Problem Solving Practice Test 05.docx

Problem Solving Practice Test 5 Question 1 6 students of nursery class are playing a game. They are standing in a circle and have to pass a ball among themselves. How many such passes are possible? 32760 15625 30 36 46656 Correct Answer : B Question 2 There are 5 boys standing in a row and 5 girls are to be paired with them for a group dance competition in a school. In how many ways can the girls be made to stand? 360 120 540 720 180 Correct Answer : B Question 3 In the editorial group’s photograph of a school all the 5 teachers are to be seated in the front row. Four girls are to be in the second row and six boys in the third row. If the principal has a fixed seat in the first row, then how many arrangements are possible? 237144 251820 502340 72000 2073600 Correct Answer : E Question 4 In how many ways can 8 people be seated at a round table? 5040 40320 2520 4914 378 Correct Answer : A Question 5 Sunita wants to make a necklace. She has 8 beads. How many different choices does she have? 2400 1200 600 250 100 Correct Answer : B Question 6 From city A to B there are 3 different roads. From B to C there are 5. From C to D there are 2. Laxman has to go from city A to D attending some work in city B and C on the way and has to come back in the reverse order. In how many ways can he complete his journey if he has to take a different while coming back than he did while going? 250 90 100 870 900 Correct Answer : D Question 7 Neetu has five identical beads each of nine different colours. She wants to make a necklace such that the beads of the same colour always come together. How many different arrangements can she have? 2534 1500 56321 42430 20160 Correct Answer : E Question 8 On a chess board one white square is chosen at random. In how many ways can a black square be chosen such that it does not lie in the same row as the white square? 1450 2920 3105 2002 1400 Correct Answer : D Question 9 How many necklaces can be made using at least 5 from 8 beads of different colours? 230 2952 5904 7695 5130 Correct Answer : B Question 10 Find the possible values of n if 30 P(n,6) = P(n+2,7). 10,15 6,7 4,25 9,10 8,19 Correct Answer : E Question 11 Using all the prime numbers less than 10 how many four-digit even numbers can be made if repetition is not allowed? 8 4 2 6 3 Correct Answer : D Question 12 There are 15 points in a plane, out of which 6 are collinear. How many pentagons can be drawn with these points? 3006 3003 2997 3005 3009 Correct Answer : C Question 13 If P(n-1,3):P(n,3) = 1:9, find n. 6 7 8 9 4 Correct Answer : D Question 14 How many four-digit numbers are there with distinct digits? 6547 10000 3600 4536 5040 Correct Answer : D Question 15 In how many ways can 9 students be seated in a row such that the tallest child and the shortest child never sit together? 564480 282240 141120 70560 23416 Correct Answer : B