X can take 7 values.
To get |X|+2) take X={−1,0,1}

=> P(|X|<2) = Favourable CasesTotal Cases = 3/7

S.P of Rs. 5000 stock = Rs.156100*5000= Rs. 7800. 

Income from this stock = Rs.12100*5000 = Rs. 600.  

Let investment in 8 % stock be x and that in 9 % stock = (7800 - x).

Therefore,  

x*890+7800-x*9108=600+70  

4x45+7800-x12=670⇔x=3600 

Therefore,  Money invested in 8 % stock at 90 = Rs. 3600.

Money invested in 9 % at 108 = Rs. (7800-3600) = Rs. 4200.

M is the brother of N and B is the brother of N. 

So, M is the brother of B

We have n(s) =52C2 52 = 52*51/2*1= 1326. 

Let A = event of getting both black cards 

     B = event of getting both queens 

A∩B = event of getting queen of black cards 

n(A) = 52*512*1 = 26C2 = 325, n(B)= 26*252*1= 4*3/2*1= 6  and  n(A∩B) = 4C2 = 1 

P(A) = n(A)/n(S) = 325/1326;

P(B) = n(B)/n(S) = 6/1326 and 

P(A∩B) = n(A∩B)/n(S) = 1/1326 

P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 = 55/221

Let S be the sample space

Then n(S) = no of ways of drawing 2 balls out of (6+4) =10C2 10 =10*92*1 =45

Let E = event of getting both balls of same colour

Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)

                =6C2+4C2 = 6*52*1+4*32*1= 15+6 = 21

Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15

Q is the son of R but R is not the mother. So, R is the Father of Q. P is married to R 

So, P is the wife of R and the mother of Q, X is the daughter of P and hence of R and so she is the Sister of Q, Y is the brother of R and Z is the brother of P. 

Clearly. Y is brother of R who is a male. So, Y and R are a pair of brothers  

Total number of elementary events = 20C2 ways =190

There are 7 white balls out of which one white can be drawn in 7C1 ways and one ball from remaining 13 balls can be drawn in 13C1 ways.

So,favourable events = 7C1*13C1

Therfore,required probability = (7C1*13C1)/20C2=91/90

D is father of A and grandfather of F. So, A is father of F. 

Thus. D and A are the two fathers. C is the sister of F So. C is the daughter of A. 

Since there is only one mother, it is evident that E is the wife of A and hence the mother of C and F. 

So, B is brother of A There are three brothers. So. F is the brother of C. 

 Clearly, A is E's Husband.