This is default featured slide 1 title

Go to Blogger edit html and find these sentences.Now replace these sentences with your own descriptions.

This is default featured slide 2 title

Go to Blogger edit html and find these sentences.Now replace these sentences with your own descriptions.

This is default featured slide 3 title

Go to Blogger edit html and find these sentences.Now replace these sentences with your own descriptions.

This is default featured slide 4 title

Go to Blogger edit html and find these sentences.Now replace these sentences with your own descriptions.

This is default featured slide 5 title

Go to Blogger edit html and find these sentences.Now replace these sentences with your own descriptions.

Monday, September 17, 2012

...........:TCS NEW PATTERN 2013:........

AFTER SOLVING THIS AND OTHERS GOT SELECTED IN TCS.............
--------------------=-------------:TCS LATEST PATTERN2012-2013:--------------------------------
1. P(x)=(x^2012+x^2011+x^2010+…...+x+1)^2-x^2012
    Q(x)=x^2011+x^2010+…+x+1
    The remainder when P(x) is divided by Q(x) is ?
2. In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water ?
3. Directions for Q. 1 to Q. 5: Refer the data:
J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.
No two among them collected the same number.
(i) 3 collected the same number as K and M together.
(ii) L collected 3 more than the cube of an integer
(iii) The no. Collected by J was the square of an integer.
(iv) Total no. Collected by K was either the square or cube of an integer.
1. The no. Collected by J was:
(1) 27 (2) 49 (3) 36 (4) 64
2. The no. Collected by K was:
(1) 16 (2) 27 (3) 25 (4) 36
3. The difference of numbers collected by L & M was:
(1) 3 (2) 2 (3) 5 (4) 9
L=12, N=11, J=27, M=14, K=36
4. A man can row 6 km/hr. in still water. If the speed of stream is 2km/hr., it takes him 3 hours to row to a place and back. How far is the place?
5. F(n) is a function...where f(f(n))+f(n)=2n+3.
F(n)=0;find f(2012) ?
6. How many vehicle registration plate numbers can be formed with digits 1,2,3,4,5(no digits being repeated)if it is given that registration number can have 1 to 5 digits ?
Options:  205  100  325  105
7. You can have registration plates of 5,4,3,2 or 1 digits
So, it's 5*4*3*2*1 + 5*4*3*2 + 5*4*3 +5*4 + 5
=120 + 120 + 60 + 20 +5
=> 325
8. A merchant buys 20kg of wheat at rs.30.00 per kg and 40kg wheat at rs.25.00 per kg.He mixes them and sell one third of the mixture at rs.26.00 per kg. The price at which the merchant should sell the remaining mixture so that he may earn a profit of 25% on his whole outlay is
Total cp = 20 * 30 + 40*25= 1600
Sp = 125/100 * 1600= 2000
Sp for 20kg mix = 26*20 =520
Rem sp = 2000-520 = 1480
As this sp is for 40 kg = 1480 / 40 = Rs37
9. Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friend will get the chocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers on two dice equals that number, the concerned person will get the chocolate. Rahul's choice was7, Ravi's choice was 9, Rajesh's choice was 10 and Rohan's choice was 11. Who has the maximum probability of winning the amount?
A) Rahul b) Ravi c) Rajesh d) Rohan
10. Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle and triangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inches respectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?
A) 24 inches b) 8 inches c) 20 inches d) 32 inches
If h is the height of triangle model, then  24*8 = 16*h/2    h= 24 inches
11. In month of jan 4 thursday and 4 sunday then on 1st jan of that month which willbe the day?
1. Monday
2. Friday
3.saturday
4. Wednesday
