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**AMCAT**

**AMCAT**

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### AMCAT Quants All Questions List

Ques. At an election there are five candidates and three members to be elected , and a voter may vote for any number of candidates not greater than the number to be elected. Then the number of ways in which a voter may vote is

Op 1: 25

Op 2: 30

Op 3: 32

Op 4: none of these

Op 5:

Correct Op : 4

Ques. There are n different books and p copies of each. the number of ways in which a selection can be made from them is

Op 1: np

Op 2: pn

Op 3: (p+1)n -1

Op 4: (n+1)p-1

Op 5:

Correct Op : 3

Ques. The sides AB, BC, CA of a triangle ABC have 3,4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices is

Op 1: 220

Op 2: 204

Op 3: 205

Op 4: 195

Op 5:

Correct Op : 3

Ques. A lady gives dinner party to five guests to be selected from 9 friends .The number of ways of forming the party of 5,given that two of the friends will not attend the party together is

Op 1: 56

Op 2: 126

Op 3: 91

Op 4: none of these

Op 5:

Correct Op : 3

Ques. Each question has four choices out of which only one is correct. A candidate has to answer four questions. The number of ways he fails to give all answers correctly, is

Op 1: 15

Op 2: 81

Op 3: 255

Op 4: 256

Op 5:

Correct Op : 3

Ques. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

Op 1: 1260

Op 2: 210

Op 3: 10C6 * 6!

Op 4: 10C5 * 6

Op 5:

Correct Op : 1

Ques. There are 10 yes or no questions. How many ways can these be answered? Op 1: 1084

Op 2: 2048

Op 3: 1024

Op 4: 100

Op 5:

Correct Op : 3

Ques. If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

Op 1: 24

Op 2: 31

Op 3: 32

Op 4: 30

Op 5:

Correct Op : 3

Ques. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

Op 1: 1/22

Op 2: 3/22

Op 3: 2/91

Op 4: 2/77

Op 5:

Correct Op : 3

Ques. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective, is:

Op 1: 4/19

Op 2: 7/19

Op 3: 12/19

Op 4: 21/95

Op 5:

Correct Op : 2

Ques. In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he has offered English or Hindi ?

Op 1: 2/5

Op 2: 3/4

Op 3: 3/5

Op 4: 3/10

Op 5:

Correct Op : 1

Ques. A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a different size. The probability that the red ball being selected is the smallest red ball, is

Op 1: 1/18

Op 2: 1/3

Op 3: 1/6

Op 4: 2/3

Op 5:

Correct Op : 3

Ques. If A and B are 2 independent events and P(A)=0.5 and P(B) = 0.4, find P(A/B):

Op 1: 0.5

Op 2: 0.4

Op 3: 0.88

Op 4: None of these

Op 5:

Correct Op : 1

Ques. A 5-digit number is formed by the digits 1,2,3,4 and 5 without repetition. What is the probability that the number formed is a multiple of 4?

Op 1: 1/4

Op 2: 1/5

Op 3: 2/5

Op 4: 1/120

Op 5: 4

Correct Op : 2

Ques. In a single throw of dice, what is the probability to get a number greater or equal to 4? Op 1: 1/3

Op 2: 2/3

Op 3: 1/2

Op 4: None of these

Op 5:

Correct Op : 3

Ques. A bag contains 5 oranges, 4 bananas and 3 apples. Rohit wants to eat a banana or an apple. He draws a fruit from the bag randomly. What is the probability that he will get a fruit of his choice?

Op 1: 3.5/12

Op 2: 7/12

Op 3: 5/12

Op 4: None of these

Op 5:

Correct Op : 2

Ques. There are two boxes A and B. Box A has three red and four blue balls. Box B has five red and two blue balls. Anya draws a ball from each bag randomly. What is the probability that both balls are red?

Op 1: 4/7

Op 2: 8/49

Op 3: 7/8

Op 4: 15/49

Op 5:

Correct Op : 4

Ques. Ravi has a bag full of 10 Nestle and 5 Cadbury chocolates. He draws two chocolates. What is the probability that he got at least one Nestle chocolate?

Op 1: 2/3

Op 2: 3/7

Op 3: 2/21

Op 4: None of these

Op 5:

Correct Op : 4

Ques. The probability of having at least one tail in 5 throws of a coin is

Op 1: 1/32

Op 2: 31/32

Op 3: 1/5

Op 4: None of these

Op 5:

Correct Op : 2

Ques. A bag contains 5 yellow and 4 brown pencils. If two pencils are drawn, what is the probability that the pencils are of the same colour?

