XAT PRACTICE QUESTIONSBy MBA - Maths By Amiya ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244
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Maths By Amiya, QUESTIONS 1. A container is full of milk. 6 litres of milk is taken out from it and, then, the container is filled with water. Next time 10 litres of the mixture is taken out and the container is filled with water such that the concentration of milk in the mixture becomes 0.75. What is the capacity of the container? a. 54 litres b. 60 litres c. 72 litres d.24 litres e. None of these 2. If a solution of milk and water in the ratio of 4:1 ( milk and water) is firstly 20% of the current solution is removed then water is added which is 20% of current solution, then 40% of the current solution is removed then water is added which is 40% of current solution. Then what is the current ratio of milk :water in the solution 3. If we sell two horses each on Rs 2000/- , one horse at 10% profit and one at 10% loss, then what would be total gain and loss in this whole transactions ? a. 1% Loss , or Rs 20 Loss b. 1% Loss , or Rs 20.20 Loss c. 1% Loss , or Rs 40 Loss d. 1% Loss , or Rs 40.40 Loss e. None of These 4. If we have two container A & B. A has 20 lit of Milk and B has 20 lit of Water. First We take 4 lit of milk from A and mix with B then take 4 lit of sol from B and put it into A. We repeat the process one more time. Then What would be ratio of Milk and Water in Container Cont ainer A ? a. 5:1 b. 5:13 c. 1:2 d.1:3 e. None of These 5. If there were only three parties in 2014 LS election BZP , LolGress & ShirdFront. It is known that BZP secured 50% more vote than LolGress , which got 20% less vote than ShirdFront. It is know that difference of votes between LolGress and and BZP is twice of that of BZP and ShirdFront. Then who won the election and and by how many number of votes wrt to party who secured second place in the election. a. BZP , 25votes b. ShirdParty, 25votes c. LolGress, 100 votes d. Can not be determined e. None of These 6. If a person leaves his house per day at the same time. When he maintain a constant speed or 30km/Hr he reaches office at 10:30 AM and when his constant speed is 40 Km/Hr he reaches at 9:30AM. What would be his constant speed if he has to reach his office at 10:00 AM sharp. a. 36.67 Km/Hr b. 37 km/Hr c.35 Km/Hr d. 34.28 Km/Hr
would 7. If velocity (m/s) is function of time and it is f(t) = 16 - 4*t , where t is in second then what would be total distance travelled travell ed in first 10 min.
8. If Ratio of Cost Price and Mark Price is 5:8 and that of % profit on sale to % discount is 2:3 then find % Discount. a.8.33% b. 16.66% c. 25% d. Cannot be determined e. Note
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Maths By Amiya, QUESTIONS 1. A container is full of milk. 6 litres of milk is taken out from it and, then, the container is filled with water. Next time 10 litres of the mixture is taken out and the container is filled with water such that the concentration of milk in the mixture becomes 0.75. What is the capacity of the container? a. 54 litres b. 60 litres c. 72 litres d.24 litres e. None of these 2. If a solution of milk and water in the ratio of 4:1 ( milk and water) is firstly 20% of the current solution is removed then water is added which is 20% of current solution, then 40% of the current solution is removed then water is added which is 40% of current solution. Then what is the current ratio of milk :water in the solution 3. If we sell two horses each on Rs 2000/- , one horse at 10% profit and one at 10% loss, then what would be total gain and loss in this whole transactions ? a. 1% Loss , or Rs 20 Loss b. 1% Loss , or Rs 20.20 Loss c. 1% Loss , or Rs 40 Loss d. 1% Loss , or Rs 40.40 Loss e. None of These 4. If we have two container A & B. A has 20 lit of Milk and B has 20 lit of Water. First We take 4 lit of milk from A and mix with B then take 4 lit of sol from B and put it into A. We repeat the process one more time. Then What would be ratio of Milk and Water in Container Cont ainer A ? a. 5:1 b. 5:13 c. 1:2 d.1:3 e. None of These 5. If there were only three parties in 2014 LS election BZP , LolGress & ShirdFront. It is known that BZP secured 50% more vote than LolGress , which got 20% less vote than ShirdFront. It is know that difference of votes between LolGress and and BZP is twice of that of BZP and ShirdFront. Then who won the election and and by how many number of votes wrt to party who secured second place in the election. a. BZP , 25votes b. ShirdParty, 25votes c. LolGress, 100 votes d. Can not be determined e. None of These 6. If a person leaves his house per day at the same time. When he maintain a constant speed or 30km/Hr he reaches office at 10:30 AM and when his constant speed is 40 Km/Hr he reaches at 9:30AM. What would be his constant speed if he has to reach his office at 10:00 AM sharp. a. 36.67 Km/Hr b. 37 km/Hr c.35 Km/Hr d. 34.28 Km/Hr
would 7. If velocity (m/s) is function of time and it is f(t) = 16 - 4*t , where t is in second then what would be total distance travelled travell ed in first 10 min.
8. If Ratio of Cost Price and Mark Price is 5:8 and that of % profit on sale to % discount is 2:3 then find % Discount. a.8.33% b. 16.66% c. 25% d. Cannot be determined e. Note
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9. If M. Pandey travels a distance in 120 days in which he took rest only for 4 hours per day and time travels with constant speed. If he is planning to travel thrice the distance with twice the speed and want to take twice more rest per day then in how many days he would cover his new task. a. 450 b. 150 c. 225 days d. Data inadequate e. NoT 10. If a person leaves his house per day at the same time. When he maintain a constant speed or 30km/Hr he reaches office at 10:00 AM and when his constant speed is 40 Km/Hr he reaches at 9:00AM. What would be his constant speed if he has to reach his office at 9:10 AM sharp. 11. Every morning Mr. Sen goes for a walk and his son cycles along. They both start together in the same direction. The walking speed of the father is one-sixth the cycling speed of his son. If Mr. Sen makes ten rounds of a circular park, then how many times will his son overtake him? a. 51 b. 49 c. 50 d. None of these Direction :- If 10 Jawans parading in a ground in a line back to back such that 2nd one is seeing the back or 1st so 10th one is seeing that of 9th with speed of 1 m/sec. There is gap of 1 m between two Jawans. Suddenly 10th Jawan from start running with speed of 2m/s towards 1st Jawan and touches him and come back without wasting any time. Then 12. Find the Total Distance Travelled By 5th Jawan during this process. 13. Find The Distance Travelled By 10th Jwana Towards 1st Jawan. 14. Find The Distance Travelled By 10th Jwana Towards his position. 15. A grocery decides to mix left over rice of five different varieties priced Rs 25, Rs 32, Rs 39, Rs, 46 and Rs 53 kg. If the store had no profit nor any loss after selling the mixture at Rs. 39 per kg then the ratio of the quantity mixed, in order could be: a. 2 : 4 : 3 : 3 : 1 b. 2 : 1 : 1 : 2 : 3 c. 1 : 1 : 2 : 1 : 2 d. 2 : 3 : 5 : 3 : 2 e. NoT 16. If the efficiency ratio of Managers, Executives, VP & CEO of doing same work is 1:2:3:4 and it is known that 4 Managers , 3 Executives ,1 VP and 1 CEO do a work in 40 days then how many days would it take to complete half of the work by 1 Manager, 1 Executive, 1 VP & 1CEO? a. 68 b. 34 c. 136 d. Data Inadequate e. NoT 17. A man purchased few oranges with the rate of 30 oranges in Rs 60/- and purchased same number of oranges but this time rate was 40 oranges in Rs 60/-. If he sold all his oranges under rate or 35 oranges in Rs 60/- , then what is the total overall aprox gain or loss % a. At Par b. 2.04 % gain c. 2.04% loss d. 4% loss e. NoT
18. If Abhisek & Sanket are standing opposite on the diameter of circular track of radius 7 m. If they start together, Abhisek moves in clockwise direction with speed of 1m/s and after every second he increases speed by 1 m/s and Shyam moves in clockwise direction with speed of 2m/s and after every second he increases speed by 2 m/s, then after 1 min of their start how many times they would meet to each other. a. 126 b. 127 c. 42 d. 41 e. NoT
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19. If Abhisek & Sanket are standing opposite on the diameter of circular track of radius 7 m. If they start together, Abhisek starts in clockwise direction with speed of 1m/s and after every second he increases speed by 1 m/s and Shyam starts in anti clockwise direction with speed of 2m/s and after every second he increases speed by 2 m/s, then after 1 min of their start how many times they would meet to each other. a. 124 b. 125 c. 42 d. 41 e. NoT 20. A,B & C three robots start from same point in the same direction of a 60 m circular track with initial speed of 1m/s , 2m/s and 4m/s respectively. When any one of two meet to each other they inter-change their velocities. and when all three meet then they stop at that point. So what would be total distance travelled by A,B & C respectively before they stop. a. 120,180&120 m b. 120 , 120 & 120 m c. 120, 120 & 180 m d. 60, 120 & 180 m e. NoT (???) 21. There are three containers A,B & C having different litters of water. First we pour 1/3 of water from container A to B then 1/4 from container B to C then 1/10 from C to A. Then after this process we have 9 litters of water in each container then how ho w much litters of water does container contai ner A have initially (if it is known that initially all have litters in water in whole numbers) a. 12 b. 9 c. 15 d. 18 e. NoT 22. If ratio of A's income to that of B is 3:4 ; ratio of B's savings to A's expenditure is 4:7 and ratio of A's Saving to his own expenditure is 1:2 then what is ratio of B's expenditure to his saving. a. 3:1 b. 5:2 c. 5:4 d. Cant be determined e. NoT 23. If ratio of population of town A to that of B is 7:9 ; total number of male population of A is equal to female population of B and female population of A to male population of B 2:3 then what is ratio male population of A to male population of B a. 1:116 b. 1:2 c. Data is not possible d. Cant be determined e. NoT 24. If ratio of population of town A to that of B is 7:9 ; total number of male population of A is equal to female population of B and female population of A to female population of B 3:2 then what is ratio male population of A to male population of B a. 14:31 b. 31:14 c. Data is not possible d. Cant be determined e. NoT
25. If to complete a work A, B & C takes individually 10, 20 & 30 days respectively. If C works on first day , A works on second day, B works on third day and then they repeat the process (same sequence) until works in not completed. After completion of the work if C get Rs 2000/- as labour cost then what is the difference between labour cost of A & B (if it is known that labour cost is distributed in the ratio of their works) a. 2500 b. 5500 c. 3000 d. 6000 e. NoT 26. What would be shortest distance between any two consecutive meeting points of Ram & Shyam on a circular track, when their speeds are 700 m/sec & 1300 m/sec and length of circular track is 132
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Km and both of them started from same point, in same direction and same time and completed 120 rounds of track. a. 22 km b. 21 Km c. 20 Km d. 23 Km e. NoT 27. If a milkman has 100 lit of milk and every time he sells 10 lit of his milk (solution) and add 20 lit of water and repeats this process two more times and then what would be ratio of milk is to water in his solution. a. 25: 23 b. 15:7 c. 45:46 d. 15:26 e. NoT 28. If a thief flew with constant speed of "T" in a straight road, and after some time a police and his dog started to chase the thief with speed of "P" and "D" respectively, such that D>P>T. In this complete journey, Dog touches the Thief and comes and touches the Police and move towards Thief and continues the process, until The Thief is caught, Then what would be ratio of "total distance covered by Dog towards Thief to total distance covered by Dog towards Police". (Police & Dog move at the same time) a. (D-T)/(D-P) b. (D+T)/(D+P) c. (D-T)/(D+P) d. (D+P)/(D-P) e. NoT 29. In a circular track of length 100 m , A starts running from a fix point with 20m/s in clockwise direction and after 2 seconds from same fix point B starts running with 10 m/s in clockwise direction than when (time after B's Start) and where (from starting point) they will meet for 3rd time if they run nonstop with their constant speed. a. 26 Sec , 60 m (clockwise) b. 18 Sec , 80 m (clockwise) c. 30 Sec , At starting point d. NoT 30. What is the approx average % increase of a quantity if t has two consecutive increase of 20% & 80% a. 50% b. 45% c. 41% d. 47% 31. If in an equilateral triangular shaped race track the mileage of a car on its sides are 12km/lit , 15km/lit and 20km/lit due to obstacles then what what would be average mileage of the car on the race track if car completes one round of track. a. 16 b. 15.67 c. 15 d. NoT
