Note: These are not sample questions, but questions that explore some of the concepts that
may be used. The intention is that you should get prepared with the concepts rather than just
focusing on a set of questions.
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1. What are the total number of divisors of 600(including 1 and 600)?
a. 24
b. 40
c. 16
d. 20
2. What is the sum of the squares of the first 20 natural numbers (1 to 20)?
a. 2870
b. 2000
c. 5650
d. 44100
3. What is∑


(
), where
is the number of ways of choosing k items from 28
items?
a. 406 *

b. 306 *

c. 28 *

d. 56 *

4. What is ∑


(
) where
is the number of ways of choosing k items from 28
items?
a.

b.

c.

d.

5. A call center agent has a list of 305 phone numbers of people in alphabetic order of names
(but she does not have any of the names). She needs to quickly contact Deepak Sharma to
convey a message to him. If each call takes 2 minutes to complete, and every call is
answered, what is the minimum amount of time in which she can guarantee to deliver the
message to Mr Sharma.
a. 18 minutes
b. 610 minutes
c. 206 minutes
d. 34 minutes6. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively.
What is the average time per call?
a. 4 minutes
b. 7 minutes
c. 1 minutes
d. 5 minutes
7. The times taken by a phone operator to complete a call are 2,9,3,1,5 minutes respectively.
What is the median time per call?
a. 5 minutes
b. 7 minutes
c. 1 minutes
d. 4 minutes
8. Eric throws two dice, and his score is the sum of the values shown. Sandra throws one die,
and her score is the square of the value shown. What is the probability that Sandra’s score
will be strictly higher than Eric’s score?
a. 137/216
b. 17/36
c. 173/216
d. 5/6
9. What is the largest integer that divides all three numbers 23400,272304,205248 without
leaving a remainder?
a. 48
b. 24
c. 96
d. 72
10. Of the 38 people in my office, 10 like to drink chocolate, 15 are cricket fans, and 20
neither like chocolate nor like cricket. How many people like both cricket and chocolate?
a. 7
b. 10
c. 15
d. 18
11. If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 1612. If f(x) = 7 x +12, what is f-1(x) (the inverse function)?
a. (x-12)/7
b. 7x+12
c. 1/(7x+12)
d. No inverse exists
13. A permutation is often represented by the cycles it has. For example, if we permute the
numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the
(132) says that the first number has gone to the position 3, the third number has gone to
the position 2, and the second number has gone to position 1, and (5 4) means that the
fifth number has gone to position 4 and the fourth number has gone to position 5. The
numbers with brackets are to be read cyclically.
If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is
represented as (1345)(2).
We may apply permutations on itself If we apply the permutation (132)(54) once, we get
2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5)
If we consider the permutation of 7 numbers (1457)(263), what is its order (how many
times must it be applied before the numbers appear in their original order)?
a. 12
b. 7
c. 7! (factorial of 7)
d. 14
14. What is the maximum value of x3y3 + 3 x*y when x+y = 8?
a. 4144
b. 256
c. 8192
d. 102
15. Two circles of radii 5 cm and 3 cm touch each other at A and also touch a line at B and C.
The distance BC in cms is?
a. 60
b. 62
c. 68
d. 64
16. In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people.
Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra,
David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with
whom and at which table are determined by the following constraints:
a. Chitra does not sit at the same table as Govind.
b. Eesha does not sit at the same table as David.
c. Farooq does not sit at the same table as Chitra.d. Akash does not sit at the same table as Babu.
e. Govind does not sit at the same table as Farooq.
Which of the following is a list of people who could sit together at table 2?
a. Govind, Eesha, Akash
b. Babu, Farooq, Chitra
c. Chitra, Govind, David.
d. Farooq, David, Eesha.
17. There are a number of chocolates in a bag. If they were to be equally divided among 14
children, there are 10 chocolates left. If they were to be equally divided among 15
children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210
chocolates are added to the bag. What is the remainder when the minimum feasible
number of chocolates in the bag is divided by 9?
a. 2
b. 5
c. 4
d. 6
18. Let f(m,n) =45*m + 36*n, where m and n are integers (positive or negative) What is the
minimum positive value for f(m,n) for all values of m,n (this may be achieved for various
values of m and n)?
a. 9
b. 6
c. 5
d. 18
19. What is the largest number that will divide 90207, 232585 and 127986 without leaving a
remainder?
a. 257
b. 905
c. 351
d. 498
20. We have an equal arms two pan balance and need to weigh objects with integral weights
in the range 1 to 40 kilo grams. We have a set of standard weights and can place the
weights in any pan. . (i.e) some weights can be in a pan with objects and some weights
can be in the other pan. The minimum number of standard weights required is:
a. 4
b. 10
c. 5
d. 621. A white cube(with six faces) is painted red on two different faces. How many different
ways can this be done (two paintings are considered same if on a suitable rotation of the
cube one painting can be carried to the other)?
a. 2
b. 15
c. 4
d. 30
22. How many divisors (including 1, but excluding 1000) are there for the number 1000?
a. 15
b. 16
c. 31
d. 10
23. In the polynomial f(x) =2*x^4 - 49*x^2 +54, what is the product of the roots, and what is
the sum of the roots (Note that x^n denotes the x raised to the power n, or x multiplied
by itself n times)?
a. 27,0
b. 54,2
c. 49/2,54
d. 49,27
24. In the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers.
If 3 + sqrt(7) is a root, which of the following must be also a root?(Note that x^n denotes
the x raised to the power n, or x multiplied by itself n times. Also sqrt(u) denotes the
square root of u, or the number which when multiplied by itself, gives the number u)?
a. 3-sqrt(7)
b. 3+sqrt(21)
c. 5
d. sqrt(7) + sqrt(3)

