Let the plane $$P:\overrightarrow r \,.\,\overrightarrow a = d$$ contain the line of intersection of two planes $$\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 6$$ and $$\overrightarrow r \,.\,\left( { - 6\widehat i + 5\widehat j - \widehat k} \right) = 7$$. If the plane P passes through the point $$\left( {2,3,{1 \over 2}} \right)$$, then the value of $${{|13\overrightarrow a {|^2}} \over {{d^2}}}$$ is equal to :
The probability, that in a randomly selected 3-digit number at least two digits are odd, is :
Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q, which are feet of these two poles. Let $${\pi \over 8}$$ and $$\theta$$ be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan2$$\theta$$ is equal to
Let p, q, r be three logical statements. Consider the compound statements
$${S_1}:(( \sim p) \vee q) \vee (( \sim p) \vee r)$$ and
$${S_2}:p \to (q \vee r)$$
Then, which of the following is NOT true?