1.In a hotel we can order two types of varities,but we can make 6 more variteis in home.One can choosethe four varities with two from hotel as must.Find how many ways one can order. a)14 b)15 c)56 d)28 As there 2 varities are fixed from hotel,so no of ways 2c2*6c2=15
2.Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape? If we are painting only 2 face of each cube then how many faces will remain unpaint??
3.If the list price of a book is reduced by Rs 5 then a person can buy 2 more books for Rs 300.the original cost of the book is a. 25 b. 30 c. 15 d. 20 A list price B No of book AxB = 300 (A-5)x(B+2) = 300 2A-5B+AB-10=300 2A-5B=10 (2A-10)A=300x5 AA-5A = 150x5 = 750 A=30
4. Ahollow cube of size 5 cm is taken with a thickness of 1 cm. it is m ade of smaller cubes of size 1 cm. if 3 faces of the t he outer surface of the cube are painted totally ho w many faces of the smaller c ubes remain unpainted? 525 900 825 513 No. of small cubes required to make the bigger cube= (5*5*5-(5-2)*(5-2)*(5-2))/1*1*1 = 98 Small cubes surfaces on one side of bigger cube= 5*5= 25 Total no of sides of small cubes= 98*6 = 588 But 3 faces of the outer surface are painted i.e. 3*25= 75 surfaces of smaller cube are painted already So remaining surfaces to be painted are= 588-75=513
5. Given 3 lines in the plane pla ne such that the points of intersection from a triangle with sides of length 20, 20 and 11 the number of points equidistant from all the 3 li nes is 0 3 1 4 4 1 point inside the triangle and other three outside the triangle
6. 80 370 ? 1550 2440 3530 a) 900 b) 840 c) 750 d) 860 answer is d) 860 10^2 - 20 = 80 20^2 - 30 = 370 30^2 - 40 = 860 40^2 - 50 = 1550 50^2 - 60 = 2440 60^2 - 70 = 3530.
7. A power unit is by the bank of a river 1500m wide. It is required to construct a po wer plant on the side of the river opposite to the power unit and 30 00mfrom the unit. A cable has to be laid lai d from the power unit to the po wer plant. The cost of laying the cable under water and on the land is Rs 100 per m and Rs 10 per m respectively. If we want to minimize the total cost of laying the cable, where should the plant be located? 750 m from the river bank 1500 m from the river bank 1200 m from the river bank 3000 m from the river bank since laying the cable under water is costly, so we should lay it al ong the perpendicular direction to the width of the river for reducing the cost, yet we have to maintain the distance of 3000 m between the power unit and power plant so power plant should be located at 1500 from the river bank.
8. If we subtract a number with y, we get 4 increase of number, once it got divided by y itself... Find that number?? according to the given condition x-y=4+(x/y) we need to work with the options here. subs x = 12 first 12-y=4+(12/y) solving this eq, we get y=6,2 so the number x will be 12 with y = 2,6 this answer is given by MONISHA and VADIVELAN M and i s correct answer
9. 8 6 17 14 35 31 75 _ 143? 6*2+2=14 4*2+3=31 31*2+4=66
10.How many 9 digit numbers are possible by using the digits 1,2,3,4,5, which are divisible by 4 if repetition of digits is allowed? 5^8 last two is divisable by 4 is condition. the possibility is 5(12,24,44,32,52) 5*5*5*5*5*5*5*5
11. There was a grandmother in a village who had two grandchild. Upon asking her younger grandchild's age she told that she is as older as many days old as her elder grandchild's age in weeks and as many days as her own age in years. The sum of the three is 130. then how old is the younger child? answer: grandmother age - 127 year. elder grand child - 127 weeks ~ 2.5 year younger child - 127 days ~ .5 year 12. The size of a program is N. And the memory occupied by the program is given by M = square root of 100N. If the size of the program is increased by 1% then how much memory now occupied? new pgm size=N+N/100 new memory=square root of 100(N+N/100)=square root of 101N
13. 33 people {a1, a2,...........,a33} meet and shake hands in a circular fashion. In other words, there are totally 33 handshakes involving the pairs, {a1,a2}, {a2,a3},..........,{a32, a33}, {a33, a1}. Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is a.11 b.13 c.24 d.50 11 the persons selected in set will be a1,a4,a7,a10,....... a1,a4,a7,a10,.... ... a25,a28,a31
14. 49 members attended the party. In that 22 are males, 17 are females. The shake hands between males, females, male and female. Total 12 people given shake hands. How many such kinds of such shake hands are possible? a) 122 b) 66 c) 48 d)1 28 12 peoples given hankshakes.so only two persons hankshakes with each other. so ues COMBINATION (BCOZ IN QUESTION SELECTION IS ASKING.)12c ASKING.)12c2=(12*11)/(2* 2=(12*11)/(2*1)=66 1)=66
15. Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter? a) 8 b) 20 c) 16 d) 1 5 let us assume peter's present age is x and paul,s y=35-x. difference of their ages i s x-(35-x)=2x-35 x-(35-x)=2x-35 peter's age was 35-x when he was paul's age and paul was of 35-x-(2x-35)=70-3x 35-x-(2x-35)=70-3x peter's present age is 2 *(70*(70-3x) 3x) which is equal s to x so, x=140-6x then x=20
16. Make six squares of the same size using twelve match-sticks. (Hint : You will need an adhesive to arrange the required figure) cube contains the 6 squares and 12 sides..... with 12 match sticks we can make a cube which consists of 6 squares
17. A solution of 25 liters contain 20% sugar, if 10 liters of the solution is evaporated, find the percentage of sugar in the final solution. it is 33.33% given 25 liters of sol has 20% sugar . qty of sugar =(20%/100%)*25 =5 lit of sugar (assume sugar qty in liter for easy calculation ). therefore 25 lit sol contain 20 lit of water and 5 liter of sugar . now the sol boils losing 10 liter of water . therefore the new 15 liter sol contains 10 liter water and 5 liter sugar . there new % of sugar is 5/15 * 100 =33.33%
18. A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet o nly if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? a) 50 b) 8 c) 60 d) 42 It is not given that how many of these items are gloves and how many are hats, if we consider that all the items are gloves then according to my opinion 32+25+2 = 59 gloves, she must take out to make sure she has a pair of each color.
19. A man was found murdured on 26.01.2008 afternoon. 1.His wife called police. 2.police questioned everyone. 3.Wife:sir,i was sleeping when the murder took place. 4.Cook:I was cooking. 5.Gardner:i was picking vegetables. 6.House-maid:i went to the post office. 7.Children:we went to the play. 8.Neighbour:we went to a marriage. police arrest the murderer immediately. who is it? the murderer is house maid, because 26th of January is national holiday so post office should be closed in that day and house maid said to the police that he/she went to post office
20. A father and his son go out for a walk-and-run every morning around a track formed by an equilateral triangle. The fathers walking speed is 2 mph and his running speed s peed is 5 mph. The sons walking walki ng and running speeds are twice that t hat of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti-clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as so on as the father starts wal king, the son starts running. Both complete the course i n 45 minutes. For how long does the fat her run? Where do the two cross eac h other? Let father runs t hours and walks (0.75-t) hours, then according to the given condition 5t+2(0.75-t)=x (for father) 10(0.75-t)+4t=x (for son) on comparing these two we will get t=2/3 hrs=40 min
on taking t=2/3 hrs, x=3.5 miles so father will run for 2/3 hrs = 40 min now let the two will cross each other after time x then according to the given condition 5x+4x=3.5 so x = 7/18 hrs = 70/3 min in this much time father will run 5*7/18 = 35/18 miles and son will walk (7/2)-(35/18) = 28/18 = 14/9 miles
21. There are seventy clerks working in a company, of which 30 are females. Also, 30 clerks are married; 24 clerks are above 25 years of age; 19 married clerks are above 25 years, of which 7 are males; 12 males are above 25 years of age; and 15 males are married. How many bachelor girls are there and how many of these are above 25? Distribution Total clerk = 70, Male = 40, Female = 30, Married clerks = 30, Male = 15, Female = 15, 25 plus married clerks = 19, Male = 7, Female = 12, 25 plus clerks = 24, Male = 12, Female = 12, 25 plus unmarried clerks = 5, Male = 5, Female = 0 so Bachelor girls = 15, none of them is above 25
43. Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the leng th of faster train? rel speed = 50-32=18 km/hr = 18000/3600= 5m/sec length of train = 5*15 =75 m
22. A man spends half of his s alary on household expenses, e xpenses, 1/4th for rent, 1/5th for travel ex penses, the man deposits the rest in a b ank. If his monthly deposits in the bank amount 50, what is his monthly salary? (a) Rs.500 (b) Rs.1500 (c) Rs.1000 (d) Rs. 900 Rs 1000. A man spends half of his salary ( 500) on household expenses, 1/4th ( 250) for rent, 1/5th (200) for tra vel expenses, the man deposits t he rest (50) in a bank
23. 2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges, 2 bananas, and 1 apple costs Rs 10. What is the cost of 3 oranges, 3 bananas and 3 apples? (a) Rs10 (b) Rs15 (c) Rs20 (d) Rs25 2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges, 2 bananas, and 1 a pple costs Rs 10. the cost of 5 oranges, 5 bananas and 5 apples = 15+10=25 the cost of 3 oranges, 3 bananas and 3 apples = 25 *3/5=15
24.If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage. (a) 40% (b) 55% (c) 35% (d) 30% let the selling price is 100 rupee on giving 25 % discount the price will be 75,on selling the object in 75 rupee profit = 25 % so original cost will be 75*100/125 = 60 now on giving 10 % discount selling cost will be 90 it means 30 rupee gain on an investment of 60 rupee so profit on investment = 30*100/60 = 50 % (correct answer) none of the option is correct
25. A man, a woman, and a child can do a piece of work in 6 days. Man only can do it in 24 days. Woman can do it in 16 days and in how many days child can do the same work? (a) 8 (b) 14 (c) 16 (d) 18 a man ,a woman a child do 6 days 1 work 1 day 1/6 part man can do 1 day 1/24 woman can do 1/16 so child can do 1 day (1/6-1/24-1/16)=1/16 so child can do 16 da ys
26. A pizza shop, there were 2 kinds of pizzas available. But now they have introduces 8 new types, a person buy two different type pizzas of new type in how many ways he can select? (a) 24 (b) 43 (c) 56 (d) 58 a person buy two different type pizzas of new type so methods will be 8*7/2 = 28
27. A box of 150 packets consists of 1kg packets and 2kg packets. Total weight of box is 264kg. How many 2kg packets are there? (a) 100 (b) 114 (c) 200 (d) 208 114. A box of 150 packets consists of 1kg pa ckets and 2kg packets. Total weight of box is 264kg. If all boxes are of 1 kg, wt will be 150 kg. Diff = 264-150 =114. so 114 boxes have wt of 2 k g instead of 1 kg.