• (5)- the call center agent first calls 301 and asks their name(worst case) then calls the middle no. i.e. (305/2)=152.5(take 152 or 153 depends on you) and asks them their name to get an idea of whether to go to left or right side of (152 (my take)) no. directory and suppose person replies R then agent will go to left side and again call (152/2=76) and asks their name and in similar way filter the list by either going to left (or right side ) and thus the list will be shortened as 305,153,76,38,19,9,4,2,1 .So minimum time= 9*2=18 mins. i hope you all will get that.
• 11 years agoHelpfull: Yes(183) No(18)
• (1)2^3*3*5^2=4*2*3=24 so its(a)
  (2)simple formula (n*(n+1)*(2n+1)/6)here n=20 so ans is (a)2870
  (3|4)it should be 2^28-1
  (9)here 24 is the largest integer that divides all three numbers 23400,272304,205248 without
  leaving a remainder so its(b)
  (10)here P(co)=10 P(cr)=15 P(coUcr)'=20 so hav to find P(co intersection cr)
  so,P(co intersection cr)=10+15-(38-20)=7 so ans is (a)
  (11)simple ..ans vll be 18.
  (12)as the function is onto as well as one one so its inverse vll b 1/(7x+12).
  (16)as C,G,F vll not sit together sp let T1->C T2->G T3->F
  now,T1/T2->D/E and remaining 1 sit of T1/T2->A/B
  so ans vll be (a) Govind, Eesha, Akash
  (18)put m=1 and n=-1 then we vll get the minimum positive value for f(m,n)
  as (a)9.
  (19)among those 257 is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder so ans is (a) 257.
  (20)The minimum number of standard weights required is 6
  these are 1,2,4,8,16,32 by these v can weight 1 to 40gm.
  (21)out of 6 faces we can choose 1 face in 6C1 ways and colour it.
  now out of left 5 faces we can choose 1 face in 5C1 ways and colour it.
  so different ways can this be done is 6*5=30.
  (22)1000=2^3*5^3 so total divisor are (4*4)
  so,number of divisors (including 1, but excluding 1000) are 16-1=15(as 1000 is excluding).
  (23)f(x) =2*x^4 - 49*x^2 +54=2*x^4+0*x^3- 49*x^2+0*x+54
  so,the sum of the roots is 0 and the product of the roots 54/2 =27
  ans is (a)27,0
  (24)the polynomial f(x) = x^5 + a*x^3 + b*x^4 +c*x + d, all coefficients a, b, c, d are integers.
  as 3 + sqrt(7) is a root other must be 3-sqrt(7).
  
