EXERCISE - A
Evaluate:
1)¹⁵C₃
2) ¹²C₉.
3) ⁵⁰C₄₇
4) ⁷¹C₇₁
5) ⁿ⁺¹Cₙ
6) ⁶ᵣ₌₁∑¹⁵Cᵣ
7) ⁸C₄+⁸C₃
8) ¹⁷C₄ +¹²C₃
**"Simplify
1) If ⁿC₇ =ⁿC₅ find n.
2) If ⁿC₁₄ = ⁿC₂₈ Find ⁿC₂₈
3) If ⁿC₁₆ = ⁿC₁₄ find ⁿC₂₇
4) if ²⁰Cᵣ=²⁰Cᵣ₊₂ find ʳC₅
5) If ¹⁸Cᵣ=¹⁸Cᵣ₊₂ find ʳC₅
6) If ⁿPᵣ=1680 and ⁿCᵣ =70 find n, r
7) If ²ⁿC₃ : ⁿC₃ =11 : 1 find n
8) If ¹⁵Cᵣ : ¹⁵Cᵣ₋₁ = 11: 5 find r.
9) If ⁿCᵣ₋₁ = ⁿC₃ᵣ find r.
10) ⁿ⁺¹Cᵣ₊₁ : ⁿCᵣ = 11 : 6 and
ⁿCᵣ : ⁿ⁻¹Cᵣ₋₁ =6 : 3 find n and r.
11) ⁿCᵣ /⁽ⁿ⁻¹⁾ C₍ᵣ₋₁₎
12) ⁽ⁿ⁻¹⁾C₍ᵣ ₋₁₎ + ⁽ⁿ⁻¹⁾Cᵣ
13) ⁿCᵣ + 2. ⁿCᵣ₋₁ + ⁿ Cᵣ₋₂
14) ¹⁸Cᵣ=¹⁸Cᵣ₊₂ Find r
15) ²ⁿCᵣ = ²ⁿCᵣ₊₂ find r.
16) ⁿC₁₂ = ⁿC₁₀ find ⁿC₂
17) ⁿPᵣ = 336 and ⁿCᵣ=56
find n and r
Find also ⁿ⁺² Cᵣ₊₁
18) ²⁰C₃ₙ = ²⁰C₂ₙ₊₅ Find n
19) ⁿC₁₀= ⁿC ₁₅ find ²⁷ Cₙ
20) ²ⁿC₃ : ⁿC₂= 12:1 find n.
21) ¹⁵C₃ᵣ = ¹⁵Cᵣ₊₃ Find the value of r.
22) ²ⁿCᵣ=²ⁿCᵣ₊₂ Find r.
22) ⁿPᵣ=6 . ⁿCᵣ Find n and r when ⁿCᵣ=56.
23) find ⁴⁷C₄+⁵ᵣ₌₁∑⁵²⁻ʳC₃.
24) Evaluate ⁴⁷C₄+²⁰C₅+⁵ᵣ₌₁∑⁵²⁻ʳC₃
25) ⁿC₄ , ⁿC₅ , ⁿC₆ are in A. P then
what is the value of n
26) ¹³C₆ + 2. ¹³C₅ + ¹³C₄ =¹⁵Cₓ find x.
EXERCISE - B
1) How many different committee of 5 members may be formed from 8 Indians and 4 foreigners.
A) 972 B)792 C)297 D) 279
2) In an examination paper 11 questions are set; In how many ways can you choose 6 questions to answer?
A) 264 B) 246 C) 462 D) 426
3) In question number 2 is made compulsory, in how many ways can you select to answer 6 questions in all.
A) 264 B) 246 C) 462 D) 426
4) In how many ways can committee of 6 men and 2 women be formed out of 10 men and 5 women
5) A committee of 10 gentleman and 5 ladies. How many different subcommittee can be formed consisting of 6 gentleman and 2 ladies.
A) 1200 B)2100 C)1300 D)3100
6) A committee consists of 10 gentlemen and 8 ladies. How many different subcommittee can be formed consisting of 5 gentlemen and 3 ladies.
A) 14000 B)14110 C)14112 D)11214
7) In how many ways can a person choose one or more of the four electric appliances? T. V, Refrigerator, Washing machine, Radiogram ?
A) 16 B) 31 C) 32 D) 15
8) A man has 8 friends. In how many ways may be invite one or more of them to a dinner ?
