theta|P_(r)=12p_(R-1)" तi "varepsilon=-

If P(11,r)=P(12,r-1) find n

If ""^(11)P_(r )= ""^(12)P_(r-1) , then r = ………….

If theta varepsilon R and i=sqrt(-1), then ((1+sin theta+i cos theta)/(1+sin theta-i cos theta))^(n) is equal to

(i) If ""^(5)P_(r)=2xx""^(6)P_(r-1) , find r. (ii) If ""^(20)P_(r)=13xx""^(20)P_(r-1) , find r. (iii) If ""^(11)P_(r)=""^(12)P_(r-1) , find r.

Find 'r' if : (i) ""^(5)P_(r )= ""^(6)P_(r-1) (ii) 5""^(4)P_(r )=6""^(5)P_(r-1) (iii) ""^(5)P_(r )=2""^(6)P_(r-1) (iv) ""^(10)P_(r+1): ""^(11)P_(r )=30 :11 .

Fine r if (i) ""^(5) P_(r) =2 ""^(6)P_(r-1) (ii) ""^(5) P_(r) = ""^(6)P_(r-1)

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

Find r if (i) ""^5P_r=2^6P_(r-1) (ii) ""^5P_r=^6P_(r-1)

Let p_(1),p_(2),...,p_(n) and x be distinct real number such that (sum_(r=1)^(n-1)p_(r)^(2))x^(2)+2(sum_(r=1)^(n-1)p_(r)p_(r+1))x+sum_(r=2)^(n)p_(r)^(2)<=0 then p_(1),p_(2),...,p_(n) are in G.P.and when Statement 2: If (p_(2))/(p_(1))=(p_(3))/(p_(2))=...=(p_(n))/(p_(n-1)), then p_(1),p_(2),...,p_(n) are in G.P.

IF ""^(20)P_(r):""^(20)P_(r-1)=15 :1 then r=