28.There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 80 , 160... in tank B.( At the end of fir st hour, B has 10 litres litre s , second hour it has 20, a nd so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely? (a) 26 hrs (b) 25 hrs (c) 5 hrs (d) 27 hrs There are two water tanks A and B, A is much smaller than B. W hile water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160... in tank B.( At the end of first hour, B has 10 litres , second hour it has 20, and so on). If tank B is 1/32 filled after 21 hours, . then tank B is 1/16 filled after 22 hours tank B is 1/8 filled after 23 hours tank B is 1/4 filled after 24 hours tank B is 1/2 filled after 25 hours tank B is fully filled after 26 hours
29. There are 10 reading spots in a room. Each reading spot has a round table. Each round table has 4 chair. If different no of persons are sitting at each reading spot. And if there are 10 persons inside the room then how many reading spots donot have atleast a single reader. (a) 5 (b) 6 (c) 7 (d) None 10 reading spots and 4 chairs ea ch total 10 persons different no. of seating must so 1st-1person 2nd-2person 3rd-3person 4th-4person by above way 10 peoples are seated so empty chairs = 10chairs - 4chairs = ans: 6chairs
52. Middle earth is a fictional land inhabited by Hobbits, Elves, dwarves and men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games . The game is as follows . A tournament is one where out of the t wo teams that play a match, the on e that loses get eliminated. The matches are played in different differe nt rounds where in every round , half of the teams get eliminated fro m the tournament. If there are 8 rounds played in a knock-out knoc k-out tournament how many matches were played? played? (a) 257 (b) 256 (c) 72 (d) 255 for two teams one will be selected and one will be eli minated so for 8 rounds 128 matches=> 64 match=> 32 =>16 => 8=>4=>2=>1 totally 128+64+32+16+8+4+2+1=255 matches were played
53.It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color? (a) 2 (b) 3 (c) 48 (d) 25 WILL BE 3 FOR SURE................ BCOZ WHEN WE TAKE OUT 3 SOCKS IT WILL BE ALWAYS OF TWO SAME COLOUR.
54. 23 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence. (a) 22 (b) 23 (c) 44 (d) 46 answer is 23 1st person with all 22 and 23 rd with 1 so ans 23
55. Which is the smallest no divides 2880 and gives a perfect square? (a) 1 (b) 2 (c) 5 (d) 6 we go by options when u divide 2880/5=576 576=24*24(perfect 576=24*24(pe rfect square)
56. The grandfather has three grandchildren, two of their age difference is 3, eldest child age is 3 times youngest child’s age and eldest child’s age is two times of s um of other two children. What is the age of eldest child? (a) 5 (8) 10 (c) 8 (d) 15 The 2nd condition given is wrong it should be two more than the age of other two children... Let the three grandchildren age be a,b and c Thus, a is youngest, c is eldest. c = 3a.........(i) c = 2+(a+b)..........(ii) => 3a = 2+a+b => 2a = 2+b Thus, the ages are..... a, 2a-2 , 3a. Two of their difference is 3. Thus, a- 2 =3 or a+2 =3 or 2a =3 a =5 or a =1 or a =3/2. Thus ages are, 5,8,15 or , 1,0 3 (not possible). or 3/2, 1, 9/2 (not possible.). The answer should be 15
57. 6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. hence the current average age h as become 45. find the age o f seventh person? (a) 69 (b) 70 (c) 40 (d) 45 ANS WILL BE 69...... SOLN- SINCE AVG AGE OF 6 PERSONS AFTER T WO TEARS IS 43....SO PRESENT AVG AGE WIL BE 41 YRS..THEREFORE TOTAL AGE=41*6=246.....NOW AGE=41*6=246... ..NOW THE 7 TH PERSON JOINS IN AND THE CURRENT AVG BECOMES 45..THEREFORE TOTAL CUURENT AGE=45*7=315.. THE 7TH PERSON AGE WILL BE (315-246)=69...
58. 3, 22 , 7, 45, 15, ? , 31 (a) 45 (b) 90 (c) 91 (d) 35 91 should be the answer...... 3*2 + 1 = 7 the digit one after other. 22*2 + 1 = 45. same as 45*2 +1 = 91
59. A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. 2 5%. However, as it turned out , 50% of the components were rejected. What is the loss to the manufacturer? (a) Rs.12000 (b) Rs.13000 (c) Rs.14000 (d) Rs.15000 Sale according to 5% loss = 1900*25 = 47500 original production cost = 47500/1.25 = 38000 Sale according to 50% loss = 10000* 25 = 25000 so loss = 38000-25000 = 13000
60. In Tnagar many buildings were under residential category.for buildings they number as 1 to 100. For shops, corporation numbered between 150 and 200 only prime numbers. how many time 6 will appear in building numbering? (a) 10 (b) 20 (c) 8 (d) 19 Building numberings are 6, 16, 26, 36, 46, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 86, 96 Shop numbering are 163, 167 Since they are asking only for buildings so answer will be 20 ( shop numbers will not be counted) Ans: 2
61. A man divides Rs.8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew, how much does each daughter receive? (a) Rs.800 (b) Rs.600 (c) Rs.200 (d) Rs.700
THERE WILL BE THREE EQUATION.. 1)5SON+4DAUGHTER+2NEPHEW=8600 2)1DAUGHTER=4NEPHEW 3)1SON=5NEPHEW BY SOLVING EQUATION 1,2,3 WE GET EACH NEPHEW WILL GET =200.. PUTTING THESE VALUE IN EQU 2 WE GWE E ACH DAUGHTER WILL GET RS 800..
62. A train starts full of p assengers. At the first station, it drops one-thir d of the passengers and takes 280 mor e. At the second station, it drops one-half of the new total and takes 12 more. On arriving at the third station, it is found to have 248 passengers. Find the number of passengers in the beginning. (a) 240 (b) 248 (c) 280 (d) 288 ans:d the passenger in the train is =x after 1 stop=x-x/3+280 after 2 stop---- (x-x/3+280)/2+12=248 solve it and ans =288
63. Two unemployed young men decided to start a business together. They pooled in their savings, which came to Rs. 2,000. They were both lucky, their business prospered and they were able to increase their capital by 50 per cent every three years. How much did they have in all at the end of eighteen years? (a) Rs. 22,781.25 (b) Rs. 24,150.25 (c) Rs. 28,140.50 (d) Rs. 18,000 Total duration = 18 years increment period = 3 years so no. of increments = 18/3 = 6 output = 2000 * (1.5)^6 = 22781.25
64.If an airplane starts at point R and travels 14 miles directly north to S, then 48 miles directly east to T, what is the straight-line distance (in miles) from T to R? (a) 25 (b) 34 (c) 50 (d) 2500 ans:c (14^2+48^2)^1/2 = (196 + 2304)^1/2 = (2500)^1/2 = 50
65.A scientist was researching into animal behavior in his laboratory. He was very interested in studying the behavior of bears. He travelled a mile to the north and reached the north pole. There he saw a bear. He then followed the bear for an 1 hour to the east with a speed of 2km/hr. After that he travelled south and reached his laboratory in 2 hours. What was the colour of the bear? (a) Black (b) White (c) Red (d) Blue This question is based on bear on poles so it should be polo bear and the color of polo bear is white. Option B
66. Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian Athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game . How many teams participated in the race? (a) 30 (b) 32 (c) 41 (d) 54 2^5=32. so ans is 32
67. A Roman was born the first day of the 35th year before Christ and died the first day of the 35th year after Christ. How many years did he live? (a) 70 (b) 69 (c) 71 (d) 72 ans is 69, not 71. 35 to 0 =35 years now 0 to 34=34 years total=35+34=69
68. There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is a)1/2 b)14/19 c)37/38 d)3/
For the probability of getting a red ball is maximized, shift 9 red balls from one box to other box with 10 green balls. balls. Then prob of getting red ball will be 1*1/2 + (9/19)*(1/2) =1/2 +9/38 =28/38=14/19 .. option b
69. A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probabilit y that Q is closer to the ce nter of the circle than the peripher y? a) 0.75 b) 1 c) 0.5 d) 0.25 Since according to requirement we have to locate Q closer to center in comparison to the circu mference, for doing this we shall make a circle in that board whose radius will be half of the radius of dartboard. now we will compare the area of inner circle to the total ar ea Answer of DIPIN is correct area of whole circle = pi*(1 foot)^2 = pi (this is according to formula area = pi*(radius)^2 similarly area of inner circle = pi*(1/2foot)^2 = pi/4 so ratio of areas of these two circles will be t he probability and that is ¼
70. Here 10 programmers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed? a) 16 b) 6 c) 10 d) 60 10
71. A man goes 50Km 5 0Km north , then turned left walked 40Km, then turned right ? In which direction he is? a) North b) South c) East d) Wes 5okm-north-->north left-west--->west turned right-north--->north(ans
72. There is 7 friends (A1, A2, A3....A7).If A1 have to have shake with all without repeat. How many handshakes possible? a) 6 b) 21 c) 28 d) 7 a1 with (a2, a3,a4,a5,a6,a7) 6 handshakes
73. 20 men handshake with each other without repetition. What is the to tal number of handshakes made? a) 190 b) 210 c) 150 d) 250 19*20/2=190
74.A game is played between 2 players and one player is declared as winner. All the winners from first round are played in second round. All the winners from second round are played in third round and so on. If 8 rounds are played to declare only one player as winner, how many players are played in first round? a) 256 b) 512 c) 64 d) 128 8 rounds means 128-64-32-16-8-4-2-1 128-64-32-16-8-4-2-1 so 128matches were played in first r ound teams= 128*2=256
75.Find the value of @@+25-++@16, where @ denotes square and + denotes sqrt. @ = ² and + = √ {[√25]²}² – √√(16)² = {[5]²}² – √√(256) = {[25]}² – √16) = 625 – 4 = 621
76. If f(0)=1 and f(n)= f(n-1)*n, find the value of f(4) f(0)=1 since f(n)=f(nf(n)=f(n-1)*n 1)*n so f(1)=f(0)* f(1)=f(0)*1=1*1=1 1=1*1=1 f(2)=f(1)*2=1*2=2 f(3)=f(2)*3=2*3=6 f(4)=f(3)*4=6*4=24....