A) 256 B)254 C) 255 D) 128
9) In how many ways a man can invite 5 friends to a dinner so that two or more of them remain present.
A) 24 B) 25 C) 26 D) 32
10) From 6 boys and 4 girls are to be selected for admission for a particular course, in how many ways can this be done if there must be exactly 2 girls?
A) 120 B)180 C) 160 D) 360
11) A person has got 12 acquaintances of whom 8 relatives. In how many ways can he invite 7 guests so that 5 of them may be Relatives ?
A) 360 B)180 C) 120 D) 336
12) At an election there are 5 candidates and 3 members are to be elected and a voter is entitled to vote for any number to be elected. In how many ways may a voter choose a vote?
A) 24 B) 23 C) 26 D) 25
13) Find out number of ways in which a cricket team consisting of 11 players can be selected out of 14 players ?
A) 364 B)286 C)720 D) 360
14) Find out how many of these will include a particular player.(from above question)
A) 364 B)286 C)720 D) 360
** In how many ways can a selection of 6 books be made from 10 books ?
15) When one specified book is always included
A) 84 B) 126 C) 120 D) 80
16) When one specified book is always excluded.
A) 126 B) 120 C) 180 D) 84
** In how many ways can a committee of 5 members be formed from 10 candidates so as to
17) Include both the youngest and oldest candidates.
A) 196 B) 65 C) 54 D) 56
18) Excluded the youngest if it includes the oldest ?
A) 196 B) 65 C) 54 D) 56
*** In how many ways can four students be selected out of twelve students if
19) Particular students are not included at all..
A) 120 B) 210 C) 340 D) 320
20) 2 particular students are included.
A) 54 B) 56 C) 57 D) 44
21) In an examination paper there are two groups each containing 7 questions. A candidate is required to attempt 9 questions but not more than five questions from any group. In how many ways can 9 questions be selected ?
A) 1470 B)1570 C)1680 D)1970
22) A candidate is required to answer 6 out of 12 questions, which are divided into two groups each containing 6 questions and he is permitted to attempt not more than four from any group. In how many different ways can he make up his choice.
A) 580 B) 680 C) 850 D) 950
23) From 6 gentleman and 4 ladies, a committee of 5 members is to be formed. In how many ways can this be done so as to include atleast one lady ?
A) 642 B) 259 C) 246 D) 586
24) In how many ways can a committee of 5 be formed from 4 professors and 6 students so as to include atleast 2 professor ?
A) 246 B) 986 C) 187 D) 186
25) In an examination paper, there are 14 questions divided into three groups of 5,5,4 respectively. A candidate is required to answer 6 questions taking atleast two questions from each of the first two groups and one question from the third group. In how many ways can he make up his choice ?
A) 1100 B)1200 C)1300 D)1400
26) A committee of 7 members is to be chosen from 6 Chartered Accountants, 4 Economist and 5 Cost Accounts. In how many ways can this be done if in the committee, there must be atleast one member from each group and atleast 3 Chartered Accounts ?
A) 3570 B)2450 C) 2670 D)6470
27) There are three sections in a question paper contains 5 questions each. A candidate has to solve any 5 questions choosing atleast one question from each section. In how many ways can be make his choice.
A) 5250 B)3250 C)2250 D) 6250
28) In how many ways can a committee of 3 ladies and 4 gentleman be appointed from a meeting consisting of 8 ladies and 7 gentleman? What will be the members of ways If Mrs. X refuses to serve in a committee if Mr. Y is a member ?
A) 1960, 1440 B) 1960, 1540 C) 1440, 1240 D) 1540, 1440
** Out of 4 officers and 10 clerks in an organisation, a committee of five consisting of 2 officers and 3 clerks is to be formed. In how many ways can this be done if
29) Any officers and any clerk can be included.
A) 720 B) 216 C)360 D) 460
30) 1 particular clerk must be on the committee.
A) 720 B) 360 C) 216 D) 380
31) 1 particular officer can't be on the committee.
A) 720 B)360 C) 300 D) 150
32) The question paper on Mathematics and Statistics contain 10 questions divided into two groups of 5 questions each. In how many ways can an examiner select 6 questions taking atleast two questions from each group?
A) 200 B) 150 C) 100 D) 250
33) Out of six teacher and four boys, a committee of eight is to be formed. In how many ways can this be done when there should be not less than four teachers in the committee.
