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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
