The number of ways in which the letters of the word $\text{'CONSTANT'}$ can be arranged without changing the relative positions of the vowels and consonants is.
- ✓$360$
- B$256$
- C$444$
- DNone of these.
Answer: A.
View full solution →Question types
Permutation and Combinations question types
303 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
303
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
186 Q→02Assertion (A) & Reason (B) MCQ
5 Q→03True False[1 Marks ]
9 Q→041 Marks Question
43 Q→052 Marks Questions
33 Q→063 Marks Question
15 Q→07Case study (4 Marks)
2 Q→08Fill In The Blanks[1 Marks ]
10 Q→Sample Questions
Permutation and Combinations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The number of non$-$negative integral solutions of $\text{x} + \text{y}+\text{z}\leq\text{n},$ where $\text{n}\in\text{N}$ is:
- ✓$\text{n}+\ ^3\text{C}_3$
- B$\text{n}+\ ^4\text{C}_4$
- C$\text{n}+\ ^5\text{C}_5$
- D$\text{n}+\ ^2\text{C}_2$
Answer: A.
View full solution →How many $3 -$ letter words with or without meaning, can be formed out of the letters of the word, $\text{LOGARITHMS,}$ if repetition of letters is not allowed:
- ✓$720$
- B$420$
- CNone of these
- D$5040$
Answer: A.
View full solution →In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament?
- A$36$
- B$30$
- ✓$15$
- D$12$
Answer: C.
View full solution →In a crossword puzzle, $20$ words are to be guessed of which $88$ words have each an alternative solution also.The number of possible solutions will be:
- A$\ ^{20}\text{P}_8$
- B$\ ^{20}\text{C}_8$
- C$515$
- ✓$256$
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If $n$ is a positive integer, then $n(n^2 - 1) (n +2)$ is divisible by $24.$
Reason: Product of $r$ consecutive whole numbers is divisible by $\angle\text{r}.$
Assertion: If $n$ is a positive integer, then $n(n^2 - 1) (n +2)$ is divisible by $24.$
Reason: Product of $r$ consecutive whole numbers is divisible by $\angle\text{r}.$
- ✓Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason $(s)(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Number of rectangles on a chess board is $^8C_2 \times\ ^8C_2.$
Reason: To form a rectangle, we have to select any two of the horizontal line and any two of the vertical line.
Assertion: Number of rectangles on a chess board is $^8C_2 \times\ ^8C_2.$
Reason: To form a rectangle, we have to select any two of the horizontal line and any two of the vertical line.
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- ✓Assertion is wrong statement but Reason is correct statement.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Number of lines formed by joining $n$ points on a circle $(\text{n}\geq2)$ is $\frac{\text{n}(\text{n}-1)}{2}.$
Reason: $\text{C}(\text{n},2)=\frac{\text{n}(\text{n}-1)}{2}.$
Assertion: Number of lines formed by joining $n$ points on a circle $(\text{n}\geq2)$ is $\frac{\text{n}(\text{n}-1)}{2}.$
Reason: $\text{C}(\text{n},2)=\frac{\text{n}(\text{n}-1)}{2}.$
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓Assertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: C.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason $(s)(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3.$
Reason: The number of ways of choosing any $3$ places, from $9$ different places is $^9C_3.$
Assertion: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3.$
Reason: The number of ways of choosing any $3$ places, from $9$ different places is $^9C_3.$
- ✓Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- CAssertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Product of five consecutive natural numbers is divisible by $4!.$
Reason: Product of $n$ consecutive natural numbers is divisible by $(n + 1)!.$
Assertion: Product of five consecutive natural numbers is divisible by $4!.$
Reason: Product of $n$ consecutive natural numbers is divisible by $(n + 1)!.$
- AAssertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
- BAssertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
- ✓Assertion is correct statement but Reason is wrong statement.
- DAssertion is wrong statement but Reason is correct statement.
Answer: C.
