Jee 2014 Booklet5 Hwt Permutations and Combinations
Short Description
Jee 2014 Booklet5 Hwt Permutations and Combinations...
Description
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [1]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
The least positive integer n for which n 1 C5 (A)
14
(B)
n 1
C6 n C7 is :
15
(C)
16
(D)
28
2.
In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit in a row so that two sisters are not sitting together is : (A) 4820 (B) 1410 (C) 2830 (D) 30240
3.
The number of words that can formed by using the letters of the word MATHEMATICS that start as well as end with T is : (A) 80720 (B) 90720 (C) 20860 (D) 37528
4.
Find the exponent of 15 in 100!. (A) 12 (B)
24
(C)
36
(D)
48
5.
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one-plate for each month). How many types of February calendars should it prepare to serve for all the possibilities in the future years ? (A) 7 (B) 14 (C) 21 (D) 28
6.
If E (A)
1 2 3 4 30 31 . . . ... . 8 x , then value of x is : 4 6 8 10 62 64
7
(B)
9
(C)
10
(D)
12
7.
Sum of all three digit numbers (no digit being zero) having the property that all digits are perfect squares, is : (A) 3108 (B) 6216 (C) 13986 (D) None of these
8.
If letters of the word SACHIN are arranged in all possible ways and are written out as in a dictionary, then the word SACHIN appears at serial number : (A) 603 (B) 602 (C) 601 (D) 600
9.
Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to : (A) 25 (B) 34 (C) 42 (D)
10.
41
For a set of five true/false questions, no student has written all correct answers, and no two students have given the same sequence of answers. What is the maximum number of students in the class, for this to be possible ? (A) 30 (B) 31 (C) 32 (D) 33
VMC/Permutation & Combination
59
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [2]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
The number of subsets of the set A a1 , a2 , . . . ., an which contain even number of elements is : (A)
2.
2 n 1
(B)
(C)
2n 2
(D)
2n
Let Tn denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If Tn 1 Tn 21 , then n equals : (A) 5
3.
2n 1
(B)
7
(C)
6
(D)
How many numbers are there between 100 and 1000 in which all the digits are distinct ? (A) 648 (B) 729 (C) 576 (D)
4
810
4.
A class consists of 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is : (A) 15 (B) 12 (C) 8 (D) 5
5.
The number of ways of permuting letters of the word ENDEANOEL so that none of the letters D, L, N occurs in the last five positions is: (A) 5! (B) 2(5!) (C) 7(5!) (D) 21(5!)
6.
How many different signals can be given using any number of flags from 5 flags of different colours ? (A) 120 (B) 205 (C) 325 (D) None of these
7.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is : (A) at least 750 but less than 1000 (B) at least 1000 (C) less than 500 (D) at least 500 but less than 750
8.
Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouces are seated next to each other, is : (A) 72 (B) 186 (C) 384 (D) 516
9.
Find the sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time. (A) 83324 (B) 93324 (C) 103324 (D)
10.
If
n
(A)
C4 , n C5 and 6
n
None of these
C6 are in A.P., then the value of n can be : (B)
VMC/Permutation & Combination
7
(C)
60
8
(D)
9
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [3]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
2.
In how many ways 5 boys and 3 girls can be seated in a row so that no two girls are together ? (A) 7200 (B) 14400 (C) 4800 (D)
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent ? (A)
3.
None of these
8 . 6 C4 . 7 C4
(B)
6 . 7 . 8C4
(C)
6 . 8 . 7 C4
(D)
7 . 6 C4 . 8C4
(D)
187
The remainder when x 1! 2! 3! 4! . . . 100! is divided by 240, is : (A)
153
(B)
33
(C)
73
4.
The number of ways in which the diagram in figure can be coloured so that each of the smaller triangles is painted with one of the three colours yellow, pink or green and no two adjacent regions are painted with the same colour, is : (A) 24 (B) 12 (C) 36 (D) 16
5.
In a class of 10 students there are 3 girls A, B, C. In how many different ways can they be arranged in a row such that no two of the three girls are consecutive. (A)
7 6
(B)
7 210
(C)
7 56
(D)
7 336
6.
