Quant Boosters  Hemant Yadav  Set 2

Number of Questions  30
Topic  Quant Mixed Bag
Solved ? : Yes
Source : Collection of solved questions from Hemant Yadav, Math faculty  FIITJEE

Q1) Let ABC be a right angled triangle with angle B = 90° and let BD be the altitude from B on to AC. Draw DE perpendicular to AB and DF perpendicular to BC. Let P, Q, R and S be respectively the incenters of triangle DFC, DBF, DEB and DAE. Find the measure of angle PDR.
[OA : 90]

Q2) If length of two altitudes of a triangle are 2 and 3, then how many integral values the third altitude can take ?
a) 2
b) 3
c) 4
d) More than 4

Q3) How many 7 digit numbers can be formed using the digits 2, 3, 4, 5, 6, 7, 8 (with repetition) such that they are divisible by 7
[OA : 7^6]

Q4) Six children are standing along the xaxis at points (0, 0), (17, 0), (40, 0), (85, 0), (173, 0), (440, 0). The children decide to meet at some point along the xaxis. What is the minimum total distance the children must walk in order to meet?

Q5) A large bottle contains a collection of coins. When you examine the contents you are amazed to discover that there is an equal number of each type of denomination: 1p, 2p, 5p, 10p, 20p, 50p, Re1, and Rs2. Even more remarkable is that if you remove one coin there will be an exact amount in rupees. What is the smallest amount, in rupees, that could be in the bottle after removing a coin?
[OA : 58]

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]