A) 45 B) 54 C) 65 D) 100
34) An examination paper consists of 12 questions Divided into two parts A and B. Part A contains 7 questions and part B contains 5 questions. A candidate is required to answer 8 questions selecting atleast 3 questions from each part. In how many maximum ways can be selected the question ?
A) 210 B) 420 C) 840 D) 144
35) In a class of 16 students, there are 5 lady students. In how many ways can 10 students be selected from them so as to include atleast 4 lady students.
A) 2770 B)2772 C)7227 D)7272
** In how many ways can 7 men be selected from 16 men so that
36)a) 4 particular men will not be there.
b) 4 particular men will always be there.
A) 792, 220 B) 792,240 C) 780,220 D) 820,220
37) In a group of 15 boys there are 7 bouy-scouts. In how many ways can 12 boys be selected so as to include
A) exactly 6 boys-scouts
B) atleast 6 boys-scouts.
A) 196,250 B) 190,252 C) 196,252 D) 196,352
38) A cricket team consisting of 11 players is to be selected from 2 groups consisting of 6 and 8 players respectively. In how many ways can the selection be made on the supposition that the group of six shall contribute no fewer than 4 players.
A) 443 B) 344 C) 544 D) 445
39) A cricket eleven is to be chosen from 13 players of whom only 4 can bowl. In how many ways can the team be selected so as to include atleast 2 bowlers ?
A) 78 B) 97 C) 88 D) 108
40) A cricket team of 11 players is to be formed from 20 players including 6 bowlers and 3 wicketkeepers. In how many ways can a team be selected so that the team contains exactly 2 wicketkeeper and atleast 4 bowlers.
A)22275 B) 27225 C) 22257 D)32275
41) How many sub-committees of five members can formed from a committee consisting of 8 gentleman and 6 ladies so as to include atleast 2 gentleman and 2 ladies ?
A) 1350 B)1300 C)1450 D)1400
42) A certain council consists of a chairman, two vice-chairman, twelve other members. How many ways can committee of 6 can be formed including always the chairman and only one vice-chairman ?
A)1000 B)900 C)990 D) 975
43) A question paper contains 12 questions, of which 7 are in Group A and 5 in Group B. The questions are serially numbered from 1 to 12. If a candidate has to answer the fourth questions and 3 other from Group A and to answer eighth question and 2 other from Group B. In how many ways can the candidate make up his choice.
A) 110 B) 115 C) 119 D) 120
44) Ten electric bulbs, of which 3 are defective are to be tried in three different points in a dark room. In how many ways the total trial the room shall be lighted ?
A) 120 B) 121 C) 119 D) 122
45) There are 10 lamps in a hall. Each of them can be switched on independently. what is the number of ways in which the hall can be illuminated.
A) 1024 B) 100 C) 1023 D) NONE
** A supreme court Bench consists of five judges. In how many ways the benches can give
46) a majority decision.
A) 16 B) 15 C) 31 D) 32
47) nagation not affecting the majority decision ?
A) 31 B) 32 C) 15 D) 16
48) There are 25 candidates, which include 5 from the scheduled castes for 12 vacancies. If 3 vacancies are reserved for scheduled castes candidates and the remaining vacancies are open to all, find the number of ways in which the selection can be made.
A) ⁵C₃ .²⁰C₉ B) ⁵C₃.²²C₉ C) ²⁵C₁₂D) n
EXERCISE - C
***There are 16 points on a plane. How many
1) Straight line
A) 120 B) 240 C) 119 D) 480 E) n
2) Triangle
A) 120 B) 240 C) 119 D) 480 E) n
3) quadrilateral
A) 120 B) 240 C) 119 D) 480 E) n
4) Pentagon may formed if there is no two points are in straight line.
A) 120 B) 240 C) 119 D) 480 E) n
** How many...... formed if no 3 points in same straight line except 4.
5) Straight line
A) 120 B) 240 C) 119 D) 480 E) n
6) Triangle
A) 120 B) 240 C) 119 D) 480 E) n
7) quadrilateral
A) 120 B) 240 C) 119 D) 480 E) n
** There are 12 points in a plane, of which 5 are collinear. Find the number of
8) triangle formed.
A) 120 B) 210 C) 180 D) 321
9) straight lines formed.
