65 + Mcqs in Combinatorics in SRMJEEE Page 1 McqOptions

1.	Consider the following two sequences,X = {-1, 1, -1, 1, ...} andY = {1, \(\frac{1}{2}\), 3, \(\frac{1}{4}\),...}.Then:
A.	both X and Y are divergent.
B.	both A and Y are convergent.
C.	X is convergent but Y is divergent.
D.	X is divergent but Y is convergent.
Answer» B. both A and Y are convergent.

Discussion

2.	How many 3 digit numbers can be formed using the numbers 6, 1, 2, 3 without repetition ?
A.	36
B.	24
C.	18
D.	12
Answer» C. 18

Discussion

3.	If \({a_n} = \sum\limits_{r = 0}^n {\frac{1}{{{n_{{c_r}}}}}}\), then \(\sum\limits_{r = 0}^n {\frac{r}{{{n_{{c_r}}}}}}\) equals
A.	(n - 1) an
B.	n an
C.	\(\frac{{n\,{a_n}}}{2}\)
D.	None of these
Answer» D. None of these

Discussion

4.	If n pigeons are assigned to m pigeonholes then one of the pigeonholes must contain at least ______ pigeons.
A.	\(\left( \dfrac{n-1}{m} \right) + 1\)
B.	\(\left( \dfrac{n-1}{m} \right) \)
C.	\(\left( \dfrac{n}{m} -1 \right) \)
D.	\(\left( \dfrac{n+1}{m} \right) -1\)
Answer» B. \(\left( \dfrac{n-1}{m} \right) \)

Discussion

5.	Let an represents the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for an?
A.	an-2 + an-1 + 2n-2
B.	an-2 + 2an-1+ 2n-2
C.	2an-2 + an-1 + 2n-2
D.	2an-2 + 2an-1 + 2n-2
Answer» B. an-2 + 2an-1+ 2n-2

Discussion

6.	How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books ?
A.	4
B.	6
C.	7
D.	9
Answer» E.

Discussion

7.	Given the recurrence relation f(n) = (n - 1) + f(n - 1), n > 72, f(2) = 1, then f(n) is:
A.	\(\dfrac{3}{2}n(n-1)\)
B.	\(\dfrac{n(n+1)}{2}\)
C.	\(\dfrac{n(n-1)}{2}\)
D.	\(\dfrac{3}{2}n(n+1)\)
Answer» D. \(\dfrac{3}{2}n(n+1)\)

Discussion

8.	Given below are two statements:Statement I: 5 divides n5 - n whenever n is a nonnegative integer.Statement II: 6 divides n3 - n whenever n is a nonnegative integer.In the light of the above statements. choose the correct answer from the options given below
A.	Both Statement I and Statement II are correct
B.	Both Statement I and Statement II are incorrect
C.	Statement I is correct but Statement II is incorrect
D.	Statement I is incorrect but Statement II is correct
Answer» B. Both Statement I and Statement II are incorrect

Discussion

9.	Find the lexicographic ordering of the bit strings given below based on the ordering 0 < 1.(A) 001(B) 010(C) 011(D) 0001(E) 0101Choose the correct answer from the options given below:
A.	001 < 010 < 011 < 0001 < 0101
B.	0001 < 001 < 010 < 0101 < 011
C.	0001 < 0101 < 001< 010 < 011
D.	001 < 010 < 0001 < 0101 <011
Answer» C. 0001 < 0101 < 001< 010 < 011

Discussion

10.	Number of binary strings of length 5 that contain no two or more consecutive zeros, is:
A.	12
B.	15
C.	6
D.	13
Answer» E.

Discussion

11.	Every bounded sequence has
A.	A divergent subsequence
B.	A convergent subsequence
C.	A divergent sequence
D.	None of these
Answer» C. A divergent sequence

Discussion

12.	If m > 1 and n ∈ N, such that 1m + 2m + 3m + ....+ nm > \(n \left( \dfrac{n+1}{k} \right)^m\), then k = ?
A.	1
B.	m
C.	2
D.	n
Answer» D. n

Discussion

13.	How many distinguishable permutations of the letters in the word BANANA are there?
A.	720
B.	120
C.	60
D.	360
Answer» D. 360

Discussion

14.	Every bounded sequence has a cluster point; then this theorem is known as:
A.	Cauchy's theorem
B.	Weierstrass theorem
C.	Bolzano-weierstrass theorem
D.	None of these
Answer» D. None of these

Discussion

15.	If ai > 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an = 1 then the greatest value of (1 + a1)(1 + a2)... (1 + an) is:
A.	22n
B.	2n
C.	1
D.	\(2^{\frac{n}{2}}\)
Answer» C. 1

