Quant Boosters  Hemant Yadav  Set 2

Q6) If A = {1, 2, 3, 4, ..., 10} and P, Q, R are subsets of A such that P U Q = R, then find the number ordered triplets (P, Q, R).
[OA : 2^20]

Q7) How many 11 digit numbers can be formed using digits 1, 2, 3, ..., 9 (repetition allowed) which are divisible by 4 ?
[OA : 9^9 * 18]

Q8) How many natural triples a, b, c are there such that (a + b)(b + c)(a + c) = 340
[OA : 0]

Q9) A and B live at opposite ends of the same street. They leave their houses at the same time and each run, at constant speed, from their house to the other house and back. The first time they meet, they are 400 meters from A's house, and the second time they meet, they are 300 meters from B's house. Both times they are traveling in opposite directions. What is the distance between the two houses?

Q10) Let a(1), a(2),..a(2011) represents the arbitrary arrangement of the numbers 1, 2,..2011. Then what is the remainder when {a(1) – 1}{a(2) – 2}..{a(2011) – 2011} is divided by 2?
[OA : 0]

Q11) Find the number of ways in which ABCDEFFFFF can be permuted such that no alphabet is at its initial position.
[OA : 120]

Q12) In a class with 20 students, 14 wear glasses, 15 wear braces, 17 wear ear rings and 18 wear wigs. What is the minimum number of students in this class who wear all four items?
(a) 4
(b) 6
(c) 7
(d) 9
(e) 10[OA : 4]

Q13) In the town there are only 2 types of coins, each worth a whole number of amount. If the highest value of amount that cannot be obtained by using any combination of the two coins is 35, then how many possible pairs of values can the coins have? (the first coin being worth 15 and the second being worth 4 is the same as the first being 4 and the second being 15)

Q14) In a triangle ABC, AC = 6 cm and D is a point on BC such that BD = AD = CD = 5 cm, then find the length of AB.
[OA : 8 cm]

Q15) If a convex Ngon has integral interior angles when measured in degrees, then what is the maximum possible value of N?
[OA : 360]

Q16) A 1000 digit number has the property that every two consecutive digits form a number that is a product of four prime numbers. The digit in the 500th position is
(a) 2
(b) 4
(c) 5
(d) 6
(e) 8[OA : 8]

Q17) A standard die with sides labelled 1 through 6 is rolled three times. Find the probability that the product of the three numbers rolled is divisible by 8.

Q18) Smallest number to be added to 17 * 20 * 23 such that it becomes a perfect square is ?

Q19) How many positive integral solutions does the equation x^2 + y^2 = 50 have?
[OA : 3]

Q20) Sum of two positive numbers a and b is 1001, then how many different values HCF(a, b) can take ?

Q21) a + b + c + d = 24, number of solutions such that a, b, c, d are distinct natural numbers

Q22) Find the minimum value of x  1 + 2x  1 + 3x  1 + 4x  1
[OA : 4/3]

Q23) There are three sugar solutions A, B and C. A is four litres with 45% concentration, B is five litres with 48% solution, C is one litre with k% solution. Now m/n litre of solution C is added to A and the remaining part is added to B such that both the resultant solutions are now 50% concentrated solutions. m and n are coprime to each other. Find the value of k + m + n.

Q24) Number of ways in which 1050 can be written as sum of:
 consecutive integers
 consecutive positive integers
 consecutive even positive integers
 consecutive odd positive integers

Q25) A kite of area K is inscribed in a circle of radius R . The length of the shorter side of kite is 7 cm . A parallelogram with shorter side 8 and area P is inscribed in the same circle. Which of the following is definitely true?
a. K > P
b. K = P
c. K < P
d. Can not say