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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
