Question Set C

CBSE 11th Mathematics Permutations and Combinations Model Questions Papers Study Material - QB365

Download CBSE Class 11th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 11th Standard CBSE Mathematics

Questions:

Multiple Choice Question

50 x 1 = 50

A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done, is _____.

(a)

216

(b)

240

(c)

600

(d)

3125

Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ...A.... Here, A refers to _____.

(a)

(b)

(c)

(d)

None of these

The number of combinations of 4 different objects A, B, C,D taken 2 at a time is _____.

(a)

(b)

(c)

(d)

The number of ways in which three girls and nine boys can be seated in two vans, each having numbered seats 3 in the front and 4 at the back, such that 3 girls are always sit together in a back row on adjacent seats, is _____.

(a)

\({ }^{\mathrm{H}} P_{9} \times 4 ! \times 3\)

(b)

\({ }^{11} P_{9} \times 4 \times 3 !\)

(c)

\({ }^{14} P_{12} \times 4 ! \times 3\)

(d)

\({ }^{14} P_{12} \times 4 \times 3 !\)

The number of natural numbers smaller than 10⁴, in the decimal notation of which all the digits are distinct is _____.

(a)

5274

(b)

5275

(c)

5276

(d)

5277

Identify the correct combination of true (T) and false (F) of the given two statements.
Statement I The number of permutations of letters of word 'ROOT' are 12.
Statement II The number of permutation of letters of word 'INSTITUTE' are \(\frac{9 !}{2 ! 3 !}\)

(a)

(b)

(c)

(d)

Consider the following statements
Statement I If 5 ⁴P_r = 6 ⁵P_r-1 ,then r = 8,3
Statement II If ⁵P_r =⁶p_r-1 ' then r = 5
Which of the above statements (s) is/are true?

(a)

Only I

(b)

Only II

(c)

Both I and II

(d)

Neither I nor II

Match the following columns and choose the correct option from the codes given below.

Column I	Column II
A. \(\frac{7 !}{5 !} \text { equals }\)	28
B.\(\frac{12 !}{(10 !)(2 !)} \text { equals }\)	42
C.\(\frac{8 !}{6 ! \times 2 !} \text { equals }\)	66

(a)

A	B	C
1	2	3

(b)

A	B	C
1	3	2

(c)

A	B	C
3	2	1

(d)

A	B	C
2	3	1

The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is _______.

(a)

432

(b)

108

(c)

(d)

10.

Suppose you have a suitcase with a number lock. The number lock has 4 wheels each labelled with 10 digits from °to 9. The lock can be opened, if 4 specific digits.are arranged in a particular sequence with no repetition. Some how, you have forgotten this specific sequence of digits. You remember only the first digit which is 7. In order to open the lock, how many sequences of 3 digits you may have to check with?

(a)

720

(b)

504

(c)

500

(d)

None of these

11.

\({ }^{15} C_{8}+{ }^{15} C_{9}-{ }^{15} C_{6}-{ }^{15} C_{7}\) is equal to .......

(a)

(b)

(c)

(d)

12.

If n = ^mC₂, then the value of ⁿC₂ is _______.

(a)

^{m + 1}C₄

(b)

^{m -1}C₄

(c)

^m+2C₄

(d)

3 x ^m+1C₄

13.

If ⁿC₁₂ = ⁿC₈, then n is equal to _______.

(a)

(b)

(c)

(d)

14.

If there are 5 different objects A, B, C,D, E. The number of combinations of 3 different objects is ...A.... Here, A refers to _______.

(a)

(b)

(c)

(d)

15.

The number of ways a team of 2 players can be formed out of a group of 3 lawn tennis players X, Y, Z is _______.

(a)

(b)

(c)

(d)

16.

Eighteen guests have 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 the other side. The number of ways in which the seating arrangement can be made, is _______.

(a)

\(\frac{11 !}{6 ! 5 !} \times 9 ! \times 9 !\)

(b)

\(9 ! \times 9 !\)

(c)

\(\frac{11 !}{6 ! 5 !} \times 5 ! 6 !\)

(d)

None of these

17.

Let T_n denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n + 1} - T_n = 21,then n equals _______.

(a)

(b)

(c)

(d)

18.

In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon is 70, then the number of diagonals of polygon is _______.

(a)

(b)

(c)

(d)

19.

The number of ways in which a mixed double game can be arranged from amongst 9 married couples, if no husband and wife play in the same game, is _______.

(a)

756

(b)

1512

(c)

3024

(d)

None of these

20.

The number of ways in which 2 black and 3 red balls can be selected from a bag containing 5 black and 6 red balls is _______.

(a)

170

(b)

190

(c)

180

(d)

200

21.