The number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two ‘–’ signs occur together is : (A) 30 (B) 35 (C) 6! 5! (D) 10!
7.
There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is : (A) 6 (B) 7 (C) 8 (D) 9
8.
If 20% of three subsets (i.e., subsets containing exactly three elements) of the set A a1 , a2 , . . ., an contains a1, then value of n is : (A)
9.
10.
15
(B)
16
(C)
17
(D)
If all the letters of the word ‘AGAIN’ be arranged as in a dictionary, what is the fiftieth word? (A) NAAIG (B) NAAGI (C) NAGAI (D)
18
NAGIA
The number of ways of selecting 4 cards of an ordinary pack of playing cards so that exactly 3 of them are of the same denomination is : (A)
2496
(B)
VMC/Permutation & Combination
13
C3 4 C3 48 (C)
61
52
C3 48
(D)
None of these
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [4]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before COCHIN is : (A) 360 (B) 192 (C) 96 (D) 48
2.
If r, s, t are prime numbers and p, q are natural numbers such that LCM of p, q is r 2 s 4 t 2 , then the number of ordered pairs (p, q) is : (A)
3.
5.
(B)
254
225
(D)
224
105
(B)
90
(C)
75
(D)
60
Six X have to be placed in the squares of figure such that each row contains at least one X. The number of ways in which this can be done is : (A)
25
(B)
26
(C)
27
(D)
30
In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent ? (A)
144
(B)
36 5
6.
(C)
The number of diagonals of a polygon of 15 sides is : (A)
4.
252
Find the value of the expression
47
C4
52 j
(C)
576
(D)
None of these
(C)
52
(D)
None of these
C3 .
j 1
(A) 7.
52
C4
C3
{1, 2, 3, 4}
(B) 7 x
5! 4!
(C)
7! 5!
(D)
6! 5!
{1, 2, 3, 4, 5, 6}
(C)
{1, 2, 3}
(D)
{1, 2, 3, 4, 5}
Px 3 is : (B)
An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 without replacement. The number of ways in which this can be done is : (A)
10.
30
The range of the function (A)
9.
(B)
C4
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by : (A)
8.
51
9!
(B)
2(7!)
(C)
4(7!)
(D)
(36) (7!)
A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to be included in a committee? (A)
5062
(B)
VMC/Permutation & Combination
6062
(C)
62
7062
(D)
8062
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [5]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
The results of 21 football matches (win, lose or draw) are to be predicted. The number of forecasts that contain exactly 18 correct results is : (A)
2.
3.
21
C3 218
5.
6.
(D)
21
C3 321 218
None of these
A polygon has 44 diagonals. Find the number of its sides. (A) 10 (B) 11 (C)
12
(D)
13
Find the total number of factors (excluding 1) of 2160. (A) 12 (B) 11
40
(D)
39
(B)
2
(C)
(D)
None of these
(D)
4
(C)
The number of positive integral solutions of the equation x1 x2 x3 x4 x5 1050 is :
If
n
1800
Cr 1 36 , n Cr 84 and 1
(B) n
1600
(C)
1400
Cr 1 126 , then the value of r is equal to :
(B)
2
(C)
3
At an election there are five candidates and three members are to be elected, and a voter may vote for any number of candidates not greater than the number to be elected. The number of ways in which the person can vote is : 25
(B)
30
(C)
35
(D)
25 23
A library has n different books and has p copies of each of the book. The number of ways of selecting one or more books from the library is: (A)
10.
321 218
(D)
(A) 9.
(C)
4
(A) 8.
C18 23
5 x 3 x y 3 y 11 If x, y 0 , 30 such that x y (where [x] denotes greatest integer x ), then number of 3 2 2 4 6 4
(A) 7.
21
There are 15 points in a plane, no three of which are in a straight line except 4, all of which are in a straight line. The number of triangles that can be formed by using these 15 points is : (A) 404 (B) 415 (C) 451 (D) 490
ordered pairs (x, y) is : (A) 0 4.
(B)
np
(B)
pn
(C)
n 1 p 1
(D)
p 1n 1
(D)
104
Determine the total number of non-negative integral solutions of x1 x2 x3 x4 100 . (A)
103
C3
(B)
VMC/Permutation & Combination
103
C4
(C)
63
104
C3
C4
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [6]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Letters of the word INDIALOIL are arranged in all possible ways. The number of permutations in which A, I, O occur only at odd places, is : (A) 720 (B) 360 (C) 240 (D) 120
2.
