Class 11 Mathematics Permutations and Combinations MCQs Set 11

STATEMENT TYPE

Question. I : The number of five digit numbers that can be formed with 0, 1, 2, 3, 5, which are divisible by 5 is 18.
II : The sum of all four digit numbers that can be formed with 1, 2, 3, 4 so that no digit being repeated in any number is 66660.
which of the above statements is true?
(a) only I
(b) only II
(c) Both I and II
(d) Neither I nor II
Answer: (b) only II

Question. I : The number of ways that 5 prizes be distributed among 4 boys while each boy is eligible for any number of prizes is \( 4^5 \)
II : The letters of the word "TOSS" are permuted in all possible ways and the words thus formed are arranged as in a dictionary, the rank of the word "TOSS" is 10
Which of the above statements is correct
(a) only I
(b) only II
(c) both I and II
(d) Neither I nor II
Answer: (c) both I and II

Question. I. The no.of ways in which 4 letters can be posted in 5 letter boxes is \( 5^4 \) ways.
II. If words are formed by taking only 4 at a time out of the letters of the word PHYSICS, then the number of words in which Y occur is 288. Which of the above statements is correct
(a) only I
(b) only II
(c) both I and II
(d) Neither I nor II
Answer: (b) only II

Question. I : The no.of permutations of n different things taken any no.of things at a time is \( ^nP_n \) (repetition not allowed)
II. The no.of permutations of n different things taken any no.of things at a time is \( ^nP_1 + ^nP_2 + ^nP_3 + \dots + ^nP_n \) (repetition not allowed)
Which of the above statements is correct?
(a) only I
(b) only II
(c) Both I and II
(d) Neither I nor II
Answer: (b) only II

Question. If the letters of the word PRISON are permuted in all possible ways and the words thus formed are arranged in dictionary order then
I: The rank of PRISON is 438
II: The rank of SIPRON is 618
(a) only I is ture
(b) only II is true
(c) both I and II are true
(d) neither I nor II true
Answer: (c) both I and II are true

Question. I: The number of ways of arranging 4 boys and 3 girls arround a circle so that all the girls sit together is 144.
II: The number of ways of arranging 6 red roses and 3 yellow roses of different sizes into a garlend so that no to yellow roses come together is 7200
(a) only I is ture
(b) only II is true
(c) both I and II are true
(d) neither I nor II true
Answer: (c) both I and II are true

ASCENDING & DESCENDING ORDERS

Question. The letters of the following words are arranged and words thus formed are kept as in dictionary. Then arrange the following in the descending order of there ranks
A : SITA   B : RAMUC   C : TEA   D : BUT
(a) DCBA
(b) ABDC
(c) ABCD
(d) BACD
Answer: (c) ABCD

Question. If a, b, c are the number of 4 digited numbers that can be formed using the digits 2, 4, 5, 7, 8 that are divisible by 3, 4, 5 respectively then the ascending order of a, b, c is
(a) a, b, c
(b) b, c, a
(c) c, b, a
(d) c, a, b
Answer: (c) c, b, a

Question. If a, b, c are the number of functions, injections, constant functions from a set containing 3 elements into a set containing 6 elements respectively then the ascending order of a, b, c is
(a) a,b,c
(b) b,c,a
(c) c,b,a
(d) c,a,b
Answer: (c) c,b,a

Question. Of the 4 letter words formed by using the letters of the word EQUATION, a, b, c are respectively the number of words begin with an vowel, begin and end with vowels, end with a consonent then the ascending order of a, b, c is
(a) a,b,c
(b) b,c,a
(c) c,b,a
(d) a,c,b
Answer: (b) b,c,a

ASSERTION & REASON

Question. Assertion (A) : The number of ways of arranging 6 boys and 5 girls alternately at circular table is 0
Reason (R) : To arrange boys and girls alternately at a circular table, they should be equal in number.
(a) A is true, R is true and R is the correct explanation for A
(b) A is true, R is true and R is not the correct explanation for A
(c) A is true, R is false
(d) A is false, R is true.
Answer: (a) A is true, R is true and R is the correct explanation for A

Question. Assertion(A): The number of quadratic expressions with the coefficients drawn from the set {0,1,2,3} is only 48 but not 64.
Reason(R): The coefficient of \( x^2 \) in the quadratic expression \( ax^2 + bx + c \) can not be ‘0’.
(a) A is true, R is true and R is the correct explanation for A
(b) A is true, R is true and R is not the correct explanation for A
(c) A is true, R is false
(d) A is false, R is true.
Answer: (a) A is true, R is true and R is the correct explanation for A

Question. Assertion: There are three doors to a room. The number of ways in which a student can enter the room and leave it by a different door is 6.
Reason: If an operation can be performed in m ways and another operation can be performed in n ways then the two operations in succession can be performed in mn ways.
(a) A is true, R is true and R is the correct explanation for A
(b) A is true, R is true and R is not the correct explanation for A
(c) A is true, R is false
(d) A is false, R is true.
Answer: (a) A is true, R is true and R is the correct explanation for A

Question. Assertion: The sum of all 4 digited numbers that can be formed using the digits 1,2,4,5,6 without repetition is 479952
Reason: Sum of all r-digit numbers formed by taking the given n digits (without zero) is (sum of all the n digits) \( \times ^{(n-1)}P_{r-1} \times (111.... r \text{ times}) \).
(a) A is true, R is true and R is the correct explanation for A
(b) A is true, R is true and R is not the correct explanation for A
(c) A is true, R is false
(d) A is false, R is true.
Answer: (a) A is true, R is true and R is the correct explanation for A

MATCHING TYPE

Question. Match the following:
1. If \( ^nP_5 : ^nP_3 = 2 : 1 \) then n =     a) 16
2. If \( ^{12}P_6 + 6 \cdot ^{12}P_5 = ^{13}P_n \) then n =     b) 8
3. If \( ^nP_4 = 1680 \) then n =     c) 6
4. If \( ^nP_5 = 12 \cdot ^nP_4 \) then n =     d) 5
(a) a,b,c,d
(b) b,c,a,d
(c) c,d,b,a
(d) d,c,b,a
Answer: (d) d,c,b,a

Question. Match the following:
Given Word     Rank
I. REMAST     a) 616
II. MASTER     b) 391
III. LUBER     c) 257
IV. ZENITH     d) 67
(a) a,b,c,d
(b) b,c,a,d
(c) c,d,b,a
(d) b,c,d,a
Answer: (d) b,c,d,a