77. In the word ECONOMETRIC S, if the first and second , third and forth ,forth and fifth, fifth and si xth words are interchanged up to the last letter, what would be the tenth letter fro m right? from right 10 th letter is O so third,fourh are interchanged O becomes N. so answer is "N
78. The cost of one pencil, two pens and four erasers is Rs.22 while the cost of five pencils, four pens and two erasers is Rs.32.How much will three pencils, three pens and three erasers cost? et the cost of 1 pencil, 1 pen and 1 eraser are respectively x, y, z. Then acc ording to the given condition 1x + 2y + 4z = 22 5x + 4y + 2z = 32 on adding these two equations we get 6x + 6y + 6z = 54 or 3x + 3y + 3z = 27
79.The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? n unit's place, the 3's are: 3, 13, 23 ... 73 103, 113, 123 ... 173 ... 703, 713, .... 773 => total number of 3's in unit's place is 8*8 = 64 in 10's place (that's 8 in decimal), the 3's are: 30, 31, 32... 37 130, 131, ... 137 ... 730, 731, .... 737 => total number of 3's in 10's place is 8*8 = 64 in 100's place (that's 64 in decimal), the 3's are: 300, 301, ... 307 310, 311 ... 317 ... 370, 371 .... 377 => total number of 3's in 100's place is 8*8 = 64 thus, the total number of 3's in total is 64 + 64 + 64 = 192
80. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color? a) 2 b) 3 c) 48 d) 25 3. when I take out 2 socks, they can be of same color or of 2 different colors. But third sock will definitely make pair with one of earlier t wo socks.
81. How many 9 digit numbers are possible by using the digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed? a) 57 b) 56 c) 59 d) 58 For a number to divisible by 4, the last two digits have to be divisible by 4 So, the units digit cannot be 1, 3 or 5 If the units units digit is 2, only 12, 32 or 52 are acceptable as the last two digits If the units digit is 4, only 24 and 44 are acceptable as the la st two digits. So, total 5 cases 12,24,32,44,52 are possible for the la st two digits. Now, the first 7 digits of the 9 digit number can be filled in 5^7 ways as ea ch place can be filled by 1, 2, 3, 4 or 5. So, desired answer = 5^7*5 = 5^8
82. 23 people are there, they are shaking hands together, how many handshakes possible, if they are in pair of cyclic sequence. (a) 22 (b) 23 (c) 44 (d) 46
this question is based on cyclic sequence so number of handshakes = n = 23 (last person will get a handshake with the first person. if these persons would be in a straight line then no. of methods = 23-1 = 22 similarly for a random handshake answer will be 23*22/2*1 = 253
83. The pace length P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pace length in meters. Bern ard knows his pace length is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed in kmph. a) 23.62 b) 8.78 c) 11.39 d) 236.16 n/P = 144 n = 144 * P P = 1.64 n = 144 * 1.64 = 236.16 approx 236 steps per minute we are ta king n in integer for it represents no. of steps now v = d / t v = 1.64 * 236 meter/minute v = 387.04 meter / minute or v = (387.04/1000)/(1/60) or v = 387.04*60/1000 = 23.2224
84. Anoop managed to draw 7 circles of equal radii with their centers on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square. a) 1:(4+ 7v3) b) 1:(2+ 6v2) c) 1:(2+ 7v2) d) (2+ 7v2):1 et the radius of circle be r let the side of square be a then diagonal of square= a*sqrt(2) This diagonal length = 12*r + 2r * sqrt(2) (because the extreme circle's radius is perpendicular to side of square.) Thus we get 12*r+2r*sqrt(2)=a*sqrt(2) r(6*sqrt(2)+2)=a r/a=1/(6*sqrt(2)+2) Thus ratio: r:a = 1:(6 *sqrt(2)+2) Ans: 1:(6*sqrt(2)+2
85.A collection of points poi nts P in the plane , a 1-set is a point in P that can be separated from the rest by a line, .i .e the point lies on one side o f the line while the others lie on o n the other side. The number of 1 -sets of P is denoted by n1(P). The minimum val ue of n1(P) over all configurations P of 5 points in the plane in general position (.i.e. no three points in P lie on a line) is a) 3 b) 5 c) 2 he meaning of this question is little complicated. In easy la nguage the question should be: There are some points in the plane. We have to make a separation between these points by forming a line in suc h a way that one point could be separate from the others. No 3 points are in a line. Maximum no of methods for plotting the line and minimum no of methods for plotting the line will be (arrangement of points i s your choice) Now Answer Is: For Maximize: The number of methods, Points should be drawn in the circu mference of the CIRCLE So a nswer would be the number of total point in the plane. For minimize: The number of methods we should draw 3 points in a TRIANGLE and all other point inside this triangle in such a way that no 3 points could be in a line. If it will be allowed to draw the points in a li ne then minimum possibilities will be 2 only, because if we take al l points in a line then you can separate only the corner points from the others. For example If we have 10 points then maximum possibilities = 10 and minimum = 3 similarly for 5 points Max = 5, Min = 3 for 19 max= 19 Min = 3
86. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every
respect. They receive identical salaries ans also write code at the same rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total? a) 6 b) 18 c) 72 d) 1 2 No of people time work 12 12 12 72 x 72 Work = No of people * time i.e. ( P1 * T1 ) / W1 = ( P2 * T2 ) / W2 (12 * 12 ) / 12 = ( 72 * x ) / 72 X = 12
87. On the planet Oz, there are 8 days in a week- Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 12:40 am. Since total hours in a day = 36 and as on earth, the hour hand covers the dial twice every day. so there will be 18 numbers from 1 to 18 in the clock. when the time will be 12:40, two hands of the clock will make an angle of 20*4 = 80 degree, here 20 is the angle between t wo numbers in the clock. now for 80 min, advancement of the hour hand will be (20/90)*40 = 80/9 so total angle = 80 + (80/9) = 800/9 = 88.889 degree if we consider the obtuse a ngle, then it will be 360-88.889 = 271.111 degree
88. Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19th century. These seem to have attacked the tomato crops in Engla nd this year. The tomato cro ps have reduced and the price of the crop has risen up . The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month? a) $27 b) $ 18 c) $45 d) $ 486 difference of cost in one box = 45-27 = 18 so for 27 boxes difference = 18*27 = 486
89. A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments. To identify the mice, the lab has prepared labels with numbers 1 to 100, by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degree Celsius. Also, not more than 2 mice can be caged together and each cage must be at least 2 sq.ft in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times the tag is numbered '4' used by the lab in n umbering these mice? a) 9 b) 19 c) 20 d) 2 1 count as 4,14,24,34,44,54,64,74, 4,14,24,34,44,54,64,74,84,94 84,94 then 40,41,42,43,45,46,47,48,49..so 40,41,42,43,45,46,47,48,49..so ans is 19
90. A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters at 10 meters per minute. However, the toy train is defective and it now produces onl y two different tunes at random. What are the odds that the toy train produces 4 consecutive music tunes of the s ame type? a) 1 in 16 b) 1 in 4 c) 1 in 8 only two different tunes are t here, so for making 4 consecutive music tu nes of the same t ype, probability = (1/2)(1/2)(1/2)(1/2)*2 = 1/8 last 2 is because of the two case (1) first tune all 4 times (2) second tune all 4 times but here the question is based on odds, so answer should be (1/8)/[(1-(1/8)] = 1/7
91. 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Answer 12 is correct. because if we take person a1 in the set then it will cover a36 and a2 for shaking hand.similarly if we take person a4 in the set then it will cover a5 and a3 for shaking hand and so on, so minimum 12 persons are required to make shake hand with rest of the people complete
92. A and B play a game of dice between them. The dice dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances c hances of winning P(A wins) = P(Die 1 lands red) * P(Die 2 lands red) + P(Die 1 lands blue) * P(Die 2 lands blue) So if r represents the number of red faces on the 2nd die and we want P( A wins) to be 0.50 (50%), then 0.50 = 4/6 * r/6 + 2/6 * (6-r)/6 0.50 = 4r/36 + (12-2r)/36 18/36 = (12-2r)/36 18/36 = 12/36 - 2r/36 6/36 = 2r/36 6 = 2r 3=r
93. Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins. The diameter of the coins should be at least 64mm and not exceed 512mm. Given a coin, the diameter of the next larger coin is at least 50% greater. The diameter of the coin must always be an integer. You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design? 5 9 6 8 64mm.........1st c oin 64mm.........1st 64+32=96.....2nd 64+32=96.....2n d c oin 96+48=144....3rd 96+48=144....3r d c oin 144+72=216...4th coin 216+108=324..5th coin 324+162=486..6th coin 486+50%of 486 exceeds 512 so 6 coins can be designed
94. A is the father of B. C is the son of D. E is the t he brother of C while D is the sister of B. how ho w is B related to E cannot be determined b'coz it is not given whether B is male or female. B is either 'aunt' or 'uncle' of E
95. In a family there are some boys and girls. All boys told that they are having equal no of brothers and sisters and girls told that they are having twice the no. of brothers than sisters. How many boys and girls present in a family? let there r b boys and g no of gals so ,when the boy is counting ,then b-1=g when the gal is counting, then b=2(g-1) so , solving above 2 eqn, we get g=3 and b=4
96. Lion tells lie on Monday, Tuesday, and Wednesday. Rat tells lie on Thursday, Friday and Saturday. Both of them speak truth on other days. Lion tells, Yesterday was one of the days which I tell lying. Rat also tells, Yesterday was one of the days which I tell lying What day was yesterday? Lion speak lies on Monday, Tuesday, Wednesday; Lion speak truth on Sunday, Thursday, Friday, Saturday; Rat speak truth on Sunday, Monday, Tuesday, Wednesday; Rat speak lie on Thursday, Friday, Saturday; Suppose, Lion tells truth on Thursday that Yesterday(Wednesday) was one of the day which he/she tell lying. Then Rat tells lie on Thursday that Yesterday(Wednesday) was one of the day which he/she tell lying. So Yesterday is Wednesday
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97. A vendor sells 1 apple for 1 penny, 2 grapes for 1 penny, 3 bananas for 1 penny. A man spends 7 penny and gives equal amount of fruits to each of his three daughters. What is the possible number of fruits each daughter ge ts? He buys 3 banana for 1 penny. 6 grapes for 3 pennies. 3 apples for 3 pennies. and then gives 1 banana , 2 grapes and 1 apple to each daughter
98. There is a die with 10 faces. It is not known t hat fair or not. 2 captai ns want to toss die for batting selec tion. What is the possible solution among the following? a) If no. is odd it is head, if no. is even it is tail b) If no. is odd it is tail, if no. is even it is head he ad c) Toss a die until all the 10 digits appear on o n top face. And if first no. in the sequence is odd then consider it as tail . If it is even consider it as head First of all it should have been given in the question that there are i ntegers from 1 to 10 written in the faces, and since it is not known that die i s fair or not, so (c) should be t he correct option
