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3E Learning, 3rd Floor, Anand Complex, Near Lalpur PS, H.B. Road Ranchi, 095 34 002244 www.facebook.com/MathsByAmiyawww.facebook.com/MathsByAmiyawww.facebook.com/MathsByAmiyawww.facebook.com/MathsByAmiya AMIYA KUMAR

Maths By Amiya, QUESTIONS 1-50

Number System

1. There are how many possible values in the form of A2A3B is divisible 11 where A & B are single digits

a. 7 b. 8 c. 9 d. 10 e. None 2. If 89: ; = 2@ 3B 4C 5D then how many different ordered pair of ;a,b> are

possible a. 3465 b. 3464 c. 1616 d. 1617 e. None of These 3. If ;1A9>^2 = BAB81 , where A and B are different digits then A+B = ? a. 4 b. 5 c. 6 d. 7 e. None of these 4. If ;AB9>^2 = CDE81 , where A, B, C, D and E are digits ;can be same> but A is a non zero

digit, then what would be Mean of all possible values B + D a. 5 b. 5.8 c. 6.2 d. 8.4 e. None of these 5. If 89: ; = 2@ 3B 4C 5D then how many different unordered ordered pair of

;a,b> are possible a. 1733 b. 1617 c. 809 d. 810 e. None of These 6. If 3/N has reoccurring decimals then how many values of K 100 are possible.

a. 15 b. 23 c. 25 d. 27 e. None of These 7. There are 10 boxes numbered 1 to 10. Each Box has some balls, balls are either weighing

1gm or 2gm and no box has mix balls. One person picked 1 balls from 1st box, 2 balls from 2nd , 4 balls from third and so on, such that he picked 512 balls from box no. 10. Then he weighs all 1023 balls and gets reading as 1099 gm. Then identify all boxes having 2gm balls?

8. How many Statement;s> is;are> correct for P=a*b*c ;i> P can be prime and if a, b & c are different non negative Numbers ;ii> P can be prime and if a, b & c are different Integers ;iii> P is always non prime if a, b & c are different Integers


a. Only One b. Two c. All Three d. None of the options are correct e. None of These

9. If there are "n" students of a batch of 3E Learning seating in a circular arrangement

facing toward the centre. It is known that their roll numbers are Integral value from 1 to "n" and they are sitting in the order of increasing roll numbers. Then what would be value of "n" if Roll number 13 is just opposite to Roll Number 29 ?

10. If @CR S @R ST

= < + =UVWX where a,b and n are non negative rational numbers and "n"

is as minimum as possible then a+b+n =? 11. If P=a*b*c, where P is a prime and a,b & c are different integer then P+a+b+c+? 12. If intersection of two twins prime pair set is a non empty set then what would be product

of all elements of union set of these two twins primes pair set.

13. What would be remainder when ;2345>_21 is divided by 20 ;N>_B denotes number N in base B a. ;5>_21 b. ;10>_21 c. ;20>_21 d. ;14>_21 e. NoT

14. Which one among the options, best show the decimal form of N/606 , where HCF;N,606>=1 , ;a,b,c,d,e.... can be similar digits, X is a non negative Integer> a. X.abcdef abcdef abcdef...... b. X.abcd abcd abcd.............. c. X.abcdefgbcdefgbcdefg.......... d. X.abcdebcdebcdebcde.......... e. NoT

15. Among options which could not be a prime number in any base ? a. 145 b. 53 c. 104 d. 312 e. All could be prime in some base

16. How many factor;s> of 11,025 has;have> even number of factors a. 3 b. 8 c. 19 d. 27 e. None of these

17. When 100 is added to 5x32xx41 and the resulting number is divided by 99, the remainder is 2 then find x a. 2 b. 3 c. More than one value be possible

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d. No such value possible

18. How many statement;s> is;are> always hold/s for real I.


23.

Arithmetic

24. 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

25. 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

26. If we sell two horses each on Rs 2000/- , one horse at 10% profit and one at 10% horse, 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


27. 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 A ? a. 5:1 b. 5:13 c. 1:2 d.1:3 e. None of These

28. 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

29. 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

30. 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 in first 10 min.