  thank u :)
• 11 years agoHelpfull: Yes(98) No(24)
• 12)
  
  f(x)=7x+12
  here we will replace f(x)=y
  now
  y=7x+12
  so x=(y-12)/7
  now just replace again y=x
  so answer f-1(x)=(x-12)/7
• 11 years agoHelpfull: Yes(56) No(9)
• Ans for que 8)137/216
  sol.
  as sample space is 216 i.e total no. of cases
  now,
  sandra's score no. of favourable cases to win
  1 0
  4 3 @(1,1)(2,1)(1,2)
  9 26 cases all pairs till 9
  16 36(as max sum is 12,n 16>12)
  25 36
  36 36
  total favourable cases= 0+3+26+36+36+36= 137
  thus,
  probablity=137/216
• 11 years agoHelpfull: Yes(50) No(5)
• 7. Isn't the answer for 7th que 3??? but the option is not der...
  Usually mode means the middle value...1,2,3,5,9. which must be 3...someone plz help me
  
• 11 years agoHelpfull: Yes(47) No(9)
• 14. from relation between AM AND GM
  AM >= GM
  (X+Y)/2 >= Sqrt(XY)
  4 >= Sqrt(XY)
  XY < = 16
  so maximum value of XY is 16
  so X^3Y^3+3XY = 4144
• 11 years agoHelpfull: Yes(38) No(0)
• 5. 1st the agent calls 152'nd no asks the name from that he come to know which half the name is present then 76,38,19,9,4,2,1. therefore totally nine calls 18 min
  
  6. average of all 5 ans: 4min
  
  15. BC line is tangent and its not a straight line parrel lo line joining their radiuses bc=sqrt(4+64)
  
  17. from the give two condition number of choclates are 38 so when this number divided by 9 yields 2 as remainder
  
  
• 11 years agoHelpfull: Yes(14) No(9)
• the correct answer for question 15 is sqrt 60
  explaination:
  as tangent make 90 degree angle with radius at the point of coincidence,by construction in figure make a parallel line BC from center of circle of radius 3cm upto radius of circle of 5cm, there a rectangle formed and a right angled triangle with hypotaneous =8cm{5+3} and perpendicular as 2cm{5-3}...now base=sqrt(64-4)=sqrt 60
  
• 11 years agoHelpfull: Yes(11) No(1)
• Hi Shiva........can u please contact me at my email id which is rudrakshsharma33@gmail.com......???? I have to ak some questions to you please contact me.
  
  Thanks
• 11 years agoHelpfull: Yes(10) No(2)
• 8. my ans is 137/216
  
• 11 years agoHelpfull: Yes(9) No(6)
• Mr. Shiva you gave a few wrong answers i guess
  answer for 21 is 2 because he stated by proper rotation of cube if one painting carries to other they are considered the same and answer for 20 is 4 the numbers are 1,3,9,27
• 11 years agoHelpfull: Yes(9) No(0)
• full solution
  
  1.a
  2.a
  3.a
  4.d
  5.a
  6.a
  7.d
  8.c
  9.b
  10.a
  11.a
  12.c
  13.d(not sure)
  14.a
  15.c
  16.b
  17.b
  18.a
  19.a
  20.a
  21.c
  22.a
  23.a
  24.a
  