A) 56 B) 57 C) 59 D) 61
** If 20 straight lines are drawn in a plane, no two of them being parallel and no three of them concurrent.
10) How many points of intersection will there be?
A) 200 B) 180 C) 210 D) 190
11) Quadrilateral.
A) 2 B) 3 C) 4 D) 6
12) Pentagon.
A) 2 B) 3 C) 5 D) 9
13) Hexagon
A) 9 B) 6 C) 10 D) 15
14) Octagon.
A) 10 B) 35 C) 20 D) 9
15) Decagon
A) 35 B) 20 C) 15 D) 25
16) A polygon has 44 diagonals. Find the number of its sides.
A) 10 B) 11 C)12 D) 14
EXERCISE - D
1) A man has five friends. In how many ways can he invite one or more of them to a dinner.
A) 32 B) 30 C) 31 D) 25
** A man has 5 German, 4 Spanish and 3 French friends. Find:
2) Total ways in which all the friends can be invited.
A) 4096 B) 4095 C)2048 D) n
3) Total ways of invitation so that there is atleast 1 German friend.
A) (2⁵-1)2⁴ B)(2⁵-1)2³ C)(2⁵-1)2⁷ D)n
4) Atleast 1 German and 1 French friend.
A) (2⁵-1)(2⁴ -1)2³.
B)(2⁵-1)(2³-1)2⁴
C)(2⁴-1)2³.2⁵ D)n
5) Atleast one friend from each country.
A) 3165 B)3290 C)3548 D)3250
6) In an examination paper 10 questions are set. In how many ways can a candidate select one or more questions to answer ?
A)1024 B)1023 C)1032 D) 512
7) In an examination paper 6 questions are set and every question has an alternative. In how many ways can the questions be answered.
A) 3⁶ B)(3⁶-1) C)2⁶ D) 6² - 1
8) A league match in football ends in a win,loss,or draw, how many ways forecast can give exactly 18 correct results out of 22 matches played ?
A) ²²C₁₈ B) ²²C₁₈ .2⁴ C) ²²C₁₈.4² D) n
9) In an examination a candidate is required to pass four different subjects. In how many ways can he fail ?
A) 14 B) 15 C) 16 D) none
EXERCISE - E
1) Out of 7 Consonants and 4 vowels, how many words can be formed, each containing 3 consonants and 2 vowels?
A) 25210 B)25000 C)25200 D)22500
2) In how many ways can the letters of the word FORECAST taken 3 at a time and the word MILKY taken 2 at a time be arranged?
A) 62700 B)67000 C)68720 D)67200
** How many different words can be formed taking 4 letters from the following words?
3) PROPORTION
A)758 B)875 C) 587 D) 578
4) EXAMINATION.
A) 2434 B)2454 C)1424 D)6424
5) EXPRESSION.
A) 2445 B)2445 C)2454 D)2544
6) MATHEMATICS.
A) 2454 B)2544 C)2445 D)2445
7) INEFFECTIVE.
A) 2241 B)2214 C)1422 D)1242
8) MORADABAD.
A) 626 B) 662 C) 226 D) 758
EXERCISE - F
** There are 8 mangoes,4 apples and 5 oranges. If any number of fruits can be selected, find:
1) Total Number of selections.
A) 269 B) 270 C) 275 D) 300
2) Total Number of selections so that there is at least 1 mango.
A) 269 B) 270 C) 275 D) 300
3) At least 1 mango and 1 apple.
A) 129 B) 108 C) 40 D) 192
4) At least 1 fruit of each type.
A) 160 B) 170 C) 190 D) 210
*** How many selections can be made by taking any letters from the words.
5) DADDY DID A DEADLY DEED
A) 1920 B)1921 C)1290 D) 1919
6) SHE SELLS SEA SHELLS
A) 1049 B)1050 C)1079 D)1080
*** There are 3 different green dice, 4 different blue dice and 5 different red dice. If any number of dice can be selected then find.
7) total number of selections.
A) 2¹² B) 2¹²-1 C) 2¹¹-1 D) none
8) there is atleast 1 green dice.
A) 2¹² B) 2¹²-1 C) (2³-1)2⁹ D) none.
9) there is atleast 1 green 1 blue dice.
A) 2¹²-1 B) 105×2⁵ C)120×2¹¹ D) n
10)there is atleast 1dice of each colour.