32. If container 1 is containing 20 litters of milk and container 2 is containing 20 litters of water. First we pour 5 litters of pure milk from container 1 to 2 and then 5 litters of solution from container 2 to 1, and repeated this process two more times. Then what would be ratio of milk : water in container 1. a. 4:1 b. 17:8 c. 76:49 d. NoT 33. If city A is in the east of city C and city C is in the west of city D who is in the east of A and west of B who is not sandwiched between any two cities and time zone difference between any two consecutive cities are 1 hour . If below is the schedule chart of two planes of a same day then when they would meet or cross each other (assuming all times are local times and all cities are in a straight line)
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Plane
Dept Time (City)
Arrival Time (City)
IoC1401
12:00PM (C)
9:00PM (B)
CoI1041
12:00PM (B)
9:00PM (C)
a. 4:30 PM (B's Local Time) c. 6:00 PM (C's Local Time) e. NoT
b. 4:30 PM (C's Local Time) d. 4:00 PM (A's Local Time)
34. Price of three types of solutions A,B& C are Rs10 per lit , Rs20 per lit & Rs 30 per lit, in which ratio we should mix A,B & C that the price per lit of new solution is Rs 23 a. 1:3:1 b. 3:3:1 c. 1:2:3 d. 2:3:5 35. If few months before price of a pen in India is Rs 100 only and currency rate was 1$= Rs. 60 . If price of pen is increased by 20% and price of Rs is also increased by 20% then what is the current price of that pen (approx) a. Rs 80 b. 1.38 $ c. 1.67 $ d. 2.4 $ e. NoT 36. It is known that ratio of selling price to mark price of a article is 3:5 and ratio of %Profit to % Mark-up is 2:5. If cost price for article is Rs 120 then what is the selling price ? a. Rs 150 b. Rs 250 c. Rs 168 d. Rs 144 e. NoT 37. If a shop keeper purchase is item from a wholesaler who gives discount of 20 % on MRP of the item, but during purchase of all items shopkeeper uses his 1200 gm wt instead of 1000 gm wt, and Shopkeeper sells his all items at 10% discount on MRP but cheated his customer by using 900gm wt instead of 1000gm wt during sell. If it is known that what he purchases in the morning sells by the evening. Then what is his actual gain %??? a. 21% b. 33.33 % c. 50% d. 66.67% e. NoT
38. If after giving discount of 30% on Dondroid-1, it is reported that there is increase of 40% in the revenue then how much % increase is recorded in the sales (unit sold) of Dondroid-1 a. 68% b. 82% c. 90% d. Cant Say e. NoT 39. A & B start from opposite end X & Y of a 20 m path and they run to & fro with their constant speed of 12 m/s & 8 m/sec respectively. Then how many times A overtakes B in the path but not on extreme ends in 2 min of journey if both start simultaneously. (overtakes means meeting when both are running in same direction) a. 60 b. 12 c. 8 d. 4 e. NoT
40. A & B start from opposite end X & Y of a 16 m path and they run to & fro with their constant speed of 10 m/s & 6 m/sec respectively. Then how many times A overtakes B in the path but not
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on extreme ends in 80 min of journey if both start simultaneously. (overtakes means meeting when both are running in same direction) a. 10 b. 8 c. 7 d. 0 e. NoT 41. A shopkeeper is using a scheme of buy 900 gm and get 100 gm to clear his stock and calming to sale at no profit no loss model but instead of 900 gm he is using 800 gm wt during sale. Then how much % profit or loss he is earning by doing this activity. a. 12.5 % loss b. 12.5 % profit c. 1.25 % loss d. 1.25 % profit e. NoT 42. If Kaif and Raina start running on boundary rope of MCG from pavilion end in opposite direction, if they meet at 30 different points on the rope then among the options which cannot be number of different meeting points if they run in the same direction a. 28 b. 16 c. 20 d. 8 e. NoT 43. If a man starts a work and after every 2 days , one extra man of same efficiency joins him then how in how many days work would complete, if same work is done by 10 men in 30 days. a. 32&11/17 b. 16 & 11/17 c. 33 & 11/17 d. NoT 44. In a day (24 hr) how many times second hand meets hour hand a. 720 b. 719 c. 1440 d. 1438 45. If a solution has ratio of milk and water in the ratio of 2:3 , if we replace 20 lit of water solution with water then repeated this process one more time then new ratio of milk : water 18:107, then what was the final volume of solution. a. 30 lit b. 50 lit c. 70 lit d. NoT 46. If the average speed of an express train between two junctions, when it stop only first and last junction is 90Km/Hr . And between same two junctions a local strains stops at 10 extra halts with average speed of 75 km/Hr then what would be average stoppage time at each halts of local train in an hour. (assume engine efficiency of both trains are same) a. 10 min b. 60 seconds c. 2 min d. 90 sec e. Not 47. If 20 lit of 20% alcohol is replaced by 4 lit of 80% alcohol then new solution is replaced by 4 lit of water the what would be ratio of alcohol and water in resultant mixture. a. 8: 17 b. 17:8 c. 32:93 d. 93:32 e. NoT 48. If fresh fruits has 90% water and dry fruit has 20% water, then to get 16kg dry fruit how much kg of fresh fruit is needed. a. 160 b. 480 c. 640 d. 960 e. NoT 49. If A takes 20 days , B takes 40 days and C takes 80 to complete a piece of work if they work alone if A starts a work on first day, on second day B works alone then and on third day C alone works and repeat the process then in what ratio their labour cost of A , B & C would be divided a. 1:2:4 b. 4:2:1 c. 47:22:11 d. 18:9:7 e. NoT
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50. A loan of Rs 3310 is paid in three equal instalments at the end of year, if interest rate is 10% compounded then what would be instalment amount a. 1200 b. 1331 c. 1441 d. NoT 51. If half life of a radioactive substance is 16 year, if initial wt of 200 kg then what would weight of this radioactive substance after 64 years. (Half-life is the amount of time required for a quantity to fall to half its value as measured at the beginning of the time period.) a. 50 kg b. 25 kg c. 12.5 kg d. 6.25 kg e. NoT 52. If Ram types 16 pages in 2 hours , Shyam types 8 pages in 3 hours and Mohan types 4 pages in 1 hours then if all three work together then in how many hours they complete a book of 396 page. a. 25 b. 27 c. 31 d. 33 53. If a man cuts 9 m long bamboo in 9 min in 9 equal parts by an axe then how much time he would take to cut 18 m long bamboo in 18 equal parts a. 1080 sec b. 540 sec c. 1147.5 sec d. 1097.5 sec e. NoT 54. If two uniform identical candles burns are lighted at the same time. If first is consumed in 12 hours and second is in 10 hours, then after how much time (in hours) being lighted was the first candle is double the length of second. (Assume each burns at constant rate and lighted at same time) a. 60/13 b. 60/11 c. 60/7 d. 5 e. NoT 55. Among the statements how many statement(s) is(are) not a possible condition (all statements are independent statements)
I. If speed of Ram from school to home is 30 km/hr then he came back with a speed X km/hr then the his average speed of this entire journey is 2X km/hr II. If Ram increases his usual speed by 7 km/hr he reaches school 30 min before his usual time but if he decreases his speed by 10 km/he he reaches school 30 min after his usual time, (considering same starting time for all cases). III. If Ram maintain a constant speed of 30 km/hr he reaches his school at 11:10AM but if move with constant speed of 50 km/hr he reaches school at 9:50 AM. To reach at 10:20 he have to move with constant speed of 40 km/hr (considering same starting time for all cases) a. Any one
b. Any two
c. All
d. None
56. If Basanti starts from Rampur to Sholhapur and after 2 hours she meets an accident and after accident her speed decreases by 2/3rd of initial speed and she takes 2.5 hour extra time (to her usual time) if accident happens after 20 km from first case then she would take 2 hour extra time (to her usual time). Then what is the distance between Rampur to Sholhapur a. 120 km b. 140 km c. 160 km d. 180 km e. NoT 57. There was only kacchi Sadak in between ZLRI & IIN-C. One day Director of IIN-C visited to ZLRI and reached ZLRI 2hr earlier than his expected time since he travelled only 50 km on kachhi
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sadak and rest on pakki sadak due to construction work which was going on under SADAK BANAO YOJNA, and next day in his return journey he saved extra 20 min than his yesterday timing since he got only 30 km as kachchi sadak and rest as pakki. Then what is the distance between ZLRI & IIN-C. (Assume speed of his car remains constant for kachhi sadak and pakki sadak but his speed is more on Pakki Sadak) a. 140 Km b. 170 km c. 190 km d. NoT 58. A fox can catch an idle hare in his 30 jumps but when fox starts to jump, same time hare also starts to jump but away from the fox and both moves in a straight line. When fox takes 2 jumps, hare takes 5 jumps but distance covered by fox in 2 jumps is same as distance covered by hare in 7 jumps, them in how many jumps fox will catch the hare. a. 75 b. 45 c. 105 d. 90 e. NoT 59. If A and B is starting on same time and same point of a circular track of radius 63 m with speed 16 m/sec and 56 m/sec in opposite directions. Whenever they meet they mark the place if place is not marked. After 1 hour, what would be minimum distance (displacement) between any two marks. a. 63*sin40 b. 44m c. 63*sin20 d.126*sin20 e. NoT 60. If number of students a class is firstly increased by a% then decreased by b% then there is no change in number of students then |b-a| = ?
a. a*b
b. b – a
c. a*b/100
d. (a+b)/100
e. NoT
Maths By Amiya - Geometry If ABCD is a trapezium such that AB||CD and AB= 80cm & CD= 20 cm. Points M & N are n non parallel sides, MN is||AB it divides trapezium in two equal halves then length of MN =? a. 30 cm b. 40 cm c. 50 cm d. NoT If two adjacent sides of a parallelogram is 10cm and 12 cm and one diagonal is 8 cm. Then what is the length of another diagonal a. 8
b.
√
√
c.
d. Data adequate or NoT
63. If a cone of radius 10 cm and of height 10 cm is filled till 5cm from its close end (tip) then sealed with a circular sheet (of negligible width) then turned upside down, then what would be the range of height of water surface inside the cone (from circular base & Assume all figures are under 100% spirit levelled) a.[0,1] b. ]1,2] c. ]2,3] d. ]3,4] e. ]4,5]
If side of an equilateral triangle ABC is 3 cm and point D is on BC such that BD=1cm then AD=? a. 2.7 cm
b.
√
c.
√
cm
d. NoT (???)
If in a plan there are four points such that AB=BC=CA=DA and angle BDC = x degree , where x is less than 180 degree , then maximum possible value of x= ?
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If AB, AC & DE are common tangents to two given circles whose centre are P & Q as shown in fig, such that AD= 6 cm , AE = 10 cm & DE= 8cm then what distance between P & Q. a. cm
√
cm
b d. NoT
is the
√
cm
c.
√
If 6cm and 8cm are length of diagonals of a rhombus then what would be length of radius of circle inscribed in this rhombus a. 2.5
b. 2.4
c.
√
d.
√
e. NoT
If in an isosceles triangle ABC , BC=4cm and circum-radius is a square of a prime number who is even then angle C = ?