• 11 years agoHelpfull: Yes(9) No(13)
• @thank u shiva i like to keep contact with shall i?
• 11 years agoHelpfull: Yes(8) No(1)
• answer for 12th is :::: (x-12)/7 here is the source :: http://www.mathsisfun.com/sets/function-inverse.html
• 11 years agoHelpfull: Yes(8) No(0)
• solution for 15 ::: sqrt(60)
  way ::: (8)^2=2^2+x^2 => x=sqrt(60), 3+5 will be hypotenuse, one side will be 5-2=2, where the length of radius of small circle 3 will be disecting radius 5, so one side of triangle will be 2,other is required bc i.e., x and hypotenuse is 5+3=8.
• 11 years agoHelpfull: Yes(8) No(9)
• 8. My ans came : 127/216
  
  solution: let score of Sandra a^2 and score of Eric be (b+c)
  favourable outcomes only at the following cases:
  
  condition: a^2> b+c
  
  a^2 b+c (favourable) no of favourable events
  ___ _______________________________________ _______________________
  1 nil 0
  4 (1,1),(1,2),(1,3) 3
  9 all pairs till (4,4) 16
  16 all pairs of (b,c) possible 36
  25 do 36
  36 do 36
  
  total num of possible outcomes = (36(for a=1)+36(for=a=2)+36+36+36+36(for a=6))
  =36*6= 216
  total num of favourable outcomes= 3+16+36+36+36 = 127
  
  so required probability= 127/216 (ans)
• 11 years agoHelpfull: Yes(8) No(20)
• The answer for 12 will be x-12/7....
• 11 years agoHelpfull: Yes(7) No(0)
• solution for qtn 8:::
  when eric rolls the dice there are 36 no.of chances for his outcome. for sandra there are 6 favourable outcomes. but for sandra to be strictly greater than eric, way is:: when its 1:she cant be greaterthan eric.she can be only when her outcomes are 2,3,4,5,6. so for 2 she'll have 1/6, for 3 =1/6,for 4=1/6,for 5=1/6,for 6=1/6,,,therefore for 5 chances add 1/6 for 5 times so ans is :: 5/6. correct me if i'm wrong guys!!
• 11 years agoHelpfull: Yes(7) No(39)
• 7) the answer should be 3 as there is a question to find median,
  first arrange numbers into order( lowest to highest)
  here 1,2,3,5,9
  and median will be the number in thwe middle hence answer should be 3.
  and avg will be 4 which is ans for 6th.
• 11 years agoHelpfull: Yes(7) No(3)
• 20)the number of min. weights needed are 4,weights are 1,3,9,27
  using these weights we could measure between 1-40.for example to measure 22,we will have (27+3+1)in one pan and 9 in other.so,31-9=22 can be weighed and so 27+9+3+1=40
• 11 years agoHelpfull: Yes(7) No(2)
• @Himanshi 600=8*3*25=2^3*3^1*5^2
  so total number of divisors of 600(including 1 and 600) are (3+1)*(1+1)*(2+1)
  =4*2*3=26
• 11 years agoHelpfull: Yes(6) No(28)
• need explanation for number 21 plz
• 11 years agoHelpfull: Yes(5) No(0)
• Answer to Question 13...
  as the cycle is(1457)(263)
  The natural order of numbers is 1,2,3,4,5,6,7
  now acc to cycle shifting the first num to 4th position ,4th num to 5th pos. 5th num to 7th pos,7th num to 1st pos.. ,the 2nd num to 6th pos, 6th num to 3rd pos,3rd nu to 2nd.
  it will take 12 steps to get the original order .as
  7361425
  5627134
  4235761
  1364527
  7621435
  5237164
  4365721
  1624537
  7231465
  5367124
  4625731
  1234567
  total 12 steps....
• 10 years agoHelpfull: Yes(5) No(0)
• 14)as am>=gm
  so x+y/2>=sqrt(xy)
  so
  4>=sqrt(xy)
  16>=xy
  x3y3=4096 and 3xy=48
  so x3y3+3xy=4144
• 11 years agoHelpfull: Yes(4) No(0)
• 3.
  Let f(x)=(1+x)^28 Using binomial theorem f(x)=∑k(28Ck)x^k. I will assume you can take care of any differentitations. Then f′(x)=∑k(28Ck)x^k−1. So xf′(x)=∑k(28Ck)x^k. So (xf′(x))′=∑k^2(28Ck)x^k−1. Now put x=1. On the right, we get our desired sum. On the left, just calculate the value of (xf′(x))′ at x=1 ans is 406*2^27
• 11 years agoHelpfull: Yes(4) No(4)
• ans for 13.If this is applied four times, the numbers 1, 4, 5 and 7 will be back in their original positions. The same will be true if you apply it eight, twelve, sixteen or any multiple of four times.
  All seven numbers will be in their original positions if you apply the permutaion (1 4 5 7) (2 6 3) a number of times that is a common multiple of 3 and 4. Find the lowest common multiple.
  
