CAREER POINT
Fresher Course for IIT JEE (Main & Advanced)–2017
Course : Fresher(XL) Batch
DAILY PRACTICE PROBLEM SHEET
Subject : Mathematics
DPPS 3
Topic : Permutation & Combination
Q.1
Consider the equation
(A) 140
xy
= 2 4 355 4 then the number of positive integral solutions of equation are
x+y
(B) 891
(C) 72
(D) None of these
Q.2
The total number of 1 word, 2 word, 3 word sentences that can be formed using all the letters of the word
SAMSUNG is
(A) 8!
(B) 18 × 7!
(C) 11 × 7!
(D) None of these
Q.3
The number of ordered pairs of positive integers (a, b) such that LCM of a and b is 23 35 117 is
(A) 105
(B) 1155
(C) 840
(D) None of these
Q.4
A group of 10 married couples is getting ready for boating, they have to split into 5 groups of 4 persons each.
The number of ways in which there will be Mr. X on the same boat with his wife is [each boat should have 2
men and 2 women]
10 9
10 9
10 9
10 9
(A)
(B) 9
(C) 9
(D)
9
( 2) 5 4
2 4
2 5
29
Statement based questions : (Q.5 to 8)
Each of these questions contains two statements. Statement-1 and Statement-2. Each of these has four
alternatives choices. You have to select the correct choice.
(A) Statement-1 is True, Statement-2 is True ; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-1.
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Q. 5
Statement-1 : When number of ways of arranging 21 objects of which r objects are identical of one type and
remaining are identical of second type is maximum, then maximum value of 13Cr is 78.
Statement-2 : 2n+1Cr is maximum when r = n.
Q. 6
Statement-1 : The number of ways of writing 1400 as a product of two positive integers is 12.
Statement-2 : 1400 is divisible by exactly three prime factors.
Q. 7
Statement-1 : The number of positive integral solutions of abc = 30 is 27.
Statement-2 : Number of ways in which three prizes can be distributed among three persons is 33.
Q.8
Statement-1 : The number of non-negative integer solution to the inequality x + y + z ≤ 2013 is 2016C3
Statement-2 : Σ(n + 1Cr – nCr) = Σ(nCr – 1)
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Passage # 1 (Q.9 & 10)
Let there are m seats in a row, out of which n are to be occupied by n persons, given m is an even number
and m > 2n.
Q.9
The number of seating arrangements such that no two persons sit side by side
(A) nCn × n!
(B) nCm – n × n!
(C) m – nPn
(D) m – n + 1Pn
Q.10
The number of seating arrangements such that each person has exactly one neighbour
(A) m – nPn
(B) m – (n/2)Cn/2 × n!
(C) m – n + 1Cn/2 × n!
(D) m – n + 1Pn/2
Passage # 2 (Q.11 to 13)
Five balls are to be placed in three boxes. Each box should hold all the five balls so that no box remains
empty.
Q.11
Q.12
Q.13
Number of ways if balls are different but boxes are identical is
(A) 30
(B) 25
(C) 21
(D) 35
Number of ways if balls and boxes are identical is
(A) 3
(B) 1
(C) 2
(D) none of these
Number of ways if balls as well as boxes are identical but boxes are kept in a row is
(A) 10
(B) 15
(C) 20
(D) 6
Q.14
There are nine different books on a shelf, four red and five are green. Number of ways in which it is possible
to arrange these books if
Column-I
Column-II
(A) the red books must be together and green books together
(P) (4) 6!
(B) the red books must be together whereas the green books may or may not be together
(Q) (8) 6!
(C) no two books of the same colour are adjacent
(R) (20) 6!
(D) if the books are arranged on a round table and no two of the three specified books are together
(S) (24) 6!
Q.15
In how many ways can 17 persons depart from railway station in 2 cars and 3 autos, given that 2 particular
person depart by same car (4 persons can sit in a car and 3 persons can sit in an auto). Let these ways are
k!
then (k + m + n) is equal to (internal arrangement of vehicle is not considered)
m !( n !) 3
Q.16
8 clay targets are arranged as shown. In how many ways can they be shot (one at a time) if no target can be
shot until the target(s) below it have been shot.
ANSWERS :
1. (B)
2. (C)
3. (B)
8. (B)
9. (D)
10. (C)
14. A → Q; B → S; C → P; D → R
4. (C)
11. (B)
15. 22
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5. (D)
12. (C)
16. 560
6. (B)
13. (D)
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7. (A)
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