12. There is a 12*6 grid...grid contains 1*1 squares. What is d total number of squares..(consider 1*1,2*2,3*3,4*4,5*5,6*6 size squares as well).
13. 7,5,9,12,18,36,47,72,?
14. 5, 9, 12, 18, 26, 36, 47, 72, _?
It is 5 ...... 12....... 26......... 47
12= 5+7
26= 12+2×7
47=26+3×7
Next is 47+4×7=75
And 9, 18, 36, 72 hence next 144
Therefore 5, 9, 12, 18, 26, 36, 47, 72, 75, 144
15. F(x)=f(f(x))=f(x^2)....how many such functions with degree >2 exist
16. The length and breadth of a field is 300x400ft, if there are 3 ants on average per square inch of field, find the approximate number of ants in field
As 300 ft=3600 inch and 400 ft=4800 inch.then area in sqr inch=17280000
1 sqr inch need 3 ant hence 17280000 sqr inch need 3*17280000 ants
17. The diagonal of a square is twice the side of equilateral triangle the ratio of Area of the Triangle to the Area of Square is?
A) 3:8 
B) 2:5
C) 3:6
D) 2:4
Ratio = sqrt3*a^2/8a^2....i.e sqrt3/8
18. A, B COMMON TO ALL THREE. THEN ATLEAST 1 ELEMNT COMMON TO 2 IE X1,X2,X2,X3,X3,X1. FINDMINIMUM ELEMENTS IN EACH GROUP.
ANSWER IS 4.
19. There are three dice, threw 3 times probability of getting 10 is ?
Possible event.......(1,3,6)(1,4,5)(1,5,4)(1,6,3)(2,2,6)(2,3,5)(2,4,4)(2,5,3)(2,6,2)(3,1,6)(3,2,5)(3,3,4)(3,4,3)(3,5,2)(3,6,1)(4,1,5)(4,2,4)(4,3,3)(4,4,2)(4,5,1)(5,1,4)(5,2,3)(5,3,2)(5,4,1)(6,1,3)(6,2,2)(6,3,1)
Total 27 possible events
Given dice is thrown 3 times
So probability is ..........3*27/216
20. What is the probability of throwing 3 dices to get a sum of 10?
21. Raj tossed 3 dices and there results are noted down then what is the probability that raj gets 10?
A) 1/72
B) 1/9
C) 25/216
D)1/8
27/216 than ans is 1/8
22. From 52 cards 3 cards drawn randomly prob of getting 1 spade , 1 red queen and 1 black king??
13C1*2C1*2C1/52C3 = 0.00235
23. A) in how many ways can 3 postcards can be posted in 5 postboxes?
      B) in how many ways can 5 postboxes hold 3 post cards?
A)5^3
B)3^5
24. The climb from foot to top of a hill 800 meters, Jack can climb at 16 meters per minute and rests for two minutes or 20meters per 2 minutes and rest for one minute. Paul can climb at 10 meters per one minute and rest for one minute or16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
A) 41 b) 42 c) 40 d) 43
Total=800m
16m per min means for 1m=800/16 =50min to climb
10m per min means for 1m=800/10=80min to climb for paul.....The total time is 2hours==120min....so, time taken for rest by paul is 120-80=40min
25. Two cyclist begin training on oval racecourse at same time the professional cyclist complete each lap in 4 sec noves take 6 minute how many minute after start will both cyclist pass at exactly same spot where they begin to cycle(a)10(b)8(C)14(D)12
26. Two points r there two person from A running to same direction with speed 20 km/hr. & 15/hr. respectively and from other end another person running to opposite direction with 30 km/hr.? Distance between  them 100 km??At what time they will meet?
27. Tim and Elan are 90km away from each other .they are starting to move towards eachother simultaneously ,tim at speed 10kmph and elect at 5kmph ,,if every hr. they double the speed ,what is distance that tim will pass until he meets elan?  (60)
28. There are 10 stepping stones numbered 1 to 10.a fly jumps from 1st stone as follows: every minute it jumps to the 4th stone from where it started -that is from 1st it would go to 5th, from 5th it would go to 9th, from 9th it would go to 3rd, etc .where would the fly be at 60th minute if it starts at 1?
Answer 1
1minute=1+4=5
1 minute=1+4=5step
2 minute=5+4=9step
3 minute=9+4=3step
4 minute=3+4=7step
5 minute=7+4=1step the same process is repeated 12*5 times hence at 60th minute fly would be at 1st step