• 10 years agoHelpfull: Yes(4) No(0)
• 20) 3^0,3^1,3^2,3^3 ARE THE STANDARD WEIGHT REQUIRED TO MEASURE 1-40;
  AS 1,3,9,27 HENCE ANS IS 4
• 10 years agoHelpfull: Yes(4) No(0)
• anyone plz solve q no 8,13 and 14
  
• 11 years agoHelpfull: Yes(3) No(0)
• 17 ans is 2
  
  number is 38
• 11 years agoHelpfull: Yes(3) No(5)
• can ny body xplain qn no:20
• 11 years agoHelpfull: Yes(3) No(0)
• the call center agent first calls 305 and asks their name(worst case) then calls the middle no. i.e. (305/2)=152.5(take 152 or 153 depends on you) and asks them their name to get an idea of whether to go to left or right side of (152 (my take)) no. directory and suppose person replies R then agent will go to left side and again call (152/2=76) and asks their name and in similar way filter the list by either going to left (or right side ) and thus the list will be shortened as 305,153,76,38,19,9,4,2,1 .So minimum time= 9*2=18 mins.
• 11 years agoHelpfull: Yes(3) No(0)
• (2) 2870 bcoz
  Sum of squares of natural numbers = (n*(n+1)*(2n+1))/6
• 11 years agoHelpfull: Yes(2) No(0)
• 14) the maximum possible value for x and y is 4 and 4.
  So (4^3)(4^3)+3(4*4)=4144
• 11 years agoHelpfull: Yes(2) No(2)
• 15) sqrt((5+3)^2-(5-3)^2))=sqrt(68)
• 11 years agoHelpfull: Yes(2) No(14)
• can anyone explain me questions 3rd and 5th
• 11 years agoHelpfull: Yes(2) No(0)
• can anyone explain the ques num 13??
• 11 years agoHelpfull: Yes(2) No(0)
• Mr Shiva, can you explain me the answer of question 3 and four............hurry..
  
• 11 years agoHelpfull: Yes(2) No(0)
• Okies got it the solution for 13 is 12.
  after 12 times numbers will appear in original order
• 11 years agoHelpfull: Yes(2) No(1)
• what's the answer for q.13?
• 11 years agoHelpfull: Yes(2) No(1)
• 14) x+y=8, assume x=4,y=4 (i.e 4+4=8)
  4^3*4^3+3*4*4=4144
  
• 11 years agoHelpfull: Yes(2) No(0)
• Q.7> may be a dummy question.......Because to solve the question, we have to first arrange the numbers in the ascending order........Then we have to fing=d the number at the middle position which will be the median..........Here since the nos are odd......So, to calculate the middle position, use the formula
  (n+1)/2 which wiil giv us the number 3, which is not amongst the options..............Thank u
• 11 years agoHelpfull: Yes(2) No(0)
• 15. If r1, r2 are the radii of two circles and d is distance between their centers, then
  (i) the length of a direct common tangent = sqrt((d)^2-(r2-r1)^2)
  SO BC= sqrt((8)^2-(5-3)^2)=Sqrt(60)
• 11 years agoHelpfull: Yes(2) No(3)
• any1 cn hlp me with the 3rd questn plzzz??
• 11 years agoHelpfull: Yes(2) No(0)
• Ans for 17 is option b)5
  solution 14*2=28+10=38
  15*2=30+8=38
  therefore by adding 210 chocolates we get,38+210=248
  248%9=5
• 10 years agoHelpfull: Yes(2) No(0)
• Ans for 17 is option b)5
  solution 14*2=28+10=38
  15*2=30+8=38
  therefore by adding 210 chocolates we get,38+210=248
  248%9=5
• 10 years agoHelpfull: Yes(2) No(0)
• 8)137/216
  