Discussion

16.	Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for an?
A.	an = an – 1 + 2an - 2
B.	an = an – 1 + an - 2
C.	an = 2an – 1 + an - 2
D.	an = 2an – 1 + 2an - 2
Answer» C. an = 2an – 1 + an - 2

Discussion

17.	How many number of times will the digit 7 be written when listing the integers from 1 to 1000?
A.	271
B.	300
C.	252
D.	304
Answer» C. 252

Discussion

18.	What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?
A.	72 * 8!
B.	144 * 8!
C.	36 * 8!
D.	9!
Answer» D. 9!

Discussion

19.	When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?
A.	25
B.	41
C.	22
D.	42
Answer» E.

Discussion

20.	What is the value of 1 1! +2 2!+3 3! + .............. n n! where n! means n factorial or n(n-1)(n-2) ............1.
A.	n (n−1) (n−1)!
B.	[(n+1)!/{n*(n−1)}]
C.	(n+1)! −n!
D.	(n+1)! −1!
Answer» E.

Discussion

21.	In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
A.	20
B.	30
C.	25
D.	600
Answer» D. 600

Discussion

22.	If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
A.	24
B.	31
C.	32
D.	30
Answer» D. 30

Discussion

23.	A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:
A.	21530
B.	8! * 360
C.	8! * 480
D.	8! * 240
Answer» D. 8! * 240

Discussion

24.	A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
A.	10
B.	12
C.	15
D.	20
Answer» D. 20

Discussion

25.	There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:
A.	10 ways
B.	30 ways
C.	60 ways
D.	80 ways
Answer» B. 30 ways

Discussion

26.	In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
A.	172000
B.	12600
C.	45920
D.	43200
Answer» E.

Discussion

27.	Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
A.	60000
B.	65000
C.	70000
D.	75000
Answer» C. 70000

Discussion

28.	There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
A.	55
B.	60
C.	25
D.	192
Answer» C. 25

Discussion

29.	How many diagonals can be drawn in a pentagon?
A.	5
B.	10
C.	8
D.	7
Answer» B. 10

Discussion

30.	After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
A.	16
B.	15
C.	13
D.	14
Answer» C. 13

Discussion

31.	In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
A.	24
B.	48
C.	96
D.	64
Answer» C. 96

Discussion

32.	A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
A.	252
B.	432
C.	462
D.	504
Answer» D. 504

Discussion

33.	Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
A.	864
B.	863
C.	865
D.	1728
Answer» E.

Discussion

34.	A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?
A.	105
B.	168
C.	189
D.	120
Answer» C. 189

Discussion

35.	In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
A.	18
B.	19
C.	17
D.	16
Answer» B. 19

Discussion

36.	A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
A.	209
B.	(4!-1)(5!-1)(6!-1)
C.	119
D.	29295
Answer» E.

Discussion

37.	From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
A.	246
B.	340
C.	290
D.	315
Answer» B. 340

Discussion

38.	There are 7 non-collinear points. How many triangles can be drawn by joining these points?
A.	35
B.	10
C.	8
D.	7
Answer» B. 10

Discussion

39.	In how many ways can six different rings be worn on four fingers of one hand?
A.	10
B.	12
C.	15
D.	16
Answer» D. 16

Discussion

40.	If 6Pr = 360 and If 6Cr = 15, find r ?
A.	5
B.	6
C.	4
D.	3
Answer» D. 3

Discussion

41.	How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
A.	6! *2!
B.	6! – 2!
C.	4!
D.	5!
Answer» D. 5!

Discussion

42.	12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.
A.	360
B.	384
C.	432
D.	470
Answer» C. 432

Discussion

43.	Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:
A.	69760
B.	30240
C.	99748
D.	42386
Answer» B. 30240

Discussion

44.	If 5* nP3 = 4* (n+1)P3, find n?
A.	10
B.	11
C.	12
D.	14
Answer» E.

Discussion

45.	A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
A.	6! × 1440
B.	18! × 1440
C.	18! ×2! × 1440
D.	None of these
Answer» C. 18! ×2! × 1440

Discussion

46.	The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
A.	242
B.	240
C.	251
D.	275
Answer» B. 240

Discussion

47.	Find the number of ways in which 8064 can be resolved as the product of two factors?
A.	22
B.	24
C.	21
D.	20
Answer» C. 21

Discussion

48.	How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
A.	256
B.	24
C.	12
D.	None of these
Answer» C. 12

Discussion

49.	10 students are to be seated in two rows equally for the Mock test in a room. There are two sets of papers, Code A and Code B. each of two rows can have only one set of paper but different that from other row. In how many ways these students can be arranged ?
A.	2775600
B.	125600
C.	7257600
D.	1200560
Answer» D. 1200560

Discussion

50.	If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be:
A.	67
B.	68
C.	65
D.	69
Answer» B. 68

Discussion

Explore topic-wise MCQs in SRMJEEE .

