If `(1)/(x)+(1)/(y)=1,` the function `a^(3)x^(2)+b^(3)y^(2)` is minimum, the `x` and `y` are

If ((x^(-1)y^2)/(x^3y^(-2)))^1.\ ((x^6\ y^(-3))/(x^2\ y^3))^(1/2)=x^a y^b , prove that a+b=-1 , where x\ a n d\ y are different positive primes.

If y=(a x+b)/(x^2+c), then (2x y_1+y) y_3=

1/(3x+y)+1/(3x-y)=3/4 and 1/(3x+y)-1/(3x-y)= -1/4

Let A = {x_(1),x_(2),x_(3),x_(4), x_(5), x_(6),x_(7), x_(8)}, B= { y_(1), y_(2), y_(3), y_(4) } . The total number of function f : A to B that are onto and there are exactly three elements x in A such that f(x) = y_(1) is :

If the slope of tangent to a curve y=f(x) is maximum at x=1 and minimum at x=0 , then equation of the curve which also satisfies (d^3y)/dx^3=4x-3 , is (A) y=x^4/6-x^3/2+x^2/2+1 (B) y=x^4/4+x^3-x^2/3+1 (C) y=x^4/4-x^3/7+x^2/3+3 (D) none of these

A plane through the line (x-1)/1=(y+1)/(-2)=z/1 has the equation (A) x+y+z=0 (B) 3x+2y-z=1 (C) 4x+y-2z=3 (D) 3x+2y+z=0

If x_(1), x_(2), x_(3) as well as y_(1), y_(2), y_(3) are in GP, with the same common ratio, then the points (x_(1),y_(1)), (x_(2),y_(2)) and (x_(3), y_(3))

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to