  Sandra's possible scores-
  1 (1)
  4 (2)
  9 (3)
  16 (4)
  25 (5)
  36 (6)
  
  So for Sandra's score=1 there will be no favorable outcomes as Eric score will always be >=2 with 2 being his least score for dice throws of 1 and 1 on both dice.
  
  Similarly for X=4 (Sandra's score)
  Dices throw of (1,1) , (1,2) , (2,1) are favorable cases.
  so P(X=4)= 3/36* 1/6= 3/216
  [ 1/6 is the probability of getting 2 on a throw of dice by Sandra (and hence the score=4) and 3 outcomes are favorable out of 36 for Eric's throw of 2 dice.
  
  Same with X=9
  Favorable Cases- (1,1), (1,2) ,(1,3) ,(1,4) ,(1,5) ,(1,6) ,(2,1) ,(2,2) ,(2,3) ,(2,4) ,(2,5) ,(2,6) ,(3,1) ,(3,2) ,(3,3) ,(3,4) ,(3,5) ,(4,1) ,(4,2) ,(4,3) ,(4,4) ,(5,1) ,(5,2) ,(5,3) ,(6,1) ,(6,2)
  so P(X=9)= 26/36*1/6 = 26/216
  
  For X=16, 25,36
  all cases are favorable as the max score of Eric can be 12 (6,6)
  Hence P(X=16)=P(X=25)=P(X=36)= 1/6* 36/36=36/216
  
  So adding all the cases-
  3/216 + 26/216 + 36/216 +36/216 + 36/216 = 137/216 (Ans)
• 9 years agoHelpfull: Yes(2) No(0)
• 14> 4144
  15> sqroot(68)
• 11 years agoHelpfull: Yes(1) No(4)
• solution for question 8:::
  
• 11 years agoHelpfull: Yes(1) No(0)
• question 22: the answer is 15 bcoz.... it include 1 but excluding 1000,
• 11 years agoHelpfull: Yes(1) No(1)
• please explain me 7th question.. isn't the median of the series (1 2 3 5 9) 3??
• 11 years agoHelpfull: Yes(1) No(0)
• For Q.3 and fourth, we have a simple Binomial formula stated below:
  The value of the binomial coefficient is easy to calculate using the formula:
  (n k) = n!/ (n-k)!
  
  So, with the help of this formula, the solution of Q.3 is (a) and Q.4 is (d)
• 11 years agoHelpfull: Yes(1) No(0)
• Can you please explain qn no 23 and 24 by justifying the answers..Let me know the answers please
• 11 years agoHelpfull: Yes(1) No(0)
• total tables-3
  chitra/govind
  chitra/fareeq
  eesha/david
  akash/babu
  That means chitra , govind, fareeq are sitting in 3 different tables.
  option 1.govind , eesha, akash are sitting together.
  2.babu, farreq, chitra = NO as chitra n fareeq are not sitting at 1 table
  3.chitra, govind, david=NO as govind and chitra are not sitting at 1 table.
  4.fareeq, david, eesha=NO as eesha n david are nt sitting together.
  ANS is 1.
• 10 years agoHelpfull: Yes(1) No(0)
• given no. are 23400,205248,272304
  these no divisible by 2,3,4,8(by division rule)(last three digit divide by 8)(sum of digit divide by 3)
  8*3
  ans. b)24
  explanation: 272304=8*2*3*3*191
  
