A bowl filled with very hot soup cools from 98$$^\circ$$C to 86$$^\circ$$C in 2 minutes when the room temperature is 22$$^\circ$$C. How long it will take to cool from 75$$^\circ$$C to 69$$^\circ$$C?

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $$x$$ times its initial resonant frequency $$\omega_0$$. The value of $$x$$ is :

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s$$^2$$)

If $$\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k$$ and $$\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k$$ then, the unit vector in the direction of $$\overrightarrow P \times \overrightarrow Q $$ is $${1 \over x}\left( {\sqrt 3 \widehat i + \widehat j - 2\sqrt 3 \widehat k} \right)$$. The value of $$x$$ is _________.