29. Given the following information who is youngest?
C is younger than a; a is taller than b;
C is younger than d;
C is older than b;
B is taller than c;
A is older than d
(1)d (2)b (3)a (4)c
30. 1!+2!+3!...+50! Divided by 5!  Remainder will be ?     (0 or 33)
31. If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
32. We have 5 sub and 6 periods so their arrangement is 6P5 and now we have 1 period which we can fill with any of the 5 subjects so 5C1
6P5*5C1=3600
33. An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
A)0.6485   b)0.6565   c)0.8645   d)none of these
Ans=c (0.8645)
Probability of no defective of x= 91/100=.91
Probability of non-defective of y= 95/100=.95
So, probability of no defective product=.91*.95=0.8645
34. There are six multiple choice questions in the examination. How many sequences of answers are possible, if the first two questions have 3 choices each, the next two have 4 choices each and last two have 5 choices each?
3c1*3c1*4c1*4c1*5c1*5c1=3600
35. The ratio of perimeter of an equilateral triangle having an altitude equal to the radius of the circle, to the perimeter of an equilateral triangle inscribed in that circle is ?
36. Arun was all bent on building a new house. He carefully got the blue print of his house designed by his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many tiles should Arun buy?
27*48/2*3=216
37. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age? A.2 b.5/2 c.3/2 d.1
F=3R.
After 8 yrs.
F+8=5/2(R+8)
2F+16=5R+16
2(3R) +16=5R+40
R=24 ROHIT
Aft further 8
Rohit == 24+8=32
Father == 24*3+8=80
80/32====5/2
38. Roy is now 4 year older than Erik and half of that amount than Lewis. If in two years Roy will be twice as old as Erick, then in two year what would be Roy age multiplied by Lewis age??
Ans is 48
Firstly two equations from 1st sentence...
Suppose Roy=x, Erik=y, Lewis=z
So x=y+4.... (1)
2nd is x=z+2... (2) (Roy is now 4 year older than Erik and half of that amount than Lewis so 4/2=2)
Also after 2 years Erik and Roy relation will b
X+2=2(y+2)... (3)
So put this into 1st equation. U will get y=2...
And then x=6, z=4(by substituting other)
Now asking multiplication after two years of Roy n Lewis is (6+2)*(4+2) =48...
39. My name is PREET. But my son accidentally types the by interchanging a pair of letters in my name. What is the probability that despite this interchange, the name remains unchanged? A.5% b.20% c.25% d.12.5%
10%   there are 10 possible pairs.  Out of which 1 will not change my name.
So probability that name remains unchanged = 1/10 = 10%
40. In how many ways can 20 identical pencils be distributed among three girls so
That each gets at least 1 pencil?
Consider 3 girls as A, B, C THEN A+B+C=20, but each one should get at least 1 pencil so giving 1 pencil to each student, the remaining pencils are 20-3=17 now A'+B'+C''=17,
Number of non-negative integers of A', B’, C’ are (17+3-1) C (3-1)
So total Combinations are 19c2=19*9 = 171
41. A sequence {An}is defined A(1)=0&A(n+1)=A(n)+2(n)WHAT IS VALUE OF A(100)(a)9902(B)9900(C)10100(D)9904
Last will be A (1) +2*99*98*.....1
Now put the value 1+2(1+2+......+99)
2+ 2*99(99+1)/2
=9902
42. The sequence {A (n)} is defined by A (1) =2 and A (n+1) =A (n) +2n. What is the value of a (100)
Let a=2, d=2, a.p formula find nth term i.e... TN=a+ (n-1) d
Where TN=100...
100=2+ (n-1)2 gives n=50.
Now sum of n terms n/2(a+l) =2550(ans).
43. In a sequence of integers, A(n)=A(n-1)-A(n-2),where A(n) is the nth term in the sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S (1000), where S (1000) is the sum of first 1000 terms.
