagonal of square is {sqrt2a}given {sqrt2a}= 2*side of triangleso side of triangle = {sqrt2a}/2 i.e a/sqrt2area of triangle = sqrt3/4*side^2......according to formulanew area = sqrt3/4*{a/sqrt2}*{a/sqrt2} i.e.........sqrt3a*a/8area of square = a^2ratio = sqrt3*a^2/8a^2....i.e sqrt3/8 

16.+17.Group MemberA--> j,k,l,nB--> j,k,l,mC--> j,k,m,nans is 4 

18.+19.Possible event.......(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)Total 27 possible eventsSo probability is ..........27/216 

20.13C1*2C1*2C1/52C3 = 0.00235 

21.First post card can be posted in any of the 5 post boxes =5c1 wayssecond post card can be posted in any of the 5 post boxes =5c1 waysthird post card can be posted in any of the 5 post boxes =5c1 ways

number of ways=5c1*5c1*5c1=125=5^3

22.First post box can hold 3 post cards in 3c1 wayssecond post box can hold 3 post cards in 3c1 waysthird post box can hold 3 post cards in 3c1 waysfourth post box can hold 3 post cards in 3c1 waysfifth post box can hold 3 post cards in 3c1 waysso number of ways =3c1*3c1*3c1*3c1*3c1=3^5 

23.Total=800m16m per min means for 1m=800/16 =50min to climb10m per min means for 1m=800/10=80min to climb for paul .....the total time is 2hours==120min.... paul works only 1 min. but it rests 1 min. so now total work with rest 2 min. so then in 80 min it will be rest (80/2)=40 times.but in case of 50 minutes rest numbers will be less.here maximum number of resets are asked.so answer is 40(c) 

24.Professional time to complete 1 lap = 4 sec noves time to complete 1 lap = 6 minutes = 360 secnow,360/4 = 90 times professional complete its lap, where noves completes its lap 1 timeso, they meet again at starting point after 6 min,12 min,18 min 

25.20-15=55+30=35now s=35km/hr,d=100km,T=?s=d/t => t=100/38=20/7 hr 

26.From Question. we can see the speed of Tim is always double than speed of Elan. Therefore, Let the Speed of Elan= X, Thenspeed of Tim= 2X, and assume that both are covering different distance in time ="t"Given: Total distance= 90 KmTherefore, 2Xt+Xt= 90 km ( where xt=distance covered by Elan &

2Xt=distance covered by Tim) Hence, Xt= 30 km,But xt is distance covered by elan, Hence Distance covered by Tim is 2Xt= 60 kmans: 60 km 

27.1minute=1+4=51 minute=1+4=5step2 minute=5+4=9step3 minute=9+4=3step4 minute=3+4=7step5 minute=7+4=1step the same process is repeated 12*5 times hence at 60th minute fly would be at 1st step 

28.(2)b because c is younger than both a and d, and c is older than b also so finally b is younger. 

29.1!+2!+3!...+50! divided by 5!remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.so remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120).so remainder is 33. 

30.We have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C16P5*5C1=3600 

31.Probability of no defective of x= 91/100=.91Probability of non-defective of y= 95/100=.95So, probability of no defective product=.91*.95=0.8645 (C) 

32.3c1*3c1*4c1*4c1*5c1*5c1=3600for any one of first three option of Q.1 we have three options in Q.2 4 option in Q.3.....this goes on... 

33.Assume dat the side of first triangle is athe perimeter is 3aso the altitude is (sqrt(3)*a)/2

it is the radius of the circlenow we know radius of circumcircle of an equilateral triangle of a side =b/sqrt(3)nowb/sqrt(3)=(sqrt(3)*a)/2or 2b=3ab=3a/2perimeter is 3*(3a/2)so ratio is 3a:(9a/2)finally 2:3 

34.27*48/2*3=216 

35.Let Ronit’s present age be X years. Then, father’s present age = (X + 3X) years = 4X years.

(4X + 8) =5/2 (X + 8)8X + 16 = 5X + 403X = 24X = 8 Hence, required ratio = (4X + 16)/(X + 16)= 48/24= 2  

36.Firstly two equations from 1st sentence...Suppose Roy=x, Erik=y, Lewis=zSo x=y+4.... (1)2nd is x=z+2... (2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)Also after 2 years Erik and Roy relation will bX+2=2(y+2)... (3)So put this into 1st equation. U will get y=2...And then x=6, z=4(by substituting other)Now asking multiplication after two years of Roy n Lewis is (6+2)*(4+2) =48   

37.Ans: 10%son can interchange a pair in 10 combination out of which only one keps the name unchanged.