Consider the following two sequences,X = {-1, 1, -1, 1, ...} andY = {1, \(\frac{1}{2}\), 3, \(\frac{1}{4}\),...}.Then:

How many 3 digit numbers can be formed using the numbers 6, 1, 2, 3 without repetition ?

If \({a_n} = \sum\limits_{r = 0}^n {\frac{1}{{{n_{{c_r}}}}}}\), then \(\sum\limits_{r = 0}^n {\frac{r}{{{n_{{c_r}}}}}}\) equals

If n pigeons are assigned to m pigeonholes then one of the pigeonholes must contain at least ______ pigeons.

Let an represents the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for an?

How many ways are there to pack six copies of the same book into four identical boxes, where a box can contain as many as six books ?

Given the recurrence relation f(n) = (n - 1) + f(n - 1), n > 72, f(2) = 1, then f(n) is:

Given below are two statements:Statement I: 5 divides n5 - n whenever n is a nonnegative integer.Statement II: 6 divides n3 - n whenever n is a nonnegative integer.In the light of the above statements. choose the correct answer from the options given below

Find the lexicographic ordering of the bit strings given below based on the ordering 0 < 1.(A) 001(B) 010(C) 011(D) 0001(E) 0101Choose the correct answer from the options given below:

Number of binary strings of length 5 that contain no two or more consecutive zeros, is:

Every bounded sequence has

If m > 1 and n ∈ N, such that 1m + 2m + 3m + ....+ nm > \(n \left( \dfrac{n+1}{k} \right)^m\), then k = ?

How many distinguishable permutations of the letters in the word BANANA are there?

Every bounded sequence has a cluster point; then this theorem is known as:

If ai > 0 for i = 1, 2, 3,..,n and a1, a2, a3, ...an = 1 then the greatest value of (1 + a1)(1 + a2)... (1 + an) is:

Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for an?

How&nbsp;many&nbsp;number&nbsp;of&nbsp;times&nbsp;will&nbsp;the&nbsp;digit&nbsp;7&nbsp;be&nbsp;written&nbsp;when&nbsp;listing&nbsp;the&nbsp;integers&nbsp;from&nbsp;1&nbsp;to&nbsp;1000?

When&nbsp;six&nbsp;fair&nbsp;coins&nbsp;are&nbsp;tossed&nbsp;simultaneously,&nbsp;in&nbsp;how&nbsp;many&nbsp;of&nbsp;the&nbsp;outcomes&nbsp;will&nbsp;at&nbsp;most&nbsp;three&nbsp;of&nbsp;the&nbsp;coins&nbsp;turn&nbsp;up&nbsp;as&nbsp;heads?

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In&nbsp;how&nbsp;many&nbsp;ways&nbsp;can&nbsp;5&nbsp;different&nbsp;toys&nbsp;be&nbsp;packed&nbsp;in&nbsp;3&nbsp;identical&nbsp;boxes&nbsp;such&nbsp;that&nbsp;no&nbsp;box&nbsp;is&nbsp;empty,&nbsp;if&nbsp;any&nbsp;of&nbsp;the&nbsp;boxes&nbsp;may&nbsp;hold&nbsp;all&nbsp;of&nbsp;the&nbsp;toys?

There&nbsp;are&nbsp;three&nbsp;prizes&nbsp;to&nbsp;be&nbsp;distributed&nbsp;among&nbsp;five&nbsp;students.&nbsp;If&nbsp;no&nbsp;students&nbsp;gets&nbsp;more&nbsp;than&nbsp;one&nbsp;prize,&nbsp;then&nbsp;this&nbsp;can&nbsp;be&nbsp;done&nbsp;in:

Find&nbsp;the&nbsp;total&nbsp;number&nbsp;of&nbsp;distinct&nbsp;vehicle&nbsp;numbers&nbsp;that&nbsp;can&nbsp;be&nbsp;formed&nbsp;using&nbsp;two&nbsp;letters&nbsp;followed&nbsp;by&nbsp;two&nbsp;numbers.&nbsp;Letters&nbsp;need&nbsp;to&nbsp;be&nbsp;distinct.