If in triangle ABC , D,E & F are points on side BC, CA & AB such that BE is median , BD:DC=1:2 & BF:FA = 2:3 then BO:OE=? [if O is point of intersection of BE & DF a. 7:4
b. 4:7
c. 5:6
d. 6:5
e. NoT
If in triangle ABC , D,E & F are points on sides BC=4cm, CA=5cm & AB=3cm such that AD, BE & CF al angle bisector and I in in-centre then AO:IO =? , [if O is point of intersection of EF & AD] a. 14:5
b. 5:15
c. 3:1
d. 1:3
e. NoT
If in a triangle ABC . D lies on the side BC and on line AD , O is point such that AO:OD=BD:DC=2:3 if we join points B & O and extend it to line AC then it cuts the line AC at E. Then AE:EC=? a. 19:4
b. 4:19
c. 4:15
d. 15:19
e. NoT
If side ratio of a triangle is 10:11:12 then what is the ratio of circum radius to in-radius a. 13:7
b. 40:19
c. 80:39
d. Can't Say
e. NoT
If radii of all four circles are consecutive terms of a G.P series then area of would be equal to a. Largest radius among all b. Product of smallest radius and 3rd largest radius c. Square of 2nd smallest radius d. Product of 2nd smallest and 3rd smallest radius
What is the maximum value of ratio of area of in-circle of a triangle to area of triangle. ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
a. 1
b. pi
c. pi / (3* sqrt(3))
d. 2
e. NoT
What would be (approx) area of a regular convex polygon with 11 sided fig whose one side is 7 cm. a. 472.916 b. 478.169 c. 458.916 d.480
that Perimeter of ABE = Perimeter of BEC & Area of ABD = Area of BDC, then
If in a triangle AB = 30, BC= 40 & CA = 50 , D and E are two points on side AC such
Length of BD = ? a. 20 b. 25 Length of BE a. 12
b. 12
c. 26.66
√
d. 23.33
c. 18
d.
e. NoT
√
e. NoT
Length of DE = ? a. 3 b. 4 c. 5 d. 6 e. NoT If a robot only moves in straight line and only takes either left or right turn and his movement path is marked by a LASER. One day he started from a point and reach at the same point and facing same direction as initially he was after taking 20 right turns that how many left turns he has taken, if he never repeated or crossed a path which is already marked and never take more than one turn on a point. a. 20 b. 16 c.24 d. (b) or (c) e. NoT
In a PQ=QR , angle PQR = and S and T are points on PR such that PS^2 + TR^2 = ST^2 then angle SQT = ? (in degre) a. 30 b. 45 c. 60 d. 75 e. NoT If the equation of one side of an equilateral triangle is 3x+4y=5 and its one vertex is (5,5) then what is its area a. 6
√
√
√
b. 12
c. 9
d. 15
e. NoT
What is the ratio of side of a hexagon to a square of maximum area inside the same hexagon a. 3 - root 3 b. 3 - root 2 c. 2 - root 3 d. 2 - root 2 e. NoT 83. If perimeter of a triangle is 24 cm then how many different triangles possible where only two sides are odd integer rest is even. a.12 b. 6 c. 3 d. NoT 84. If length of minor arc created of a chord AB is equal to radius of the circle . then angle OAB = ? (where O is the centre of circle and A & B are on the centre) a. 1 rad b. 2pi -1 rad c. pi - (1/2) rad d.60 degree
What would be diameter of circle whose two chords AB and CD make angle of 90 at point E such that , CE=2 cm, CD= 9 cm & EB= 3 cm. a. 12 cm
b.
√
c.
√
d. NoT
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https://www.facebook.com/MathsByAmiya/photos/840413596010758/
√
What would be radius of circle of maximum area inside a sector of a circle whose radius is 12 cm and central angle of sector is 60 a. 6cm
b. 4 cm
c.
d.
√
e. NoT
There are how many convex polygon possible such that integral angles are in AP and integer and the smallest angle is 30 a. 8
b. 17
c. 3
d. 4
e. NoT
90. If angle ABC=angle BCA, BF=7 cm, CE= 5 cm , DE= 9 cm Then EF =?
a. 3 cm d. 4 cm
b. 3.4 cm e. NoT
c. 3.6
91. If in a ∆ABC, AB=16 cm, BC= 30 cm & CA= 34 cm and I is incetre of the triangle then IA =?
a. 6 cm
√
b. 2
c. 8 cm
d.
√
e. NoT
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√
92. What would be side of inscribed square PQRS having maximum area inside a triangle ABC such PQ lies on side BC, angle ABC=30 , angle ACB=60 and side AC= 6 cm
√ √
a.
b.
√ √
c.
√ √
d.
√
e. NoT
93. If in a triangle ABC, AB is also a side of a regular hexagon and AC is side of a regular pentagon then what is the measurement (in degree) of angle BAC ? a. 60 b. 114 c. 120 d. 108 e. NoT 94. https://www.facebook.com/MathsByAmiya/photos/859153280803456 95. If the semi-perimeter of right angled triangle is 154 cm and smallest median is 72 cm then what would be area of the triangle.
a. 1600 cm^2
b. 1440 cm^2
c. 1540 cm^2
d. Data inadequate
e. Not
Algebra
= = in If
then
a. -1
b.0
c.-5
d.5
What would be remainder if a. 0
b. 1
What would be coefficient of a. 3 b. -23
is divided by
c. x
d. -x
for
c. -3
d. 23
What would be coefficient of x^50 in the expansion of a. 3
b. 12
c. 31
d. 56
e. NoT
If roots of equation x^2 + bx + 30 =0 are integers then what would be sum of all values of b a. 72
b. 465
c. 0
d. -465
e. -72
= , = & = = ec If
then for real a,b & c ;
then what would be digital sum of N a. 9 b. 2 c. 5 d. 7
e. NoT
What would be minimum value of a. 78 b. 75 c. 39
e. NoT
d. 57
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If
= then
a. -1
b. 0
c. 1
=?
d. 2
=
If
and then for how many positive values of x less than 6 would give
|f(x)| = 1 a. 0
b. 2
c. 3
d. 4
e. Cant Day or NoT
if n! seconds is equivalent to 6 weeks then n = ? a. 9 b. 10 c. 15 d. 16
e. NoT
If a and b are roots of x^2 - 7x + 9 =0 and the quadratic equation whose roots are (a^2 7a + 10) & (2b^2 - 14b +15) is a. x^2 + 2x +3 =0 b. x^2 - 2x -3 =0 c. x^2 + 2x -3 =0 d. NoT
If
√ then
a. Independent of m c. Independent of m & n both
For real x, what is the range of a. Positive Real c. Negative Real
b. Independent of n d. Dependent on both m & n
b. Non negative Real d. All Real Numbers
If "a" and "b" are the roots of equation minimum value of a. - 15 b. -11 c. -7
=
then
If a. x^2 - 4x + 6=0 c. x^3 + 6x + 6 =0
is
=
then what would be
d. NoT
b. x^3 + 6x -6=0 d. x^3 - 6x - 6 =0
| |=
What would be sum of all possible values of x, if a. 0 b. -20 c. 20 d. NoT
For real values a, b & c if a+b+c=0 then roots of equation (a + b - c)x^2 + ( a - b + c) x + ( -a + b + c)=0 a. Imaginary b. Irrational c. Rational
d. Equal
For how many values of "x" there is an isosceles triangle with sides 3x-5, x+3 , 7-x ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
a. 0
b. 1
c. 2
d. 3
If roots of x^2 + mx + n =0 is 2 more than roots of x^2 + nx + m =0 then m+n=? a. 4 b. 2 c. -2 d.-4 For how many natural numbers "n" less than equal to 50 a. 15
b. 16
c. 17
d. NoT
is an integer
(Based on an old Question)
What would be sum of all coefficient excluding constant term of (x+7)(x+5)(x+3)....(x3)(x-5)(x-7) a. 0 b. -11025 c. -14400 d. NoT Sum of imaginary roots of 4x^3 - 12x^2 + 9x -27 =0 lies in the close interval of a. [-12,-3] b. [-2,2] c. [3,5] d. [6,12] e. NoT
If
= = = = then
a. 1/2
b. 7/5
c. 5/7
d. 2
e. NoT
If a^2 + b^2 + c^2 = 11 , ab + bc + ca = 35 then (a+b+c)^3 = ? a. 729 b. 1331 c. 1000 d. Can't be determined
e. NoT
√ √ =
What would be sum of all integral values of x for which a. 0 b. 9 c. -9 d. 10 e. NoT If for real x and y a. 5
=
b. 3/5
c. 5/3
then what is the value of d. 1/5
e. NoT
a, b, c, d, e and f are four integers such that a+b+c+d+e+f = 5. What would be the minimum possible value of 1/a+1/b+1/c+1/d+1/e+1/f ? a. - 4
b. - 78/125
c. - 49/10
d. - infinity
e. NoT
If a^2 + a*e= 10 , b^2 + b*f= 21, c^2 + c*d= 75, d^2 + d*c= 6,e^2 + e*a= 6 and f^2 + f*b= 15 then maximum value of a+b+c+d+e+f = ? a.
√ = b. 19
c. 20
d. infinite
e. NoT
What is the range of 5x^2 + 2x + xy + y^2 for real x and y a. [0, [ b. [-4/19 , c. [-3/19 , [ d. [-4/19 , If a. 1
[
e. NoT
then x^37 + x^31+x^25+...+x^7+x =? b. 0 c. x d. -x e. NoT
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Miscellaneous 126. In how many ways a boy can reach the top of stairs which contain 11 steps, when he can take any number of steps less than equal to 5 steps every time ? a. 1024 b. 464 c. 912 d. 1793 e. Not 127. How many of the statement(s) is(are) false I. The difference between any two consecutive primes is always prime II. The difference between any two consecutive primes is always composite III. Speed average of any two speeds is always less than twice of speed of slower IV. For a given perimeter , Circle has maximum area among all 2-D figures (figures in a single plane). a. 1 b.2 c. 3 d. 4 128. If there are 12 straight lines in a plane, such that, no two lines are parallel and no three pass through same point then how many new lines would be created by joining the point of intersections of these 12 lines. a. 1473 b.1485 c. 1497 d. NoT 129. Odds in favour of "Ram will say truth" is 3:4 then what would be probability that after a fair dice throw Ram claimed its 3 a. 1/14 b. 23/42 c. 3/23 d. NoT 130. Odds in favour of "Ram will say truth" is 3:4 then what would be probability that in a fair dice throw Ram says 3 and its 3 on dice. a. 1/14 b. 23/42 c. 3/23 d. NoT 131. Four fair dices are thrown 243 times. Throw of four dice one times is termed as a set (of four dice). If all numbers which appeared on dices are noted down on a paper set wise. Then how many set we could expect all numbers greater than 1 but less than 6. a. 16 b. 52 c. 48 d. 96 e. NoT 132. It is knows that Zee Loo is a planet in Loo-Zee Galaxy, where sex ratio of infants is 800 (sex ratio is ratio of female out of 1000 mails). What would probability of two girl children of King of Zee Loo if it is known that he has two children only one of them is girl and both are not twins. a. 1/3 b. 2/3 c. 1/7 d. 2/7 e. Not 133. What would be probability of a point O lying inside a square ABCD such that angle AOB is an acute angle a. pi/4 b. 1/2 c. (5*pi/6) + (root 3)/4 d. (5*pi/6) - (root 3)/4 e. NoT 134. What would be probability of a point O lying inside a square ABCD such that angle AOB & BOC both are acute angles a. pi/4 b. 1/2 c. (5*pi/6) + (root 3)/4
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d. (5*pi/6) - (root 3)/4
e. NoT
On 28 Oct 1986 Imran Khan and Abdul Qadir were stars in 'Mission Impossible'. Read Di rection : the score chart and analyse the data. If you have any problem to understand any term try to correlate with same term in other column. All are having basic mathematical operations. It is known that only 3 bowlers did bowl. Extras was not added in either bowlers account (Runs Given by a bowler) or batsman account (Runs Scored by a batsman). Extras are only By lb (leg by) and all extras are scored in different balls, and these balls were not added in batsman account of ball faced. It is known that last wicket and first wicket was not taken by same bowler. R- Run , M--Match, B- Ball Faced, 4s & 6s- Number of 4s & 6s resp.SR- Strike Rate(= R/B * 100). Econ- Economy (=R/O) , W- Wicket Taken, O- Over, In a over there are always 6 valid balls. All figures are rounded off to double digit decimals. (Score Card Courtesy - ESPN)
135.
