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?
Let R1 and R2 be relations on the set {1, 2, ......., 50} such that
R1 = {(p, pn) : p is a prime and n $$\ge$$ 0 is an integer} and
R2 = {(p, pn) : p is a prime and n = 0 or 1}.
Then, the number of elements in R1 $$-$$ R2 is _______________.
The number of real solutions of the equation $${e^{4x}} + 4{e^{3x}} - 58{e^{2x}} + 4{e^x} + 1 = 0$$ is ___________.