[keerthi_koch]

Originally Posted by lonewolf7

what is the last digit of the sum of factorial of first 100 natural numbers???

evry number from 5 onwards will hav a 0 in its factorial...so the units digit can be calculated by adding up the factorial for the first 4 numbers
so it is 1+2+6+24=33

so units digit is 3

[MaskedMenace]

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# Miss Susie a famous psephologist, constructs a venn diagram to study the voting pattern among a sample of 5000 voters.The survey requires the voter to identify election issues from among a list of five issues.A voter may identify none,one,or more than one of the issues listed as an election issue.How many different regions should the venn diagram contain ?

# There are 15 points in space, of which 5 points lie on the same plane and the other 10, no four points are in the same plane.Find the number of distinct planes which are determined by the 15 points.

# From the first 20 natural numbers, a combination of 3 distinct numbers is selected and then arranged in ascending order.How many such combinations can be picked so that the average of the extreme numbers gives the middle element ?

# Five points A,B,C,D,E lie on a line L1 and points P,Q,R,S,T lie on a line L2. Each of the five points on L1 is connected to each of the points on L2, by means of straight lines terminated by the points.Then Excluding the given points,The maximum number of points at which the lines can intersect is ?

[jigar_p_civil]

Originally Posted by MaskedMenace

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# Miss Susie a famous psephologist, constructs a venn diagram to study the voting pattern among a sample of 5000 voters.The survey requires the voter to identify election issues from among a list of five issues.A voter may identify none,one,or more than one of the issues listed as an election issue.How many different regions should the venn diagram contain ?

# There are 15 points in space, of which 5 points lie on the same plane and the other 10, no four points are in the same plane.Find the number of distinct planes which are determined by the 15 points.

# From the first 20 natural numbers, a combination of 3 distinct numbers is selected and then arranged in ascending order.How many such combinations can be picked so that the average of the extreme numbers gives the middle element ?

# Five points A,B,C,D,E lie on a line L1 and points P,Q,R,S,T lie on a line L2. Each of the five points on L1 is connected to each of the points on L2, by means of straight lines terminated by the points.Then Excluding the given points,The maximum number of points at which the lines can intersect is ?

Ya menacebhai u r true .......... Lack Activity ALL ARE in RECESSION

# From the first 20 natural numbers, a combination of 3 distinct numbers is selected and then arranged in ascending order.How many such combinations can be picked so that the average of the extreme numbers gives the middle element ?

here number from 1 to 20

average so extreme number definitely divided by 3

possible number 3,6,9,12,15,18

3 not possible
6 combination 126
9 combination 139/239
12 combination 1,4,12/2,4,12/3,4,12

same for 15 & 18

so total combination 5*6/2=15

[lonewolf7]

# From the first 20 natural numbers, a combination of 3 distinct numbers is selected and then arranged in ascending order.How many such combinations can be picked so that the average of the extreme numbers gives the middle element ?

ans) i think that here "average of the extreme numbers " means (max+min)/2

based on that

thought process: the average of two nos. will always lie exactly between them. in other words the two extreme numbers can be represented as " n+x " and " n-x" where n is the middle element.

so for 1,2...20.
max value of x is 9, thus possibl combo are 11(+-)9 and 10(+-)9
for x=8,posib combo is 12,11,10,9(+-
similarly for x=2 there are 18 possib combo.(19,18..2)+-(1)
thus total possible combination is 2+4+6...+18=2*(1+2+...9)
=90 possible combo

[lonewolf7]

sorry puys in last post for x=8,posib combo is 12,11,10,9(+- ) 8 should be there in place of the smiley with goggles..

[STALWART]

Originally Posted by MaskedMenace

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# Miss Susie a famous psephologist, constructs a venn diagram to study the voting pattern among a sample of 5000 voters.The survey requires the voter to identify election issues from among a list of five issues.A voter may identify none,one,or more than one of the issues listed as an election issue.How many different regions should the venn diagram contain ?

There are five number of issues . So any one issue cud be selected in two ways i.e. is either PRESENT or ABSENT in any voter's choice. So total no. of different regions in venn diagram will be 2^5 = 32.

Sayonara

[jigar_p_civil]

Originally Posted by MaskedMenace

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# Miss Susie a famous psephologist, constructs a venn diagram to study the voting pattern among a sample of 5000 voters.The survey requires the voter to identify election issues from among a list of five issues.A voter may identify none,one,or more than one of the issues listed as an election issue.How many different regions should the venn diagram contain ?

# There are 15 points in space, of which 5 points lie on the same plane and the other 10, no four points are in the same plane.Find the number of distinct planes which are determined by the 15 points.

# From the first 20 natural numbers, a combination of 3 distinct numbers is selected and then arranged in ascending order.How many such combinations can be picked so that the average of the extreme numbers gives the middle element ?

# Five points A,B,C,D,E lie on a line L1 and points P,Q,R,S,T lie on a line L2. Each of the five points on L1 is connected to each of the points on L2, by means of straight lines terminated by the points.Then Excluding the given points,The maximum number of points at which the lines can intersect is ?

# Miss Susie a famous psephologist, constructs a venn diagram to study the voting pattern among a sample of 5000 voters.The survey requires the voter to identify election issues from among a list of five issues.A voter may identify none,one,or more than one of the issues listed as an election issue.How many different regions should the venn diagram contain ?

i am not sure but here intersection of 4 circles

because 5th issue(no vote) out side of region

so inner region inside venn diagram=2^4 and 1 outside

so and is 17

[STALWART]

Originally Posted by MaskedMenace

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# There are 15 points in space, of which 5 points lie on the same plane and the other 10, no four points are in the same plane.Find the number of distinct planes which are determined by the 15 points.

Any 3 points in 3-D makes a plane. 15 points wud have made 15C3 planes had no 4 points been in the same plane. But here 5 points are given to be in the same plane, so, we have to deduct 5C3 from the total number of planes. So the required answr is 15C3 - 5C3 + 1 = 446

Sayonara

[contact_nipun]

Originally Posted by MaskedMenace

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# Five points A,B,C,D,E lie on a line L1 and points P,Q,R,S,T lie on a line L2. Each of the five points on L1 is connected to each of the points on L2, by means of straight lines terminated by the points.Then Excluding the given points,The maximum number of points at which the lines can intersect is ?

Let us take two lines

--*--------*--------*--------*-------*------
A B C D E

--*--------*--------*--------*-------*------
P Q R S T


When A is joined to all P,Q,R,S,T 5 line segments are made
secondly when B is connected to all these five points BT wil not intesect ne line
BP will account for 4 intersection points
similarly,BQ will account for 3 intersection point
BR will account for 2 intersection point
BS will account for 1 intersection point

i.e (4+3+2+1) points till now
for CP,CQ,CR,CS,CT we have (8+6+4+2) pts resp.
so on....

total points = 1+2+3+4+8+6+4+2+12+9+6+3+16+12+8+4
=(1+2+3+4)(1+2+3+4)
=10*10=100

hence 100 intesection pts in all

Did i get it right..??

[MaskedMenace]

The answers for the above ones

# 32

#446

#90

#60

respectively