136.
137.
What is the Econ of Abdul Quadir a. 1.72 b. 1.68 c. 1.52
d. Cant Say
e. NoT
What is the SR of HA Gomes a. 28.57 b. 40.00 c. 0.00
d. Cant Say
e. NoT
How many wicket(s) were taken by Imran Khan a. 4 b. 6 c. 5 d. Cant Say
e. NoT
138. Who had taken wicket of MD Marshall a. Imran Khan b. Abdul Quadir d. Washim Akram e. NoT
c. Either (a) or (b)
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139. If there are 5 identical boxes carrying some identical balls. If we only know the total weight (including balls) of each box then from which additional information we can find the weight of a ball a. HCF of number of balls in each box is 1 b. Numbers in each box are distinct c. HCF of difference of number of balls of any two box is 1 d. HCF of sum of number of balls of any two box is 1 e. From any one of the information alone (given above) we can't find wt of a ball 140. TIMEXians are inhabitants of Planet TIMEX. They are immortal and their reproduction is asexual in nature. It is known that every TIMEXian produces two new baby TIMEXian in a year so by 1 TIMEXian, we will have total 3 TIMEXian in next year. Few of the TIMEXian shifted to planed WATCH and after 8 year their population is 65610 (on WATCH), then there were how many TIMEXian shifted to planet WATCH ? a. 8 b. 9 c. 3 d. 10 e. NoT 141.
inco=
If a. 13
b. 6
then 7 tan B + 13 cosec A = ? c. -13 d. Cant Say
142. If probability of Ram is killing Shyam in a bullet shot is 1:3 and that of Shyam to Ram is 1:4. If they alternate fire a bullet on each other then what would be probability that Ram is killed in a bullet shot by Shyam if it is known that Ram fired the first bullet and a single bullet shot kills a man. a. 1/6 b. 1/3 c. 1/2 d. NoT 143.
If sin 27 = x/y then sec 27 - sin 63 = ? a.
b.
c.
d. 0
144.
If 2 - cos^2 A = 3*sin A * cos A, and sin A cos A then tan A =? a. 1/2 or 1 b. 0 or 1 c. 2/3 or 1 d. 1/3 or 1
145.
If tan 6A * tan 3A =1 then tan 24A =?, if A is an acute angle. a. root 3 b. root(1/3) c. - root3 d. - root (1/3)
146. 10 lines are in place such that no two are parallel or passing through a common point then number of maximum close regions is a. 56 b. 20 c. 36 d. NoT 147.
There are exactly how many four digits number which has exactly two different digits a. 720 b. 900 c. 783 d. NoT
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148. Mr. Kumar has 10 different keys and a lock and out of 10 keys only one can open the lock. If he tries to open the lock by using the keys one after another (keeping aside the failed ones). What is the chance that 7th key will work. a. 7/10 b. 1/10 c. 1/2^7 d. None of these 149. If ax+3y=7 and 27x + by = 9 are two parallel lines for non negative of a and b then min value of a+b is a. 27 b. 24 c. 30 d. 18 e. NoT 150. Average of 10 consecutive terms of an A.P is A, if next 10 terms are also added then what would be new average______ 151.
=
What would be value of m for which 7x - 24y + m =0 is tangent to curve a. b. c. d. e. NoT
152. If 3456 is written as product of few integers (a*b*c*d*....) then what would be minimum absolute sum of all those integers. (Absolute Value means magnitude without negative sign) a. 0 b. 1 c. 2 d. 5 e. NoT 153. Consider an equation [log_B_1] +[log _B_2] +…..[log_B_N] = N here [N] is greatest integer function and log_B_N is log of N in base B then for natural number B, N = ? a. B b. B^2 c. B^2 + B - 3 d. B^2 + B - 2 e. NoT
In one clock has only 10 segments instead of 12 segments and each sub segments has 5 sub segments, i.e 1 hour has only 50 min and clock has only 10 hours. Then what would be angle between hands if this clock is showing 8:25
a. 102.5
b. 120
c.126
d. 130
e. NoT
In how many ways 10 person can be arranged in a circle such that Ram and Shyam always sit together and among Mohan, Priya and Ram no two sit together a. 43200
b. 60480
c. 14400
d. 28800
e. NoT
There would be how many trailing ’ at the end of total number of way of arranging
boys and 100 girls in a row such that no two boys and no two girls sit together. a. 24
b. 24^2
= √ b.
c. 48
d. 49
c.
e. NoT
co d.
e. NoT
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What is minimum value of N for which "1246*1248*1250*1252 + N" is a perfect square
If N =122333444455555....., is 301 digit number then what would be remainder if N would be divided by 250 a. 232 b. 169 c. 72 d. NoT (???) If the HCF of a pair of natural numbers is 13 and their LCM is 5460 then how many such pairs be possible a. 24 b. 12 c. 8 d. 4 e. NoT If the HCF of a pair of natural numbers is 13 and their sum is 5460 then how many such pairs be possible a. 96 b. 48 c. 24 d. 12 e. Not If the HCF of a pair of natural numbers is 13 and their product is 5070 then how many such pairs be possible a. 24 b. 12 c. 8 d. 4 e. NoT What would be highest power of 2 in 15^1024 - 1 a. 10 b. 12 c. 14 d. 16 What would be highest power of 2 in 13^1024 - 1 a. 10 b. 12 c. 14 d. 16
what would be sum of digits of decimal part of a. 8 b. 125 c. 26 d. 17
e. NoT
If 680! = m*(100!)^n , where n is the max possible natural number & m is a natural too then n =? a. 5 b.6 c.7 d.8 What would be remainder when 5183^70 is divided by 71
=
then unit digit of (a+b) a. 1 b. 3
c. 5
d. 7
where a & b are integral co-primes e. NoT
If F is set of all factors of factors of 1000, then what would be sum of all different elements of F. a. 2340 b.2340^2 c. 2340^2340 d. NoT
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+ = What is the digital sum of
; where
is greatest integer less than equal
to N, digital sum is continuous summation of digits till single digit. a. 2
b. 3
c. 7
d. 9
e. Not
If H HCF of all six digits number abcdef , where abc are consecutive increasing digits and def are consecutive decreasing digits (e.g 234876). Then what would be remainder if H is divided by 5 a. 1 b. 2 c. 3 d. 4 e. NoT What would be minimum number of different cuts required to divide a bigger cube in to 1320 smaller identical cubes/cuboids a. 37 b. 24 c. 30 d. 33 e. Not
is divided by 29
( )
What would be remainder if a. 1 b. 14 c. 28
What would be remainder if a. 1
b. 2
d. 15
c. 7
d. 9
is divided by 23
e. NoT
What is value of a + b + c, where a, b & c are integers with minimum one even integer I. II. a+b+c is a prime a. Question can be answered with the help of statement I alone, b. Question can be answered with the help of statement II alone, c. Question can be answered with the help of both statements together, d. Question cannot be answered even with the help of both statements together.
For three integers a,b & c I.
II. |a+b+c| is a prime
For three different integers a, b & c I. a. If I is true then II is definitely false c. Both can be true at a time
II. |a+b+c| is a prime b. If II is true then I is definitely false d. II can be true but I can't be true
Number of digits in 20! =??? a. 19 b. 20 c. 21
d. 22
If N mod A = x ; x mod B=y & y mod C = z , where A, B and C are 5 , 8 and 11 in any order then maximum value of (x+y+z) = ? a. 12 b. 14 c. 16 d.17 e. NoT For how many natural number N ( a. 14 b. 24 c. 28
; N^7 gives remainder 1 when divided by 56 d. 27 e. NoT
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If a three digits number XYZ is multiple of N then it is also known that YZX & ZXY are multiples of N. then among the following which could be value of N. where X, Y & Z are different digits and could be 0 a. 23 b. 32 c. 47 d. 37 If 152720168 - X = N^2 , where X and N are non-negative integers , then among the options which could be value of X a. 2 b. 3 c. 4 d. 8
If N! has N digits then there would be how many 0's at the end of factorial of sum of all such N if converted into base M where M is maximum value of N for given condition a. 30 b. 28 c. 32 d. 22 e. NoT For how many natural number N less than equal to 100, such that (N+10)! is divisible by N^2 a. 75 b. 78 c. 79 d. 21 e. NoT For positive integer N less than equal to 10, if (N!)*m is a perfect square where m is the least possible natural number then how many different values of m be possible (for different values of N). a. 20 b. 9 c. 8 d. 7 e. NoT If N = 1000a + 100b + 10c + d & n = a + b + c + d Where a, b, c & d are distinct non zero digits then Maximum value of N/n = ? If N = 1000a + 100b + 10c + d & n = a + b + c + d Where a, b, c & d are distinct non zero digits then Minimum value of N/n = ? If N! is divisible by N^K then what is the maximum value of K is possible where K is a natural number and N is composite number is less than 100. a. 18 b. 15 c. 10 d. 21 e. NoT
If N! is divisible by N^K then what is the maximum value of K is possible where K is a natural number and N is a number is less than 100. a. 18 b. 15 c. 10 d. 21 e. NoT If N=2^13 -2^6 then what would be sum of all factors of N a. N b. More than N but less than 2*N c. 2*N d. More than 2*N but less than 3*N e. NoT What would be right most two non zero digits of 100th root of 20^20^20 a. 24 b. 76 c. 04 d. 16 e. NoT ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
Maximum number of different digits in the decimal of P/37 , where P is prime other than 37 is ________ ??? a. 3 b. 6 c. 12 d. 36 What would be remainder when (1234)_18 is divided by (17)_18. (N)_B denotes number N in base B a. (10)_10 b. (A)_18 c. (13)_18 d. (13)_10 e. NoT If N= 3^4*a^b and N in base c = 31400 , where a, b, & c are distinct natural nubmbers then a+b+c= ? a. 13 b. 17 c. 15 d. Cant Say e. NoT If a ten digits number is multiple of 11 & 9091 and its 2nd, 5th, 6th, 8th & 9th digits (from right) are 4,7,3,5 &2 respectively then what would be remainder if N is divided by 101 a. 0 b. 37 c. 73 d. cant say e. NoT (???) What would be unit digit of LCM of 23^13+1 & 23^13-2 a. 2 b.4 c. 6 d. 8 e. 0
If I is the integral value of square root of 232*233*234*235then what would be digital sum of I a. 3 b. 5 c. 7 d.9 e. NoT If log 5 (base10) =0.69897 then there would be how many zero's after decimal in the decimal part of 1/2^100 a. 39 b. 100 c. 30 d. 69 e. NoT If in a Fibonacci (T[n+2] = T[n] + T[n+1]) sequence whose all terms are integers with none of the term is unity and difference of 10th term and 9th term of a is 1111 then what is the sum of 7th and 6th term a. 45 b. 11 c. 56 d. 34 e. NoT If M and N are two distinct primes such that, when M divides N^2 - 1 and N divides M^2 4 in both case remainder is 0, then what would be sum of all distinct p ossible value of "M+N" a. 3 b. 13 c. 31 d. 43 e. NoT If product of 4 numbers has 16 factors and their sum is not an even number then how many different remainders could be possible if product is divides by 6 a. 2 b. 3 c. 4 d. NoT What would be 122nd digits after decimal of 22/7 a. 1 b.4 c. 2 d. 8 For how many different numbers M & N , M! - N! is a perfect square of an integer a. 0 b. 1 c. 3 d. More than 3
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There are how many prime factors of 12480 a. 4 b. 9 c. 56 d. NoT What is the sum of all different possible valued of "a" such that both "abc" and "bca" are three digits perfect squares a. 6 b. 1 c. 7 d. 8 There are how many number(s) in decimal system be possible such that its equivalent in base 6 has 4 digits but that in base 4 it has 6 digits a. 1295 b. 271 c. 217 d. 272 e. NoT If kumar writes all numbers from 1to 10,000 from left to right and make a single number then in this number there are how many 12 are visible in single number. a. 430 b. 413 c. 432 d. 412 e. NoT What would be last two digits of a. 15
b.35
c. 55
d. 75
e. NoT (???)
