Permutations and Combinations-Quiz-14

Permutations and Combinations Quiz-14

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: Number of ways in which two persons A and B select objects from two different groups each having 20 different objects such that B selects always more objects than A (including the case when A selects no object ) is (2⁴⁰− ⁴⁰C₂₀)/2 Statement 2: The sum ∑_0<e;i<j<e;n ⁿC_iⁿC_j = (2²ⁿ - ²ⁿC_n)/2

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q2.Statement 1: The number of positive integral solutions of 𝑎𝑏𝑐 = 30 is 27
Statement 2: Number of ways in which three prizes can be distributed among three persons is 3³

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q3.  Statement 1: The number of different car licence plates can be constructed if the licences contain three letters of the English alphabet followed by a three digit number is (26)³×(900)(if repetitions are allowed). Statement 2: The number of permutations of 𝑛 different things taken 𝑟 at a time when each things may be repeated any number of times is 𝑛^𝑟

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q4. Statement 1: The sum of the digits in the tens place of all numbers formed with the help of 2, 3, 4, 5 taken all at a time is 84.
Statement 2: The sum of the digits in the units place of all numbers formed with the help of 𝑎₁,𝑎₂,….𝑎_𝑛 taken all at a time is (𝑛−1)!(𝑎₁ + 𝑎₂+...+𝑎_n) (repetition of digits is not allowed)

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q5.Statement 1: Number of rectangle on a chess board is ⁸𝐶₂ × ⁸𝐶₂ Statement 2: To form a rectangle we have to select any two of the horizontal line and any two of the vertical line

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q6. Statement 1: Number of terms in the expansion of (𝑥+𝑦+𝓏+𝑤)⁵⁰ is ⁵³𝐶₃ Statement 2: Number of non-negative solution of the equation 𝑝+𝑞+𝑟+𝑠 = 50 is ⁵³𝐶₃

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q7.Statement 1: Number of ways in which India can win the series of 11 matches is 2¹⁰.(if no match is drawn) Statement 2: For each match there are two possibilities, either India wins or loses

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q8.Statement 1: Total number of five-digit numbers having all different digits and divisible by 4 can be formed using the digits {1,3,2,6,8,9} is 192 Statement 2: A number is divisible by 4, if the last two digits of the number are divisible by 4

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q9.Statement 1: A number of four different digit is formed with the help of the digits 1, 2, 3, 4, 5, 6, 7 in all possible ways. Then, number of ways which are exactly divisible by 4 is 200 Statement 2: A number divisible by 4 if unit place digit divisible by 4

•  (a)
•  (b)
•  (c)
•  (d)

Solution

Q10.Statement 1: If 𝑝,𝑞 < 𝑟, the number of different selections of 𝑝 + 𝑞 things taking 𝑟 at a time, where 𝑝 things are identical and 𝑞 other things are identical, is 𝑝 + 𝑞 − 𝑟 + 1 Statement 2: If 𝑝,𝑞 > 𝑟, the number of different selections of 𝑝 + 𝑞 things taking 𝑟 at a time, where 𝑝 things are identical and 𝑞 other things are identical, is 𝑟 − 1

•  (a)
•  (b)
•  (c)
• (d)

Solution

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