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 

here, small cube shped brick=12 we know, surface of cube=6 x (arm)2 total surface of 12 bric=12x6x(1)2=72 now, length= 3 cm width= 2 cm height=2 cm rectangle er surface=2(ab+bc+ca)=2[(3x2)+(2x2)+(2x3)=32 small-big=72-32=40  

probablity=10/20 x 9/19 x 8/18=2/19

3.2 people live in 1 house hold 1 people live in 1/3.2 house hold 48000 people live in 48000/3.2 house hold=15000 household in 1 household the is 1.2 dvd in 15000 household 1.2x15000=18000 dvd

suppose, distance=D we know, time=distance/speed at time of going=D/6 t time of coming=D/4 here, D/6+D/4=1 or,D=12/5 miles goes 1 mile in 1/6 hour goes 12/5 milein 1/6 x 12/5 hour=2/5 hour =24 minutes

Afia, in 15 days does 1 work in 4 days does 4/15 work Bbul, in 20 days do 1 work in 4 days do 4/20 work both of them do together=(4/15+4/20)=7/15 part left=(1-7/15)=8/15 

prime factors of following  numbers are, 6=2x3 7=1x7 8=2x2x2x2 9=3x3 so,L.C.M=2x3x3x7x4=504

boys =45% so,girls=100-45=55%

boys went to picnic=40%  of 45 %=18% girls went to picnic=55% of 20%=11% total student=(18+11)=29%

suppose, people like both x% total people 100% here, x%=(63+76)%-100%=39%

samiras age=20 farzanas age=60 suppose, x years ago farzana was five times of samira according to question, (20-x)5=60-x or,4x=40 or,x=10  

damage insured=50000 tk damage paid by company=56000 tk damage extra paid=6000 tk 

left books=(29-2)+(32-4)+1=56

suppose, total people 100 60% means, 60  people gve 60 tk, then total= 60x60=3600 tk people remain= 40  money remin=3600x100/75=4800-3600=1200 tk so  remaining per people donate =1200/40=30 tk

The minimum value of 10% including tax =- 35.50+3.55 = 39.05

And the maximum value of 15% including tax = 35.50+ 5.325 = 40.825

So, the total amount will be paid Tk. 39 and tk. 41

Here, x = 2y = 3z

So, x=3z

And 2y=3z

So, y=(3/2)z

xyz=36

So,  3z×(3/2)z×z=36

=> 9z3=72

=> z3=8

So, z=2