Let ƒ(x) = a^x (a > 0) be written as
ƒ(x) = ƒ₁ (x) + ƒ₂ (x), where ƒ₁ (x) is an even function of ƒ₂ (x) is an odd function.
Then ƒ₁ (x + y) + ƒ₁ (x – y) equals

If the system of linear equations

x – 2y + kz = 1
2x + y + z = 2
3x – y – kz = 3

has a solution (x,y,z), z $$ \ne $$ 0, then (x,y) lies on the straight line whose equation is :

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is :

The vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y+ 4z = 5 which is perpendicular to the plane x – y + z = 0 is :