Basic Concepts Of Permutations And Combinations

20 Questions  I  By Sweetsalman123
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1.  N articles are arranged in such a way that 2 particular articles never come together. The number of such arrangements is
A.
B.
C.
D.
2.  The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is
A.
B.
C.
D.
3.  The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
A.
B.
C.
D.
4.  The number of different factors the number 75600 has is
A.
B.
C.
D.
5.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»51«/mn»«mi»c«/mi»«/msub»«mn»31«/mn»«/msub»«/math» is equal to Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»51«/mn»«mi»c«/mi»«/msub»«mn»20«/mn»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo».«/mo»«msub»«msub»«mn»50«/mn»«mi»c«/mi»«/msub»«mn»20«/mn»«/msub»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo».«/mo»«msub»«msub»«mn»45«/mn»«mi»c«/mi»«/msub»«mn»15«/mn»«/msub»«/math» D.None of these
A.
B.
C.
D.
6.  The number of 4 digit numbers greater than 5000 can be formed out of the digits 3, 4, 5, 6 and 7 (no. digit is repeated). The number of such is
A.
B.
C.
D.
7.  The number of arrangements of the letters in the word FAILURE, so that vowels are always! coming together is
A.
B.
C.
D.
8.  The number of numbers lying between 10 and 1000 can be formed with the digits 2,3,4,0,8,9 is
A.
B.
C.
D.
9.  At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. The number of ways a voter choose to vote is
A.
B.
C.
D.
10.  The value of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mi»r«/mi»«mo».«/mo»«/mrow»«mrow»«mi»r«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mn»10«/mn»«/munderover»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»r«/mi»«msub»«mi»p«/mi»«mi»r«/mi»«/msub»«/msub»«/math» Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»11«/mn»«mi»P«/mi»«/msub»«mn»11«/mn»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»11«/mn»«mi»P«/mi»«/msub»«mn»11«/mn»«/msub»«/math»-1 C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»11«/mn»«mi»P«/mi»«/msub»«mn»11«/mn»«/msub»«/math»+1 D.None of these
A.
B.
C.
D.
11.   nPr can also written as Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»n«/mi»«mo»!«/mo»«/mrow»«mrow»«mi»n«/mi»«mo»-«/mo»«mi»r«/mi»«mo»§nbsp;«/mo»«mo»!«/mo»«/mrow»«/mfrac»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»n«/mi»«mo»!«/mo»«/mrow»«mrow»«mi»r«/mi»«mo»!«/mo»«mo»(«/mo»«mi»n«/mi»«mo»-«/mo»«mi»r«/mi»«mo»)«/mo»«mo»!«/mo»«/mrow»«/mfrac»«/math» C.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»r«/mi»«mo»!«/mo»«/mrow»«mrow»«mi»n«/mi»«mo»-«/mo»«mi»r«/mi»«mo»!«/mo»«/mrow»«/mfrac»«/math» D.None of these
A.
B.
C.
D.
12.  The number of ways in which 12 students can be equally divided into three groups is 
A.
B.
C.
D.
13.  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mn»4«/mn»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn»3«/mn»«/msub»«/msub»«/math» is evaluated as
A.
B.
C.
D.
14.  The number of ways the letters of the word COMPUTER can be rearranged is
A.
B.
C.
D.
15.  The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is Options: A.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»12«/mn»«mi»c«/mi»«/msub»«mn»4«/mn»«/msub»«mo»§#215;«/mo»«msub»«mn»5«/mn»«msub»«mi»c«/mi»«mn»3«/mn»«/msub»«/msub»«/math» B.«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«msub»«mn»17«/mn»«mi»c«/mi»«/msub»«mn»7«/mn»«/msub»«/math» C.4950«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#215;«/mo»«/math»(7)! D.None of these
A.
B.
C.
D.
16.  If . nP3: nP2 =3:1, then n is equal to
A.
B.
C.
D.
17.  The number of ways in which 7 boys sit in a round -table so that two particular boys may sit together is
A.
B.
C.
D.
18.  The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3, 4, 5, 6, 7 is
A.
B.
C.
D.
19.  5 letters are written and there are five letter-boxes. The number of ways the letters can be dropped into the boxes, are in each
A.
B.
C.
D.
20.  There are 12 points in a plane of which 5 are collinear. The number of triangles is
A.
B.
C.
D.
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