Permutation and Combination Test 2

Directions For Questions

Directions∶ Answer these questions on the basis of the information given below ∶An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …., 9 such that the first digit of the code is non-zero (digits repetition not allowed). The code, handwritten on a slip, can however potentially create confusion, when read upside-down for example, the code 91 may appear as 16. Agency will not consider such confusion as there codes.

How many codes are there starting with 6 or ending with 8?

Directions For Questions

Directions∶ Answer these questions on the basis of the information given below ∶An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …., 9 such that the first digit of the code is non-zero (digits repetition not allowed). The code, handwritten on a slip, can however potentially create confusion, when read upside-down for example, the code 91 may appear as 16. Agency will not consider such confusion as there codes.

How many codes are there for which no such confusion can arise?

Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose the possible answer.

Quantity A∶ Suppose there are 4 teachers, 6 students and 3 guardians. What are the various ways in which a committee of 7 members can be formed, such that the committee has at least 3 students and 2 guardians?

Quantity B∶ 590.

Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: There are 17 points in a plane out of which 6 are collinear. Find the number of lines that can be formed from 17 points.Quantity B: In how many different ways can the letters of the word DETAILS be arranged in such a way that the vowels occupy only the even positions?

Rajesh along with Reena accepted the order to prepare x number of dresses. For the order, 44.44% of the material is prepared by Reena and rest is prepared by Rajesh. It is found that 14.29% of dress prepared by Reena is defective and for Rajesh, the number is 16.67%. If one of the dresses had been picked up from the bunch, what is the probability that it is prepared by Rajesh and it is in good condition?

Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

A box contains 6 Red balls, 5 White balls, 3 Black balls and 6 Blue balls.

Quantity A: If three balls are drawn at random then the probability that all the balls are either white or blue.Quantity B: If three balls are drawn at random then the probability that all are of different colours.

Directions: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.

What is the probability of selecting a prime number in the set of first ‘x’ natural numbers?

I. x is a prime number just greater than 10.II. x = 14.

Given below are two quantities named A & B. Based on the given information, you have to determine the relation between two quantities. You should use the given data and your knowledge of Mathematics to choose between possible answers.

A bag contains 12 five rupee coins, 11 two rupee coins, and 4 half rupee coins. If 3 coins are selected at random, then

P(A): Probability that the sum of the three coins is maximum.P(B): Probability that each coin is of different value.

There are three different bags. Each of them has N balls. But first bag has red balls, second bag has blue balls and third bag has green balls. Three balls are taken each from first and second bags and put in the third bag. Now, a ball is randomly chosen from third bag. The probability that this ball is green is 5/7. What is the value of N?

A bag contains ten fruits. Among them, four are orange and six are apples. If four of them are drawn together, the probability that exactly three are apples and exactly two are apples is ___ and  ____ respectively/.

Which of the following options satisfies the two blanks in the question?

A. 4 / 21, 1 / 84

B. 4 / 21, 3 / 84

C. 2 / 21, 1 / 42D. 8 / 21, 6 / 7

A pack of the card contains some Black cards, Red cards and Blue cards such that the probability of picking a Black card is 2/7 and the probability of picking a Red card is 1/2. If all the cards are numbered starting from 1, 2, 3, …. and so on, then what is the probability of getting one card numbered as multiple of 3 or 7 out of the total cards.

A child who has learnt to spell a word is asked by his teacher to spell a 7 letter word. He remembers the middle five letters of the word. However, he is sure that the first letter is a consonant and the last letter is a vowel. What is the probability that he spells the word correctly?

 A small spherical substance was accidently dropped into a cylindrical vessel of height 42 cm and radius 30 cm filled with water. A small cylindrical glass of height 7 cm and radius 5 cm was used to take some water from it. What is the probability that the small spherical substance gets transferred to the glass?

Directions For Questions

Directions: There are total 10 teachers and 20 students in the group. Based on the given information, answer the following questions.

Find the number of ways in which 10 teachers can be equally divided into five groups.

Directions For Questions

Directions: There are total 10 teachers and 20 students in the group. Based on the given information, answer the following questions.

A committee is to be formed of 2 teachers and 3 students in such a way so that a particular teacher is included and 2 particular students are excluded. In how many number of ways it can be done?