99. Amrith told to Anand in front of a Photo that "He is the son of my father’s son". Find who is in the picture if amrith have no brothers and sisters. a) Amrith himself b) Amrith's Uncle c) Amrith's Father d) Amrith's son d Amrith's father's son is Amrith His son is in the picture
100. Middle earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and elves are peaceful creatures that prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournament is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds, where in every round; half of the teams get eliminated fro m the tournament. If there are 8 rounds playe d in knock out tournament, how many matches were played? a) 257 b) 256 c) 72 d) 255 256->128->64->32->16->8->4->2->1 Thus initially ter wer 256 teams. But wat is askd is the numbr of matches that were played to rea ch the winner. The number of matches for 8 rounds is: 128->64->32->16->16->8->4->2->1 128+64+32+16+8+4+2+1=255 ans
101.10 people are there, they are shaking hands together, how many hand shakes possible, if they are in no pair of cyclic sequence. a) 45 b) 9 c) 12 d) 10 a)45 1st person shakes hand with 9 others=9 ha ndshakes then 2nd person shakes hand with 8 others(ie excluding 1st person)=8 handshakes .... finally 9th person=1 hanshake and 10th person=0 handshake so total=9+8+7+6+5+4+3+2+1=45 handshake
102. A speaks truth 70% o f the time; B speaks truth 80% of the time. What is the probability that both are c ontradicting each other? p(a)=0.7 p(b)==0.8 as both are independent events,the pro to contradict each other is: a)a tells truth while b tells fal sei.e.(0.7* sei.e.(0.7*0.2)+ 0.2)+
b)a tells false while b tells truth i. e.(0.3*0.8) results 0.38
103. In a family 7 children don’t eat spinach, 6 don't eat carrot, 5 don't eat beans, 4 don't eat spinach & carrots, 3 don't eat carrot & beans, 2 don't eat beans & spinac h. One doesn’t eat all 3. Find the no. of children do not spinach only=2 do not carrot only=0 do not beans only=1 do not spinach & carrots only=3 do not beans & carrots only=2 do not spinach & beans only=1 do not all three=1 total 10 children(2+0+1+3+2+1+1
104. There are 9 cards. Arrange them in a 3*3 matrix. Cards are of 4 colors. They are red, yellow, blue, green. Conditions for arrangement: one red card must be in first row or second row. 2 green cards should be in 3rd column. Yellow cards must be in the 3 corners only. Two blue cards must be in the 2nd row. At least one green card in each row YRG BBG YGY
105. Is z less than w? z and w are real numbers. (I) z^2 = 25 (II) w = 9 To answer the question, a) Either I or II is sufficient s ufficient b) Both I and II are sufficient but neither of the m is alone sufficient c) I & II are sufficient d) Both are not sufficient b Neither is alone sufficient because they show no relation between z and w But when both are considered we get value of both z and w, so can answer the qn
106. A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the are of t he larger field is greater gre ater than the area of the s maller field by what amount? (a) 6K (b) 8K (c) 12K (d) 7K answer :7k area of small =k area of large 8k result = 8k-k =7k
107. Nine equal circles are enclosed in a square whose area is 36sq units. Find the area of each circle pi square units side of square 6 units diameter of circle 2 units radius of circle 1 unit area of circle pi*1*1=pi(3.14) sq unit
108. Amongst Ram, Sham and Gobind are a doctor, a lawyer and a police officer. They are married to Radha, Gita and Sita (not in order). Each of the wives have a profession. Gobinda wife is an artist. Ram is not married to Gita. The The lawyer’s wife is a teacher. Radha is married to the police police officer. Sita is an expert cook. Who’s Who’s who? Ram(doctor)-Sita(cook) Sham(lawyer)-Gita(teacher) Gobind(police officer)-Radha(artist)
109.In a group of five people, what is the probability of finding two persons with the same month of birth robability of having the month of birth of all 5 persons different = 12 *11*10* *11*10*9*8/12*12*12*12* 9*8/12*12*12*12*12 12 = 55/144 so answer for the given case = 1-(55/144) = 89/144
110.There are seventy clerks working in a company, of which 30 are females. Also, 30 clerks are married; 24 clerks are above 25 years of age; 19 married clerks are above 25 years, of which 7 are males; 12 males are above 25 years of age; and 15 males are married. How many bachelor girls are there and how many of these are above 25 Distribution Total clerk = 70, Male = 40, Female = 30, Married clerks = 30, Male = 15, Female = 15, 25 plus married clerks = 19, Male = 7, Female = 12, 25 plus clerks = 24, Male = 12, Female = 12, 25 plus unmarried clerks = 5, Male = 5, Female = 0 so Bachelor girls = 15, none of them is above 25
111. In a market 4 men are standing. The average age of the four before 4years is 45, after some days one man is added and his age is 49. What is the average age of all? suppose total age of four ppal = x so before 4 years , the total was x-16 so that the avg ( before 4 yrs) = (x-16)/4 =45.. x=196 now after some days 49yrs is bei ng added. So avg is , (x+49)/5 = (196+49)/5 = 49
112. two years before paul's age is 2 times the alice age and present age of paul is 6 times the alice .what is present paul's age can't evaluate because if alice age before 2 year is x then paul's age =2x and now 2x+2=6(x+2) which can;t be solved so either this question is incorrect or It can't be evaluated
113. what to do for: 1.cyclic handshake 2.acyclic handshake 3.when to apply n(n-1)/2 . for cyclic >> no. of handshakes is = no. of peoples. 2. for acyclic>> no. of handshakes is = no. of peoples - 1. 3. when everyone is shaking hands with everyone else a pply n(n-1)/2
114. age of the 2 people are in ratio 6:5 after how many years,their ratio will be 8:7 The age of the two friends were in the ration of 6:5. If the sum of their ages is 55. Then a fter how many years their ratio will become 8:7? a) 11 b) 7 c) 10 d) 12 ans=c
115. Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles cir cles on either side. Find Fi nd the ratio of the radius of the circ les to the side of the square. a 1:(2+ 7√2) b 1:(2+ 6√2) c 1:(4+ 7√3) d (2+ 7√2):1 Let the radius of circle be r let the side of square be a then diagonal of square= a*sqrt(2) This diagonal length = 12*r + 2r * sqrt(2) (because the extreme circle's radius is perpendicular to side of square.) Thus we get 12*r+2r*sqrt(2)=a*sqrt(2) r(6*sqrt(2)+2)=a r/a=1/(6*sqrt(2)+2)
Thus ratio: r:a = 1:(6 *sqrt(2)+2) Ans: 1:(6*sqrt(2)+2)
116. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person perso n declares that the person next to him on his right is guilty. The rig htmost person is not questioned. Which of the following possibilities are true?(a) All suspects are lying or the leftmost suspect is innocent. (b) All suspects are lying and the leftmost suspect is innocent a)If all suspects are lying then first one is also lying so he can't be innocent therfore "or" is correc
117. Worker W produces n units in 5 hours. Workers V and W, wor kers independently but at the same time, produce n units in 2 hours. How long would it take V alone to produce n units? w produces n/5units/hr or 2n/5 in 2hrs. as v&w together produce n in 2hrs, v alone produces n-2n/5=3n/5 in 2hrs.so to produce n units,v takes 2*5/3=10/3hrs
118. The bacteria have the probability of split into 3 and probability to die is 1/3rd of the total bacteria. Let the probability is P. Some of them survived with probability 1/5.Then which among the following relation is true? a)P=1/3+1/5*3 b)P=1/5*(1/8-3) a)P=1/3+1/5*3
119. Mr. Das has 3 sons whose ages are respectively a, b, c. The grandfather has bought a cycle for the eldest son, mother has bought a bag for the youngest one which cost Rs. 150/. The sum of two age of the elder son and one son is 15. The difference of the age of sons is 3 & 2. Then what of the age o f the elder son In this question there is an additional information "The grandfather has bought a cycle for the eldest son, mother has bought a bag for the youngest one which cost Rs. 150/." which seems absurd, but there is a hidden info of elder, eldest and youngest son in it. given eldest son age = a elder son age = b youngest son age = c according to given conditions b+a = 15 OR b+c=15 and a-b = 3, b-c = 2, OR a-b = 2, b-c = 3 there are 4 combination 1) a+b = 15, a -b = 3, b-c = 2 (9,6,4) 2) a+b = 15, a -b = 2, b-c = 3 (8.5,6.5,3.5) 3) b+c = 15, a -b = 3, b-c = 2 (11.5,8.5,6.5) 4) b+c = 15, a -b = 2, b-c = 3 (11,9,6)
120. A school yard contains only bicycles 7 4 wheeled wagons.On tuesday,the total no. of wheels in the schoolyard was 114. what would be the possible no. of bicycles? #M40001259 is a question which can be solved only i f there would be options.The question writte n is A school yard contains only bicycles 7 4 wheeled wagons.On tuesday,the total no. of wheels in the schoolyard was 114. what would be the possible no. of bicycles? In this question "7" is wrong . It should be "and
121. A cube painted red on two t wo adjecent faces and black o n the faces opposite to the red faces a nd green on the remaining remai ning faces is cut into sixty-four smaller cubes of equal size. 21. How many cubes are there which have no face painted 8 cubes are there which hav no face painted cube is cut in 64(4^4) small cubes(4 rows of 4 columns each) inner cubes(2,3 rows 2,3 columns) sre not painted....
122. Entry ticket to an exhibition ranges from 1p to 31p. You need to provide exact change at the counter. You have 31p coin. In how many parts will u divide 31p so that u will provide the exact change required and carry as less coins as possible? a) 4 b) 5 c) 6 d) 7 minimum possible combinations are 5 as 1,2,4,8,16 if we require any amount we can give as a combination of others
for ex. if we require 12p 8+4
123. B is taller than j and 3 pillars. P is shorter than B and 2 pillars is j shorter/taller than P? a) yes b) no c) may be d) can’t find cant find as no relatio for the question is given
124. If there are 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if there were 58 wheels are parked there a)10 b) 33 c) 22 d) non this type of questions can be solved by only guessing the anws 10*4=40 if(58-40)/2 ==0 then ans is true otherwise no
125. A man whose age is 45 yrs has 3 sons named John, Jill, jack. He went to a park weekly twice. He loves his sons very much. On a certain day he found the shop keepers selling different things. An apple cost 1penny, 2chocalate costs 1penny & 3 bananas cost 1 penny. He has bought equal number of apple, choco late & banana for each so n. If the total amount he invest is 7 penny then how many he has bought from each piece for his so n? a) 1app, 1cho, 1 banana b)1 app, 2cho,3 banana c)1app, 2cho, 1banana c) as he buys equal items for each son we can divide 3 bananas equally 1 each(so 3 bananas=1penny) we require min 6 choc for e qual distribution(so 6 choc=3 penny) we require min 3 apples for equal distribution(so 3 apples=3 penn
126. John buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque with his neighbor and gave change to John. Jo hn. After 2 days, it is kno wn that cheque is bounced. Shop keeper paid the amount to his neighbor. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper? a)loss 23 b)gain 23 c)gain 54 d)Loss 54 Loss of dollar 23. Cycle of 19 dollar + Rs 4 cash given to john.
