For the first order reaction A $$\to$$ B, the half life is 30 min. The time taken for 75% completion of the reaction is _________ min. (Nearest integer)

Given : log 2 = 0.3010

log 3 = 0.4771

log 5 = 0.6989

The total number of lone pairs of electrons on oxygen atoms of ozone is __________.

The vector $$\overrightarrow a = - \widehat i + 2\widehat j + \widehat k$$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $$\overrightarrow b $$. Then the projection of $$3\overrightarrow a + \sqrt 2 \overrightarrow b $$ on $$\overrightarrow c = 5\widehat i + 4\widehat j + 3\widehat k$$ is :

The minimum value of the function $$f(x) = \int\limits_0^2 {{e^{|x - t|}}dt} $$ is :