If
1 4
Cn
(A)
1 5
Cn
1 6
3
, then value of n is :
Cn
(B)
4
(C)
1
(D)
2
3.
Three straight lines l1, l2 and l3 are parallel and lie in the same plane. Five points are taken on each of l1, l2 and l3. The maximum number of triangles which can be obtained with vertices at these points, is : (A) 425 (B) 405 (C) 415 (D) 505
4.
The number of ways of arranging 20 boys so that 3 particular boys are separated is : (A) 9(16!) (B) 15(16!) (C) 15(17!)/2
5.
7.
None of these
The number of ways in which n distinct objects can be put into two different boxes so that no box remains empty, is : (C)
2n 2
(D)
n2 2
The value of 1.1! + 2.2! + 3.3! + . . . . . + n.n! is : (A) (n + 1)! (B) (n + 1)! + 1
(C)
(n + 1)! – 1
(D)
None of these
The number of the factors of 20! is : (A) 4140 (B)
(C)
4204
(D)
81650
2n 1
(A) 6.
(D)
(B)
n2 1
41040
8.
The number of five digit numbers that can be formed by using digits 1, 2, 3 only, such that three digits of the formed number are identical, is : (A) 30 (B) 60 (C) 90 (D) None of these
9.
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is : 8 (A) 38 (B) 21 (C) 5 (D) C3 n
10.
k
Cr equals,
k m
(A)
n 1
Cr 1
(B)
VMC/Permutation & Combination
n 1
Cr 1
m
Cr
(C)
64
n 1
Cr 1
m
Cr 1 (D)
n 1
Cr 1 m Cr 1
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [7]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order ? (A) 360 (B) 240 (C) 120 (D) 480
2.
If nCr denotes the number of combinations of n things taken r at a time, then the expression n
C r 1 n C r 1 2 n C r
Equals : (A) 3.
n2
(B)
Cr 1
n 1
Cr
(C)
n 1
Cr 1
(D)
Three dice are rolled. The number of possible outcomes in which at least one die shows 5 is : (A) 215 (B) 36 (C) 125 (D)
n2
Cr
91
4.
Six boys and six girls sit along a line alternatively in x ways ; and along a circle (again alternatively in y ways), then : (A) x=y (B) y = 12x (C) x = 10y (D) x = 12y
5.
A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways, in which this can be done is : (A) 240 (B) 3125 (C) 600 (D) 216
6.
The number of ways in which two teams A and B of 11 players each can be made up from 22 players so that two particular players are on the opposite sides is : (A) 369512 (B) 184755 (C) 184756 (D) 369514
7.
Let an 10n n! for n 1 . Then an takes the greatest value when n equals : (A)
8.
9.
10.
20
(B)
18
(C)
6
(D)
9
The greatest number of points of intersection of n circles and m straight lines is : (A)
2mn m C2
(C)
m
C2 2
(B)
C n
2
(D)
1 m m 1 n 2m n 1 2
None of these
The number of times the digit 3 will be written when listing the integers from 1 to 1000 is : (A) 269 (B) 300 (C) 271 (D)
302
There are three pigeon holes marked M, P, C. The number of ways in which we can put 12 letters so that 6 of them are in M, 4 are in P and 2 are in C is : (A) 2520 (B) 13860 (C) 12530 (D) 25220
VMC/Permutation & Combination
65
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [8]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 6
1.
50
The value of
C4
56 r
C3 is :
r 1
(A)
56
C3
(B)
56
C4
(C)
55
C4
(D)
55
C3
2.
25 lines are drawn in a plane. Such that no two of them are parallel and no three of them are concurrent. The number of points in which these lines intersect, is : (A) 300 (B) 315 (C) 325 (D) 450
3.
The number of subsets of a set containing n distinct objects is :
4.
(A)
n
C1 n C2 n C3 . . . n Cn 1
(B)
2n 1
(C)
n
C0 n C1 . . . n Cn
(D)
2n 1
The number of 10 digit numbers that can be written by using the digits 0 and 1 is : (A)
210
(B)
29
(C)
210 2
(D)
10!