If N= 1*1! + 2*2! + 3*3! + 4*4! +.....+ 49*49! ; then what would be remainder if N is divided by 53 a. 27 b. 26 c. 25 d. 0 e. NoT If three digits of the number 78932279178745, are omitted such that the result is as large as possible. Then what would be sum of all three digits a. 6 b. 9 c. 16 d. 17 e. NoT
How many statement(s) is (are) always correct for real a & b I. If then II. If then or a < b III. If then IV. If then or a < b V. If then or a < b a. 0 b. 1 c. 2 d. 3 e. More than 3
CHOTU SESSION VERBAL #XAT DIRECTIONS for questions 141 to 145: In the following questions, select the pair of words that express a relationship similar to the pair in capitals. 141. PECUNIARY : MONEY a] jejune : youth b] arbitrary : temper c] tectonic : structure d] specious : value
142. ACROPHOBIA : HEIGHTS a] logophobia : sound b] nelophobia : power c] pediophobia : pedestrian d] photophobia : light
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143. ECLIPSE a] nascent b] inappropriate c] peripatetic d] apogee
: : : :
: UNVEILING pedigree inapt eclectic perigee
144. BARD a] troubadour b] toreador c] bugler d] tipster
: : : :
: POET dancer bullfighter thief drunkard
145. ANTEDILUVIAN : PRIMEVAL a] neoteric : recent b] annul : deplete c] replete : spasmodic d] historic : palpable DIRECTIONS for questions 146 to 155: Given below are 10 sentences followed by questions based on the same. Read the sentences and, then, answer the questions accordingly.
1] Sara named her pet Alsatian „Tot‟. 2] „Laetitia heard the front door bang and, then, a huge crash outside the house‟. Joe read the last line of Scott‟s „The Mulberry Tree‟. 3] Carrick to Smith: Please explain the full form of MRI, which you mentioned only in brief during your presentation. 4] When asked to describe the beautiful mountains, Ramesh said, “They rise out of the mist like alert soldiers,
all tough and silent, all blue and ice, all ready to impose their will on the hapless climber”. 5] The police recorded the statement of Alistair who, according to Mr. Sequeira, had allegedly broken into his house in a state of drunken stupor. 6] Ismail was very surprised to see a red car in one of the scenes of the Biblical film Ben Hur and decided to write about it in his school report on the film based in the ancient times and and wrote about it in his school project.
7] Saurav cried in jest, “For sooth, I have not stolen your watch; just borrowed it without asking you!” 8]
Reeves was quite alone in the room when Mohan caught him having a conversation with himself.
9]
Leena decided to follow Cassia‟s advice of ending each of the episodes of the TV serial on a
cryptic note so that the audience would be anxious to know what happened next.
10] The captain of the ship bellowed, “All hands on deck!” 146. Who used an archaic term? a] Ramesh b] Mr. Sequeira
c] Laetitia
d] Saurav
147. Who used a palindrome? a] Reeves b] Sara
c] Alistair
d] Captain
148. Who used an imagery? a] Cassia b] Reeves
c] Scott
d] Ramesh
149. Who used an abbreviation? a] Smith b] Carrick
c] Captain
d] None of these
150. Who used the idea of a cliffhanger? a] Alistair b] Saurav c] Leena
d] Joe
151. Who made use of an anachronism?
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a] Reeves
b] Smith
c] Ismail
d] Mohan
152. Who used a synecdoche? a] Cassia b] Captain
c] Alistair
d] Sara
153. Who used an onomatopoeia? a] Joe b] Ismail
c] Leena
d] Scott
154. Who made an allegation? a] Smith b] Alistair
c] Mr. Sequeira
155. Who held a soliloquy? a] Reeves b] Leena
c] Captain
d] None of these
d] Sara
DIRECTIONS for questions 156 and 157: Choose the correct alternative to complete the sentences. 156. The property was snapped up quickly, but the transaction was done ___________. a] according to Hoyle b] up to the mark c] after a fashion d] at the top of the tree 157. Shalini felt that the best way to get noticed in the Art Competition. among a teeming host of newcomers, was to be totally shocking; to base her film on a theme very ___________. a] art nouveau b] à la mode c] avant garde d] Florentine DIRECTIONS for questions 158 to 160: Given below are some quotations of famous personalities followed by 4 options that sum up the main idea of the quotation. For each question, select the option that best conveys the main idea of the quotation.
158. “Consistency is the last refuge of the unimaginative.” - Oscar Wilde a] b] c] d]
Consistent people are unimaginative. When all else fails, unimaginative people often hide under the cover of consistency. People often hide their lack of imagination under the guise of consistency. People embellish their weak imagination by calling it consistent behaviour.
159. “It‟s not the size of the dog in the fight, it‟s the size of the fight in the dog.” - Mark Twain a] The desire to fight is more important than the ability to fight. b] Strength seldom determines the outcome of a fight. c] The desire to win is more important in a fight. d] All of the above
160. “Aromatic plants bestow no spicy fragrance while they grow; But crush‟d or trodden to the ground, Diffuse their balmy sweets around.” - Oliver Goldsmith a] b] c] d]
We do not know what we are capable of unless pushed to the extremes. Adversity brings out the best in us, something which we were unaware of till then. Everyone has strengths, but few realize them unless pushed to prove them. The best can be achieved only if one is forced to prove it.
DIRECTIONS for questions 161 to 175: Choose the correct the alternative for each question. 161. The question that all managers have to understand properly is how to get the most out of people, and, at the same time, get them excited. The underlined phrase can be best replaced by:
a] „get along famously‟. c] „get a handle on‟.
b] „get it in the neck‟. d] „gather steam‟.
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162. Sam is extremely pessimistic and also imparts a negative influence on his teammates. He can be called a:
a] „bad egg‟.
b] „bad apple‟.
c] „bag of bones‟.
d] „paper tiger‟.
163. Which of the following describes a person who argues only for the sake of argument and adopts a position that he himself does not believe in? a] Devil‟s Advocate b] Dirty Dog c] Vicar of Bray d] Agony Aunt 164. Which of the following is another name for an angel? a] Volpone b] Salamander c] Reeve
d] Cherubim
165. If „Theocracy‟ refers to the rule of religious leaders, „Plutocracy‟ refers to the rule of the: a] wealthy.
b] philosophers.
c] politicians.
d] scientists.
166. A person who protests against or breaks established beliefs and traditions is an: a] idolator. b] iconodule. c] iconoclast. d] ethnocentric. 167. Select the option that arranges the following words from low to high in ascending order according to their implications. a] think, cogitate, ponder, ruminate b] think, ponder, cogitate, ruminate c] ponder, ruminate, think, cogitate d] ruminate, cogitate, ponder, think
168. Which of the following most closely implies „to annoy someone extremely‟? a] exasperate
b] irritate
c] enrage
d] provoke
169. Which of the following would be used to say that a person is uneasy and nervous? a] mesmerize b] fidget c] astonish d] petrify 170. The following words are almost similar in meaning, but there is a subtle difference in their meanings. Which of the following has the most neutral connotation? a] titter b] chortle c] snigger d] laugh 171. When he realized that his brother had a strong business acumen and could soon override him in their family business, he decided to restrict his brother‟s freedom and say in business issues. He was trying to: a] put the clocks back. b] keep a close eye on his brother. c] close the book on his brother. d] clip his brother‟s wings.
172. „Oblique‟ is to „outright‟ as „bombast‟ is to ______________. a] „terse‟ b] „rhetorical‟ c] „inane‟ d] „captious‟
173. To watch someone closely in a way that makes the person uncomfortable is to:
a] be up to one‟s neck in something. c] get something in the neck.
b] breathe down somebody‟s neck. d] be neck – deep in something.
174. As „sharpness‟ is of a „razor‟, „slyness‟ is of a ________________. a] „snake‟ b] „crocodile‟ c] „fox‟ d] „stork‟
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175. The following are different sets of beliefs about religion and God. Identify the option that does not correspond to the stated pattern. a] Cosmology, Mythology, Scientology, Ontotheology b] Positivism, Agnosticism, Atheism, Non-atheism c] Mysticism, Esotericism, Shamanism, Spiritualism d] Judaism, Hinduism, Confucianism, Zoroatrianism
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Maths By Amiya, QUESTIONS & Solutions 1. [b]. 60 litres
4. [e] None of These 13:5
8. [c] 25%
2. 8:27
5. [d] Can not be determined
9. [c] 225 days
3. [d] 1% Loss , or Rs 40.40 Loss
10. 720/19 km/hr 6. [d] 34.28 Km/Hr 11. [c] 50 7. 104 m
Direction :- If 10 Jawans parading in a ground in a line back to back such that 2nd one is seeing the back or 1st so 10th one is seeing that of 9th with speed of 1 m/sec. There is gap of 1 m between two Jawans. Suddenly 10th Jawan from start running with speed of 2m/s towards 1st Jawan and touches him and come back without wasting any time. Then 12. Find the Total Distance Travelled By 5th Jawan during this process. 13. Find The Distance Travelled By 10th Jwana Towards 1st Jawan.
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14. Find The Distance Travelled By 10th Jwana Towards his position.
15. Sol: [d] Since given rice are Rs 25 and Rs 53 kg & Rs 32, and Rs, 46 are equidistance from required rice so among options the answer should be [d] we need equal quantities of each type of rice and could take any ratio but equal. 16. [b] 34 17. [c]. 2.04% loss, take total number of orange purchased in one transaction = LCM(30,40,35) and work 18. [d]. 41 Distance travelled by ram = 60*61/2 = 1830 Distance travelled by shyam = 60*61= 3660
Relative distance (same direction) = 3660-1830= 1830m 1st meeting at 66 m , and rest at so rest 44 m, rest distance =1830-66 =1794 Perimeter of Track = 44 m. number of meetings in 1808 m = [1764/44] = 40 So total 41 meetings since the initial distance between them was 22 m only, and after first meeting they should travel 44 m for next meeting.
19. [b]. 125 Distance travelled by ram = 60*61/2 = 1830 Distance travelled by shyam = 60*61= 3660
Relative distance (opposite direction) = 3660+1830= 5490m 1st meeting at 22 m , and rest at so rest 44 m, rest distance =5490-22 =5468 Perimeter of Track = 44 m. number of meetings in 5424 m = [5468/44] = 124 So total 125 meetings since the initial distance between them was 66 m only, and after first meeting they should travel 44 m for next meeting. 20. [c]. 120, 120 & 180 m Relative speed of two :- 1 m/s meeting time - 60 sec Relative speed of two :- 2 m/s meeting time - 30 sec Relative speed of two :- 3 m/s meeting time - 20 sec All three first time after 60 sec. and after 60 sec they stop.
