[" 42.The inequalities "y(-1,z-4,y(1)<=0" and "y(3,(-5)" are known to hold for "y=ax^(2)+bx+c" then "],[" the least value of 'a' is "]

The inequalities y(-1)>=-4,y(1) =5 are known to hold for y=ax^(2)+bx+c then the least value of 'a' is:

The values of x, y, z for the equations x-y+z=1, 2x-y=1, 3x+3y-4z=2 are

Let N be the number of triplets (x,y,z) where x,y,z in[0,2 pi] satisfying the inequality (4+sin4x)(2+cot^(2)-y)(1+sin^(4)+z)<12sin^(2)-z Find the value of (N)/(2)

The value of |(2 y_(1)z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) y_(2) z_(1),2y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),2y_(3) z_(3))| , is

The value of |(2 y_(1)z_(1),y_(1) z_(2) + y_(2) z_(1),y_(1) z_(3) + y_(3) z_(1)),(y_(1) z_(2) y_(2) z_(1),2y_(2) z_(2),y_(2) z_(3) + y_(3) z_(2)),(y_(1) z_(3) + y_(3) z_(1),y_(2) z_(3) + y_(3) z_(2),2y_(3) z_(3))| , is

Show that the lines (x-1)/(2)=(y-2)/(y-1)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z intersect

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

If x y+y z+x z=1 ,then prove that x/(1-x^2)+y/(1-y^2)+z/(1-z^2)=(4x y z)/((1-x^2)(1-y^2)(1-z^2)

Solve the following inequation : 2y - 3 lt y + 1 le 4y + 7 , if : y in (Integers)

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(z y-z)+cot^(-1)(z x+1)/(z-x)