1. A club with x members is organised into 4 committees according to
the following rules :
(i) Each member belongs to exactly 2 committees
(ii) Each pair of committees has exactly 1 member in common.
Then find the value of x….?
2.The no. of integer lying between 3000 and 8000(both included) that
have at least 2 digits equal.
3.The coefficient of x^4 in the expansion of (1+x-2x^2)^7 is .
4. A closet has pairs of shoes. The no ways in which 4 shoes can be
chosen from it so that there be no complete pairs.
5. Distance passed over by a pendulum bob in successive swing are 16,
12, 9, 6.75..cm. Then the total distanced traversed b the bob before
it come to rest is (in cm) A. 60 B. 64 C.65 D.67.
6 The point (2,1), (8,5) and (x,7) lie on a straight line , find the
value of x..?.
7.Eight singers participate in an art festival where m songs are
performed. Each song is performed by 4 singers, and each pair of
singers performs together in the same number of songs. Find the
smallest m for which this is possible. A. 12 B.14 C.16 D.18
When two fat fish of identical volume were placed inside the tank,
the water level rose to a height of 25 cm.
(a) What is the volume of one fat fish?
(b) How many small turtles of volume 250 would be needed to replace
the fish?
10. In D ABC, ÐC = 90, ÐA = 30 and BC = 1. Find the minimum of the
length of the longest side of a triangle inscribed in ABC (that is,
one such that each side of ABC contains a different vertex of the
triangle).
11. Starting at (1, 1), a stone is moved in the coordinate plane
according to the following rules:
(i) From any point (a, b), the stone can move to (2a, b) or (a, 2b).
(ii) From any point (a, b), the stone can move to (a-b, b) if a >
b, or to (a, b-a) if a < b.
For which positive integers x, y can the stone be moved to (x,y)?
12. The numbers from 1 to 100 are written in an unknown order. One
may ask about any 50 numbers and find out their relative order. What
are the fewest questions needed to find the order of all 100 numbers?
A. 5 B.6 C.7 D. none of these.
13. Let k be a fixed odd positive no. find minimun value of x^2 +^2,
where x, y are nonnegative interger and x+y =k.?
14. How many natural number less than 10^8 are there , whose sum of
digit = 7.?
15. All permutations of the letter a, b, c, d, e were written down
and arranged in alphabetical order as in dictionary. Thus in
arrangement abcde is in the first place and edcba in last , find the
position of debac.?
16. If the area of circumcircle of a regular polygon with n sides is
A then the area of circle inscribed in polygon is..(in term of A) ?
17. Find the no. of rational number m/n where m ,n are relatively
prime positive no. satisfying m<n and mn = 25!..?
18. Let ABC be an isosceles triangle with AB = BC = 1 cm and angle A
= 30 . Find the volume of solid obtained by revolving the triangle
about the line AB. ?
19. A rectangle OACB with 2 axes as sides , the orgin O as a vertex
is drawn in which length OA is 4 time the width OB . A circle is
drawn passing through the point B and C touching OA at its min-point
, thus dividing the rectangle into 3 parts . Find
the ratio of areas of these 3 parts. ?
20. The 3 side of triangle are x^2+x+1 , 2x+1 and x^2 –1. Then the
largest of 3 angle of triangle is…?
21. The distance between town A and B is 1000 k.m. A load containing
10000 kg of jaggery is to be transferred from A to B. A camel is the
only source of transport. However, the camel is unique. It can
maximum carry a load of 1000 kgs. Further, for it is
a voracious eater, and for every k.m. it travels, it eats a kilo of
the jaggery which it is carrying.
What is the maximum amount of jaggery that can be transferred from A
to B ?
22. A farmer has four straight pieces of fencing: 1, 2, 3, and 4
yards in length. What is the maximum area he can enclose by
connecting the pieces?
23. What will be the remainder when CAT is divided by 5 , given that
CAT is written in a base in which exactly all the letters are used .
?
24.On the sides of an acute triangle ABC are constructed externally a
square, a regular n-gon and a regular m-gon (m, n > 5) whose
centers form an equilateral triangle. Prove that m = n = 6, and find
the angles of ABC.
25. Find all real numbers x such that X [x [x [x]]] = 88:
26. Two players take turns drawing a card at random from a deck of
four cards labeled 1,2,3,4. The game stops as soon as the sum of the
numbers that have appeared since the start of the game is divisible
by 3, and the player who drew the last card is the
winner. What is the probability that the player who goes first wins?
27. Find all triples (x, y, n) of positive integers with gcd(x, n +
1) = 1 such that x^n + 1 = y^n+1.
28. The point P lies inside an equilateral triangle and its distances
to the three vertices are 3, 4, 5. Find the area of the triangle.
29. A triangle ABC has positive integer sides, angle A = 2 angle B
and angle C > 90. Find the minimum length of the perimeter of ABC.
Additional Question:
A survey was conducted in a city to determine the choice of channel
(DD, BBC and CNN) among viewers in viewing the news. The viewership for these
three channels is 80, 22 and 15 percent respectively. Five percent of the respondents do not view news at all. What is the maximum percent of viewers who watch all the three channels?
1)22 2)15 3)11
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