5.
The number of arrangements of the letters of the word BANANA in which two N’s do not appear adjacently is : (A) 40 (B) 60 (C) 80 (D) 100
6.
Given that n is odd, the number of ways in which three numbers in AP can be selected from 1, 2, 3, . . . ., n is : (A)
n 12 2
(B)
n 12 4
(C)
n 12 2
(D)
n 12 4
7.
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
8.
The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the sides of the octagon is : (A) 24 (B) 52 (C) 48 (D) 16
9.
Rakshit is allowed to select (n + 1) or more books out of (2n + 1) distinct books. If the number of ways in which he may not select all of them is 255, then value of n is : (A) 3 (B) 4 (C) 5 (D) 11
10.
The units digit of 17 2009 112009 7 2009 is : (A)
1
(B)
VMC/Permutation & Combination
8
(C)
66
2
(D)
5
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [9]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
In a cricket championship there are 36 matches. The number of terms, if each plays 1 match with other are : (A) 9 (B) 10 (C) 8 (D) 12
2.
Four dice are rolled. The number of possible outcomes in which atleast one dice shows 2 is : (A) 625 (B) 671 (C) 1023 (D)
3.
If
2 n 1
Pn 1 :
(A)
2 n 1
1296
Pn 3 : 5 , then n =
5
(B)
4
(C)
3
(D)
2
4.
20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host ? (A) (B) (C) (D) None of these 20 2 18 18
5.
Assuming that no two consecutive digits are same the number of n-digit numbers is : (A) (B) (C) 9n n 9
(D)
n9
6.
There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope is : (A) 119 (B) 44 (C) 59 (D) 40
7.
The number of ways of selecting atleast 4 candidates from 8 candidates is : (A) 270 (B) 70 (C) 163
8.
m 1
C2 .
n 1
C2
(B)
m
C2 . n C 2
(C)
m 1
C2 . n C 2
The number of ways in which 6 rings can be worn on 4 fingers of one hand is : 6 (A) 46 (B) C4 (C) 64 m
10.
None of these
There is a set of m parallel lines intersecting a set of another n parallel lines in a plane. The number of parallelograms formed is : (A)
9.
(D)
nr
n 1
(D)
m
(D)
24
(D)
None of these
C2 .
C2
Cn
r 0
(A)
n m 1
Cn 1
(B)
VMC/Permutation & Combination
nm2
Cn
(C)
67
n m3
C n 1
HWT/Mathematics
Vidyamandir Classes DATE :
TIME : 30 Minutes
MARKS : [ ___ /10]
TEST CODE : P&C [10]
START TIME :
END TIME :
TIME TAKEN:
PARENT’S SIGNATURE :
This test contains a total of 10 Objective Type Questions. Each question carries 1 mark. There is NO NEGATIVE marking. Choose the correct alternative. Only one choice is correct. 1.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is : (A) 9 (B) 12 (C) 10 (D) 14
2.
The number of positive odd divisors of 216 is : (A) 4 (B) 6
3.
4.
8
The number of ways in which 9 persons can be divided into three equal groups is : (A) 1680 (B) 840 (C) 560
(D)
12
(D)
280
(D)
9 2
(D)
48
In how many ways a garland can be made from exactly 10 flowers ? (A)
5.
(C)
(B)
10
9
(C)
29
How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7 ? (A) 12 (B) 24 (C) 36
6.
The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is : (A) 55 (B) 66 (C) 77 (D) 88
7.
The number of subsets of {1, 2, 3, . . . . , 9} containing atleast one odd number is : (A) 324 (B) 396 (C) 496
(D)
512
8.
The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is : (A) 2454 (B) 2452 (C) 2450 (D) 1806
9.
If
16
(A) 10.
Cr
16
31
Cr 2 , then
r
Pr 3 = (B)
120
(C)
210
(D)
840
In how many ways can 21 English & 19 Hindi books be placed in a row so that no two Hindi books are together ? (A) 1540 (B) 1450 (C) 1504 (D) 1405
VMC/Permutation & Combination
68
HWT/Mathematics
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