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

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 :

Let $$\overrightarrow a = 3\widehat i + 2\widehat j + 2\widehat k$$ and $$\overrightarrow b = \widehat i + 2\widehat j - 2\widehat k$$ be two vectors. If a vector perpendicular to both the vectors $$\overrightarrow a + \overrightarrow b $$ and $$\overrightarrow a - \overrightarrow b $$ has the magnitude 12 then one such vector is :

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = $$\left[ {\matrix{ 2 & 3 \cr 5 & { - 1} \cr } } \right]$$, then AB is equal to :