Let m and M be respectively the minimum and maximum values of

$$\left| {\matrix{ {{{\cos }^2}x} & {1 + {{\sin }^2}x} & {\sin 2x} \cr {1 + {{\cos }^2}x} & {{{\sin }^2}x} & {\sin 2x} \cr {{{\cos }^2}x} & {{{\sin }^2}x} & {1 + \sin 2x} \cr } } \right|$$

Then the ordered pair (m, M) is equal to :

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

Identify the correct output signal Y in the given combination of gates (as shown) for the given inputs A and B.

A particle of charge q and mass m is moving with a velocity $$ - v\widehat i$$ (v $$ \ne $$ 0) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field $$\overrightarrow B = {B_0}\widehat k$$ , the maximum value of v for which the particle will not hit the screen is :