  23400=8*3*3*5*5*13
  
  205248=8*8*3*13*13
  highest common factor=24
  22)find divisors between 1 to 1000 including 1 and excluding 1000
  sol: 1000=2*2*2*5*5*5
  no. of divisors=1,2,4,5,8,10,20,25,40,50,100,125,200,250,500
  ans.a)15
  19)given no are 90207,127986,232585
  h.c.f=257
  a).257
  
  
  
  
  
  
  
  
  
  
• 10 years agoHelpfull: Yes(1) No(0)
• plz explain me how the ans of first is (a)
• 11 years agoHelpfull: Yes(0) No(0)
• 19 A
  take hcf of any two number by continous division method
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• @Rudraksh Sharma ohh sure..u r wellcome sobhandutta91@gmail.com
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• Soumadeep can explain why ans of 15??
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• @GOUTHAM ANUSH I think your are right... answer of ques 7 is 3.
  
  even for reference http://www.purplemath.com/modules/meanmode.htm
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• 15) use Pythagoras theorem=√25*2+9*2=√68
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• 4th answer is D
  
• 11 years agoHelpfull: Yes(0) No(3)
• can anyone explain the solution for 17 how the number is 38??
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• explain 9th... s tat trial nd error??
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• frnds plz explain questn no. 8..
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• Plz some one post the solution of Q 3,4 and 13...very urgent
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• ans of 13) is a 12
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• Ans of 16: (a) Govind, Eesha, Akash
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• i need the answers for the question to verify with the answer i got
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• any1 can help me out with the 13th q plzzz??
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• 15)answer is sqrt 60.
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• 2)
  here by using this below formula we can helpful do it
  (n(n+1)(2n+1))/6=2870 ;here n=20
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• 2. 1^2+2^2+......+20^2
  sum of square continuous no=(n(n+1)(2n+1))/6
  (20*21*41)/6=2870
  ans. a)2870
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• 1. divisor from 1 to 600 both are including
  600=2*2*2*3*5*5
  so 1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
  to find factor and multplie to each other to find new no.
  ans.24
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• 17)
  ans.2
  x*14+10=x*15+8
  x=2
  total no chocolate=38
  add chocolate multiply by 210*3=630 which is completely divide by 9
  so remainder 38%9=2
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• 23)ax^2+bx+c =0 product of roots = c/a
  
  sum of roots = -b/a so answer is 54/2 , 49/2
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• 19) find GCD( greatest common divisor) between 90207 and 232585 then u get answer a)257
  
  example :- gcd between 39 and 412
  
  39)412(10
  390
  --------------
  22)39(1
  22
  -------
  17)22(1
  15
  -----------
  7)17(2
  14
  ----------
  3)7(2
  6
  ---------
  1)3(3
  0
  --------
  0
  
  so GCD between 39 and 422 is 1
  
  
  22) 1 ,2,4,5,8,10,16,20,40,50,100,125,200,250,500 so total 15 divisors
  
  method if 1000 divide by 1 u get 1000 quotient same as it is 1000 divide by 1000 u get 1
  
  like that 1000/2 = 500 like that 1000/500=2 so both 2 , 500 are divisors
  
  hence 1x1000 2x500 4x250 5x200 8x125 10x100 20x50 40x25
  
  here condition is divisor must be less than 1000 so eliminate 1000 from list then we get total 15 divisors less than 1000
  
  answer a)15
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• Okay, consider the cycle (1 4 5 7). If this is applied four times, the numbers 1, 4, 5 and 7 will be back in their original positions. The same will be true if you apply it eight, twelve, sixteen or any multiple of four times.
  
  For (2 6 3) this happens after three, six, nine, etc applications.
  
  All seven numbers will be in their original positions if you apply the permutaion (1 4 5 7) (2 6 3) a number of times that is a common multiple of 3 and 4. Find the lowest common multiple.
  Ans:12
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• 54 is the answer
  
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• Why I cant see solutions above?
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