[Initial A & B] [Initial B & C] [Initial A & C]
Speed Change
Time
0 sec
speed 4&1
speed 4&2
speed 4&1
speed 2&1
20 sec
30 sec
40 sec
60 sec
Robots
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A
1
4
2
2
Stop
B
2
2
4
1
Stop
C
4
1
1
4
Stop
Distance Covered
Total Distance
A
0
20
40
20
40
120
B
0
40
20
40
20
120
C
0
80
10
10
80
180
=, =, =
21. [a]. 12
After solving, A=12, B=8 & C = 7 Or alternate do reverse calculation and find A.........B........C 9.........9........9 9.........9........10 9.........(12-3)........10
9.........12........7 12-4.........12........7 12.........8........7 (ans) 22. [b]. 5:2 23. [b]. 1:2 24. [a]. 14:31 25. [c]. 3000 Their work ratio C:A:B = 4:11:5 ; so answer is 3000
26. [b]. 21 Km Ratio of their speeds = 13:7 , so number of meetings points = 13-7 = 6 , all 6 meeting points ar uniformly distributed. For minimum distance between any two make 60 as central angle, so minimum distance would be radius of track. Perimeter of track = 132 Km = 2*pi*r => r= 21 km.
27. [e]. NoT Milk/ Total = (90/110)*(100/120)*(110/130) = 15:26 So Milk : Water = 15:11 28. [d]. (D+P)/(D-P)
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29. [a]. 26 Sec , 60 m (clockwise) In first 2 sec, A covers 40 m. Their Speed Relative = 10m/s Initial Distance between them for first meeting = 100-40 = 60 m (concept : faster chase slower) Meeting time of first meeting (After B's Start) = (Initial Distance)/( Speed Relative) = 60/10 = 6 sec For next meeting Initial Distance = 100 m (Concept- Initial Distance is length of track , since this time, both are starting from same point) Meeting time for next meetings = 100/10 = 10 sec So time for 3rd meeting after B's Start = 6 + 2*10 = 26 Sec For where, In 26 Sec, B would cover 260 m, i.e 60 m (clockwise) from start 30. [c]. 41% Avg % change is GM of multiplying factor of % changes = so approx 47%
√ =
31. [c]. 15 For same distance avg of mileage = HM(Given Mileages)
= HM(12,15,20)=
=
32. [c]. 76:49 During first process, Ratio = a:b During second process, Ratio = a^2 + b^2 : 2ab During third process, Ratio = a^3 + 3ab^2 : 3a^2b + b^3 = 76:49 [a=20,b=5] 33. [d]. 4:00 34. [d]. 2:3:5 check by options
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1.4696
35. [d]. 2.4 $ Current price of that pen in Rs = Rs 120. Current currency rate is 1.2$ = Rs 60 So Current price of Pen = Rs 120 = 2.4 $ 36. [e] NoT 216 Since ratio of selling price to mark price of a article is 3:5 so Discount % = (2/5)*100 = 40% %Profit : % Mark-up = 2:5 Let %Profit = 2x & %Mark-up=5x So 2x = 5x - 40 + (5x*(-40))/100 x= 40 So %Profit 2x= 80% Since cost price = Rs 120 so S.P= Rs 216 37. [c] 50% 38. [e] Not 100% 39. [e]. NoT [0] Time of meetings (in opposite direction) is given by (2n-1)*D/Speed Relative , where D is length of path. In this case D= 20 & Speed relative = 20 m/s , so meeting times are 1sec, 3sec , 5 sec and so on. so in 2min=120 Sec there would be 60 meetings (in opposite direction) including extreme ends. Total round covered by faster (A) in 120 sec = 120 /(20/12) = 72 rounds They meet 12 times on extreme ends We know that faster meets or overtake slower in its every round except if they meet at extreme ends then this meeting is including in a meeting of two rounds. so they either meet or over take 72-12 = 60 times. in 2 min Thus, there would be 60-60 = 0 meeting possible which are over takes. 40. [e]. NoT – 0 Time of meetings (in opposite direction) is given by (2n-1)*D/Speed Relative , where D is length of path. In this case D= 16 & Speed relative = 16 m/s , so meeting times are 1sec, 3sec , 5 sec and so on. so in 80 Sec there would be 40 meetings (in opposite direction) including extreme ends.
Total round covered by faster (A) in 80 sec = [80 /(16/10)] = 50 rounds Number of meeting at extreme end in 80 sec = 0 We know that faster meets or overtake slower in its every round except if they meet at extreme ends then this meeting is including in a meeting of two rounds. ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
so they either meet or over take 50-0 = 50 times. in 80 min Thus, there would be 50-40 = 10 meeting possible which are over takes. 41. [b]. 12.5 % profit 42. [c]. 20 If their Speed Ratio = a:b then a+b= 30 , where a and b are co-primes then {a , b} = {1,29} , {7,23}, {11,19}, {13,17} Number of different meeting points in same direction |a-b|= 28, 16, 8 or 4 On an escalator if Jhon takes 5 steps then in same time Rashi takes 8 steps. If Jhon takes 35 steps to reach first floor from the ground floor and Rashi takes 80 steps from first floor to ground floor by the same escalator then how much full steps of escalator would be visible if escalator is in idle position. Steps of Jhon 5S
Steps of Rashi 8S
Help/Opposition by Escalator 8D
40S
40D
35S
56D
43. [c]. 33 & 11/17
53. [c]. 1147.5 sec= 17*9/8 min = 1147.5 sec
44. [d]. 1438 54. [c]. 60/7 45. [b]. 50 lit 46. [b]. 60 seconds
55. [b]. Any two , I & II are not a valid condition
47. [c]. 32:93
56. [b]. 140 km
48. [e]. NoT 128
57. [b] 170 km (Speed Kacchi = 10 km/hr, Speed Pakki = 12 km/hr)
49. [c]. 47:22:11 58. [c] 105 50. [b]. 1331 59. [d].126*sin20 51. [c]. 12.5 kg 60. [d]. (a+b)/100 52. [b]. 27
[d]. NoT
=√
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https://www.facebook.com/MathsByAmiya/photos/528568450528609/
√ = √ ⇒ = = =(√ ) √ = =
62. [b]. By Apollonius ,
; where a is half of another diagonal.
so diagonal = 63. [a].[0,1]
Vol of water (tip is downside) =
Vol of water (circular base downside) =
[b].
If
then
Ans : 150 degree [c].
√
cm
We have Radius of Circle of centre Q = 2 cm [inradius of triangle, and Radius of circle of centre P = 6 cm
[ ex radius =
=
]
Since ADE is a right angled triangle so we can work on this by co-ordinate geometry . Assume D is origin So coordinate of Q = (2,-2) [IVth quadrant] & co-ordinate of P = (-6,-6) [IIIrd Quard] So QP =
√
cm
[By Distance Formula]
https://www.facebook.com/MathsByAmiya/photos/812283092157142/
= √ = = [b]. 2.4
or can apply
Ans: 15 or 30 or 75 or 120 degree (since angle A=30 or 150 degree, and we dont know which two angles or sides are equal) [b]. 4:7 [c]. 3:1 ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
[c]. 4:15
= & = ⇒ = = () = () = = [c]. 80:39
For a=10x , b=11x & c=12x =>
[d]. Product of 2nd smallest and 3rd smallest radius
where r is inradius and rest are exradius of a triagnle.
[c]. pi / (3* sqrt(3)) ; [c] , for equilateral triangle. [c]. 458.916 For a given perimeter, Area of a circle is maximum . Perimeter of this polygon is 77 cm , consider it as a circle of circumference = 77cm so the area of this circle is approx 472. so area of polygon should be less than 472 , hence [c] [d]. 23.33; Median [b]. 12
√
; Best is coordinate geometry
[c] 5, Best is coordinate geometry [d]. (b) or (c) Take Left turn as 90 degree and right turn as 270 as internal angle of a closed polygon, and we know sum of all internal angles = 180(n-2) , n is vertex Here 90*l + 270*r = 180 (l+r-2) , by question r=20, we get l=24 Now, Take Left turn as 270 degree and right turn as 90 as internal angle of a closed polygon, and we know sum of all internal angles = 180(n-2) , n is vertex Here 270*l + 90*r = 180 (l+r-2) , by question r=20, we get l=16 So either 24 or 16.
[b]. 45 ; solve by options or coordinate or sine formula
√
[b]. 12
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[e]. NoT https://www.facebook.com/MathsByAmiya/photos/584494198269367/ 83. [d]. NoT 84. [c]. pi - (1/2) rad
[b].
√
https://www.facebook.com/MathsByAmiya/photos/840413596010758/ [b]. 4 cm
Ans: 10 cm^2 https://www.facebook.com/MathsByAmiya/photos/509985899053531/ [e]. NoT 180*(n-2)=(n/2)(2a+(n-1)d), here a=30 For convex polygon we get only 2 set of values 90. [c]. 3.6 https://www.facebook.com/MathsByAmiya/photos/853093624742755/ 91. [e]. NoT
Inradius = 6 , so centre (6,6) and A=(0,16) so IA= 92. [c].
√ √
√ = √ =√
https://www.facebook.com/MathsByAmiya/photos/532772120108242/ 93. [e]. NoT (cannot be determined) 94. https://www.facebook.com/MathsByAmiya/photos/859153280803456 Ans: [b] 95. [c]. 1540 cm^2 Area = (s – c)*s = 1540 cm^2 https://www.facebook.com/MathsByAmiya/photos/861355437249907/
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[d].5 Sol: Whenever you get a bakwas question of algebra where one polynomial is given and to find value of another polynomial then we just divide required polynomial by first polynomial and remainder is our answer (just by synthetic division) so
= = = = So required answer is 5
[c]. x;This question has second type of divisor
mod = x by putting in polynomial Since this remainder is smaller degree than given divisor so remainder would be x only
= =, = = =, =
Two important Divisors 1. If divisor is then it's multiple is , now put in dividend (P(x)) and get the remainder (R(x)) by . a. If R(x) is smaller degree than given Q(x) then R(x) is your required remainder. b. Otherwise divide R(x) by Q(x) by synthetic division. 2. If divisor is now put .
then it's multiple is , in dividend (P(x)) and get the remainder (R(x)) by
a. If R(x) is smaller degree than given Q(x) then R(x) is your required remainder. b. Otherwise divide R(x) by Q(x) by synthetic division. [d]. 23 The expansion of
by power erie or taylor erie for = in So coefficient of Is
=1*1 + 3*1 + 6*1 + 7*1 + 6*1= 23 [c]. 31 [c] 0
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[b]. 2, N=38 Adding all and after arranging, we get a^2 + 6a +9 + b^2 + 4b + 4 +c^2 + 10c + 25 = 0 (a+3)^2 + (b+2)^2 + (c+5)^2 =0
ec = tan == = = = = = = [d]. 57
[b]. 0
[b]. 2, tan function (trigo) [b]. 10 [c]. x^2 + 2x -3 =0 Since a and b are roots of x^2 - 7x + 9 =0 so, a^2 - 7a + 9 =0 & b^2 - 7b + 9 =0 , then the values of new roots a^2 - 7a + 10=1 & 2b^2 - 14b +15= -3 So equation whose roots are 1 & -3 is x^2 + 2x -3 =0 [b]. Independent of n Let
⇒
= √
-m)(x+n)=0, thus x=a only since x cant be -n a negative, so it is independent of n
[d]. All Real Numbers [b]. -11 min(a^2 + b^2) = min((a+b)^2 - 2ab) = min((m-2)^2 - 2(m+3)) = -11 [d]. x^3 - 6x - 6 =0
| |=, | |= [c]. 20
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| | | | =, | | | | = = = = = = =
|x-5|=1 or 2 , x= 4,6, 3 & 7 then sum of all possible x is 4 + 6 + 3 + 7 =20 [c]. Rational
[c]. 2 Sides are 3x-5, x+3 , 9-x, If 3x-5= x+3 , x=4 then sides are 4,4,5 If 3x-5= 7-x , x=3 then sides are 4,6,4 (triangle not possible) If x+3= 7-x , x=2 then sides are 1,6,5 So only 2 values are possible for x [d].-4 For getting equation whose roots are 2 more than roots of x^2 + nx + m =0 , we put x=x-2 in equation, so we get (x-2)^2 + n(x-4)x + 4 -2n+m = 0 which is same as given equation x^2 + mx + n =0 So, x^2 + (n-4)x + 4 -2n+m = x^2 + mx + n So, n-4 = m & 4 -2n+m = n , so, m=0, n=-4 so, m+n = -4
m = ⇒ n
= = = = ⇒ , [c]. 17
Say ,
Then
So,
, so there are total 16 possible values of
n , since K should be odd.
