If the equation of the locus of a point equidistant from the points `(a_1,b_1)` and `(a_2,b_2)` is `(a_1-a_2)x+(b_2+b_2)y+c=0`, then the value of C is

Correct Answer - C The equation of the hyperbola is `(x^(2))/(9)-(y^(2))/(16)=1` The equation of the tangent is `y=mx+sqrt(9x^(2)-16)` `"or sqrt(9m^(2)-16)=2sqrt5` `"or "m= pm2` or a + b = sum of roots...

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)...

`P_1` is midpoint of `A_1A_2`. `therefore" "P_1-=((x_1+x_2)/(2),(y_1+y_2)/(2))` `P_2` divides `P_1A_3` in `1:2`. `therefore" "P_2-=((2((x_1+x_2)/2)+x_3)/(2+1),(2((y_1+y_2)/2)+y_3)/(2+1))` `-=((x_1+x_2+x_3)/(3),(y_1+y_2+y_3)/(3))` Now, `P_3` divides `P_2A_4` in ` 1:3` `therefore" "P_3-=((3.((x_1+x_2+x_3)/3)+x_4)/(3+1),(3.((y_1+y_2+y_3)/3)+y_4)/(3+1))` `-=((x_1+x_2+x_3+x_4)/(4),(y_1+y_2+y_3+y_4)/(4))` Proceeding in this manner, we...

Correct Answer - A We have `(1)/(2)|{:(x_1,,y_1,,1),(x_2,,y_2,,1),(x_3,,y_3,,1):}|=|{:(a_1,,b_1,,1),(a_2,,b_2,,1),(a_3,,b_3,,1):}|or (1)/(2)|{:(x_1,,y_1,,1),(x_2,,y_2,,1),(x_3,,y_3,,1):}|=(1)/(2)|{:(a_1,,b_1,,1),(a_2,,b_2,,1),(a_3,,b_3,,1):}|` Hence, the area of triangle with vertices `(x_1,y_1),(x_2,y_2),(x_3,x_3)` is the same as the area of triangle with vertices `(a_1,b_1),(a_2,b_2),(a_3,b_3)`. Hence, the two triangles...

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 - B Put `x = i` `(1+i)^(5) = (a_(0) - a_(2) + a_(4)) + i(a_(1)-a_(3)+a_(5))` `rArr |1+i|^(5) = |(a_(0) - a_(2) + a_(4)) + i(a_(1) - a_(3) + a_(5))|`...

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...

Correct Answer - C `(c )` Centre `(5,0)`, radius `=5sqrt(2)` `:.` Equation of the circle `(x-5)^(2)+y^(2)=50` For `x=1`, `y^(2)=34`. Total number of integral points `=(5+5+1)`. Similarly for `x=2,3,…..12` Finally number of...

Correct Answer - A `(a)` First arrange `12` persons `A_(4),A_(5),….A_(15)` in `"^(15)P_(12)` ways There remains `3` places. Keep `A_(1)` in the first place and arrange `A_(2)`, `A_(3)` in the remaining two...

Correct Answer - Inconsistent