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1 What could be the greatest possible natural number in set P?
2 What is the smallest number of elements in set P?
3 Which of the following must always be included in the set P?
d.More than one of these
4 ABCD is a quadrilateral such that the bisectors of the four interior angles meet at a point O is ? (AOB)= 57degree , calculate angle ?(COD) [in degrees]
5 a, b and c are positive numbers satisfying a2 + b2 + c2 = 12 .Find the minimum/maximum possible value of the sum of the sum of the three numbers.
a. 6, minimum
b. 6, maximum
c. 12 , minimum
d. 12, maximum
6 ABC is right angle triangle at B. AD and CE are two medians drawn from A and C respectively. If AC = 5 cm and AD = (3?5)/2 cm. Find the length of CE
c. 5 cm
7 A chord of length 32 cm is placed inside a circle of radius 20cm and a point whose distance from the center of the circle is 13 cm is marked on the chord. Calculate the length of the segment of the chord.
a. 21 cm & 11 cm
b. 19cm & 13 cm
c. 16 cm each
d. 18cm & 14 cm
8 If A = 255, B = 1714 and C = 3111 , then which of the following is a correct ascending/descending order of the values A , B and C ?
9 The integers x, y, and z are each perfect squares, and x > y > z > 0 . If x, y, and z from an arithmetic progression, find the smallest possible value of x.
10 The smallest positive integer x with 24 divisors is
11 In the given figure , AD and BC are two chords extended to meet at E. if ? (BAD) = 60 degree and CE = DE, which of the following is true
a.BE > 2AD
b.BE = 2AD
c.BE < 2AD
12 Which of the following statements are true?i. 1011 > 1110 ii. 2021 > 2120
c.Both I & II
d.Neither I nor II
13 Maya Bought a certain number of mynahs and bulbuls spending a total amount Rs. 5350. The cost of each mynah is Rs.200 and that of a bulbul is Rs.250 > If Maya had bought as many as Mynahs as the bulbuls she actually bought, and vice versa, she would have spent less than what she actually did. What is the minimum number of bulbuls she could have bought?
14 Tickets for the senior prom were Rs. 1 each for boys and 65 paise each for girls. Although there were more boys than girls at the dance, the percentage of boys who did not go was twice the percentage of the girls who did not go. The total senior class enrolment is 81, and there are 54 boys. If the total receipt from the prom tickets was Rs. 39, what was the total attendance at the prom?
15 V is an 8 digit number of which 7 digits are zero. If V2 has 16 digits, then how many different values of V are possible ?
16 ection for question 16 to 18 X, Y and Z are playing a game. There are number of matchsticks on a table. Each person has to pick up at least one matchstick and at most two matchsticks , in turn. The person who picks up the last matchstick loses. X, Y and Z takes turns in that order – till all the match sticks are picked up. Each person plays intelligently such that , to the extent possible , he does not lose even if the other two players collude. 16. How many matchsticks should X and Y respectively pick in their first chance , so that Z is certain to lose if X and Y play with the common objective of making Z lose ? ( There were 7 matchsticks to start with.)
a. ( 1, 1)
b. ( 1, 2)
c. (2, 1)
d. ( 2, 2)
17 If there are 5 matchsticks at some point of time in the game , and youy are told that Y later lost the game , then whose turn it to pick up matchsticks at the point of time ?
d.can not be determined
18 What is the smallest number of matchsticks greater than 5 at the beginning, that would ensure that Z will lose, given that X and Y work towards making Z lose?
19 Every natural number n x can be expressed as sum of two distinct composite numbers , x is also a natural number . The minimum value of x is
20 The average weight of 5 men and 5 boys is 112.5 . One man drops out and 2 boys join the group. A man's weight is 25% more than the weight of a boy. Assuming that all men are of equal weight and all boys are of equal weight , what will be the average weight of the new group closest to ?
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