Ans: 3
44. In base 7, number is written only using digit0, 1, 6.a number 135in base 7 is 1*7^2+3*7+5=75in base10.what is sum of base7 numbers1234&6543in base 7? (A) 11101(B) 11110(C) 10111(D) 11011
Ans: b) 11110
Explanation:
Convert the number from base 7 to base 10
Base 7(1234) = base 10(466)
Base 7(6543) = base 10(2334)
Sum of 466 + 2334 = 2800
Convert to base 7
Base 10 (2800) ===> 11110
45. M,N,O,P ARE DIFFERENT INDIVIDUAL M IS DAUGHTER OF N; MIS SON OF P;WHICH FOLOWING TRUE (a)M IS DAUGHTER OF P (B)IF B IS DAUGHTER OF N THEN M AND B ARE SISTER (b)IF C IS GRANDDAUGHTER OF O ,C AND M ARE SISTERS(d)P AND N ARE BROTHER
46. Which of following true: A occur only B or C occur B occur D&E occur if C not occur g occur if A and F occur option A occur whenever F occur2) F never occur3) G not occur if D not occur (3584) 4) none of these
47. House1 is older than H2, H3 is taller than H4, and H4 is older than H1... (I)H1 is older than H3 (ii) H2 is taller than H4 (a) only 1 (b) both (c) neither (d) only2
48. Apple costs L rupees per kilogram for first 30kgs and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67and for 36kgs of Apples is 12.48 then the cost of first 10 kegs of Apples is
A) 3.50 b) 10.53 c) 1.17 d) 2.8
30L+3Q=11.67
30L+6Q=12.48
------------
3Q=.81 Q= .27
From that L=0.362 cost of 10 kg apple is 10*.362=3.6
49. The letters in the word ABUSER are permuted in all possible ways and arranged in alphabetical order then find the word at position 49 in the permuted alphabetical order?
A) ARBSEU
B) ARBESU
C) ARBSUE
D) ARBEUS
AB**** =4! = 24 ways
AE****=4! =24 ways next word is 49th so
AR**** in alphabetical order **** will be BESU
Ans is B
50. X,Y,W,Z ARE INTEGER THE EXPRESSION X-Y-Z IS EVEN&Y-W-Z ODD IF X IS EVEN THEN WHICH OF FOLLOWING IS TRUE(a)Y MUST BE ODD(b)Y-Z MUST BE ODD(c)W MUST BE ODD(d)Z MUST BE ODD
Ans. (c) W must be ODD
X-Y-Z=even and X even no.
Hence (y-z) must be even because (even -even = even)
And y-w-z=y-z-w=odd and (y-z) is even so W must be odd because (even - odd=odd)
Hence option (c) is correct
51. The milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk and half water?
Mr and Mrs smith had invited 9 of their friend and their spouses for party at wiki beachresort.the stand for group photograph if Mr smith never stand next to Mrs smith then how many way group arrange in row
(A) 20!
(B) 19! +18!
(C) 18*19!
(D) 2*19!
52. A father purchases dress for his three daughters. The dresses are of same colour but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress...
53. An empty tank is filled with an inlet pipe 'A' in 42 minutes. After 12 minutes an outlet pipe 'B' is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe 'C' opened into the same tank, which can fill the tank in 35 minutes and the tank is filled find the time taken to fill the tank?
54. There are three buckets. Of 8, 5 n 3 litres...out of which only 8 ltr buckets is fully filled...u have to fill exact 4-4 ltr liquid in 8 and 5 litre bucket by using only these buckets in minimum number of steps.
55. 16 meters per minute and rest for 2 minutes. If take has to reach the top in exactly two hours. What is the maximum number of rests that he can take?
A) 41 b) 42 c) 40 d) 43
56. There are 4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A) 1 b) 6 c) 9 d) 5
57. N! Have 13 zeros than what is the highest and lowest value of n??
65! Will have 13 +2= 15 zeros.55! , 56! .59! Will have 13 zeros. Lowest value of n=55 highest value of n =59
58. N is an integers and N>2 at most how many integers among N+2,N+4,N+5,N+6 and N+7 are prime integers?
A) 1, b) 3, c) 2, d) 4
If n=3 than 5 7 8 9 10 so prime no. 2