31. 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

32. 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

33. 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.


34. 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 :Direction :Direction :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

35. Find the Total Distance Travelled By 5th Jawan during this process. 36. Find The Distance Travelled By 10th Jawana Towards 1st Jawan. 37. Find The Distance Travelled By 10th Jawana Towards his position.

38. 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

39. 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

Miscellaneous

40. If after "n" year a calendar repeats itself for the first time then what would be maximum

value of "n" a. 6 b. 11 c. 28 d. 40 e. None of These

41. If the Distance between Ranchi to Gaya is 300 km. We are covering this distance with the help of a Bullock cart and with 900 apples . But we can put max 300 apples on Bullock Cart, and Ox of Bullock cart travelled 1 Km after eating 1 apple which is loaded on the cart.


42. What would be total number of ways to distribute all 58 identical balls among 10 children, such that all would get minimum one ball and each would get different number of balls.

a. 10! b. 2*10! c. 3*10! d. 6*10! e. NoT 43. Maximum how many points can be possible in a space such that all are equidistance to

each other. a. 3 b. 4 c. 5 d. More than 5 e. NoT Below table iBelow table iBelow table iBelow table is a Result Chart of City School, s a Result Chart of City School, s a Result Chart of City School, s a Result Chart of City School, which has equal number of students in all which has equal number of students in all which has equal number of students in all which has equal number of students in all classesclassesclassesclasses

Class % of students Who failed in Final

Examination

Ratio of Male(M) & Female(F) Students

M:F

Who Failed Who Passed

6 15% 3:2 2:3

7 25% 1:4 2:1

8 35% 3:4 9:4

9 20% 1:1 1:1

44. What is the ratio of "Male, wrote Class 7th exam and failed" to "Female, wrote class 9th

exam and passed" a.10:1 b. 4:1 c. 1:10 d. None Of These

45. Which Statement is Correct a.. There are 48% of total students are Male b. There are 42% of total students are Male and failed c. There are 14 % of total students are Female and failed d. None Directions :Directions :Directions :Directions :---- Dood-Yo-Smart, a student of Xarvard , is fond of cryptology and created his own coding system. We just know few things about his codes, which are

He has given alphabetical codes to all numbers, Only Alphabets M, A, T, H, S have assigned different numbers among 1, 5, 10, 50 &

100 not in particular order rest number would be formed by arrangements of these alphabets only.

In his code : TA = 51 , AM = 9, MH= 15, SM= 110, T HA = 56 TT=S SA H=106 & 104= S AH

46. What would be code of 209 a. SS MA b. MM SA c. SS MH AAA d. SS AM e. NoT

47. M AM + HS + SM = ? a. SS MH b. MH SA c. SS MM AH d. AAA S e. NoT


48. Maximum how many different points can be possible in a space such that all are equidistant to each other. a. 3 b. 4 c. 5 d. More than 5 e. NoT

49. What would be total number of ways to distribute all 58 identical balls among 10

children, such that all would get minimum one ball and each would get different number of balls.

a. 10! b. 2*10! c. 3*10! d. 6*10! e. NoT 50. minimum dei@| + }ad@| + +f + }adh}@;~> + dh}@;~> + }af@;~>


k

Maths By Amiya, ANSWERS 1-50

Number System

1. Sol: [b]

Different Possible Cases Total Cases

2*A + B = 5 2

2*A + B = 16 5

2*A + B = 27 1

Total cases 8 2. Sol: [d] 89: ; = 2@ 3B 4C 5D = 2T 3B 5D So Number of Ordered Pair ;a,b>= ;2*10+1> ;2*3+1>* ;2*5+1>= 1617 3. Sol: [d] Since last two digits of square are 81 so last two digits of 1A9 would be either 50*n 9 Number Square