A) 2¹²-1 B)3200 C) 3255 D) none.
EXERCISE - G
1) divide 12 items in two groups so that each containing 8 and 4 items.
A) 12!/8! B) 12!/8!4! C) 8!4/12! D)n
** In how many ways can 12 apples be divided equally among
2) 2 boys.
A)12!/6! B)12!/(2!)⁶ C)12!/(6!)² D)n
3) 3 boys.
A) 12!/3! B) 12!/4! C) 12!/(4!)³ D) 12!/(3!)⁴
4) 4 boys.
A) 12!/(3!)⁴ B) 12!/4! C) 12!/(4!)³ D) n
5) 6 boys.
A) 12!/(2! B) 12!/(2!)⁶ C) 12!/(6!)³ D) n
*** In how many ways can 20 books be equally divided amongst:
6) 2 boys.
A) 20!/(10!)² B) 20!/(5!)⁴ C) 20!/(4!)⁵ D) 20!/(2!)¹⁰
7) 4 boys.
A) 20!/(10!)² B) 20!/(5!)⁴ C) 20!/(4!)⁵ D) 20!/(2!)¹⁰
8) 5 boys.
A) 20!/(10!)² B) 20!/(5!)⁴ C) 20!/(4!)⁵ D) 20!/(2!)¹⁰
9) 10 boys.
A) 20!/(10!)² B) 20!/(5!)⁴ C) 20!/(4!)⁵ D) 20!/(2!)¹⁰
10) The three different sections of a Library need the services of 3,4,5 workers respectively. If 12 workers are available. In how many ways can they be allotted to different sections.
A) 27620 B)22770 C)27270 D)72270
*** In how many ways can 9 students be divided
11) equally into 3 groups
A) 270 B) 260 C) 280 D) 300
12) 3 groups as 2,3,4.
A) 270 B) 260 C) 280 D) 300 E) n
EXERCISE - H
1) Mathematics paper is divided into three sections. A, B, C consisting of 6,7 and 8 questions respectively. Four questions are to be answered from each section. Find the number of total ways of selecting the questions from the paper by a student.
A) 176 B) 166 C) 159 D) 186
2) there are 5 copies of University physics, 8 copies of University chemistry, 3 different books on law and 2 different books on History in a library. Find the number of ways in which one or more than one book can be selected.
A)1728 B)1729 C)1727 D) none
3) There are 5 green dyes, 4 different dyes and 3 different red dyes. How many combination of dyes can be chosen taking atleast one green and one blue dye?
A) 210 B) 420 C) 560 D) 600
4) There are 'n' different video films and 'p' cassettes of each film in a video Library. Find the number of ways in which one or more than one video cassettes can be selected.
A) (p+1)ⁿ B) (p+1) C)(p+1)ⁿ-1 D) n
5) How many selection can a child make 4 milk chocolates, 5 sugar candies and 6 chewing gums?
A) 120 B) 180 C) 209 D) 210
Mg. A- R.1
1) ⁸C₃ = ?
a) 65 b) 56 c) 72 d) 27 e) none
2) ⁴⁵C₄₂ = ?
a) 14 b) 141 c) 1419 d) 14190 e) none
3) ⁵C₃ + ⁵C₄ = ?
a) 1 b) 12 c) 15 d) 21 e) none
*** In how many ways can a committee of 5 be formed from 10 persons in which
4) the eldest and the youngest will be included
a) 56 b) 65 c) 7 d) 70 e) none
5) the eldest will be included but the youngest will not be included?
a) 56 b) 65 c) 7 d) 70 e) none
6) In how many ways can 2 consonants and one vowels be selected from the word PROBLEM?
a) 10 b) 20 c) 21 d) 30 e) none
7) There are 5 girls in a group of 12 students. In how many ways 5 Students can be selected so as to include exactly 2 girls.
a) 30 b) 35 c) 350 d) 530 e) none
8) From 6 men and 4 women a committee of 5 is to be formed. In how many ways can this be done so as to include at least one women?
a) 246 b) 426 c) 642 d) 462 e) 264
9) Find the number of committees of 5 members that can be formed from 6 gentlemen and 4 ladies if each committee has atleast one lady and two gentlemen?