TCS NEW PATTERN 2013 SOLUTION

http://adityasrmca.co.cc/
http://adityasrmca.co.cc/----------------------------------:TCS NEW PATTERN 2013 SOLUTION:------------------------


1.  If 3y + x > 2 and x + 2y3, What can be said about the value of y?
A. y = -1
B. y >-1
C. y <-1
D. y = 1
Answer: B

Multiply the second equation with -1 then it will become - x - 2y - 3.  Add the equations.  You will get y > -1.

2. If the price of an item is decreased by 10% and then increased by 10%, the net effect on the price of the item is
A. A decrease of 99%
B. No change
C. A decrease of 1%
D. An increase of 1%
Answer: C

If a certain number is increased by x% then decreased by x% or vice versa, the net change is always decrease.  This change is given by a simple formula (x10)2= (1010)2= 1%.  Negitive sign indicates decrease.

3. If m is an odd integer and n an even integer, which of the following is definitely odd?
A. (2m+n)(m-n)
B. (m+n2)+(mn2)
C. m2+mn+n2
D. m +n
Answer: C and D (Original Answer given as D)

You just remember the following odd ± odd = even; even ± even = even; even ± odd = odd
Also odd x odd = odd; even x even = even; even x odd = even.

4.  What is the sum of all even integers between 99 and 301?
A. 40000
B. 20000
C. 40400
D. 20200
Answer: D

The first even number after 99 is 100 and last even number below 301 is 300.  We have to find the sum of even numbers from 100 to 300.  i.e., 100 + 102 + 104 + ............... 300.
Take 2 Common.  2 x ( 50 + 51 + ...........150)
There are total 101 terms in this series.  So formula for the sum of n terms when first term and last term is known is n2(a+l)
So 50 + 51 + ...........150 = 1012(50+150)
So 2 x 1012(50+150) = 20200

5. There are 20 balls which are red, blue or green.  If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
A. 4
B. 5
C. 6
D. 7
Answer: B

Given R + B + G = 17; G = 7; and R + G < 13.  Substituting G = 7 in the last equation, We get R < 6.  So maximum value of R = 6

6.  If n is the sum of two consecutive odd integers and less than 100, what is greatest possibility of n?
A. 98
B. 94
C. 96
D. 99
Answer : C

We take two odd numbers as (2n + 1) and (2n - 1).
Their sum should be less than 100. So (2n + 1) + (2n - 1) < 100 4n < 100.
The largest 4 multiple which is less than 100 is 96

7. x2 < 1/100, and x < 0 what is the highest range in which x can lie?
A. -1/10 < x < 0
B. -1 < x < 0
C. -1/10 < x < 1/10
D. -1/10 < x
Answer: A

Remember:
(x - a)(x - b) < 0 then value of x lies in between a and b.
(x - a)(x - b) > 0 then value of x does not lie inbetween a and b. or ( , a) and (b, ) if a < b
x2 < 1/100
(x21/100)<0(x2(1/10)2)<0(x1/10)(x+1/10)<0
So x should lie inbetween - 1/10 and 1/10.  But it was given that x is -ve. So x lies in -1/10 to 0

8.  There are 4 boxes colored red, yellow, green and blue.  If 2 boxes are selected, how many combinations are there for at least one green box or one red box to be selected?
A. 1
B . 6
C. 9
D. 5
Answer: 5

Total ways of selecting two boxes out of 4 is 4C2 = 6.  Now, the number of ways of selecting two boxes where none of the green or red box included is only 1 way.  (we select yellow and blue in only one way).  If we substract this number from total ways we get 5 ways.

9. All faces of a cube with an eight - meter edge are painted red.  If the cube is cut into smaller cubes with a two - meter edge, how many of the two meter cubes have paint on exactly one face?
A. 24
B. 36
C. 60
D. 48
Answer : A

If there are n cubes lie on an edge, then total number of cubes with one side painting is given by 6×(n2)2.  Here side of the bigger cube is 8, and small cube is 2.  So there are 4 cubes lie on an edge. Hence answer = 24

10. Two cyclists begin training on an oval racecourse at the same time.  The professional cyclist completes each lap in 4 minutes; the novice takes 6 minutes to complete each lap.  How many minutes after the start will both cyclists pass at exactly the same spot where they began to cycle?
A. 10
B. 8
C. 14
D. 12
Answer: D

The faster cyclyst comes to the starting point for every 4 min so his times are 4, 8, 12, .........  The slower cyclist comes to the starting point for every 6 min so his times are 6, 12, 18, .........  So both comes at the end of the 12th min.

