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JEE Mains Super40 Revision Series

PERMUTATION AND COMBINATION

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1 11461

JEE Mains Super40 Revision Series PERMUTATION AND COMBINATION

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to beselected and arranged in a row on a shelf so that the dictionary is always in the middle.Then the number of such arrangements is (1) less than 500 (2) at least 500 but less than750 (3) at least 750 but less than 1000 (4) at least 1000

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2 11643


The number of integers greater than that can be formed, using the digits without repetition, is :


3 11685


If all the words (with or without meaning) having five letters, formed using the letters ofthe word SMALL and arranged as in a dictionary; then the position of the word SMALL is: (1) 46th (2) 59th (3) 52nd (4) 58th


4 13892 JEE Mains Super40 Revision Series PERMUTATION AND COMBINATION

6, 0003, 5, 6, 7 and 8,

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lf are prime numbers and are the positive integers such that their LCM of is then the numbers of ordered pair of is (A) (B) (C) (D)


5 19697


A man has friends, of them are ladies and are men. His wife also has friends, of them are ladies and 4 are men. Assume and have no common friends.Then the total number of ways in which and together can throw a party inviting 3ladies and 3 men, so that 3 friends of each of and are in the party, is : 469 (2) 484(3) 485 (4) 468


6 30331


The number of triangles that can be formed with 10 points as vertices of them beingcollinear, is 110. Then is a. b. c. d.


7 30355


A person predicts the outcome of 20 cricket matches of his home team. Each match canresult in either a win, loss, or tie for the home team. Total number of ways in which hecan make the predictions so that exactly 10 predictions are correct is equal to a.

b. c. d.


8 30361


Let there be circles in a plane. The value of for which the number of radicalcenters is equal to the number of radical axes is (assume that all radical axes and radicalcenters exist and are different). a. b. c. d. none of these


r, s, t p, q p, q

r2t4s2, (p, q) 252 254 225 224

X 7 4 3 Y 73 X Y

X YX Y

nn 3 4 5 6

^ 20C10 × 210 ^ 20C10 × 320 ^ 20C10 × 310 ^ 20C10 × 220

n ≥ 3 n

7 6 5

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Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10passengers enter the train during the journey with 10 different ticket of two class. Thenumber of different sets of tickets they may have is a. b. c. d. none of these


10 30377


In a certain test, there are question. In the test, students gave wrong answers toat least questions, where if the total number of wrong answersgiven is 2047, then is equal to a. b. c. d.


11 30557


The number of arrangements of the letters of the word BANANA in which the two N's donot appear adjacently is a. b. c. d.


12 30563


A fivedigit number divisible by 3 is to be formed using the digits without repetition. The total number of ways this can done is (a) (b) (c) (d)



Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chaireach. First, the women choose the chairs from amongst the chairs marked 1 to 4, andthen the men select th chairs from amongst the remaining. The number of possiblearrangements is a. b. c. d. none of these


^ 15C10 ^ 20C10 ^ 30C10

n 2n − i

i i = 1, 2, ............. , nn 10 11 12 13

40 60 80 100

0, 1, 2, 3, 4, and 5,216 240 600

3125

^ 6C3 ×4 C2 ^ 4P2 ×4 P3 ^ 4C2 ×4 P3

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14 30603


A bag contains four onerupee coins, two twentyfive paisa coins, and five tenpaisacoins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag?(Consider coins of the same denominations to be identical.) a. b. c. d.


15 30620


The total number of positive integral solution of is equal to a. b. c. d. none of these


16 30676


An ndigit number is a positive number with exactly Nine hundred distinct ndigitnumbers are to be formed using only the three digits The smallest valueof for which this is possible is (a) (b) (c) (d)


17 30686


A sevendigit number without repetition and divisible by 9 is to be formed by using sevendigits out of The number of ways in which this can be done is (a) (b) (c) (d) non of these



Messages are conveyed by arranging four white, one blue, and three red flags on a pole.Flags of the same color are alike. If a message is transmitted by the order in which thecolors are arranged, the total number of messages that can be transmitted if exactly sixflags are used is a. b. c. d.

71 72 73 80

15 < x1 + x2 + x3 ≤ 20685 785 1125

n2, 5, and 7.

n 6 7 8 9

1, 2, 3, 45, 6, 7, 8, 9.9 ! 2(7 !) 4(7 !)

45 65 125 185

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19 30698


The number of threedigit numbers of the form such that and is a. b. c. d.


20 30737


The letters of the word COCHIN are permuted and all the permutations are arranged inan alphabetical order s in an English dictionary. The number of words that appear beforethe word COCHIN is a. b. c. d.


