A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25 cm/sec, then the rate (in cm/sec.) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is 1 m above the ground is :

The equation y = sinx sin (x + 2) – sin² (x + 1) represents a straight line lying in :

If the truth value of the statement p $$ \to $$ (~q $$ \vee $$ r) is false (F), then the truth values of the statements p, q, r are respectively :

If the volume of parallelopiped formed by the vectors $$\widehat i + \lambda \widehat j + \widehat k$$, $$\widehat j + \lambda \widehat k$$ and $$\lambda \widehat i + \widehat k$$ is minimum, then $$\lambda $$ is equal to :