11. M, N, O and P are all different individuals; M is the daughter of N; N is the son of O; O is the father of P; Among the following statements, which one is true?
A. M is the daughter of P
B. If B is the daughter of N, then M and B are sisters
C. If C is the granddaughter of O, then C and M are sisters
D. P and N are bothers. 
Answer: B

From the diagram it is clear that If B is the daughter of N, then M and B are sisters.  Rectangle indicates Male, and Oval indicates Female.



12. In the adjoining diagram, ABCD and EFGH are squres of side 1 unit such that they intersect in a square of diagonal length (CE) = 1/2.  The total area covered by the squares is

A. Cannot be found from the information
B. 1 1/2
C. 1 7/8
D. None of these
Answer:  C


Let CG = x then using pythogerous theorem CG2+GE2=CE2
  x2+x2=(1/2)22x2=1/4x2=1/8
Total area covered by two bigger squares = ABCD + EFGE - Area of small square = 2 - 1/8 = 15/8


13. There are 10 stepping stones numbered 1 to 10 as shown at the side.  A fly jumps from the first stone as follows; Every minute it jumps to the 4th stone from where it started - that is from 1st it would go to 5th and from 5th it would go to 9th and from 9th it would go to 3rd etc.  Where would the fly be at the 60th minute if it starts at 1?
A. 1
B. 5
C. 4
D. 9

Answer : A

Assume these steps are in circular fashion. 
Then the fly jumps are denoted in the diagram.  It is clear that fly came to the 1st position after 5th minute.  So again it will be at 1st position after 10th 15th .....60th. min.

So the fly will be at 1st stone after 60th min.

 

14. What is the remainder when 617+1176  is divided by 7?
A. 1
B. 6
C. 0
D. 3
Answer: C

617 = (71)17 =
17C0.71717C1.716.11.....+17C16.71.11617C17.117

If we divide this expansion except the last term each term gives a remainder 0.  Last term gives a remainder of - 1.

Now From Fermat little theorem, [ap1p]Rem=1
So [1767]Rem=1

Adding these two remainders we get the final remainder = 0

15. In base 7, a number is written only using the digits 0, 1, 2, .....6.  The number 135 in base 7 is 1 x 72 + 3 x 7 + 5 = 75 in base 10.  What is the sum of the base 7 numbers 1234 and 6543 in base 7.
A. 11101
B. 11110
C. 10111
D. 11011
Answer: B

In base 7 there is no 7.  So to write 7 we use 10.  for 8 we use 11...... for 13 we use 16, for 14 we use 20 and so on.
So from the column d, 4 + 3 = 7 = 10, we write 0 and 1 carried over.  now 1 + 3 + 4 = 8 = 11, then we write 1 and 1 carried over.  again 1 + 2 + 5 = 8 = 11 and so on



16. The sequence {An} is defined by A1 = 2 and An+1=An+2n what is the value of A100
A. 9902
B. 9900
C. 10100
D. 9904
Answer: A
We know that A1 = 2 so A2=A1+1=A1+2(1)=4
A3=A2+1=A2+2(2)=8
A4=A3+1=A3+2(3)=14
So the first few terms are 2, 4, 8, 14, 22, ......
The differences of the above terms are 2, 4, 6, 8, 10...
and the differences of differences are 2, 2, 2, 2.  all are equal.  so this series represents a quadratic equation.
Assume  An = an2+bn+c
Now A1 = a + b + c = 2
A2 = 4a + 2b + c = 4
A3 = 9a + 3b + c = 8
Solving above equations we get a = 1, b = - 1 and C = 2
So substituting in An = n2+bn+c = n2n+2
Substitute 100 in the above equation we get 9902.