View full solution →State True or False for the following statement:
In a steamer there are stalls for $12$ animals, and there are horses, cows and calves (not less than $12$ each) ready to be shipped. They can be loaded in $3^{12}$ ways
View full solution →In a steamer there are stalls for $12$ animals, and there are horses, cows and calves (not less than $12$ each) ready to be shipped. They can be loaded in $3^{12}$ ways
State True or False for the following statement:
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table.
The number of ways in which the seating arrangements can be made is $\frac{11!}{5!6!}(9!)(9!) .$
View full solution →Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table.
The number of ways in which the seating arrangements can be made is $\frac{11!}{5!6!}(9!)(9!) .$
State True or False for the following statement:
There are $12$ points in a plane of which $5$ points are collinear, then the number of lines obtained by joining these points in pairs is $^{12}C_2 –\ ^5C_2 .$
View full solution →There are $12$ points in a plane of which $5$ points are collinear, then the number of lines obtained by joining these points in pairs is $^{12}C_2 –\ ^5C_2 .$
State True or False for the following statement:
To fill $12$ vacancies there are $25$ candidates of which $5$ are from scheduled castes. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is $^5C_3 \times\ ^{20}C_9 .$
In each if the Exercises from $60$ to $64$ match each item given under the column $C_1$ to its correct answer given under the column $C_2 .$
View full solution →To fill $12$ vacancies there are $25$ candidates of which $5$ are from scheduled castes. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is $^5C_3 \times\ ^{20}C_9 .$
In each if the Exercises from $60$ to $64$ match each item given under the column $C_1$ to its correct answer given under the column $C_2 .$
State True or False for the following statement:
Three letters can be posted in five letterboxes in $35$ ways.
View full solution →Three letters can be posted in five letterboxes in $35$ ways.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: atmost 3 girls?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: atleast 3 girls?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
If $^n{C_8}{ = ^n}{C_2}$ . find $^n{C_2}$.
View full solution →How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if all letters are used but first letter is a vowel?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
A bag contains 5 black balls and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
It is required, to seat 5 men, and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
In an examination a question paper consist of 12 questions divided into two parts i.e. part I and part II containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
The English alphabet has 5 vowels and 21 consonants. How many words with 2 vowels and 2 different consonants can be formed from the alphabet?
How many $6-$digit numbers can be formed from the digits $0, 1, 3, 5, 7$ and $9$ which are divisible by $10$ and, no digit is repeated?
View full solution →Republic day is a national holiday of India. It honours the date on which the constitution of India came into effect on 26 January 1950 replacing the Government of India Act (1935) as the governing document of India and thus, turning the nation into a newly formed republic.
Answer the following question, which are based on the word "REPUBLIC".
(i) Find the number of arrangements of the letters of the word 'REPUBLIC'.
(a) 40300 (b) 30420 (c) 40320 (d) 40400
(ii) How many arrangements start with a vowel?
(a) 12015 (b) 15120 (c) 12018 (d) 15100
(iii) Which concept is used for finding the arrangements start with a vowel?
(a) Permutation (b) FPM (c) Combination (d) FPA
(iv) If the number of arrangements of the letters of the word 'REPUBLIC' is abcde, the (a + b + $\mathbf{c}+\mathbf{d}+\mathbf{e})$ is
(a) 10 (b) 9 (c) 8 (d) 15
(v) If the number of arrangements start with a vowel is abcde, then $(\mathbf{a}+\mathbf{b})-(\mathbf{d}+\mathbf{e})$ is
(a) 2 (b) 3 (c) 4 (d) 5
View full solution →Answer the following question, which are based on the word "REPUBLIC".
(i) Find the number of arrangements of the letters of the word 'REPUBLIC'.
(a) 40300 (b) 30420 (c) 40320 (d) 40400
(ii) How many arrangements start with a vowel?
(a) 12015 (b) 15120 (c) 12018 (d) 15100
(iii) Which concept is used for finding the arrangements start with a vowel?