How&nbsp;many&nbsp;diagonals&nbsp;can&nbsp;be&nbsp;drawn&nbsp;in&nbsp;a&nbsp;pentagon?

In&nbsp;a&nbsp;hockey&nbsp;championship,&nbsp;there&nbsp;are&nbsp;153&nbsp;matches&nbsp;played.&nbsp;Every&nbsp;two&nbsp;team&nbsp;played&nbsp;one&nbsp;match&nbsp;with&nbsp;each&nbsp;other.&nbsp;The&nbsp;number&nbsp;of&nbsp;teams&nbsp;participating&nbsp;in&nbsp;the&nbsp;championship&nbsp;is:

From&nbsp;6&nbsp;men&nbsp;and&nbsp;4&nbsp;ladies,&nbsp;a&nbsp;committee&nbsp;of&nbsp;5&nbsp;is&nbsp;to&nbsp;be&nbsp;formed.&nbsp;In&nbsp;how&nbsp;many&nbsp;ways&nbsp;can&nbsp;this&nbsp;be&nbsp;done,&nbsp;if&nbsp;the&nbsp;committee&nbsp;is&nbsp;to&nbsp;include&nbsp;at&nbsp;least&nbsp;one&nbsp;lady?

There&nbsp;are&nbsp;7&nbsp;non-collinear&nbsp;points.&nbsp;How&nbsp;many&nbsp;triangles&nbsp;can&nbsp;be&nbsp;drawn&nbsp;by&nbsp;joining&nbsp;these&nbsp;points?

In&nbsp;how&nbsp;many&nbsp;ways&nbsp;can&nbsp;six&nbsp;different&nbsp;rings&nbsp;be&nbsp;worn&nbsp;on&nbsp;four&nbsp;fingers&nbsp;of&nbsp;one&nbsp;hand?

If&nbsp;6Pr&nbsp;=&nbsp;360&nbsp;and&nbsp;If&nbsp;6Cr&nbsp;=&nbsp;15,&nbsp;find&nbsp;r&nbsp;?

How&nbsp;many&nbsp;words&nbsp;can&nbsp;be&nbsp;formed&nbsp;by&nbsp;re-arranging&nbsp;the&nbsp;letters&nbsp;of&nbsp;the&nbsp;word&nbsp;ASCENT&nbsp;such&nbsp;that&nbsp;A&nbsp;and&nbsp;T&nbsp;occupy&nbsp;the&nbsp;first&nbsp;and&nbsp;last&nbsp;position&nbsp;respectively?

If&nbsp;5*&nbsp;nP3&nbsp;=&nbsp;4*&nbsp;(n+1)P3,&nbsp;find&nbsp;n?

Find&nbsp;the&nbsp;number&nbsp;of&nbsp;ways&nbsp;in&nbsp;which&nbsp;8064&nbsp;can&nbsp;be&nbsp;resolved&nbsp;as&nbsp;the&nbsp;product&nbsp;of&nbsp;two&nbsp;factors?

How&nbsp;many&nbsp;ways&nbsp;can&nbsp;4&nbsp;prizes&nbsp;be&nbsp;given&nbsp;away&nbsp;to&nbsp;3&nbsp;boys,&nbsp;if&nbsp;each&nbsp;boy&nbsp;is&nbsp;eligible&nbsp;for&nbsp;all&nbsp;the&nbsp;prizes?

If&nbsp;letters&nbsp;of&nbsp;the&nbsp;work&nbsp;KUBER&nbsp;are&nbsp;written&nbsp;in&nbsp;all&nbsp;possible&nbsp;orders&nbsp;and&nbsp;arranged&nbsp;as&nbsp;in&nbsp;a&nbsp;dictionary,&nbsp;then&nbsp;the&nbsp;rank&nbsp;of&nbsp;the&nbsp;word&nbsp;KUBER&nbsp;will&nbsp;be:

How many number of times will the digit 7 be written when listing the integers from 1 to 1000?

When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

What is the value of 1 1! +2 2!+3 3! + .............. n n! where n! means n factorial or n(n-1)(n-2) ............1.

In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?

There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:

Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.

How many diagonals can be drawn in a pentagon?

In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:

From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?

There are 7 non-collinear points. How many triangles can be drawn by joining these points?

In how many ways can six different rings be worn on four fingers of one hand?

If 6Pr = 360 and If 6Cr = 15, find r ?

How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

If 5 nP3 = 4 (n+1)P3, find n?

Find the number of ways in which 8064 can be resolved as the product of two factors?

How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?

If letters of the work KUBER are written in all possible orders and arranged as in a dictionary, then the rank of the word KUBER will be: