Permutations and Combinations-Quiz-15

Permutations and Combinations Quiz-15

Dear Readers,

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
.

Q1. Statement 1: (𝑛²)!/(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 (𝑛²)!/(𝑛!)^𝑛

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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 ¹⁰𝐶₅ 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.

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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 ³⁰𝐶₂

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q6. Statement 1: The number of non-negative integral solutions of 𝑥₁+𝑥₂+𝑥₃+...+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

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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 2²⁰ Statement 2: ⁴²𝐶₀+ ⁴²𝐶₁+ ⁴²𝐶₂+⋯+ ⁴²𝐶₂₁ = 2⁴¹

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q9.Statement 1: Number of ways in which 10 identical toys can be distributed among 3 students, if each receives atleast one toys is ⁹𝐶₂ Statement 2: Number of positive integral solutions of 𝑥 + 𝑦 + 𝓏 + 𝑤 = 7 is ⁶𝐶₂

•  (a)
•  (b)
•  (c)
•  (d)

Solution

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 ¹³𝐶_𝑟 is 78 Statement 2: ^2𝑛+1𝐶_𝑟 is maximum when 𝑟 = 𝑛

•  (a)
•  (b)
•  (c)
• (d)

Solution

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