Number Square

Number Square

109 11881

209 43681

309 95481 141 19881

241 58081

159 25281

259 67081 191 36481

291 84681

So its 159^2 = 25281 , A=8, B=2 4. Sol: [e] Since last two digits of square are 81 so last two digits of 1A9 would be either 50*n 9 Number Square B D B+D 109 11881 0 1 1 141 19881 4 9 13 159 25281 5 5 10 191 36481 9 6 15


209 43681 0 3 3 241 58081 4 8 12 259 67081 5 7 12 291 84681 9 4 13 309 95481 0 5 5 So, Mean = 9.33 359^2=128881 ;can't be since square is 5 digits only> Different possible value of B+D are, 1, 3, 5, 10, 12, 13, 15 so mean = 59/7 = 8.42.. 5. Sol: [d] 89: ; = 2@ 3B 4C 5D = 2T 3B 5D So Number of Ordered Pair ;a,b>= [;2*10+1> ;2*3+1>* ;2*5+1>+1]/2= 1617 6. Ans[e] None of these, Hint:- For non reoccurring, N should be in the form of 0 ] 2 3

5 100 , mhbh _12

14. Ans : [d]

15. Ans : [d] , it is an even number in all the bases


16. Sol: [c] 11025 = 3^2 * 5^2 * 7^2 Odd number of factors means number should be perfect square. Among factors of 11025, there are 3 perfect square of primes. So we can choose perfect squares from these 4 perfect squares in 2^3 ways = 8 So 8 factors have odd number of factors [Why 2^3, since all perfect squares of prime has two options either selected or not selected] Rest 27-8 = 19 have even number of factors

17. Sol: No such value possible since we get remainder 1,4 & 7 only by 9 for any value of x.

18. Sol: [a] , all are false for some critical values

19. Sol: a*b*c*d = 2^3 * 3^4 Ordered pair All positive Integral = c;6,3>*c;7,3> Case I : All Positive = c;4,4> Case II : Two positive, two negative = c;4,2> Case III : All negative : c;4,0> Total cases = c;6,3>*c;7,3> *[ c;4,4> + c;4,2> + c;4,0> ] = 5600 20. Sol: 27 , all 25 primes and 2 perfect numbers ;6 & 28> 21. Sol: b. 40! + 41! + 42! +43! has 10 0's so total zeros would be 10*5! = 1200

22. Ans : 2 2 23. Ans : ;i>

Arithmetic

24. Ans : [b]

25.

26. Ans: [d]


27. Ans: [e] None of These 13:5 Concept Video - https://www.youtube.com/watch?v=Ymw1FagUH0c

28. Ans: [d]

29. Ans: [d]

30. Ans: 104 31. Ans: [c] 32. Ans: 225

33. Concept Video - https://www.youtube.com/watch?v=3cOgrEhhc1E

34. [b] 49 ;overtake , 50 meetings>

35. 36. 37. 38. 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.

39. Ans : [b] 34

Miscellaneous

40. Sol: [c]

It would be 40, when its a calendar of leap year and less than ;Non Leap Century - 28> v.z 1888, 1884

41. Ans : 160 42. Sol : [c] If we have 55 balls then we can distribute in


Boys 1 2 3 4 5 6 7 8 9 10

Balls 1 2 3 4 5 6 7 8 9 10

And total no of such distribution = 7! Now we have 3 balls left this would be distributed in last three boys and we could divide rest three balls in only three different VALID arrangements of ;1,1,1> , ;0,1,2> & ;0,0,3> so total such arrangements = 3*10! 43. MAns : [b]

Sol:

44. [d] 45. [c]

Class Students in class

(Let) Who failed Who Passed Total

Failed Pass M F M F M F

6 100 15 85 9 6 34 51 43 57

7 100 25 75 5 20 50 25 55 45

8 100 35 65 15 20 45 20 60 40

9 100 20 80 10 10 40 40 50 50

400 95 305 39 56 169 136 208 192

% 23.75% 76.25% 9.75% 14.00% 42.25% 34.00% 52.00% 48.00%

Sol: Following Roman Number system with A -1 H- 5 M- 10 T-50 S- 100

46. . d 47. . c.

48. Sol: [b] Tetrahedron 49. Ans : [c] 3*10!

50. Ans : 7

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