127. Inspired by fibonacci series sanket decided to create is own series which is 1,2,3,7,7,22,15,67,.... what number come immediately before 67? the series is a combination of two series... First one is 1, 3, 7, 15, 31, 63, ... (2^n - 1, n = 1, 2, 3, ...) Second one is 2, 7 (= 2 + 5), 22 (= 7 + 5*3), 67 (= 22 + 5*3*3), 202 ( = 67 + 5*3*3*3) 5*3*3*3),, ... Combining, we get 1, 2, 3, 7, 7, 22, 15, 67, 31, 202, 63, ... So, if it is number before 67, then it is 15 and if it i s number after 67, then it is 31, followed by 202 and so on..
128. if there are 30 cans out of them one is poisened if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisened ca n? A)3 B)2 C)6 D)1 we will need 1 mouse only. first let the mouse taste the first can. then after some time(say 1min) the mouse tastes 2nd can. in this way in 30 mins the mouse will taste all the thirty cans. after 14 hrs and x mins the mouse will die. here the value of x is between 1 and 30. If suppose the poison was in 7th can the mouse will die in 14 hrs and 7 mins... hence only 1 mouse is needed.
129. A Sheet of paper has state ments number from 1 to 20.Statement n says "At least n of the statements on t his sheet are true".which statements are true and which are false. a.The even no statements are true an d the odd no statements are false. b.the 1st 13 statements are false and rest are true. c.the 1st 6 statements are true and rest are f alse d.the odd no statements are true and even no. are false
For this type of Questions, follow this: At least- Ist half are true, Last half are false Exactly- Last second one is true or (N-1)th Statement is true Almost- All are true. So correct answer is (C
129. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? (a) 360 (b) 480 (c) 720 (d) 5040 the word leading contains 7 different letters,when the vowels eai r always together they can be supposed to form 1 letter then we have to arrange l dng (eai) now,5 letters can be arranged in 5! ways=120 ways the vowels (eai)can be arranged in 3! ways=6ways required no of ways =12 0*6=720 so ans is c
130. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together? (a) 4 (b) 10 (c) 15 (d) 16 L.C.M. of 2,4,6,8,10,12 is 120. So they toll once together in 2 minutes. In 30 minutes they toll together for 30/2 + 1 times= 16 times. Ans is (D)
131. In a restaurant with a staff of 5 members, the avg age is 45 yrs. after 5 years, a person joins them and the avg age is again 45 yrs. what is the age of 6th perso n? as the 6th person join after 5 years so the avg age of 5 person after years=45+5=50 now, 6th person joins so, (5*50+x)/6=45 x=20
132. A vessel is in the form of a hollow cylinder mounted on a hollow hemisphere. the diameter of the hemisphere is 14cm, and the total height vessel is 3cm. find the outer s urface area of the vessel surface area of hemisphere part= 2*(pi)*d^2/4=308 surface area of cylindrical part= 2 *(pi)*r*h=132 thus total SA=440 cm2
133. The ratio of sum of s quares of first n natural numbers to square of sum of first n natural numbers is 1 7:325. the value of n is (a)15(b)25(c)35(d)30 (e)none of these sum of square of n terms =n(n+1)(2n+1)/6 -------------- eq no.1 square of sum of n terms =n^2(n+1)^2/4 ---------------eq no. 2 eq 1/2 (2n+1)2 17 ------- = ---n(n+1)3 325 only 25 satisfies thi
134. Father's age was five times his son's age 5 years ago and will be three times the son's age after 2 yrs. what is the ratio of their present ages? let son's present age is = x year so son's age 5 year ago was (x-5) and father's age was 5(x-5) that ti me and after two years son's age would be (x+2) and then father's age would be 3(x+2) hence it is clear that 5(x-5)+7 = 3(x+2) and after solving we get x = 12 so son's present age is 12 years and so father's present age is 5(12-5)+5=40 s0 the ratio of present age of father and son respectively is 40:12 or10:3
135. Monthly income of X and Y are in the ratio 1:3 and their expenses are in the ratio 19:40. X saves 18,860 less than Y and in total they save 36,020. what are their respective incomes x-19y=8580,3x-40y=27440........solve them x-19y=8580,3x-40y=27440........solve ans a=10480,b=31440
136. A point A(x,y)divides the segment joining point B(5,-1)and C(-10,4)in the ratio 3:2. find the value of X and Y X=(m*x2+n*x1)/(m+n) Y=(m*y2+n*y1)/(m+n) (-4,2
137. There is Ferarri and a Benz car.Benz speed is 10km/h and it covers 10 km. if the Ferarri goes 3 times faster than benz,in how much time Ferarri would take to cover the same distance? since benz takes 60 min ferrari takes 20 min
138. One card is drawn from a well shuffled deck of 52 cards: Finds the probability of getting i)a king of red color ii)a black car 2 red king so i)2/52=1/26 26 black card ii)26/52=1/
139. There are 3 boys A,B,C and 2 girls D,E. D always sit right to A.girls never sit in extreme positions and in the middle position. C always sits in the extreme positions. who is sitting immediate right to E possible arrangements are ADBEC BEADC CEADB so after E there is either C or A
140. 6 persons standing in queue with different age group, after two years their average age will be 43 and seventh person joined with them. hence the current average age h as become 45. find the age o f seventh person now avg age of 6 persons is(43-2)=41 total age 41*6=246 total age of 7 person = 45*7=315 then the age of 7th person=(315person=(315-246)=69; 246)=69; other short process--now the avg age of6 person =41 7th person make it 45, then the 6 other persons' age increase 4. total increased age=4*6=24. then 7th person's age i=24+45=69
141. a two digit num "ab" is six times the sum of its d igits. find the value of b^a two digit number = (10*a + b) sum of its digits = a + b then, (10*a + b) = 6*( a + b) 10a - 6a = 6b - b a/b = 5/4 a=5 and b=4 the no is 54, which is 6 * (5 + 4). b^a = 4^5=4x4x4x 4^5=4x4x4x4x4 4x4 = 1024
142. the price of a maruti car rises by 30% while the sales of the car came down by 20%. what is the percent change in the total revenue? (a)-4(b)4(c)-2(d)0(e)none of thes Assume that price is 100 and sales are also 100. Total revenue is 100*100=10000(100%). Now price price increased by 30%. S o new price is 130. Similarly new sales are 80. N ow revenue is 130*80=10400(104%)= So total change is 4%
142. A,B,C are the mechanisms used seperately to reduce the wastage of fuel by 30%,40%,10%.What will be the fuel economy? The question should be "what will be the economy when all mechanisms are combined?" Think that fuel wastage i s 100. Now A reduces this by 30 % =70. B reduces 40% from 70 = 70-[40% of 70] = 70 -28= 42. Similarly 42-[10% of 42] = 37.8. Its wastage. So t otal economy will be 100-37.8= 62.2%
143. An athlete decides to run the same distance in 1/4th less time that she usually took. by how much percent will she have to increase her average speed let initial velocity = u and time taken = t since athlete decides to run the same distance i n 1/4th less time, then new time taken will be t-(t/4) = 3t/4 let the new volocity = v then for the same distance u*t = v*(3t/4) on solving we get v = 4u/3 so increment = 4u/3 - u = u/3 so % increment in speed = 33.33%
144. A metal strip of width 'X'cm. 2 metal strips are placed one over the other, then the combine length of 2 strips is 'Y'. if 'Z' strips are placed in that manner.what is the final width of that management? Total width= xz Y is irreleven
145. Find the number of trailing Zeroes in 52! here trailing zeros would be c ontributed by totl no of 2s and 5 s. Just calculate the multiples of 5 upto 52. i.e 52/5 = 10 multiples. now multiples of next power of 5 i.e 25 are 25 and 50=2 hence total factors contributing to trailing zeros= 10+2 = 12 hence no of trailing zeros i n 52! would be 12
146. A boy bought a roll A of 56 inches wide and 141 yards long. he also bought B of 77 inches wide of length 333 years. time taken for cutting A into 1 yard piece is 2 seconds.time taken to cut into 141 pieces of 1 yard each is how much? roll A is 141 yards long To cut 1 yard piece it takes 2 seconds no of pieces = 141-1=140(at 140th cut obviously it becomes 141 pieces) so, time taken=140*2=280......
147. There is a doll that can make 2 musical sounds. it makes 2 musical sounds after being defective. what is the probability that the same musical sound would be produced 5 times consecutively here are two sounds A and B, In first chance the doll can produce any of the t wo sounds so probability = 1 After that for making the sa me sound to be produced, probability = 1/2 similarly for the other chances t hus answer will be 1*(1/2)*(1/2)*(1/2)*(1/2) = 1/16
148. There are 11 boys in a family. youngest child is a boy.what is the probability that all are boys? (1/2)^10
149. 3 friends A,B,C measures their weights in some order in 7 rounds as follows: A,B,C,AB,BC,AC,ABC. Final round measure is 155kg.find the avrg weight of all the 7 rounds. given filanl round weight=155=a+b+c now a+b+c+(a+b)+(b+c)+(a+c)+(a+b+c) =4a+4b+4c=4(a+b+c) =4*155=620 now the average weight=620/7=88.5714
150. six friends go to pizza corner where there are different types of pizza available. six different flavours are there and they have to select 2 flavours from 6 flavours.In how many ways they can select? 6c2 then ans is 6*5/1*2=15
151. if a person moves 15km straight and turns 45 km right and moves 15km straight again,then how much distance does he need to walk to reach the starting point?