21 30743


Let . The total number of unordered pairs of disjoint subsets of isequal a. b. c. d.


22 30794


Among the 8! [permutations of the digits 1, 2, 3..., 8, consider those arrangements whichhave the following property. If we take any five consecutive positions the product of thedigits in these positions is divisible by 5. The number of such arrangements is equal to a. b. c. d. none of these



The total number of times, the digit 3 will be written when the integers having less than 4digits are listed is equal to a. b. c. d.

xyz x < y z ≤ y 276285 240 244

360 192 96 48

S = 1, 2, 3, 4 S25 34 42 41

7! 2. (7 !) ^ 7C4

300 310 302 306

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24 30812


The total number of ways in with three distinct numbers in A.P. can be selected from theset is equal to a. b. c. d. none of these


25 30818


In a polygon, no three diagonals are concurrent. If the total number of points ofintersection of diagonals interior to the polygon is 70, then the number of diagonals of thepolygon is a. b. c. d. none of these


26 30824


A man has three friends. The number of ways he can invite one friend everyday fordinner on six successive nights so that no friend is invited more than three times is a.

b. c. d.


27 30875


Number of ways in which 25 identical things be distributed among five persons if eachgets odd number of things is


1, 2, 3, ............24 66 132 198

20 28 8

640 320 420 510

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28 30885


There are three copies each of four different books. The number of ways in which they

can be arranged in a shelf is. a. b. c. d.


29 30892


The total number of ways in which number of identical balls can be put in numberedboxes such that ith box contains at least number of balls is a.

b. c. d. none of these


30 30896


Let denote the number of triangles, which can be formed using the vertices of aregular polygon of sides. It ,then equals a. b. c. d.


31 30897


In a group of boys, two boys are brothers and six more boys are present in the group. Inhow many ways can they sit if the brothers are not to sit along with each other? a.b. c. d. none of these


12!

(3 !)4

12!

(4 !)3

21!

(3 !)44!

12!

(4 !)33!

n2 n(1, 2, 3, .......... n) i

.n2

Cn − 1 .n2 − 1 Cn − 1 . Cn − 1

n2 + n − 2

2

Tnn Tn + 1 − Tn = 21 n 5 7 6 4

2 × 6!^ 7P2 × 6! ^ 7C2 × 6!


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32 30938


Fifteen identical balls have to be put in five different boxes. Each box can contain anynumber of balls. The total number of ways of putting the balls into the boxes so that eachbox contains at least two balls is equal to a. b. c. d.


33 30946


If parallel lines in a plane are intersected by a family of parallel lines, the number of

parallelograms that can be formed is a. b.

c. d. none of these


34 30956


There are white and black balls, each set numbered Thenumber of ways in which the balls can be arranged in a row so that the adjacent balls areof different colors is a. b. c. d.


35 30958


Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed inenvelopes so that each envelope contains exactly one card and no card is placed in theenvelope bearing the same number and moreover cards numbered 1 is always placed inenvelope numbered 2. Then the number of ways it can be done is a. b. c. d.


.9 C5 .10 C5 .6 C5 .10 C6

m n

mn(m − 1)(n − 1)1

4

mn(m − 1)(n − 1)1

4m2n21

4

(n + 1) (n + 1) 1 → n + 1.

(2n + 2)! (2n + 2)! × 2 (n + 1)! × 2 2(n + 1)!2

264 265 5367


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36 30972


In an examination of nine papers, a candidate has to pass in more papers than thenumber of paper in which he fails in order to be successful. The number of ways in whichhe can be unsuccessful is a. b. c. d.


37 30984


Ten IIT and 2 DCE students sit in a row. The number of ways in which exactly 3 IITstudent sit between 2 DCE students is

none of these


38 44581


How many different nine digit numbers can be formed from the number byrearranging its digits so that odd digits occupy even positions (a) (b) (c) (d)


39 69577


A rectangle with sides of lengths units is divided into squaresof unit length. The number of rectangles which can be formed with sides of odd length, is(a) (b) (c) (d) non of these


256 256 193 319

(A) .10 C3 × 2! × 3! × 8! (B)10! × 2! × 3! × 8! (C) 5 ! × 2! × 9! × 8! (D)

2233558816 36 60 180

(2n − 1) and (2m − 1)

m2n2 mn(m + 1)(n + 1) 4m + n − 1


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40 183555


If then (a) (b) (c) (d) non of these


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nCr − 1 = 36, nCr = 84 and nCr + 1 = 126, n = 8, r = 4n = 9, r = 3 n = 7, r = 5


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