Op 1: 5/108

Op 2: 1/6

Op 3: 5/18

Op 4: 4/9

Op 5:

Correct Op : 4

Ques. A single letter is drawn at random from the word, “ASPIRATION”, the probability that it is a vowel is?

Op 1: 1/2

Op 2: 1/3

Op 3: 3/5

Op 4: 2/5

Op 5:

Correct Op : 1

Ques. The probability that a man can hit a target is 3/4. He tries 5 times. The probability that he will hit the target at least three times is:

Op 1: 291/364

Op 2: 371/464

Op 3: 471/502

Op 4: 459/512

Op 5:

Correct Op : 4

Ques. An unbiased dice is rolled 3 times. The probability that the value on the dice is not more than 4 in any of the 3 rolls is:

Op 1: 8/27

Op 2: 1/27

Op 3: 26/27

Op 4: 2/3

Op 5:

Correct Op : 1

Ques. Probability of occurrence of event A is 0.5 and that of event B is 0.2. The probability of occurrence of both A and B is 0.1. What is the probability that none of A and B occur?

Op 1: 0.3

Op 2: 0.4

Op 3: 0.7

Op 4: None of these

Op 5:

Correct Op : 2

Ques. An unbiased coin is tossed 5 times. If tail appears on first four tosses, then probability of tail appearing on the fifth toss is:

Op 1: 1/2

Op 2: 1

Op 3: 0

Op 4: 4/5

Op 5:

Correct Op : 1

Ques. X and Y are two independent events. The probability that X and Y occur is 1/12, and the probability that neither occur is 1/2, the probability of occurrence of X can be:

Op 1: 1/3

Op 2: 1/5

Op 3: 1/2

Op 4: 1/10

Op 5:

Correct Op : 1

Ques. An unbiased coin is tossed n times. If the probability of getting 4 tails equals the probability of getting 7 tails, then the probability of getting two tails is:

Op 1: 55/2048

Op 2: 3/4096

Op 3: 1/1024

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Sudhanshu and Pankaj stand in a circle with 10 other persons. If the arrangement of the person is at random, then the probability that there are exactly 3 persons between Sudhanshu and Pankaj is?

Op 1: 9/11

Op 2: 2/11

Op 3: 1/11

Op 4: None of these

Op 5:

Correct Op : 2

Ques. Three numbers are chosen from 1 to 30 randomly. The probability that they are not consecutive is:

Op 1: 1/145

Op 2: 144/145

Op 3: 139/140

Op 4: 1/140

Op 5:

Correct Op : 2

Ques. A bag is full of 20 bananas and no other fruit. Rajeev draws a fruit from the bag. What is the probability that he will draw a banana?

Op 1: 1

Op 2: 0

Op 3: 1/2

Op 4: None of these

Op 5:

Correct Op : 1

Ques. An unbiased dice is rolled 5 times and the outcomes are 1, 2, 3, 4 and 5 respectively. If it is rolled again, what is the probability that the outcome is 6?

Op 1: 1

Op 2: 5/6

Op 3: 1/6

Op 4: None of these

Op 5:

Correct Op : 3

Ques. The probability of drawing an apple from a bag of fruits is 6/25. How many apples should Ravi draw, so that there is a chance he will draw 12 apples on average?

Op 1: 25

Op 2: 50

Op 3: 12

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is the probability for a day to be Sunday?

Op 1: 1/7

Op 2: 1/5

Op 3: 52/365

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Rani has a bag with three blue and three yellow coins. She takes out a coin, sees its colour and puts it back in the bag. She does this thrice. What is the probability that she saw all blue coins.

Op 1: 1/8

Op 2: 1/2

Op 3: 1/3

Op 4: None of these

Op 5:

Correct Op : 1

Ques. Shikhar has a bag with 2 balls, each of which can be black or white with equal probability. Now, he draws out a ball and it turns out to be black. After this event, what is the probability that both balls are black?

Op 1: 1/2

Op 2: 1/4

Op 3: 1

Op 4: None of these

Op 5:

Correct Op : 1

Ques. A coin is tossed thrice. What is the probability that the first toss of coin lands head, second tail and third lands tail as well?

Op 1: 1/16

Op 2: 3/8

Op 3: 1/8

Op 4: None of these

Op 5:

Correct Op : 3

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