straight=15km,and right turn =45+15=60, distance to the starting point = square root (15^2 + 60^2)=square root (3825)=61.85 this answer is given by KALPANA G and is the correct a nswer Here it is to be informed that straight doesn't show any particular direction
152. The age of two people is in the ratio 6:6. if the sum of their ages is 44.after how many years would the ratio be 8:7? The ratio given is 6:6 means both are same in age it means it will be impossible to make their a ge ratio 8:7 now if we consider the suggestion given by RISHABH, then present ratio = 6:5 = 24:20 sum of ages = 44 so ages are 24 and 20 let after x years ratio will be 8:7 , so (24+x)/(20+x) (24+x)/(20+x) = 8/7 on solving the equation we get x = 8
153. Variables R and S are related by the equation R=(1/S^2). Now is S is increased by 10%. What will happen to R? Let s=10 s'=11 r=1/100 r'=1/121 decrease= (1/100-1/121)/(1/100)=17. (1/100-1/121)/(1/100)=17.4 4
154. A bag contains 4 white and 3 black balls, 2 balls are drawn at a time, randomly in succession. What is the probability that both the balls drawn are white in color, if the first ball is not replaced after the first draw. 4/7*3/6=2/7
155. A car manufacturer produces only red and blue models which come out of the final testing area completely at random. What are the odds that 5 consecutive cars of the same color will come through the test area at any one time? a)1 in 16 b)1 in 125 c)1 in 32 d)1 in 25 he probability for the question will be 1/16 and answer of KAPIL is ri ght but question is saying about odds and odds mean favorable probability/non favorable probability = (1/16)/(15/16) = 1/15 odds has two category 1) in favour 2) against odds in favour = favorable probability/non favorable probability odds against = non favorable probability/ favorable probability
156. A pie is to be divided among 20 people. A man eats 3 pieces, a woman eats 2 pieces and a child eats ½ a piece of pie. What is the number of men, women children, so that 20 people in total and everyone get the same pie? There are 20 pieces of pie in all. 7 women, 1 man, 12 children 5 women, 1 man, 14 children 4 women, 2 men, 12 childre n third option total number of persons are 18 so it would be wrong. in a option 7*2 + 1*3 + 12*1/2 = 23 pie so it would also be wrong now 2nd option 5*2 + 1*3 + 14*1/2 = 20 so b option is correc
157. Suppose n is an integer, s uch that the sum of the digits of n is 2 , and 10^10 < n < 10^11 10 ^11 . The number of different values for n is: (i) 11 (ii) 10 (iii) 9 (iv) a)11 10000000001(first 10000000001(f irst number) now 1 can be placed in 9 other positions to give 9 numbers 20000000000 , one more number total=1+9+1=11
158. Alan, Steven and Marwick dug up 9 nuggets. Their weights were 154,16,19,101,10,17,13,46 and 22 kgs. They took 3 each. Alan’s weighed twice as much as Steven’s. How heavy were Marwick’s nuggets alan=46,22,16=84 "take big two digit even no's for alan" steven=10,19,13=42 "here try to make sum of 42 with remainin small 2 digit odd no's" remainin=154,101,17=marwic
159. If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms? let the radius of umbra and penumbra are 2k and 6k. Then as given radius of umbra=40cm so 2k=40 k=20 radius of penumbra=20* penumbra=20*6=120 6=120 area of penumbra ring around the umbra=area of penumbra-area of umbra 22/7*[(120)^2-(40)^2] =40288.57cm^2
160. How many numbers can be formed using all of 1,2,3,4,5(without repetition),when the digit at the units place must be greater than that in the tenth place? (a)54(b)40(c)60(d)48(e)36 total methods without any restriction = 5*4*3*2*1 = 120 now for units place to be greater than tens place , only one method out of the set of two will be correct. ex: 12 & 21 only one will be valid so answer will be 120/2 = 60
161. The average age of all boys in the class is 16.66,while the average age of all girls in the same class is 18.75.Thus the average marks of all 40 students in the class is 17.5.what is the number of girls in the class? (a)12(b)16(c)18(d)20 (e)data insufficient question will be correct if we use marks in the place of age ans : x*18.75 + (40-x)*16.66 = 40*17.5 on solving we get x = 16
162. There are 6 positive and 8 negative numbers. Four numbers are choosen at random and multiplied.the probability that the product is positive is: (a)500/1001 (b)503/1001 (c)303/1001 (d)101/1001 (e)505/1001
163. There is a die with 10 faces. It is not known that fa ir or not. 2 captains want to toss die for batting selection. What is the possible solution among the following? a) If no. is odd it is head, if no. is even it is tail b) If no. is odd it is tail, if no. is even it is head he ad c) Toss a die until all the 10 digits appear on o n top face. And if first no. in the sequence is odd then consider it as tail . If it is even consider consi der it as head. Since "It is not known that the dice is fair or not.", so you should confirm about all the faces hence answer will be c
164. which of the following has the highest standard deviation? A.3,0,3,0,3,0 B.-3,-3,-3,-3,-3 C.3,3,3,3,3,3 D.-3,3,-3,3,-3, .option is D take option d-->mean=(-3+3-3+3-3+3)/6=0; (-3-0)^2+(3-0)^2+(-3-0)^2+(3(-3-0)^2+(30)^2+(-3-0)^2+(3-0)^2+(-3-0)^2+(30)^2+(-3-0)^2+(3-0)^2=54. 0)^2=54. Sd = sqrt(54/6)=9
165. The population of bacteria culture doubles every 2 minutes.approximately how many minutes will it take for the population to grow from 1000 to 500,000 bacteria? (A)10 (B)12 (C)14 (D)18 (E)20 To maximise probability, transfer all r ed balls except 1 from box1 to box2.So now box1 will have 1 red ball and box2 will have 19(9red + 10 green)balls. Now probability of selecting box1 from those is 1/2. Since there is 1 red ball only, prbability of selecting red ball will be 1. So for box1 total is (1/2)(1)=1/2. Similarly for box2 it s (1/2)(9/19). Add both you get 14/19
166. Pace length is distance between rear of consecutive footprints. For a old man walking Berghian's formula is n/p=144, where n is number of steps per minute and p is pace le ngth which equals 164 cm.Find c m.Find the sped of walking in kmp no of steps per minute=144*1.64 length of one step=1.64 speed=144*1.64*1.64 speed=144*1. 64*1.64 =387.30m/s speed=387.30*60/1000=23.23 speed=387.30* 60/1000=23.23 a
167. A class photograph has to be taken.the first row consists of 6 girls who are sitting.20 boys are standing behind.The two comer position are reserved for the two tallest boy.In how many ways can the students be arranged? (A)18!*720 (B)6!*1440 (C)18!*2!*1440 (D)18!*1440 (E)none of these
168. Given 3 lines in the plane such that the points of intersection for m a triangle with sides of length 20, 20 and a nd 30, the number of points equidistant from all the 3 li nes is a)1 b)3 c)4 d)0 Answer will be (c) There will be four points satisfying the given condition one point will be incentre of the circle and other three will be excentre
169. Peter and paul are 2 friends.Sum of their ages is 35 years.Peter is twice as old as paul was when peter was as old as paul is now.What is the present age of peter? supposing Peter’s age is e and Paul’s age is a We have a + e = 35………………….. (1) Now when Peter was Paul’s age which means (e - a) years ago Peter would have been e - (e - a) = a which is Paul’s age now Paul would have been a - (e - a) = 2a - e We have been given that Peter’s age is twice what Pauls was, so e = 2(2a - e) = 4a - 2e which gives 3e = 4a………………….. (2) For ease of use if a + e = 35; the n 3a + 3e = 105 = 3a + 4a from (2) above Thus 7a = 105 a = 15; e = 20 So Peter is 20 years and Paul is 15 years. The sum is 35 years and when Peter was 15
170. A game is played between 2 players and one player is declared as winner. All the winners from first round are played in second round. All the winners from second round are played in third round and so on. If 8 rounds are played to declare only one player as winner, how many players are played in first round 2^8=256 teams
171. Alok and Bhanu play the following min-max game. Given the expression N=9+X+Y-Z Where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their o ptimal strategies, the value of N at the end of the game would wo uld be 27 0.0 20 1 First Read the question carefully, According to the given question all the numbers will be decided by alok and first 2 would be put by bhanu whereas alok will put the 3rd one. So for getting maximum alok will tell 7 a s the first Number two cases arise
1) if bhanu will put this number as Z then 9, 9 will be the next 2 number. and 9+x+y-z = 20 2) if bhanu will put this number X, then alok will tell 4 or 5 as next number. if bhanu will put 4 or 5 as Z then alok will put 9 a s Y. So N will be 9+x+y-z= 9+7+9-4 = 21 OR 9+7+9-5 = 20 IF bhanu will put 4 or 5 as Y then alok will put 0 as Z 9+x+y-z = 9+7+4-0 = 20 OR 9+7+ 5-0 = 21 So if both are playing with there best effort then 9+x+y-z will be 20 20 is the correct a nswer
172. Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins. • The diameter of the coins should be at least 64mm and not exceed 512mm. • Given a coin, the diameter of the next larger coin is at least 50% greater. • The diameter of the coin must always be an integer. You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design? a9 b5 c8 d6 6 coins with dia 64,96,144,216,324,486 mm
173. Alok and Bhanu play the following min-max game. Given the expression N = 12 + X*(Y - Z) where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their o ptimal strategies, the value of N at the end of the game would wo uld be a 12 b3 c 30 d 69 Solution 12. Crame this x*(y-z)=18; x+(y-z)=11; x-y-z=2; x-y-z=2;
174. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The right most person is not questioned. Which of the following possibilities are true? A. All suspects are lying or the leftmost suspect is innocent. B. All suspects are lying and the leftmost suspect is innocent . Neither A nor B Both A and B B only A only A only If all suspects are lying then left most is guilty. becuse e very one said the the person right to them is guilty.Only the left most person is not mentioned.so he might be guilty. Or if any one's statement is true then definitely the leftmost is i nnocent.because he is not mentioned guilty by anyone. so only one is possible at a time. they ar e connected with or compound statement. So A only true. In B t hey used and keyword. both condition cannot occur at a time . So b is not true
175. One day Alice meets pal and byte in fairyland. She knows that pal lies on Mondays, Tuesdays and Wednesdays and tells the truth on the other days of the week byte, on the other hand, lies on Thursdays, F ridays and Saturdays, but tells the truth on the o ther days of the
week. Now they make the following statements to Alice – pal. Yesterday was one of those days when I lie byte. Yesterday was one of those days when I lie too. too . What day is it? a) Thursday b) Tuesday c) Monday d) Sunda according to the given data, the ans is thursda
176. A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning? a) 3 red and 3 blue faces b) 2 red and remaining blue c) 6 red and 0 blue d) 4 red re d and remaining blue ANS is 3 red and 3 blue faces Let 2 dice contains x no of red faces and y no of blue faces probability of winning A=(4/6)*(x/6)+(2/6)*(y/6) A=(4/6)*(x/6)+(2/6)*(y/6) probability of winning B=(2/6)*(x/6)+(4/6)*(y/6) both probabilities are equal according to t he given condition therfore 4x+2y=2x+4y x=y hence x=3 and y=3
177. A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probabilit y that Q is closer to the ce nter of the circle than the peripher y? a) 0.75 b) 1 c) 0.5 d) 0.25 the aresa of circle is pi*r^2 and fro ques we understand dat radius 0.5 so we get pi/4 the area of dartboard is pi*r^2 pi pi/4/pi 0.25
178. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game? a)1/9 b)4/9 c)5/9 d)2/3 2/3*2/3+1/3*1/3 5/9
179. Given a collection collectio n of points P in the plane, a 1 -set is a point in P that t hat can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie o n a line) is a)3 b)5 c) 2 d)1 ans is 3... consider a triangle. any point placed inside it will not form a 1-set point..... only the three vertices give the value of n1(P)
180. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope Zero. If one letter is in wrong envelope, one other letter must also be in wrong envelope. So zero is the probability that exactly 1 l etter is inserted in an improper envelope
181. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2.
