1)When a four digit number is multiplied by N,the four digit number
repeats itself to give an 8 digit number .If four digit number has
all distinct digits then N is a multiple of ?

a)11 b) 37 c)73 d) 27

Ans 73

2)Find the greatest and least values of

f(x) = x^4 +x^2+5 / (x^2+1)(x^2+1)

for real x

a)5,0.95 b ) 5,-1 c)4,0 d)3,2

Ans a

3)Out of m persons sitting at a round table in how many ways no two
of the persons

A,B, C are sitting together?

a)m(m-1)(m-2) b)m(m-2)(m-3) c)m(m-4)(m-5) d)m(m-1)

Ans c

4)A bookworm starts eating pages of a book from a certain page number
in ascending order of page numbers without missing a single page
between the first and last pages eaten by it .When it finished with
its job it counts the sum of the page numbers of

all the pages eaten and finds that the sum is 198.Find the page
number where it stopped eating?The cover page of the book is page
number 1 and the worm always eats both sides of a sheet.

a)11 b) 22 c) 33 d ) 44

Ans c

5)The number from 1 to 33 are written side by side as follows :
123456...........33.If this number is divided by 9 what is the
remainder?

a)0 b)1 c)3 d) 6

Ans c

6) A positive three digit number X is such,when divided in two
unequal three digit number,the larger part is the aritmetic mean of X
and the smaller part.How many values can X take?

a)300 b)234 c)198 d)None

Ans b

7)A 101 digit number 222.........2X3...333 is formed by repeating
the digit 2,50 times followed by the digit X and then repeating the
digit 3,50 times.The number is a multiple of 7.Find the value of X.?

a)2 b)3 c ) 4 d ) 5

Ans d

8) There are ten coin making machine.Nine of them produces coins of
10 gm each while the tenth machine produces coins with 11 gm weight .
If one has a weight measuring instrument to measure weight in
grams,how many minimum number of readings are required

to determine which machine produces heavier coins?

a)1 b)3 c)4 d)None of these

Ans a

9)A student is solving a maths problem.He attempts to solve a
particular problem where he has to determine the sum of the squares
of the roots of the given polynomial.

The print having faded over time,he can see only 3 terms of the fifth
degree polynomial

x^5-11x^4+....-13=0 is all that is visible.He still manages to find
the answers What is it given that -1 is the root and all other roots
are integers?

1)171 2)173 3)169 4)None

Ans 2

10) The number 444444....(999 times) is definitely divisible by:

a)22 b)44 c)222 d)444

Ans c

11)If a three digit number is divided into three two digit numbers
and if all these three two digit numbers from an A.P. with a common
difference of 20.How many three digit numbers satisfy this condition?

a)54 b)45 c)46 d) 55

Ans c

12) If first 23 terms of the series 1,11,111 are added together ,what
digit would occupy the thousands place?

a)3 b)0 c)9 d)2

Ans d

13)A chord is drawn arbitrarily in a given circle.What is the
probability that the length of the chord is less than or equal to the
radius of the circle?

a)0.5 b)0.25 c)0 d)0.33

Ans d

14) Ravi,Deepak and Amod started out on a 100 mile journey.Ravi and
Deepak went by car at the rate of 25mph,while Amod walked at the
rate of 5 mph.After a certain distance,Deepak got off and started
walking at 5 mph,while Ravi drove back for Amod and

got him to the destination in the car at the same time that Deepak
arrived.

Q)What is the time taken by Amod to finish the journey?

a)6 b)7 c)8 d)None

Ans c

Q)What was the total distance(in miles) travelled by Ravi?

a)100 b)200 c)250 d)150

Ans b

15)How many natural numbers are factors of 7560 and multiples of 14?

a)20 b)22 c)24 d)28

Ans. c)

16)Definition:If a,k and n are positive integers with k>1,and
n=k*a ,then a is called

proper divisor of n.How many positive integers less than 54 are equal
to the product of their proper divisors?

a)1 b)8 c)10 d)14

Ans d

17) Given that A is a six digit number with unit digit of 1,and B is
a natural number which is the fourth root of A,what is the largest
possible value of B?

a)23 b)29 c)31 d)37

Ans 31

18)How many integers greater than 40,00,000 and less than 90,00,000
are perfect squares?

a)100 b)999 c)1000 d)1999

19)Six integers are selected from 1 to 100 in such a way that the
smallest positive difference between any two of them is as large as
possible.What is this difference?

a)16 b)17 c)19 d)20

20)How many different points in the xy plane are at a distance of 5
from the origin and have coordinates (a,b) ,where a and b are
integers?

a)4 b)6 c)8 d) 12

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