How many number lying between 999 and 10000 can be formed with the help of the digits 0,2, 3, 6, 7, 8, when the digits are not be repeated?

(a)

100

(b)

200

(c)

300

(d)

400

22.

The number of arrangements can be made with the letters of the word 'MATHEMATICS' in which all vowels are together, is _______.

(a)

120920

(b)

120930

(c)

120940

(d)

120960

23.

The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time, is _______.

(a)

93321

(b)

93322

(c)

93323

(d)

93324

24.

Fill in the blanks.
I. The number of permutations of n objects, where P objects are of the same kind and rest are all different equals ...A....
II. The number or permutations of n objects, where P₁ objects are of one kind, P₂ are of second kind, P_k are of k^th kind and the rest, if any, are of different kind is ...B....
Here, A and B refer to

(a)

\(\frac{n !}{P ! 2 !}, \frac{n !}{\left(P_{1}+P_{2}+\ldots+P_{k}\right) !}\)

(b)

\(\frac{n !}{P !}, \frac{n !}{P_{1} ! P_{2} ! \ldots P_{k} !} \)

(c)

\(\frac{P !}{n !}, \frac{\left(P_{1}+P_{2} \ldots+P_{k}\right)}{n !}\)

(d)

None of the above

25.

The number of 5-digit telephone numbers having atleast one of their digits repeated is _______.

(a)

90000

(b)

10000

(c)

30240

(d)

69760

26.

The total number of 9-digits numbers which have all different digits is _______.

(a)

10!

(b)

(c)

9 x 9!

(d)

10 x 10!

27.

In a class of 10 students there are 3 girls A, B, C. The number of different ways they can be arranged in a row such that no two of three girls are consecutive are _______.

(a)

4! x 300

(b)

7! x 336

(c)

6! x 300

(d)

6! x 336

28.

Consider the following statements
Statement I \({ }^{n} P_{r}=\frac{n !}{(n-r) !}, 0 \leq r \leq n\)
Statement II \({ }^{n} P_{r}=n(n-1)(n-2) \ldots \ldots . .(n-r+1)\), \(0 \leq r \leq n\)
Which of the above statement (s) is/are true?

(a)

Only I

(b)

Only II

(c)

Both I and II

(d)

Neither I nor II

29.

The number of permutations of n different things taken r at a time, when repetition is allowed, is _______.

(a)

rⁿ

(b)

n^r

(c)

\(\frac{n !}{(n-r) !}\)

(d)

None of these

30.

p(n -1, r) + r . P (n -1, r -1) equals _______.

(a)

P(n-1,r+1)

(b)

P(n,r-1)

(c)

P(n, r)

(d)

P(n + I, r + I)

31.

If (n + 1)! = 12 x (n - 1)! then the value of n is equal to

(a)

(b)

(c)

(d)

32.

The value of 1.1!+2·2!+ 3·3!+ .... +n·n! is _______.

(a)

(n + 1)!

(b)

(n + 1)!+ 1

(c)

(n + 1}!-1

(d)

n!+1

33.

If \(\frac{1}{9 !}+\frac{1}{10 !}=\frac{x}{11 !}\) then x is equal to _______.

(a)

100

(b)

110

(c)

(d)

121

34.

Match the following columns and choose the correct option from the codes given below.

Column I	Column II
A.5! equals	5040
B.7! equals	120
C.8! equals	4920
D.7! - 5! equals	40320
E.4! - 3! equals	18

(a)

A	B	C	D	E
1	2	3	4	5

(b)

A	B	C	D	E
2	1	3	4	5

(c)

A	B	C	D	E
2	1	4	3	5

(d)

A	B	C	D	E
5	4	3	2	1

35.

Fill in the blanks.
I. When n = 6, r = 2, the value of \(\frac{n !}{(n-r) !}\) is ...A....
II. When n = 9, r = 5, the value of \(\frac{n !}{(n-r) !}\)... B....
III. When n = 5, r = 2, the vaIue of \(\frac{n !}{(n-r) !}\)... C...
IV. 3! + 4! = 7! is ...D....
Here, A, B, C and D refer to

(a)

A\(\rightarrow\) 10, B\(\rightarrow\) 15120, C\(\rightarrow\) 10, D\(\rightarrow\) false

(b)

A\(\rightarrow\) 30, B\(\rightarrow\)15120, C\(\rightarrow\) 20, D\(\rightarrow\) true

(c)

A\(\rightarrow\) 30, B\(\rightarrow\) 15120, C\(\rightarrow\)10, D\(\rightarrow\) false

(d)

None of the above

36.