Which of the following is true? a) In order to win, Alo k should remove O1 on his first t urn. b) In order to win, Alo k should remove one of the coins differe nt from O1 and O2 on his firs t turn. c) In order to win, Alo k should remove O2 on his first turn. d) Alok has no winning strategy b) In order to win, Alok should remove one of the coins different from O1 a nd O2 on his first turn
182. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race? 37.8
183. A sheet of paper has st atements numbered from 1 to 40. For each value of n from 1 to 4 0, statement n says "At "A t least n of the statements on this sheet are true." Which statements are true and which are false? a The even numbered statements are true and the odd numbered are false. b The first 26 statements are false and the rest are true. c he first 13 statements are true and the re st are false. d The odd numbered statements are true true and the even numbered numbered are false. ans is c) The first 13 statements are true and the re st are false. when atleast one of the statement is true, first one will be true. first n no. of statements must be true. When any one statement becomes false,all the stat ements also becomes false
184. 10 suspects are rounded by t he police and questioned about a bank robbery. Only one of t hem is guilty. The suspects are m ade to stand in a line and each person perso n declares that the person next to him on his right is guilty. The rig htmost person is not questioned. Which of the following possibilities are true? All suspects are lying or the leftmost suspect is innocent.
185. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? In base 8 System the digits are 0,1,2,3,4,5,6,7. The building numbers from 1 to 1000 in ba se 8. The number of 3s in one digit numbers is "1" The number of 3's in two digit numbers(30,31, numbers(30,31,32,33,34,35,36,37, 32,33,34,35,36,37,13,23,43,53, 13,23,43,53,63,73) 63,73) is 15. The number of 3's in t hree digit numbers is (300......307,310.. (300......307,310....317,320..... ..317,320.....327,330...337,340. 327,330...337,340....347,350.... ...347,350....357,360.....367, 357,360.....367,370......377 370......377 AND 103,203,.....703,113....... 103,203,... ..703,113.......713.......AND 713.......AND 130....773.)60+56+56 So total number is 1+15+56+56+60=192 HINT::Use permutations Principle.......
186. Entry ticket to an exhibition ranges from 1p to 7p. You need to provide exact change at the counter. You have 7p coin. In how many parts will you divide 7p so that you will provide the exact change required and carry as less coins as possible? Divide 7p into 3 parts such as 1p,2p,4p.So we can provide Exact change at t he counter.i.e 1p for 1p(if the tick et is 1p . 2p for 2p.//if the ticket is 2p 1p and 2p for 3p // if the ticket is 3p 4p for 4p 1p and 4p for 5p 2p and 4p for 6p 1p and 2p and 4p for 7p
187. Given a collection collectio n of 36 points P in the plane and a point equidistant from all points in P, which of the following are necessarily true? A. The points in P lie on a circle.
B. The distance between any pair of points in P is larger than the distance between X and a point in P a) A and B b) Neither A nor B c) B only d) A onl d)A only Soln: all points in a circle are equidistant from a given point.
188. In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6? Ans : 1/5 XYZ x takes 3 nos (1,2,3) Y takes 10 values(0-9) Z takes 3 values (4,5,6) 3*10*3=90 Prob= 90/450=1/5
189. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ' At least n of o f the statements on this sheet are false. ' Which statements are true and which are false First 35 statements are true and last 35 are false. Also if it is atmost n of the stat ements on this sheer are false then ans is all a re false. if it is exactly n statements on this sheet are false then ans is69th statement is true and rest are false.
190. Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two te ams from each group enter the se mi finals (after which the winner is decided by knockout). However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the cup ns is : (2/3)^10 + (8/3)*(2/3)^ (8/3)*(2/3)^9 9 given that prob. of India winning the match is 2/3. taking that India wins the semi-final and final.Prob is (2/3)^2 this gets multiplied to the league stage... in league stage, if In dia has won all the games, the prob. of winning is (2/3)^10 for the 10 matches played...if Indian hadanyone of mathches the prob. Is (8/3)*(2/3)^9 (8/3)*(2/3)^9 Where 8/3 Is pob for for loss
191. There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner. What is the probability that they don't coll ide? Ans:1/4 Let the corners of triangle be A,B,C There are 8 pssible ways in which ant can move 1. A to B, B to C, C to A 2. A to B, B to C, C to B 3. A to B, B to A, C to A 4. A to B, B to A, C to B 5. A to C, C to B, B to A 6. A to C, C to B, B to C 7. A to C, C to A, B to A 8. A to C, C to A, B to C Out of which, there are only two cases under which the ants won't collide : A to B, B to C, C to A and A to C, C to B, B to A probability =2/8=1/4
192. Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number. 285714 If its rightmost digit is placed at it s left end, then new number is 428571 which is 50% larger than the original number 285714.
193. Consider a number 235, where last digit is the sum of first two digits i.e. 2 + 3 = 5. How many such 3-digit numbers are there? Ans: 45 101,112,123,134,145,156,167, 101,112,123,134, 145,156,167,178,189,202,21 178,189,202,213,224,235,246, 3,224,235,246,257,268,279,3 257,268,279,303,314,325,,336,3 03,314,325,,336,347,358,369,4 47,358,369,404,415,426,437, 04,415,426,437,448,459,505,51 448,459,505,516,527,5 6,527,5 38,549,606,617,628,639,707, 38,549,606,617, 628,639,707,718,729,808,819, 718,729,808,819,909 909
194. Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3-dimensional objects. The rupee notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins. • The diameter of the coins should be at least 64mm and not exceed 512mm. • Given a coin, the diameter of the next larger coin is at least 50% greater. • The diameter of the coin must always be an integer. You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design? a9 b 5 c 8 d 6 6 coins with dia 64,96,144,216,324,486 mm. mm.
195. Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles circ les on either side. Find the ratio r atio of the radius of the cir cles to the side of the square. a (2+ 7√2):1 b 1:(2+ 6√2) c 1:(2+ 7√2) d 1:(4+ 7√3) Let the radius of circle be r let the side of square be a then diagonal of square= a*sqrt(2) This diagonal length = 12*r + 2r * sqrt(2) (because the extreme circle's radius is perpendicular to side of square.) Thus we get 12*r+2r*sqrt(2)=a*sqrt(2) r(6*sqrt(2)+2)=a r/a=1/(6*sqrt(2)+2) Thus ratio: r:a = 1:(6 *sqrt(2)+2) Ans: 1:(6*sqrt(2)+2)
196. One day Alice meets pal and byte in fairyland. She knows that pal lies on Mondays, Tuesdays and Wednesdays and tells the truth on the other days of the week byte, on the other hand, lies on Thursdays, F ridays and Saturdays, but tells the truth on the o ther days of the week. Now they make the following statements to Alice – pal. Yesterday was one of those days when I lie byte. Yesterday was one of those days when I lie too. too . What day is it? a) Thursday b) Tuesday c) Monday d) Sunday Thursday
197. Given a collection collectio n of points P in the plane, a 1 -set is a point in P that t hat can be separated from the rest by a line, .i.e the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie o n a line) is a)3 b)5 c) 2 d)1 ans is 3... consider a triangle. any point placed inside it will not form a 1-set point..... only the three vertices give the value of n1(P).
198. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope Zero. If one letter is in wrong envelope, one other letter must also be in wrong envelope. So zero is the probability that exactly 1 l etter is inserted in an improper envelop
199. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2.
Which of the following is true? a) In order to win, Alo k should remove O1 on his first t urn. b) In order to win, Alo k should remove one of the coins differe nt from O1 and O2 on his first t urn. c) In order to win, Alo k should remove O2 on his first turn. d) Alok has no winning strategy. option B is cirrect. If Alok removes coin either from O1 or O2, then there will be only 1 ordinary coin b/w special coins.Then obviously Bhanu will remove that coin in his turn and wins. So Alok should not touch O1 and O2 i n his first turn
200. Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well sh uffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums to a number between 2 and 12. Which total would be likely to appear more often – 8,9 or 10? a) 8 b)All are equally likely c)9 d)10 the best solution will be 7, and there will be total 6 cases for this choice (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) but this one is not in the choices so out of the 4 choices givem 8 will be the best choice. For this choice there are 5 methods (2,6), (3,5), (3,5), (4,4), (5,3), (6,2) similarly for 9 there ar e 4 choices (3,6), (4,5), (5,4), (6,3) for 10 there are 3 choices (4,6), (5,5), (4,6) Answer is (a)
201. A man goes north 37km.turns left goes 2km.turns right goes 17km.turns right goes 2km. find distance b/w starting ending point. a) 54 b) 27 c) 81 d) 67 Since man moves 2 km east and 2 km west so distance between initial a nd final points will be (37+17)km = 54km
202. There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is a) 3/4 b) 37/38 c) 1/2 d) 14/19 plz explain answer 14/19 To maximise probability of red ball, Move 9 red balls in other box such that one box contains 1 red ball and other box contains 9 red and 10 green balls, then probability of getting red ball = 1/2 *1 + 1/2*9/19 = 1/2+9/38= 28/38=14/19
203. 30 teams enter a hockey tournament.A team is out of the tournament if it loses 2 games. What is the maximum number of games to be played to decide one winner? a) 61 b)59 c)30 d)60 b)59 Out of 30 teams 29 teams will lose 2 games each which makes count 58 And winning team may also lose one match that adds with the count 58+1=59
204. Entry ticket to an exhibition ranges from 1p to 31p. You need to provide exact change at the counter. You have 31p coin. In how many parts will u divide 31p so that u will provide the exact change required and carry as less coins as possible? a)4 b)5 c)6 d)7 1,2,4,8,16...... 5 coin s 1,2,4,8,16....
