Permutations and Combinations is one of the most important chapters of Algebra in the JEE syllabus and other engineering exams. For JEE Mains, it has 4% weightage and for JEE Advanced, it has 5% weightage..

**This section contain(s) 10 questions numbered 1 to 10. Each question contains statement 1(Assertion) and statement 2(Reason). Each question has the 4 choices (a), (b), (c) and (d) out of which only one is correct.**

a)Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

b)Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1

c)Statement 1 is True, Statement 2 is False

d)Statement 1 is False, Statement 2 is True

.

a)Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1

b)Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1

c)Statement 1 is True, Statement 2 is False

d)Statement 1 is False, Statement 2 is True

**Q1.**Statement 1: (𝑛

^{2})!/(𝑛!)

^{𝑛}is a natural number for all 𝑛 ∈ 𝑁 Statement 2: Number of ways in which 𝑛2objects can be distributed among 𝑛 persons equally is (𝑛

^{2})!/(𝑛!)

^{𝑛}

**Q2.**In a shop there are five types of ice-creams available. A child buys six ice-creams Statement 1: The number of different ways the child can buy the six ice-creams is

^{10}𝐶

_{5}Statement 2: The number of different ways the child can buy the six ice-creams is equals to the number of different ways of arranging 6 A’s and B’s in a row.

**Q3.**Statement 1: Number of ways in which 30 can be partitioned into three unequal parts, each part being a natural number is 61 Statement 2: Number of ways of distributing 30 identical objects in three different boxes is

^{30}𝐶

_{2}

**Q4.**Statement 1: Number of ways in which Indian team (11 players) can bat, if Yuvraj wants to bat before Dhoni and Pathan wants to bat after Dhoni is 11!/3! Statement 2: Yuvraj, Dhoni and Pathan can be arranged in batting order in 3! Ways

**Q5.**Statement 1: Number of zeros at the end of 50! Is equal to 12 Statement 2: Exponent of 2 in 50! is 47

**Q6.**Statement 1: The number of non-negative integral solutions of 𝑥

_{1}+𝑥

_{2}+𝑥

_{3}+...+𝑥

_{𝑛}= 𝑟 is

^{ 𝑟+𝑛−1}𝐶

_{𝑟}Statement 2: The number of ways in which 𝑛 identical things can be distributed into 𝑟 different groups is

^{𝑛+𝑟−1}𝐶

_{𝑛}

**Q7.**Statement 1: The number of ways in which 𝑛 persons can be seated at a round table, so that all shall not have the same neighbours in any two arrangements is (𝑛−1)!/2 Statement 2: Number of ways of arranging 𝑛 different beads in circles in which is (𝑛−1)!/2

**Q8.**Statement 1: Number of ways of selecting 10 objects from 42 objects of which, 21 objects are identical and remaining objects are distinct is 2

^{20}Statement 2:

^{42}𝐶

_{0}+

^{42}𝐶

_{1}+

^{42}𝐶

_{2}+⋯+

^{42}𝐶

_{21}= 2

^{41}

**Q9.**Statement 1: Number of ways in which 10 identical toys can be distributed among 3 students, if each receives atleast one toys is

^{9}𝐶

_{2}Statement 2: Number of positive integral solutions of 𝑥 + 𝑦 + 𝓏 + 𝑤 = 7 is

^{6}𝐶

_{2}

**Q10.**Statement 1: When number of ways of arranging 21 objects of which 𝑟 objects are identical of one type and remaining are identical of second type is maximum, then maximum value of

^{13}𝐶

_{𝑟}is 78 Statement 2:

^{2𝑛+1}𝐶

_{𝑟}is maximum when 𝑟 = 𝑛