Find the number of ways of arranging 15 students `A_1,A_2,........A_15` in a row such that (i) `A_2`, must be seated after `A_1 and A_2`, must come af

Here, `tan^(_1) ((a_(1) x- y)/(a + a_(1) y)) = tan^(-1) ((a_(1) - (y)/(x))/(1 + a_(1) (y)/(x))) = tan^(-1) a_(1) - tan^(-1) (y)/(x)` `tan^(-1) ((a_(2) -a_(1))/(1 + a_(2) a_(1))) = tan^(-1)...

Correct Answer - B `OM_r=OA_r+(OA_(r+1)-OA_(r))/(2)` `=(OA_(r)+OA_(r+1))/(2)` `=(1)/(2){OA_1xxk^(r-1)+OA_(1)xxK^(r)}` `=(OA_1)/(2)(1+k)k^(r-1)` `therefore sum_(r=1)^(oo)OM_(r)=(OA)/(2)(1+k)sum_(r=1)^(oo)k^(r-1)` `=(OA_1))/(2)(1+K)xx(1)/(1-k)` `(OA)/(2)xx(1+(OA_2//OA_1))/(1-(OA_2//OA_1))=(OA _(1)(OA_1+OA_2))/(2(OA_1-OA_2))`

Correct Answer - D Let (h,k) be the point on the locus. Then by the given conditions, `(h-a_1)^1+(k-b_1)^2=(h-a_2)^2+(k-b_2)^2` or `2h(a_1-a_2)+2k(b_1-b_2)+a_2^2+b_2^2-a_1^2=0` `h(a_1-a_2 )+k(b_1-b_2)+(1)/(2)(a_2^2+b_2^2-a_1^2-b_1^2)=0` .....(1) Also, since (h,k) lies on the given locus,...

Correct Answer - C Let the probability that a man aged x dies in a year p. Thus the probability that a man aged x does not die in a year...

`cos B = (c^(2) + a^(2) - b^(2))/(2ca)` or `a^(2) - (2c cos B) a + c^(2) - b^(2) = 0` This equation has roots `a_(1) and a_(2)` `rArr a_(1)...

Correct Answer - B `(b)` For the first place `5` players (excluding the oldest) and for the remaining place `5` (including the oldest)players are available. `:.` No of ways `=5xx5xx4xx3xx2xx1=600`

Correct Answer - A `(a)` Total no. of arrangement if all the girls do not seat side by side `=["all arrangement"-"girls seat side by side"]` `=8!-(6!xx3!)` `=6!(56-6)=6!xx50` `=720xx50=36000`

Correct Answer - A `(a)` The possible arrangements of teachers and students can be as follows : `(i) T S S T S S T S S` `(ii) S T S...

Correct Answer - A `(a)` The other five letters (other than `G`, `R`, `L`, `A`, `S`, `N`) in `11` places can be arranged in `"^(11)P_(5)` ways. Then three remains six places....

Correct Answer - 43200