[b]. -11025 For sum of all coefficients including constant, put x=1 , and we get 0 For constant term put x=0 , so we get 11025 as constant term , So sum of all coefficient excluding constant term = - 11025
= = = = , [b]. [-2,2]; its 0. roots are 3, [d]. 2
a=3k, b=2k, c=5k, d=2k
[d]. Can't be determined, since a+b+c=
, so a+b+c=
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[c]. -9, -4, -3 & -2
=⇒ =⇒= = = = – – [c]. 5/3
So,
[c]. - 49/10 a, b, c, d, ..... are integers (It can be +ve or can be ve). For minimum required value the sign should be ve and magnitude should be maximum that is possible when any five of them = -5 and remaining one = 10. Then required value = -5+1/10 = -49/10.
[b]. 19 By making combinations of two and adding we get a^2 + 2*a*e+e^2= 16, so, a+e= b^2 + 2*b*f+f^2= 36, so, b+f= c^2 + 2*c*d+d^2= 81, so, c+d= So Max a+b+c+d+e+f = 19
[d]. [-4/19 ,
[, by making perfect square
[c]. x;x^6=-1 126. [c]. 912 Total n umber of di ff er ent ways in whi ch a boy can reach the top of stai rs whi ch contain N steps, when he can take any number of steps less than equal to " r " steps ever y tim e i s Nth ter m of ser ies woul d general term i s
=
= = = = ∑ =
In how many ways a boy can reach the top of stairs which contain 10 steps, when he E.g. 1 can take any number of steps less than equal to 2 steps every time ? Sol: 89 We want to find 10th term which is sum of two preceding terms (sin ce one can take max 2 steps at a time). Or
, which is
1
1 2 3 5 8 13 21 34 55 89 In how many ways a boy can reach the top of stairs which contain 11 steps, when he E.g. 2 can take any number of steps less than equal to 5 steps every time ? Sol: 912 We want to find 11th term which is sum of five preceding terms (since one can take max 5 steps at a time).
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1
1
2
4
8
16
31
61
120
236
464
912
, I & II are definitely false and III not always it depend upon the distance covered 127. [c]. 3 in both speeds. 128. [b].1485 https://www.facebook.com/MathsByAmiya/photos/746191142099671/ 129. [b]. 23/42
Required Probability = 130. [c]. 3/23
Required Probability =
=
=
131. [c]. 48 Probability of getting greater than 1 and less than 6 on A Dice throw = 4/6 = 2/3
So Prob of getting greater than 1 and less than 6 in a set (of four dice) = This probability means out of 81 trials we would get 16 required events So out of 243 trials total number of required outcome is 48
=
132. [d]. 2/7 Cases are { bg, gg, gb } So Required probability = {gg}/( { bg, gg, gb })
= =
133. [e]. NoT;1 - pi/8 https://www.facebook.com/MathsByAmiya/photos/784502371601881/ 134. [c]. (5*pi/6) + (root 3)/4 https://www.facebook.com/MathsByAmiya/photos/784502371601881/ 135. (b) 1.68 (Run = 16 , O= 9.3, 9.3 is a cricket term not used to Calculate Econ 9.3 means 9 overs and 3 balss, mathematically its 9.5 overs , so 16/9.5 = 1.68) 136. (b) 40(By adding Runs we can get Run Scored By HA & By counting Balls column we can get ball faced by HA; Ball Faced By all batsmen should be= Total Balls Of Innings - 2(extras), SO R=2 & B=5)
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137. (a) 4 138. (b)
139. [c] with (c) HCF of difference of wts of box would be wt of one ball 140. [d]. 10 Their population after nth year = 3^n if in start there was only 1 TIMEXian So x*3^8=65610 then x=10 141. [a]. 13 142. [b]. 1/3 ; Sol: 2/3*1/4 + 2/3*3/4*2/3*1/4 + 2/3*3/4*2/3*3/4*2/3*1/4+..... = 1/3 143. [b]. x^2/ (y*root(y^2 - x^2)) 144. [a]. 1/2 or 1 145. [a]. root 3 A= 10, since tan6A = cot 3A , tan 240 = root3 146. [c]. 36
d. NoT
147. [c] 783 Case I - Non zero digits Sub case A: Three same one different = 9*8*(4!/3!)
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Sub case A: Two same and another two same = 9*8*(4!/(2!*2!)) Case II - With Zero (starting with non zero) Sub case I - Only one 0 = 9*(3!/2!) Sub case II- Two zeros= 9*(3!/2!) Sub case III- Three zeros= 9 Total= 9*8*(4!/3!) + 9*8*(4!/(2!*2!)) + 9*(3!/2!) + 9*(3!/2!) + 9= 783 148. [b] 1/10 ; 9/10*8/9*7/8*6/7*5/6*4/5*1/4=1/10 149. [d] 18,
150. Cant say, A+5d 151. [e] ; x^2 + y^2 - 100 =0 is a circle whose centre is (0,0) and radius is 10, so for being a
tangent
=√ so m =
152. [a] 0 153. [d]. B^2 + B – 2 ; best is to solve by taking some value of base B
⇒ min ⇒ min=
[c].126 Min Hand 50 min Hour Hand 500 min Angle by Hour & Min Hand in 1 min Angle by 1 seg = 36 So angle for 8:25 = 8*36 - 25*6.48= 126
[a]. 43200 ; 2*6!*P(6,2)=43200 Since M & P has problem , we will arrange them in the last, first arrange 8 people including (R,S) So we have total (R,S), a,b,c,d,e,f (i.e. only 7 bundles out of 8) So they can be arranged in (7-1)!=6! [(n-1!) since circle] and R & S in 2 ways So total arrangement in circle of these 8 ppl = 6!*2! Now 7 bundles (R,S), a,b,c,d,e,f would create 7 different places (places in between them) for M & P, but both both cant sit near to R so only 6 places for these two. total ways for M & P = P(6,2) So required ways for all 10 = 6!*2!*P(6,2) = 43200
ling ’
[c]. 48 Ways = 2*100!*100! i.e. 48 trai [e]. NoT
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16 = 2^4 Product of four consecutive numbers of an AP + d^4 is always a perfect square , where d is common difference of AP [b]. 169 N= 1234...... Single digits = 1+2+3...+9 = 45 Double digits = 2* (10+11+12+.....) let the maximum number in the series be "n" Total digits = 45 + (n-10+1)(2*10 + (n-10+1 - 1)*1 = 9 + (n-9)(n+10) =n^2 +n -45
(By AP Sum)
Since there are 265 digits , so n= 18 , till 18 we would get 297 digits so we need 4 more digits i.e. 1919 So, N= 122333.....18181919 For divisible by 250 we need to check last three digits, 919 N mod 250 = 919 mod 250 = 169
[c]. 8 Let number be 13*m & 13*n then LCM = 13*m*n=5460
⇒ m*n = =
Since m & n are co-primes so , Total number of co-prime product pairs = So total 8 pairs are possible
=
[4 is total number of prime in 420]
[b]48 Let number be 13*m & 13*n then Sum = 13*(m+n)=5460 m+n=420 Since m and are co primes so , co-prime sum pair =
=[ ]= == ⇒ m*n = = =
[d]4 Let number be 13*m & 13*n then Product = 13^2*m*n=5070 Since m & n are co-primes so , Total number of co-prime product pairs = So total 4 pairs are possible
[3 is total number of prime in 420]
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[c] 14 15^1024 - 1 = (15^2^10) - 1 So highest power of 2 = 10+4 = 14 ; extended by 4 since 15 = 2^4 -1 https://www.facebook.com/MathsByAmiya/photos/587854111266709/ [b]12 13^1024 - 1 = (13^2^10) - 1 So highest power of 2 = 10+2 = 14 ; extended by 2 since 13 is not in the form of 2^n 1 https://www.facebook.com/MathsByAmiya/photos/587854111266709/
= [a]8
So decimal part of
is 1/125= 0.008 , so sum of digits of decimal part = 8
[b]6 If we have to find either power of 2 in both or 97 in both (biggest or smallest prime) In 100! there are 97; 2's (i.e. 2^97 in 100!) & 1 times 97 (i.e. 97^1 in 100!) & in 680! there are 676, 2's (i.e. 2^676 in 680!) and only 7 times 97 (i.e. 97^7 in 680!) We have 7 bundles of 97^1 in 680! but only 6 bundles of 2^97 in 2^676 So, we have only 6 bundles of 2^97 in 2^676 so only n=6 Ans : 0
= = = = == = ()( ) = [b] 3
; Unit digit of a + b = 3
[a]. 2340
This is nothing but sum of all factors of 1000 =
1000 = 2^3*5^3 Sum of all different factors = (1+2+2^2 + 2^3) + 5^1*(1+2+2^2 + 2^3) + 5^2*(1+2+2^2 + 2^3) + 5^3*(1+2+2^2 + 2^3) = 2340 [d]. 9
e. Not
= =
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==
Digital Sum (
)
Digital Sum (9+9*49)
9
[c]. 3; number is 3*37 = 111 mod 5 = 1 [d]. 33; Since we want minimum number so we have to cut in all three directions along x-axis, y-axis, and z-axis. and cut would be depend upon factors or required number of smaller cubes. 1320 = 10*11*12 (all factors are closer, so we will get minimum cut) For 10 parts we need 9 different cuts (assume along x-axis), For 11 parts we need 10 different cuts (assume along y-axis) & For 12 parts we need 11 different cuts (assume along z-axis), So total cuts= 9+10+11 = 30 [A]; 1
=( ) =( ) = = [b]2 [d]. Question cannot be answered even with the help of both statements together. [c]. Both can be true at a time [c]. Both can be true at a time [a] https://www.facebook.com/MathsByAmiya/photos/813110062074445/ [d] 17 ; A=11 , & x=9 & B=5 and C=8, so 9+4+4 = 17 [e] NoT 1; [N must be co-prime of 56 for 1 as remainder] Cyclicity of 56 is 6 so for coprime N, N^7 mod 56 = N , So N has only one value which is 1. I [d] 37 either check by options. or since XYZ, YZX and ZXY are multiples of N so their sum would be. XYZ+YZX+ZXY = 100X+10Y+Z+100Y+10Z+X+100Z+10X+Y =111X+111Y+111 =111(X+Y+Z) so N would be factor of this sum , means factor of 111, hence N=37 [c]. 4, check last two digits after subtraction [c]. 32 ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
There would be 4 such N be possible, which are 1, 22,23 & 24. Sum of all values is 60 70! = 2^67*3^32*K = 2^1*(8^22)*3^28*K So there would be 22 zeros You should know - http://goo.gl/dae4F7 [c] 79 ; all numbers from 1 to 100 excepts prime more than 10 [c]8 , except 4! & 3! and 8! & 9! rest would have distinct m. : max for N=9321 : min for N=1289 : [d] , 90! is divisible by 90^21 [e] for 1! we can get a bigger value (biggest ) of K [c]. 2*N; its a perfect number (read perfect number) http://en.wikipedia.org/wiki/Perfect_number#Even_perfect_numbers [b]. 76 [a] 3 [d]. (13)_10 (1234)_18 = (6538)_10 & (17)_18 = (25)_10 6538 mod 25 = 13 in base 10 = (D)_18
[d]. Cant Say; a=16 , b=2 , c=9 or a=2 , b=8 , c=9 then a+b+c= either 17 or 19 [b] 37 11*9091*34527= 100001*34527 = 3452734527 mod 101 = 37 [d] 8 Gap between both the numbers is 3 , so their HCF would either 1 or 3 (if they are divisible by 3) HCF(23^13+1 , 23^13-2) = 3 since they difference these two numbers are 3 and both are divisible by 3 HCF*LCM=Product of Number 3* LCM = ----4 (4 as unit digit of product of (23^13+1) & (23^13-2)
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So Unit digit of LCM should be 8 [c]7; Digital Sum of 232*235 = 7 (this holds for product of four consecutive numbers)
= = = log =log == [c]. 30
So there would 30 , 0's after decimals
[e] NoT there are two possible values [e] NoT, infinite for M=2 [b] 3; 0,2,4 primes with 2 [b] 4 [d]. More than 3 ; 1!-0!= 0, 2!-1!=1, 2!-0!=1, 3!-2!= 4......so d..? [b]9 [c]7, (1 and 6), (144, 441) &(256,625) [d]. 272 base 6 has 4 digits = numbers [6^3,6^4-1]= [216,1295] base 4 has 6 digits = numbers [4^5,4^6-1]= [1024,4095] [d] 412, solve by formation of number There are how many 4 digits numbers are possible such that whose all digits are prime and when we add 15 in the number resulting number has only primes as digits [d]. 75
= = = = = So
[By CRT]
[c]. 25 [d]. 17 ©AMIYA KUMAR ; Maths By Amiya, 3E Learning, Ranchi 9534002244 www.fb.me/MathsByAmiya
[a] 0
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CHOTU SESSION VERBAL #XAT: Solution 141. „Pecuniary‟ is „fiscal‟ or related to money and „tectonic‟ is related to the „structure of the earth‟s surface‟. [d] is irrelevant. [a] and [b] have pairs of words that share a quality – thing relationship. Thus,
148. An „imagery‟ is the creation of „mental images‟ that signifies sensory perception referred to in a literary work. Ramesh uses imagery to describe the mountains. Hence, [d].