17.Find the number of rectangles from the adjoining figure (A square is also considered a rectangle)
A. 864
B. 3276
C. 1638
D. None

Answer: C

To form a rectangle we need two horizontal lines and two vertical lines.  Here there are 13 vertical lines and 7 horizontal lines.  The number of ways of selecting 2 lines from 13 vertical lines is 13C2 and the number of ways of selecting 2 lines from 7 horizontals is 7C2. So total rectangles = 7C2x13C2

18. A, B, C and D go for a picnic.  When A stands on a weighing machine, B also climbs on, and the weight shown was 132 kg.  When B stands, C also climbs on, and the machine shows 130 kg.  Similarly the weight of C and D is found as 102 kg and that of B and D is 116 kg.  What is D's weight
A. 58kg
B. 78 kg
C. 44 kg
D. None
Answer : C

Given A + B = 132; B + C = 130; C + D = 102, B + D = 116
Eliminate B from 2nd and 4th equation and solving this equation and 3rd we get D value as 44.

19.  Roy is now 4 years older than Erik and half of that amount older than Iris.  If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age?
A. 28
B. 48
C. 50
D. 52
Answer: 48

20. X, Y, X and W are integers.  The expression X - Y - Z is even and the expression Y - Z - W is odd.  If X is even what must be true?
A. W must be odd
B. Y - Z must be odd
C. W must be odd
D. Z must be odd
Answer: A or C (But go for C)

21.  Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Waikiki Beach resort.  They stand for a group photograph.  If Mr Smith never stands next to Mrs Smith (as he says they are always together otherwise). How many ways the group can be arranged in a row for the photograph?
A. 20!
B. 19! + 18!
C. 18 x 19!
D. 2 x 19!
Answer: C

22.  In a rectanglular coordinate system, what is the area of a triangle whose vertices whose vertices have the coordinates (4,0), (6, 3) adn (6 , -3)
A. 6
B. 7
C. 7.5
D. 6.5
Answer: A

23. A drawer holds 4 red hats and 4 blue hats.  What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
A. 1/2
B. 1/8
C. 1/4
D. 3/8
Answer: B

24. In how many ways can we distribute 10 identical looking pencils to 4 students so that each student gets at least one pencil?
A. 5040
B. 210
C. 84
D. None of these
Answer: C

25. The prime factorization of intezer N is A x A x B x C, where A, B and C are all distinct prine intezers.  How many factors does N have?
A. 12
B. 24
C. 4
D. 6
Answer: A

26. Tim and Elan are 90 km from each other.they start to move each other simultanously tim at speed 10 and elan 5 kmph. If every hour they double their speed what is the distance that Tim will pass until he meet Elan 
A. 45
B. 60
C. 20
D. 80
Answer: B

27. A father purchases dress for his three daughter. The dresses are of same color but of different size .the dress is kept in dark room .What is the probability that all the three will not choose their own dress.
A.  2/3
B.  1/3
C.  1/6
D.  1/9
Answer: B

28. N is an integer and N>2, at most how many integers among N + 2, N + 3, N + 4, N + 5, N + 6,  and N + 7 are prime integers?
A. 1
B. 3
C. 2
D. 4
Answer: C

29. A turtle is crossing a field.  What is the total distance (in meters) passed by turtle? Consider the following two statements
(X) The average speed of the turtle is 2 meters per minute
(Y) Had the turtle walked 1 meter per minute faster than his average speed it would have finished 40 minutes earlier

A. Statement X alone is enough to get the answer
B. Both statements X and Y are needed to get the answer
C. Statement Y alone is enough to get the answer
D. Data inadequate
Answer: B

30. Given the following information, who is youngest?
C is younger than A; A is talled than B
C is older than B; C is younger than D
B is taller than C; A is older than D

A. D
B. B
C. C
D. A
Answer: B

31. If P(x) = ax4+bx3+cx2+dx+e has roots at x = 1, 2, 3, 4 and P(0) = 48, what is P(5)
A. 48
B. 24
C. 0
D. 50
Answer: A

bobby car