a) 24 b) 42 c) 60 d) 72 e) none
10) Aquestion paper consists 12 questions of which 7 are in group A and 5 in group B. The questions are serially numbered from 1 to 12. If a candidate has to answer the fourth question and 3 others from group A and to answer eighth question and 2 others from group B, in how many different ways can the candidate make up his choices ?
a) 100 b) 110 c) 120 d) 150 e) none
*** A committee of 5 is to be formed from 6 ladies and 4 gentlemen. In how many ways this can be done so that the committee contains
11) exactly two ladies
a) 32 b) 40 c) 60 d) 82 e) 110
12) at least two ladies.
a) 200 b) 240 c) 246 d) 252 e) 280
13) at most two ladies.
a) 60 b) 62 c) 64 d) 66 e) 68
14) Find the numbers of different words that can be formed from 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word.
a) 249 b) 24948 c) 2494800 d) 24948000 e) 249480000
*** In a plane that 10 points out of which no 3 are collinear except the four which lie on a straight line. By joining these 10 points, how many
15) straight line obtained
a) 40 b) 42 c) 44 d) 46 e)
16) triangles may be obtained.
a) 110 b) 112 c) 114 d,) 116 e) 118
17) How many Triangles can be formed by joining the singular points of a decagon ? How many diagonals will it have ?
a) 120,45 b) 122, 46 c) 124, 48 d) 12658 e) 110,46
18) A man has six friends. In how many ways can he invite one or more of his friends in an occasion ?
a) 60 b) 61 c) 62 d) 63 e) 65
19) There are 5 questions in a questions paper. Each question has an alternative question. In how many ways can a student choose one or more than one question ?
a) 242 b) 246 c) 248 d) 240 e) 250
20) Of the 14 articles, 10 are of the same type and each of the remaining is of different type. Find the number of combinations of 10 articles are taken at a time ?
a) 10 b) 12 c) 14 d) 16 e) 18
21) In how many ways can one or more balls can be selected from 5 deuce balls all alike, 4 tennis balls are all alike 3 rubber balls are alike.
a) 119 b) 120 c) 121 d) 122 e) 123
22) In how many ways from 5 rupees notes, 2 two Rupees notes and one coin of each of 1 rupee, fifty paise and twenty paise can be donated to a poor fund ?
a) 144 b) 143 c) 142 d) 146 e) none
23) how many different factors can be found for the numbers 858
a) 14 b) 15 c) 16 d) 23 e) none
24) How many different factors can be found for the number 75600
a) 119 b) 120 c) 122 d) 126 e) 129
Mg. A- R.2
*** In how many ways can 10 different types of fruits
1) be divided into two parts where each part must have at least one fruit.
a) 633 b) 634 c) 667 d) 637 e) 720
2) be divided between two persons where each of them can have at least one fruit
a) 1000 b) 1020 c) 1022 d)1026 e) 1320
3) be divided into two parts where there are 4 fruits in one part and 6 fruits in the other parts.
a) 200 b) 210 c) 212 d) 242 e) 240
4) be divided equally between two persons.
a) 240 b) 242 c) 250 d) 252 e) 260
5) be divided into two equal parts?
a) 120 b) 122 c) 124 d) 126 e) 128
** How many ways 12 different books can be divided
6) into 3 groups consisting 3, 4 and 5 books respectively.
a) 277 b) 2772 c) 27720 d) 277200 e) 278
7) equally among 3 persons
a) 34 b) 346 c) 3465 d) 34650 e) 346500
8) equally into three groups ?
a) 57 b) 577 c) 577 d) 5575 e) 57750
9) An exercise contains 12 questions. From them how many greatest number of different bunches of questions consisting same number of questions in each bunch can be made ? how many questions are there in each bunch of questions ?
a) 6,924 b) 924, 6 c) 8, 694 d) 6, 948 e) none
10) The result(win, lose or draw) of 10 football matches are to be predicted. How many different forecasts can contain exactly 6 correct results?
a) 33 b) 336 c) 3360 d) 33600 e) 3360000
11) From 5 boys and 4 girls, how many different selections can be made so as to include at least one boy and one girl?
a) 465 b) 475 c) 485 d) 495 e) 505
12) If 20 straight lines be drawn in a plane, no two of them being parallel and no 3 of them concurrent, how many points of intersection will be there ?
a) 180 b) 190 c) 200 d) 210 e) 220
13) If n parallel straight lines in a plane are intersected by m parallel straight lines, how many different parallelograms are there in the network thus formed?