10 combinations for change are PRPEPEPTRERERTEE ETET

so the probability that despite this interchange, the name remains unchanged = 1/10 = 10%   

38.consider 3 girls as A,B,C THEN A+B+C=20, but each one should get atleast 1 pencil so giving 1 pencil to each student,the remaining pencils are 20-3=17now A'+B'+C''=17,number of non negative integers of A',B',C' are (17+3-1)C(3-1)so total Combinations are 19c2=19*9 = 171   

39.A(100)= A(99)+2(99)A(100)= A(98)+ 2(98)+2(99)A(100)= A(97)+2(97)+2(98)+2(99)||LYA(100)= A(1)+ 2(1+2+3+4+.......97+98+99)

NOW; 1+2+3.......+97+98+99= 99(2+98)/2= 4950(SUM OF AN A.P)

A(100)= 0+ 2(4950)= 9900    

40.A(100)=we can write A(99+1) as A(n+1) is given so i broke it in n+1 form.then A(99+1)=A(99)+2*99;in this way A(99)=A(98)+2*99*98

in this way....last will be A(1)+2*99*98*.....1now put the value 1+2(1+2+......+99)2+ 2*99(99+1)/2=9902   

41.actually answer is 1...consider the soln...given A(1)=1,A(2)=1.so, A(3)=A(2)-A(1) acc to the given formula A(n)=A(n-1)-A(n-2)A(3)=1-1=0.similarliy,A(4)=A(3)-A(2)=0-1=-1.A(5)=A(4)-A(3)=-1-0=-1.A(6)=A(5)-A(4)=-1-(-1)=0.after 6th term seq is repeating like...1,1,0,-1,-1,0...after every 6 termsso the sum of these 6 terms are 1+1+0+(-1)+(-1)+0=0.now we have to find sum of 1000 terms...now consider in splitted pattern,likesum of first 600 terms is 0...(as consider 1,1,0,-1,-1,0 as one sequence,now consider 166 seq i.e 166*6=996 terms)so the sum of first 996 terms is 0...after that 4 terms come i.e 1,1,0,-1so the sum of last 4 terms = 1+1+0+(-1)=1.   

42.Explanation:Convert the number from base 7 to base 10Base 7(1234) = base 10(466)Base 7(6543) = base 10(2334)Sum of 466 + 2334 = 2800Convert to base 7Base 10 (2800) ===> 11110 

43.3) G nt occure if D not occurea=>b or cb=>d & ef=>c not

g =>a & f1) a occure whenevr f :- depen on c where as 'a' can occure if 'c' not ..so this is not true2) f nevr occure => depnd on c only n c is indipendent ...if c not occure f will occure ....so this is also not true3) g not occure if d not:-g depnd on a & f ...if d not ocuure b will not occure (as b=>d&e) a will occure if c occure...if c occure f will not occure ...hence g will not occure...this is true  

44.(c)neither, is the answer.We can't relate heights of 2 & 4 coz relation b/w heights of 4 and 2 isn't given(4 is 'OLDER' than 2, we can't say anything about their height);also no relation is stated b/w ages of 1 & 3, so neither of i and ii is correct.    

45.30L+3Q=11.6730L+6Q=12.48------------3Q=.81 Q= .27from that L=0.362 cost of 10 kg apple is 10*.362=3.6  

46.AB**** =4! = 24 waysAE****=4! =24 ways next word is 49th soAR**** in alphabetical order **** will be BESUAns is ARBESU  

47.milk in A=4/7 water in A=3/7 let x quantity of mixture from A be added to Cmilk in B=2/5 water in B=3/5 let y quantity of mixture from B be added to Chence,milk added from a + milk from b= 4x/7+2y/5water added from a + water from b= 3x/7+3y/5these two shud be equal as ratio in c is same for milk nd watertherefore,(4x/7+2y/5)/(3x/7+3y/5)=1on solving,x/7=y/5or x:y=7:5 

48.(C) 19!*18bcoz along with mr and mrs smith can be arranged in 19!*2 (2 bcoz of mr and mrs smith arrangement) all together can be arranged in 20! ways so no mr and mrs smith can be arranged in 20!-19!*2 =19!*18 

49.Total selections=3!=6

Proper Selections: A B CA C BC B AB A C (ie. total 4)

Improper selection: B C A , C A B (ie. total 2)Probability for improper selection= 2/6 = 1/3 

50.let the tank be filled in n minutes after opening tap Cnow total part of tank filled=[(n/42)-(n/30)+(n/35)]now(12/42)-(6/30)+(6/42)+[(n/42)-(n/30)+(n/35)=1solve for n we get n=40.5 minutesthereforetotal time= 40.5min + 12min(when A was opened) + 6 min(when B was opened)= 58.5 min 

51.A person works only 1 min. but it rests 2 min. so now total work with rest 3 min. so than in 1 hour it will be rest 20 times and in next 1 hour 20+20=40 times it will take. 

52.ans is 5combinations of the 4 boxes likered, yellowred,greenred,blueyellow,greengreen,blue 

53.Here we have to consider only the 5,10,15,20.... these terms..so form (5,10,15,20,30,35,40,45,55 ) we got 1 no of zero from each.

Now from 25(5*5) and 50(5*5*2) we got 2 no of zeroes form each.so upto 55 factorial we get (9+4)= 13 zeroes.so 55! is the smallest value and 59! is the largest value.   

54.For N=3 we have - 5,7,8,9,10 so 2 primeFor N=4 we have - 6,8,9,10,11 so 1 primeFor N=5 we have - 7,9,10,11,12 so 2 primeFor N=6 we have - 8,10,11,12,13 so 2 prime& so on.... So max no of Primes are 2