(a) Permutation (b) FPM (c) Combination (d) FPA
(iv) If the number of arrangements of the letters of the word 'REPUBLIC' is abcde, the (a + b + $\mathbf{c}+\mathbf{d}+\mathbf{e})$ is
(a) 10 (b) 9 (c) 8 (d) 15
(v) If the number of arrangements start with a vowel is abcde, then $(\mathbf{a}+\mathbf{b})-(\mathbf{d}+\mathbf{e})$ is
(a) 2 (b) 3 (c) 4 (d) 5
Five students Ajay, Shyam, Yojana, Rahul and Akansha are sitting in a playground in a line.
Based on the above information, answer the following questions.
(i) Total number of ways of sitting arrangement of five students is
(a) 120 (b) 60 (c) 24 (d) None of these
(ii) Total number of arrangement of sitting, if Ajay and Yojana sit together, is
(a) 60 (b) 48 (c) 72 (d) 120
(iii) Total number of arrangement 'Yojana and Rahul sitting at extreme position' is
(a) 24 (b) 36 (c) 48 (d) 12
(iv) Total number of arrangement, if shyam is sitting in the middle, is
(a) 24 (b) 12 (c) 6 (d) 36
(v) Total number of arrangement sitting Yojana and Rahul not sit together, is
(a) 72 (b) 120 (c) 60 (d) 144
Based on the above information, answer the following questions.
(i) Total number of ways of sitting arrangement of five students is
(a) 120 (b) 60 (c) 24 (d) None of these
(ii) Total number of arrangement of sitting, if Ajay and Yojana sit together, is
(a) 60 (b) 48 (c) 72 (d) 120
(iii) Total number of arrangement 'Yojana and Rahul sitting at extreme position' is
(a) 24 (b) 36 (c) 48 (d) 12
(iv) Total number of arrangement, if shyam is sitting in the middle, is
(a) 24 (b) 12 (c) 6 (d) 36
(v) Total number of arrangement sitting Yojana and Rahul not sit together, is
(a) 72 (b) 120 (c) 60 (d) 144
Fill in the Blank.
The number of permutations of n different objects, taken $r$ at a line, when repetitions are allowed, is ______.
View full solution →The number of permutations of n different objects, taken $r$ at a line, when repetitions are allowed, is ______.
Fill in the Blank.
If $^nP_r= 840,\ ^nC_r = 35,$ then $r = \_\_\_\_\_\_.$
View full solution →If $^nP_r= 840,\ ^nC_r = 35,$ then $r = \_\_\_\_\_\_.$
Fill in the Blank.
A committee of $6$ is to be chosen from $10$ men and $7$ women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee.
[Hint: At least $3$ men and $2$ women: The number of ways $=\ ^{10}C_3\times\ ^7C_3 +\ ^{10}C_4 \times\ ^7C_2 $. For $2$ particular women to be always there: the number of ways $=\ ^{10}C4 +\ ^{10}C_3\times\ ^5C_1 .$ The total number of committees when two particular women are never together = Total – together.]
View full solution →A committee of $6$ is to be chosen from $10$ men and $7$ women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee.
[Hint: At least $3$ men and $2$ women: The number of ways $=\ ^{10}C_3\times\ ^7C_3 +\ ^{10}C_4 \times\ ^7C_2 $. For $2$ particular women to be always there: the number of ways $=\ ^{10}C4 +\ ^{10}C_3\times\ ^5C_1 .$ The total number of committees when two particular women are never together = Total – together.]
Fill in the Blank.
$^{15}C_8 +\ ^{15}C_9\ –\ ^{15}C_6\ –\ ^{15}C_7 = \_\_\_\_\_\_.$
View full solution →$^{15}C_8 +\ ^{15}C_9\ –\ ^{15}C_6\ –\ ^{15}C_7 = \_\_\_\_\_\_.$
Fill in the Blank.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
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