they do not share the same relationship as the root pair. Hence, [c].
149.
142. „Acrophobia‟ is a fear of „heights‟. „Logophobia‟ is a fear of „words‟. „Nelophobia‟ is a fear of „glass‟. „Pediophobia‟ is fear of „children‟. „Photophobia‟ is the fear of „light‟. Hence, [d].
word or phrase. Thus, MRI stands for Magnetic Resonance imaging. This is used by Smith, as he has already mentioned it in brief during his presentation. Hence, [a].
143.
150.
The relationship between the given pair is one
An „abbreviation‟ is a shortened form of a
A „cliffhanger‟ is a melodramatic narrative,
of antonyms. „Eclipse‟ and „unveiling‟ are antonyms. Similarly, „pedigee‟ is the point nearest to the earth, while „apogee‟ is the point farthest from the earth. „Peripatetic‟ means going from place to place in order to work; „eclectic‟ means choosing from a wide variety. They don‟t share the same relat ionship. [a]
especially in films, serially published novels, etc., in
& [b] are irrelevant. Hence, [d].
151.
which each section „ends‟ at a suspenseful moment, so that the audience will wait for the next episode. Leena uses a cliffhanger on the advice of Cassia. Hence, [c].
An „anachronism‟ is placing an event, person,
item, or verbal expression in the wrong historical 144. A 'bard' is a 'poet' or one who composes poetry. A 'toreador' is a 'bullfighter'. A 'bugler' is one who uses the bugle (a musical instrument), used typically for sounding military signals. A 'bugler' must, hence, not be confused with a 'burglar' who is a thief. A 'drunkard' is described as a 'tippler' and not a 'tipster'. A 'tipster' is one who sells tips or
information to bettors or speculators. A „troubadour‟ is a wandering singer or minstrel. Hence, [b].
period. A „car scene‟ in a film based on Biblical times is totally out of place. Ismail used this anachronism in his school report. Hence, [c].
152.
a part is used to designate the whole or the whole to designate a part. When the captain of the ship bellows „All hands‟, he r efers to his/her crew – i.e., a part for a whole. Hence, [b].
145. 'Antediluvian' and 'primeval' are synonyms and mean very old, old-fashioned, or out of date; 'antiquated' or 'primitive'. Similarly 'neoteric' is synonymous to 'recent' and also means 'modern'. All other options are irrelevant. Hence, [a].
153.
146.
154.
An „archaic term‟ is a word, expression,
spelling, or phrase that is out of date in the common speech of an era, but still deliberately used by a writer, poet, or playwright for artistic purposes.
„For sooth‟, which means in truth, is an archaic
A „synecdoche‟ is a figure of speech in which
An „onomatopoeia‟ is a figure of speech in
which the sound of the words is made to suggest or echo the sense. Joe reads aloud the lines showing onomatopoeia, in Scott‟s novel. Thus, it is Scott who used the figure of speech. Hence, [d].
An „allegation‟ is a public statement that is
made without giving proof, accusing somebody of doing something that is wrong or illegal. Mr. Sequeira made the allegation against Alistair of breaking into his home. Hence, [c].
term and is used by Saurav. Hence, [d].
155. 147. A „palindrome‟ is a word, sentence, or verse that reads the same way backward or forward. „Tot‟, which means a small amount or a young child, is a palindrome and is used by Sara. Hence, [b].
A „soliloquy‟ is a speech made to oneself; a
monologue. Reeves is caught speaking to himself by Mohan. Hence, [a]. 156. „According to Hoyle‟ means in keeping with the established rules. „Up to the mark‟ means good
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enough. „After a fashion‟ means to a certain degree, not satisfactorily. „At the top of the tree‟ means in the highest position or rank in a profession or career. Given the context of the sentence – a business transaction – the best fit would be option [a]. Hence, [a].
157.
„Art nouveau‟ is a style of decorative art and
architecture that uses complicated designs based on natural shapes. Since the sentence is talking about film-making and not art or architecture, option [a] is
ruled out. „À la mode‟ means fashionable and does not fit the context. „Florentine‟ is used for food items and is a dish too. Thus, only „avant garde‟, which means
means to acquire an understanding of, can replace the underlined phrase. Hence, [c].
162. A person who cannot be trusted is called a „bad egg‟; hence, the expression cannot be used in the context. A person who is underweight is called „a bag of bones‟ and „paper tiger‟ refers to a person or institution that looks powerful but is actually weak. Therefore, [c] and [d] are also negated. A person who is bad and has a negative influence on others
is called a „bad apple‟. Hence, [b]. 163.
A person who is untrustworthy is called a
„dirty dog‟. „Vicar of Bray‟ refers to a person
new and very modern ideas in art, music or literature, that are sometimes surprising, fits in well with the meaning of the sentence. Hence, [c].
who changes his beliefs and principles to stay popular with his superiors. A person who advises
158. Oscar Wilde says, through this quotation, that people who lack imagination, in order to cover up this lack, call it uniformity, consistency, a highly prized concept. Option [a] makes the generalization that all consistent people are unimaginative. Option [d] is
who argues only for the sake of argument. Hence, [a].
incorrect as the quote is not about „weak imagination‟
A „reeve‟ is an administrative officer of a district or town. „Cherubim‟ means a winged celestial being or
but of a total lack of imagination. Between options [b] and [c], [b] is a better answer – „when all else fails‟ corresponds with „last refuge‟ of the quotation – it implies that, when nothing else works, lack of imagination is dubbed uniform action, which is actually the meaning of the quotation. Hence, [b].
159.
Mark Twain‟s quote means that the outcome of
a fight is decided by the determination to keep fighting rather than having the strength and skills to fight. Option [d] is only partly true. Option [b] contradicts the quotation because it implies that sometimes strength is enough to win a fight. Only option [a] gives the right meaning. Hence, [a].
160.
Oliver Goldsmith‟s quote means that one‟s
strength is proved in the face of adversity. Option [a] is incorrect, as it is not the intensity of the circumstances but the hardships that make us prove our strengths. Options [c] and [d] do not bring in the hardship angle. Also, option [d] distorts the meaning. Only option [b] gives the right meaning of the quotation. Hence, [b].
people on their personal problems is called an „agony aunt‟. The term „devil‟s advocate‟ refers to a person
164. „Volpone‟ is another name for fox. „Salamander‟ is a mythical being that looks like a lizard and is believed to be able to live in fire.
an angel. Hence, [d].
165.
„Plutocracy‟ refers to a government or state
in which the wealthy class rules. Hence, [a].
166. An „idolater‟ is a person who worships idols in an unquestioning manner. An „iconodule‟ is one who serves images. An „iconoclast‟ is a person who opposes accepted beliefs and traditions.
„Ethnocentricism‟ is the belief in the superiority of one‟s ethnic group or culture. Hence, [c]. 167. „Ponder‟ means to consider or think about something deeply and thoroughly. „Cogitate‟ means to ponder hards and „ruminate‟ means to reflect on a matter over and over again. Therefore, the correct sequence should be: think, ponder, cogitate, ruminate. Only [b] gives the correct sequence. Hence, [b].
168.
„Irritate‟, „enrage‟ and „provoke‟ are
synonymous and mean to disturb or annoy someone.
But „to exasperate‟ someone means to irritate or 161.
„To get along famously‟ cannot fit in the
context because it means to have a good relationship with somebody. Option [b] also cannot be used in the context because it means to be punished or criticized for something. „To gather steam‟ means to progress at
an increasing speed. Only „to get a handle on‟, which
provoke somebody to a high degree. Hence, [a].
169.
To „mesmerize‟ someone means to fascinate
somebody almost in a hypnotic manner; whereas, to
„astonish‟ means to surprise someone. „Petrify‟ means to turn into stone out of fear or any strong emotion.
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Only „fidget‟, which means to move about restlessly
antonym. „Bombastic‟ means verbose or
or nervously, is the appropriate word. Hence, [b].
pretentious; hence, its antonym would be
„Titter‟ means to laugh quietly in an embarrassed way. „Chortle‟ is to laugh loudly in amusement and „snigger‟ means to laugh in an unpleasant way at somebody‟s mistakes. „Laugh‟ is 170
the most general term, which is not indicative of any strong or particular emotion like the other options. Hence, [d].
171.
„To put the clock back‟ means to return to a
situation that existed in the past and does not explain the context properly. Option [b] is inadequate because „to keep a close eye‟ means to just watch somebody carefully and does not imply curtailing
„terse‟, meaning concise or pithy. „Rhetorical is synonymous to „bombastic‟; „inane‟means severely critical. Therefore, none of these can be the correct answer. Hence, [a].
173. „To be up to one‟s neck in something‟ means to be very busy with something. „To get something in the neck‟ means to be punished or criticized for something that one has done. „To save somebody‟s neck‟ means to prevent something bad from happening to someone. „To breathe down one‟s neck‟ means to pay very close attention to what one does
in such a way that it worries the person. „To be neck – deep in work means to be deeply involved
someone‟s powers or freedom. „To close the book on something‟ means to stop doing something because
in something. Hence, [b].
one no longer believes in its success; hence, it does not fit the context. „To clip somebody‟s wings‟ means
174. „Sharpness‟ is an essent ial quality of a razor; similarly, „slyness‟ is associated with a fox. Hence,
to restrict a person‟s freedom or powers. Hence, [d].
[c].
172. „Oblique‟ means not straight or direct. „Outright‟, which means straightforward, is its
175.
„Positivism‟ is a belief concerning philosophy
and not religion or God. Hence, [b].
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