a)mn b) mn(m-1) c)mn(m-1)(n-1) d) mn/4 e) mn(m-1)(n-1)/4
14) how many of combination and permutation can be formedd by the letters of the word STATISTICS tekan 4 at a time
a)34,386 b) 34,396 c) 36,352 d) 38,342 e) none
15) Four different letters are written and the corresponding correct addresses are written on 4 envelopes. One letter can be placed in one envelope. Find the number of way so that all the letters are wrongly placed
a) 8 b) 9 c) 10 d) 12 e) 14
16) If ²ⁿCₓ = ²ⁿCₓ₊₂ . Then x is
a) n b) 2n c) n+1 d) 2n-1 e) n -1
17)ⁿCₓ+3. ⁿCₓ₋₁ + 3.ⁿCₓ₋₂ + ⁿCₓ₋₃= ?
a) n b) 1 c) 0 d) ⁿ⁺³Cₓ e) none
18) value of ⁶C₂+ ⁶C₄ + ⁶C₆ is
a) 24 b) 26 c) 31 d) 32 e) 34
19) If ⁿPₓ = ⁿCₓ then value of x is
a) 0 b) 1 c) 0 or 1 d) 0 and 1 e) none
*** In how many different ways can a team of 9 persons be formed from 15 persons so that 3 particular persons
20) always be in the team ?
a) 900 b) 910 c) 924 d) 960 e) none
21) be never in the team
a) 20 b) 22 c) 200 d) 220 e) 240
*** In how many ways can a committee of 5 men be formed from 10 men so as to
22) include both the eldest and the youngest
a) 52 b) 54 c) 56 d) 58 e) 60
23) Exclude the youngest if it includes the eldest ?
a) 178 b) 186 c) 196 d) 1200 e) none
24) In how many different ways can two vowels and 2 consonants together be selected from the word LOGARITHM.
a) 42 b) 44 c) 45 d) 48 e) 50
Mg. A R. 3
1) value of ¹²C₀ is
a) 0 b) 1 c) 2 d 12 e) none
2) value of ²⁰C₂₀ is
a) 0 b) 1 c) 2 d 12 e) none
3) value of ¹⁰C₅ is
a) 2 b) 252 c) 52 d) 22 e) 25
4) In the election of the student's Council 15 students are elected of which 6 are girls. In how many ways can a sub- committee of 6 students be formed from the elected students where 2 girls will be in each committee?
a) 1800 b) 1890 c) 1920 d) 1990 e) 1920
5) 8 prizes are to be distributed by a lottery The first participant picks up five tickets from a box containing 50 tickets. In how many different ways can he extract them so that exactly two tickets are winning.
a) 321 b) 3211 c) 3214 d) 32144 e) 321440
6) 5 students from each class XI and class XII and 3 representative from teachers are in a sports committee of a school. In how many ways can a sub committee be formed by taking 2 students from each of class XI and class XII and one from the teachers ?
a) 100 b) 200 c) 300 d) 400 e) 500
7) A box contains 50 tickets numbering 1 to 50. 5 tickets are drawn from the box and are arranged in ascending order of the numbers on tickets as x₁ < x₂< x₃<x₄ <x₅. In how many selections will x₃ =30.
a) 771 b) 7714 c) 77140 d) 771400 e) none
8) A committee of 4 is to be formed from 5 men and 6 women. How many commity can be formed if each committee contains atleast one woman.
