The system of linear equations
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a² – 1) z = a + 1 then

Let $$0 < \theta < {\pi \over 2}$$. If the eccentricity of the

hyperbola $${{{x^2}} \over {{{\cos }^2}\theta }} - {{{y^2}} \over {{{\sin }^2}\theta }}$$ = 1 is greater

than 2, then the length of its latus rectum lies in the interval :

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is :

If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be