Let the number of persons= n

Number of handshakes by first person= n- 1

(As he cannot handshake with himself)

Number of handshakes by second person = n- 2

(As he has already handshaked with first person)

Number of handshakes by third person= n- 3

.

.

Number of handshakes by second last i.e. ( n- 1)th person= n- (n- 1)= 1

Number of handshakes by last i.e. nth person= n- n= 0

So,

Total number of handshakes=(n- 1)+ (n- 2)+ (n- 3)+ 1+ 0

= 0+ 1+ 2+ 3+ ...........(n- 1)

= Sum of first (n- 1) terms

= (n- 1)(n- 1+ 1)/2

= n(n- 1)/ 2

So, Total number of handshakes= n(n- 1)/2

According to question,

n(n- 1)/ 2= 66

=> n^2 - n= 132

=> n^2- n- 132= 0

=> n^2- 12n+ 11n- 132= 0

=> n(n- 12) + 11(n- 12)= 0

=> (n- 12)(n+ 11) = 0

n= 12 or n= - 11(which is not possible as no. Of persons cannot be negat 

Original side length: x New side length: x + 10% x = 1.1 x Original area = x^2 New area = (1.1 x)^2 = 1.21 x^2 So we've increased area by factor of 1.21 = 1 + 0.21 = 1 + 21% So we've increased area by 21%

sons current age=42/2=21

so,4 years back sons age was=21-4=17

Angus Stewart Deaton, FBA[1] (born 19 October 1945) is a British-American economist. In 2015, he was awarded the Nobel Memorial Prize in Economic Sciences for his analysis of consumption, poverty, and welfare

The European Union (EU) is a politico-economic union of 28 member states that are located primarily in Europe.[11][12] It covers an area of 4,324,782 km2, with an estimated population of over 508 million. The EU operates through a system of supranational institutions and intergovernmental-negotiated decisions by the member states.[13][14] The institutions are: the European Parliament, the European Council, the Council of the European Union, the European Commission, the Court of Justice of the European Union, the European Central Bank, and the Court of Auditors. The European Parliament is elected every five years by EU citizens.

Saina Nehwal is an Indian badminton player, former world no.1 in Women's Singles . She is the first Indian to win a medal in Badminton at the Olympics. She achieved this feat by winning the Bronze medal at the London Olympics 2012 on 4 August 2012.

Time difference 1 PM-7AM=6 Hour=360 minute

3 Minutes gains from 5 second

1 minutes gains from 5/3 second

360 minutes gains from 5×360/3

                                   =600 second = 10 min

the watch will indicate:1 PM + 10 min=1:10 PM

a2+b2=29

=> (a-b)2+2ab=29

=> (3)2+2ab=29

=> 2ab=20

=> ab=10 (Ans.)

11 would have been a correct answer as well.

Mr. Rafim can do 1 days=1/15 parts

and Mr. Shafin can do 1 days=1/30 parts

(Mr. Rafim+ Mr. Shafin) can do 1 days=(1/15 +1/30) parts

“         “                   “                   “              = 1/10 parts

(Mr. Rafim+ Mr. Shafin),

  1/10 parts can do = 1 day

 So,  1  part   “      “  = 10 days

Part of the total vote against the issue-

=6/(9+6)

=6/15

=2/5