a) 352 b) 325 c) 3250 d) 32500
**** A committee of five is to be formed from 6 men and Four Women. In how many ways can this be done when
9) the committee contains at least one woman
a) 24 b) 246 c) 42 d) 426 e) none
10)
one there is no District sent to form the committee a candidate the gas to answer 6 questions out of 10 questions and those 10 questions are divided into two groups is containing 5 questions the candidate is to ask to choose the leak at least two questions one is group in how many different ways can the candidate make up choice in a cricket team of 14 players how many different teams of 11 players can be selected keeping at least four bowlers in the team in how many ways can a cricket team of 11 cricketers be chosen from the batsman and 6 greater than the number of batsman box contents to a blanks up with 5 are defective in which how many ways can a sample of 6 be selected at random from the box was to incluid at least 3 defective lens equation paper contains 14 question of which is group of A and B contains 5 question and Group C contains 4 questions a candidate is asked to answer 6 question and to choose at least two questions each from A and B and at least one from Group C in how many different ways can the candidate the 6 questions how many communication can be formed from Tekken 4 tickets at a time from a ticket amount 12345678 where is combination conference at least one all and one even number ticket in a question paper and B contents 5 question the questions are seriously number from 1 to 12 even examination is to answer the 7th question and three others from the group A and to answer the 12th questions and two others from group B and how many different ways can the examine make up his choice in how many ways can a committee of three ladies and 4 gentleman be formed from 8 ladies and civil gentleman what will be the number of cases of Mrs X reduces the member in how many ways can I committee of 6% be pound taken at least 3 gentleman and two ladies from tangent seven lady where two particular ladies recruites to serve the same committee together and question paper that 7 question and broken 4 question and group B and how many ways can 6 questions containing at least two questions at most questions from group B B selected how many different words can be formed by taking to consonants from 9 different consonants in 3 Bible from 5 different find the number of arrangement that can be made by taking 3 letters from the word forecast aeroplane that are 11 points of which 4 are coal in your Note 3 of the remaining are collinear how many different straight lines can be formed by joining the points in a plane there are 12 points of which five are coal in your Note 3 of the remaining are colonial how many straight lines Triangles maybe formed by joining the points that are in points on a plane of which Note 3 hour on a straight line except which are all in straight line find the number of straight lines Triangles can be found joining the points determine the number of diagonals of polygon of inside the number of diagonals of a polygon is 44 how many Triangles can be formed by joining the angular determine the number of diagonals of polygon of nxit the number of diagonals of polygon is 44 how many Triangles can be formed by joining the angular points of the polygon there are five points and 10 points respectively on two parallel straight lines how many Triangles can be form taking these point as the vertices in a plane 4 points out of 15 points lie on the straight line and another 5 points in lie on the straight line the two lines are parallel no 3 of the remaining 6 find the number abstract lines Triangles that can be found by joining this 15 points a candida has to seat in an examination of 6 subject and will be declare as passed if he passes any subject in how many ways can he filled in how many can a person subscribed to a poor fund out of one 10 rupees 15 Rupees 1 to rupees 11 rupees notes in an election that 7 candidates and four members are to be selected a voter is entitle to vote for any number of candidates not greater than to be selected in how many ways to a hotel basket contains 5 and I call and this one each of Apple guava and pear and how many different ways can 5 roots we taken from the basket if the ratio of the combination of two and difference in taken any number of them at a time and that are pain different things can taken any number of them at anytimes is 1025 is 21 find the value of n question paper rate how many ways a students can answer one or more questions the box contents for 1 rupees coin 350 calls 225 coins in how many ways can one or more coins be taken from the box han maine different factors can 115 have find the number of different factors of 3528 which are greater than 1 and less than 3528 and how many ways it sketch pens of different colours can be divine to 2 group so that each group contain at least one pain between two person so that each can have at least one pain into two group so that one group and the other as 5 page how many ways five mangoes of different size is can be divided into 3 groups such that the contents 456 respectively equally among 3% equal into 3 groups in a plane that are 11 points opposite no 3 are collinear find the greatest number of polygon of equal number of side that can be formed by joining this points what is the number of sides of each polygon prove that the greatest value of if the twice the greatest value of without repetition of digits how many different numbers are four digits can found with the digit 0 1 2 3 4 5 6 so that the digit number descending order ascending order there are three mango the different size is 4 oranges of different sizes to Apple of different size how many combination approach can we make taking at least coin the Indian Cricket is to play 5 test match against CC cricket 11 in the next winter the result of this five matches win loss or draw are to be predicted how many different forecast can obtain all the five character results and how many ways can the creeve and after board how many words are four letters can be formed from 7 capital letters 3 Bhave sim 4 consonants so that each word begin with the capital and contains at least one bhavel all the letters of each word begin being different find how Numb number of combination and permutation of the letter of the word accountancy taking 4 at a place in how many ways 9 lakh things you depended to groups between 2% a polygon has 44 diagonals the number of its sides is 11789 in a football Championship there are played 36 matches every teams played one match with each other the number of teams participated in the champions 8 and 18 circle 6 circle how many Triangles can be formed by joining this points find the number of chords passing through the point in the plane 13 straight lines meet at a point find the number of angles in between the straight lines
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