.1.ABCD is a quadrilateral such that the bisectors of the four interior angles meet at a point O is Ð (AOB)= 57degree , calculate angle Ð(COD) [in degrees]
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.2. In the given figure , AD and BC are two chords extended to meet at E. if Ð (BAD) = 60 degree and CE = DE, which of the following is true 
- a.BE > 2AD
- b.BE = 2AD
- c.BE < 2AD
- d.None
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- 3. How many ordered pairs of integers (a, b), are there such that their product is a positive integer less than 1000?
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- 4.Chris and his wife invited a total of 10 families on their marriage anniversary. While the host family had just the two members, each family invited consisted of four members. If every person in the party shook hands with every other person belonging to a different family exactly once, then find the number of handshakes that took in the party.
total no. of persons in the party = 10X4 + 2
= 42
let everyone is shaking hand to other including the member of his own family
then the total no. of handshakes = 41+40+39+38+ ----+3+2+1 = 861
no. of handshakes between family members = 10X5 +1 ( 1 for the host family)
= 51
therefore total n of handsakes = 861- 51 = 810
Let angle A = 2a, angle B = 2b, angle C = 2c and angle d = 2d
we know that 2a +2b+2c+2d = 360
a+b+c+d = 180
c+ b = 180 - (a+d)
for the triangle AOB a+d+57= 180 i.e. a+d = 123
for the triangle COD c+b+x =180 (let angle COD = x )
180 - ( a+d) +x= 180
180 - 123 +x = 180
therefore x = 123
hi madam,
i think it must b 861-61=800
cos in 10 families ,the no.of handshakes between them will b
10*(3+2+1)=60 and
the couple willl account for another 1 ..
so its 61 not 51.
If I'm right can u reward me with
Its 800 in deed.
hi ......the solution is 800 and not 810...
it can be easily with help of permut and combination
Hey Nilay Could you please explain how to solve it using combination principles
Sol. 2 : AD x DE = BC x CE
but DE = CE ; AD = BC or AE = BE
Tringle ABE is Isosceles ; Ang BAE = Ang ABE = 600 ; Ang AEB = 600
Triangle ABE is Equilateral; AB = BE = AE or BE = ?
any one try further
Sol. 2 : AD x DE = BC x CE
but DE = CE ; AD = BC or AE = BE
Tringle ABE is Isosceles ; Ang BAE = Ang ABE = 600 ; Ang AEB = 600
Triangle ABE is Equilateral; AB = BE = AE or BE = ?
any one try further
Thanks for making out my mistake, yes your ans is correct, but I am going o reward you with that HA..HA..HA..
Hi guys,
I am new to CAT4MBA...had been participating in forums of other web sites...thought of trying this site too... :)
total members in the party are 40 guests + 2 hosts....
if there is no restriction total handshakes among guests wld be...
40C2 = 780
every guest handshaking with every host = 80
so total 860..
now each family members among them do not handshake...
so 4C2 x 10 = 60 handshakes are extra...
so total handshakes = 860 - 60 = 800
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