The number of ways in which 3 prize can be distributed to 4 childrens, so that no child gets all the three prizes, are ______.

(a)

(b)

(c)

(d)

None of these

37.

A sequence is a ternary sequence, if it contains digits 0, 1and 2. The total number of ternary sequences of length 9 which either begin with 210 or end with 210, is ______.

(a)

1458

(b)

1431

(c)

729

(d)

707

38.

A telegraph has 5 arms and each arm is capable of 4 distincts positions, including the position of rest. The total number of signals that can be made is ______.

(a)

1024

(b)

1023

(c)

1022

(d)

1021

39.

Sabnam has 2 school bags, 3 tiffin boxes and 2 water bottles. In how many ways can she carry these items ( choosing one each)?

(a)

(b)

(c)

(d)

40.

Mohan has 3 pants and 2 shirts. The.number of different pairs of a pant and shirt he can wear are ______.

(a)

(b)

(c)

(d)

None of these

41.

If ⁿ⁺¹C₃ = 2.ⁿC₂ then n is equal to ______.

(a)

(b)

(c)

(d)

42.

If C₀ + C₁ + C₂ +...+C_n = 256 then ²ⁿC₂ is equal to ______.

(a)

(b)

105

(c)

120

(d)

130

43.

⁶C₁ + ⁶C₂+⁶C₃+⁶C₄+⁶C₅+⁶C₆ is equal to ______.

(a)

(b)

(c)

(d)

none of these

44.

If ⁿC_r+ⁿC_r+1=ⁿ⁺¹C_x then x is equal to ______.

(a)

r-2

(b)

r-1

(c)

n+1

(d)

r+1

45.

If ^mC₂ = ⁿC₁ then ______.

(a)

m = 2n

(b)

m(m-1) = 2n

(c)

m = 2n(n+1)

(d)

none of these

46.

If ⁴⁰C_r+2 = ⁴⁰C_r-2 then r is equal to ______.

(a)

(b)

(c)

(d)

47.

The number of arrangements of the letters of the word BHARAT taking 3 at a time is ______.

(a)

(b)

120

(c)

(d)

48.

The number of ways in which 8 men can be arranged in a row so that three particular men are seated consecutively is ______.

(a)

6! \(\times\)3!

(b)

(c)

9! \(\times\) 3!

(d)

none of these

49.

The number of ways to arrange the letters of the word HAPPY are ______.

(a)

120

(b)

(c)

(d)

50.

Total number of words formed by 3 vowels and 5 consonants taken from 4 vowels and 7 consonants is equal to ______.

(a)

75360

(b)

60480

(c)

54230

(d)

none of these

Visit QB365-SLMS - https://www.qb365.in/slms/

Answers Key:

Multiple Choice Question

50 x 1 = 50

(a)
216

(b)
6

(b)
\({ }^{11} P_{9} \times 4 \times 3 !\)

(a)
5274

(d)
TT

(d)
Neither I nor II

(d)

A B C

2 3 1

(b)
108

10.

(b)
504

11.

(a)
0

12.

(d)
3 x ^m+1C₄

13.

(a)
20

14.

(d)
10

15.

16.

(a)
\(\frac{11 !}{6 ! 5 !} \times 9 ! \times 9 !\)

17.

(b)
7

18.

(b)
20

19.

20.

(d)
200

21.

22.

(d)
120960

23.

(d)
93324

24.

(b)
\(\frac{n !}{P !}, \frac{n !}{P_{1} ! P_{2} ! \ldots P_{k} !} \)

25.

(d)
69760

26.

27.

(b)
7! x 336

28.

29.

(b)
n^r

30.

31.

(b)
3

32.

33.

(d)
121

34.

35.

36.

37.

(b)
1431

38.

(b)
1023

39.

(b)
12

40.

(b)
6

41.

(d)
5

42.

43.

(a)
63

44.

(d)
r+1

45.

(b)
m(m-1) = 2n

46.

(a)
20

47.

(d)
72

48.

(a)
6! \(\times\)3!

49.

(d)
60

50.

(b)
60480

CBSE 11th Mathematics Permutations and Combinations Model Questions Papers Study Material - QB365 Set C

QB365 Student Learing Managemnet System

Std: 11th Standard CBSE - Mathematics

chapter: Permutations and Combinations - Model Questions Papers

Visit QB365-SLMS - https://www.qb365.in/slms/ Complete Questions and Answers

Questions:

Visit QB365-SLMS - https://www.qb365.in/slms/

Answers Key:

NEW MCQ Practice Test - CBSE Class 11

Mathematics CBSE Class 11 MCQ Practice Test

CBSE Class 11 MCQ Practice Test

11th Standard CBSE Study Materials