### AMCAT Quantitative Aptitude Previous Years Question answers with Solutions 6

Ques 151 : Choose the correct answer.

A polygon has 44 diagonals, the number of its sides is

Option 1 : 10

**Option 2 : 11**

Option 3 : 12

Option 4 : 22

Ques 152 : Choose the correct answer.

The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line is

Option 1 : 105

Option 2 : 115

Option 3 : 175

**Option 4 : 185**

Ques 153 : Choose the correct answer.

There are 5 letters and five addressed envelopes. the number of ways in which all the letters can be put in wrong envelopes is

Option 1 : 119

**Option 2 : 44**

Option 3 : 59

Option 4 : 40

Ques 154 : Choose the correct answer.

The number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated is

Option 1 : 960

**Option 2 : 2880**

Option 3 : 288

Option 4 : 576

Ques 155 : Choose the correct answer.

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

Option 1 : 25

Option 2 : 30

Option 3 : 32

**Option 4 : none of these**

Ques 156 : Choose the correct answer.

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

Option 1 : np

Option 2 : pn

**Option 3 : (p+1)n -1**

Option 4 : (n+1)p-1

Ques 157 : Choose the correct answer.

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

Option 1 : 220

Option 2 : 204

**Option 3 : 205**

Option 4 : 195

Ques 158 : Choose the correct answer.

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

Option 1 : 56

Option 2 : 126

**Option 3 : 91**

Option 4 : none of these

Ques 159 : Choose the correct answer.

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

Option 1 : 15

Option 2 : 81

**Option 3 : 255**

Option 4 : 256

Ques 160 : Choose the correct answer.

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?

**Option 1 : 1260**

Option 2 : 210

Option 3 : 10C6 * 6!

Option 4 : 10C5 * 6

Ques 161 : Choose the correct answer.

There are 10 yes or no questions. How many ways can these be answered?

Option 1 : 1084

Option 2 : 2048

**Option 3 : 1024**

Option 4 : 100

Ques 162 : Choose the correct answer.

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?

Option 1 : 24

Option 2 : 31

**Option 3 : 32**

Option 4 : 30

Ques 163 : Choose the correct answer.

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:

Option 1 : 1/22

Option 2 : 3/22

**Option 3 : 2/91**

Option 4 : 2/77

Ques 164 : Choose the correct answer.

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:

Option 1 : 4/19

**Option 2 : 7/19**

Option 3 : 12/19

Option 4 : 21/95

Ques 165 : Choose the correct answer.

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 ?

**Option 1 : 2/5**

Option 2 : 3/4

Option 3 : 3/5

Option 4 : 3/10

Ques 166 : Choose the correct answer.

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

Option 1 : 1/18

Option 2 : 1/3

**Option 3 : 1/6**

Option 4 : 2/3

Ques 167 : Choose the correct answer.

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

**Option 1 : 0.5**

Option 2 : 0.4

Option 3 : 0.88

Option 4 : None of these

Ques 168 : Choose the correct answer.

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?

Option 1 : 1/4

**Option 2 : 1/5**

Option 3 : 2/5

Option 4 : 1/120

Option 5 : 4

Ques 169 : Choose the correct answer.

In a single throw of dice, what is the probability to get a number greater or equal to 4?

Option 1 : 1/3

Option 2 : 2/3

**Option 3 : 1/2**

Option 4 : None of these

Ques 170 : Choose the correct answer.

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?

Option 1 : 3.5/12

**Option 2 : 7/12**

Option 3 : 5/12

Option 4 : None of these

Ques 171 : Choose the correct answer.

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?

Option 1 : 4/7

Option 2 : 8/49

Option 3 : 7/8

**Option 4 : 15/49**

Ques 172 : Choose the correct answer.

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?

Option 1 : 2/3

Option 2 : 3/7

Option 3 : 2/21

**Option 4 : None of these**

Ques 173 : Choose the correct answer.

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

Option 1 : 1/32

**Option 2 : 31/32**

Option 3 : 1/5

Option 4 : None of these

Ques 174 : Choose the correct answer.

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?

Option 1 : 5/108

**Option 2 : 1/6**

Option 3 : 5/18

Option 4 : 4/9

Ques 175 : Choose the correct answer.

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

**Option 1 : 1/2**

Option 2 : 1/3

Option 3 : 3/5

Option 4 : 2/5

Ques 176 : Choose the correct answer.

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:

Option 1 : 291/364

Option 2 : 371/464

Option 3 : 471/502

**Option 4 : 459/512**

Ques 177 : Choose the correct answer.

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:

**Option 1 : 8/27**

Option 2 : 1/27

Option 3 : 26/27

Option 4 : 2/3

Ques 178 : Choose the correct answer.

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?

Option 1 : 0.3

**Option 2 : 0.4**

Option 3 : 0.7

Option 4 : None of these

Ques 179 : Choose the correct answer.

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

**Option 1 : 1/2**

Option 2 : 1

Option 3 : 0

Option 4 : 4/5

Ques 180 : Choose the correct answer.

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:

**Option 1 : 1/3**

Option 2 : 1/5

Option 3 : 1/2

Option 4 : 1/10