205. the cost of manufacturing a popular model car is made up of three items:cost of raw material,labour and overheads- in a year the cost of three items were in the ration of 4:3:2.next year the cost of the raw material rose by 10% ,labour cost increased by 8% but overhead reduced by 5%.then %increase int the price of the car ? a)7.67% b)6% c)0.54% d)9.54% before increase total cost = 4+3+2=9, after increasing the cost = 9.54 so increase of .54 over 9 , equal to 6%
206. If a pipe can fill the tank within 6hrs.But due to leak it takes 30 min more.Now the tank is full then how much time will it take to empty the tank throught the leak.? a)78 b)56 c)66 d)59 78 hour Let capacity be 6litres then pipe takes 1litre/hour pipe/leak = 6/6.5 litre/hour(as they are inveresly proplational) so leak = 1/13 litre per hour for 6 litres it will take 13*6 = 78 hour
207. Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players ta ke turns. A turn consists of moving the coi n on the top to a positio n i below the top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on to p when it's a player's turn the n the player wins the game. Initially, the gold coinis the third coin from the top. Then Alice has no winning strategy. In order to win, Alice's first move should be a 1-move. In order to win, Alice's first move can be a 0-move or a 1-move. In order to win, Alice's first move should be a 0-move. in order to alice first move should be 1-move
208. The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed in kmph. n/1.64 = 144 n = (144 * 1.64) = 236.16 No. of steps per minute = 236.16 Distance per minute = (236.16 * 164) cm Distance per minute = 0.3873024 km Distance per hour = 23.238144 Speed = 23.238144 km/h
209. A car is traveling at uniform speed. The driver sees a milestone showing a two digit number which is a perfect square, after traveling for an hour the driver sees another milestone with the same digits in reverse order and after another hour the driver sees another milestone containing the same two digits as part of a three digit number. What is the speed of the car? (A) 30 kmph (B) 40 kmph (C) 50 kmph (D) 60 kmph (E) 45 kmph first milestone driver see is 16,second is 61,&third is 106. so total distance traveled by him=106-16=90km time taken=2h so speed=distance/time=90/2=45kmph hence (e) is the ans.
210. A man divides Rs.8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew, how much does each daughter receive? Let x be amount with nephew then with daughter 4x and with son 5x as,there are 5 sons,4 daughters, 2 nephews the amount is share in ratio 5*5x:4*4x:2*2x 5*5x:4*4x:2* 2x i.e., 25:16:2 total amount is 8600, total parts is 43(it is sum of ratios 25,16,2) so value of x is 8600/43= 200 the share of daughter is (16*200)/4 ans:800
211. A garrison of 3300 men has provisions for 32 days when supplied at the rate of 850 g per head. At the end of 7 days, a reinforcement arrives, and it is found that the prov isions can last for 17 days more when supplied at the rate r ate of 825 g per head. What is the strength of the reinforcement? (a) 1700 (b) 1000 (c) 3000 (d) 2700 3300 men -> 32 days -> 850 g/head After 7 days, 3300 men -> 25 days -> 850 g/head After reinforcement = 'x' arrives,
(3300+x) men -> 17 days -> 825 g/head Now, men count is inversely proportional to th e days for survival So, 3300*850 -> 1/25 (3300+x)*825 -> 1/17 Solving the above two we get, 3300 + x = (3300*850*25)/(17*825) So, x = 5000-3300 = 1700
212. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is: (a) 1 hour (b) 2 hours (c) 3 hours ( d) 4 hours suppose avg speed of aircraft is v km/hr,and it takes t hr to trip 600 km. then t=600/v.......(1) now avg speed slowed down by 200 km/hr and it takes 30 more minutes t hat means now it ta kes t+30/60=t+1/2 hr and speed i s v-200 now time=distance/speed=>t+1/2=600/(v-200) 2t+1=1200/(v-200) (2t+1)(v-200)=1200 (2t+1)((600/t)-200))=1200 (2t+1)((600/t)-200))=12 00 from (1) on solving it t= -3/2 or 1 time cant be -ve,hence answer is 1 hr.
213. A garrison of 3300 men has provisions for 32 days when supplied at the rate of 850 g per head. At the end of 7 days, a reinforcement arrives, and it is found that the prov isions can last for 17 days more when supplied at the rate o f 825 g per head. he ad. What is the strength of the reinforcement? (a) 1700 (b) 1000 (c) 3000 (d) 2700 Answer : (a)1700 Now since after 7 days r einforcement arrives,let us first find out how much amount of provisions is left over: (32-7)*3300*0.850 (32-7)*3300*0.850 = 70125 So now this amount will suffice for x number of men for 17 days at 0.825kg per head so , x*0.825*17 = 70125. Form this we get x = 5000. So totally number of men is 5000 which gives reinforcement as 5000-3300 = 1700
214. There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is a)1/2 b)14/19 c)37/38 d)3/4 14/19 1/2 + 1/2 *9/19 = 1/2(1+9/19) =(1/2 )*(28/19) = 14/19
215. A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. 2 5%. However, as it turned out , 50% of the components were rejected. What is the loss to the manufacturer? answer : (b)13000 Now as per her assumption of 5% failing , he will sell 1900 at 25rs earning 47500 which is his Selling Price(SP).Consider Cost Price(CP) as x and given profit as 25%, using formula (CP)[1+ profit]=SP we can substitute and find CP as 38000 (this is CP for 2000 goods). Now since only 50% passed test, 1000 goods were sold at 25rs i.e he got 25000. his loss is hen ce 38000-25000 = 13000
216. A man divides Rs.8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew, how much does each daughter receive? (a) Rs.800 (b) Rs.600 (c) Rs.200 (d) Rs.700 Let us say each nephew received rupees x So each daughter will get 4x and each son will get 5x There are 2 nephews, 4 daughters and 5 sons So 2(x)+4(2x)+5(5x) = 8600 43x = 8600 x = 200 sp each daughter gets 4x or 4 *200 = 800
217. Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian Athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race?
(a) 30 (b) 32 (c) 41 (d) 54 ans b)32 final round 2 teams (then only decide one winner) previous round 4 teams(include final round teams plus other two eliminated teams) previous round 8 teams(include next round team plus e qual no.of members that is 4+4) like wise ,, in general 2^5=32
218. If an airplane starts at point R and travels 14 miles directly north to S, then 48 miles directly east to T, what is the straight-line distance (in miles) from T to R? (a) 25 (b) 34 (c) 50 (d) 2500 ans c)50 R |14miles | |s- - - - T 48 miles so using pythagoras theorm rs^2+st^2=rt^2 14^2+48^2=2500 that is rt=50
TCS Overview
Established: 1968 Founder: JRD TATA CEO: N.Chandrasekhran Chief Operating officer: S. Mahalingam Global corporate affairs: Phiroz Vandervala Chairman: Ratan Tata Vice chairman: S. Ramdorai
1.Global network delivery model (GNDM) 2. CMMI level 5 company in quality framework. 3. Workforce: 198500 trained it consultants across 42 countries 4. revenue : $ 8.2 billion last fiscal till march 2011 5. Awards:
2009 sap pinnacle award
2010 Golden peacock award
2010 M.A.K.E individual operating unit(ipo) a ward.
6. Tcs has 50 subsidiaries out of which 20 are directly held and 37 are indirectly held.
Aponlie
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TCS Role in :
Aadhar project (unique identification authority of india )
Tata Consultancy Services Ltd.
Purchase of Biometric Devices 10-03-2010
Tata Consultancy Services Ltd.
Re-Design, Development, Maintenance and Support of UIDAI Web Portal 11-06-2010
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Leading European marathon with 33,000 participants, will be renamed as “TCS Amsterdam Marathon”
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Tata Consultancy Services (TCS) provides information technology and management consulting services to organizations in more than 53 countries. The company offers e-business, application development and maintenance, architecture and technology consulting, engineering, security, infrastructure development and management, and quality consulting services. In addition, TCS offers software packages for business functions s uch as applications f or electronic banking, insurance billing, customer relationship management, and hospital management. It caters to f inance and banking, insurance, telecommunication, transportation, retail, manufacturing, pharmaceutical, and utility industries. The company was founded in 1968 and is based in Mumbai, India. It has more than 150 offices worldwide. TCS operates as a subsidiary of T ata Sons Ltd. In the early 1990s, the Indian IT outsourcing industry grew tremendously due to the Y2K bug and the launch of a unified European currency, Euro. TCS pioneered the factory model for Y2K conversion and developed software tools which automated the conversion process and enabled third-party developers and clients to make use of it. [9] In 1999, TCS saw outsourcing opportunity in E-Commerce and related solutions and set up its E-Business division with ten people. By 20 04, EBusiness was contributing half a billion dollars (US) to TCS. [10] On 9 August 2004, TCS became a publicly listed company, company,[11] much later than its rivals, Infosys Infosys,, Wipro and Mahindra Satyam. Satyam. During 2005, TCS ventured into a new area for an Indian IT services c ompany - Bioinformatics. Bioinformatics.[12] In 2008, the company went through an internal restructuring exercise t hat executives clai m would bring about agility to the organization. [13] In 2011, the company entered the Small and medium enterprises (SME) market with cloud cloud-based -based offerings. [14
Tata Research Development and Design Center TCS established the first software research center in India, the Tata Re search Development and Design Center, in Pune Pune,, India in 1981. TRDDC undertakes research in Software engineering, engineering , Process engineering and Systems Research. Researchers at TRDDC also developed Master-Craft (now called TCS Code Generator Framework [22]) a Model Driven Development software that can automatically create code based on a model of a software, and rewrite the code based on the user's needs. [23] Research at TRDDC has also resulted in the development of Sujal, a l ow-cost water purifier that can be manufactured using locally available resources. TCS deployed thousands of these filters i n the Indian Ocean Tsunami disaster of 2004 as part of its relief activities. [24] This product has been marketed in India as Tata swach, swach, a low cost water purifier. [25
Type
Public company
Traded as
BSE: 532540 BSE: NSE:: TCS NSE
Industry
IT services IT consulting
Founded
1968
Headquarters
Mumbai,, Maharashtra, India Mumbai
Area served
Worldwide
Key people
Ratan Tata (Chairman) S Ramadorai (VC VC)) N. Chandrasekaran (CEO & MD MD))
Products
TCS Bancs Digital Certification Products Healthcare Management Systems
Services
Outsourcing BPO Software Products
Revenue
US$ 8.355 billion (2011) [1]
Profit
US$ 2.024 billion (2011) [1]
Total assets
US$ 7.215 billion (2011) [1]
Total equity
US$ 5.499 billion (2011) [1]
Employees
202,039 (Q1, 2011) [1]
Parent
Tata Group
