If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are mutually perpendicular vectors having magnitudes $$1,2,3$$ respectively, then $$\left[\begin{array}{lll}\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}} & \overline{\mathrm{b}}-\overline{\mathrm{a}} & \overline{\mathrm{c}}\end{array}\right]=$$

$$\int \frac{\sec ^8 x}{\operatorname{cosec} x} d x= $$

Two rotating bodies $$P$$ and $$Q$$ of masses '$$\mathrm{m}$$' and '$$2 \mathrm{~m}$$' with moment of inertia $$I_P$$ and $$I_Q\left(I_Q > I_P\right)$$ have equal Kinetic energy of rotation. If $$\mathrm{L}_P$$ and $$\mathrm{L}_Q$$ be their angular momenta respectively then

A sound wave is travelling with a frequency of $$50 \mathrm{~Hz}$$. The phase difference between the two points in the path of a wave is $$\frac{\pi}{3}$$. The distance between those two points is (Velocity of sound in air $$=330 \mathrm{~m} / \mathrm{s}$$ )