Recent questions in Engineering Mathematics

1
How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1? I got answer 9C2=36.Answer given 45
1 vote
2
It is known that a bus will arrive at random at a certain location sometime between 3:00 P.M. and 3:30 P.M. A man decides that he will go at random to this location between these two times and will wait at most 5 minutes for the bus. If he misses it, he will take the subway. What is the probability that he will take the subway?
3
Prove that at a party where there are at least two people, there are two people who know the same number of other people there.
4
Show that there are at least six people in California (population: 37 million) with the same three initials who were born on the same day of the year (but not necessarily in the same year). Assume that everyone has three initials.
1 vote
5
Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.
6
Show that in a group of five people (where any two people are either friends or enemies), there are not necessarily three mutual friends or three mutual enemies.
1 vote
7
Assume that in a group of six people, each pair of individuals consists of two friends or two enemies. Show that there are either three mutual friends or three mutual enemies in the group.
8
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games
9
if (x lg x)=4608 , then how to calculate value of x ? Base is 2
10
How many bit strings of length 10 contain either five consecutive 0s or five consecutive 1s? I got 382.Is it correct?
11
How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1} a) that assign 1 to exactly one of the positive integers less than n?
12
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
13
every total ordered set is distributive.
14
$\lim_{x\rightarrow 0}\sin \left( \frac{1}{x}\right)$ (a) 1 (b) 0 (c) does not exist (d) none of these
1 vote
15
$\lim_{x\rightarrow 0}\frac{ \sin x^{\circ}}{x}$
16
$\lim_{x\rightarrow 0} \left( \frac{1}{x^{2}} -\frac{1}{\sin^{2}x} \right)$
17
$\lim_{\theta \rightarrow 0} \frac{ 1-\cos \theta }{ \theta \sin\theta }$
1 vote
$\lim_{x\rightarrow 0} \frac{e^{x}-e^{\sin x}} {x-\sin x}$
$\lim_{x\rightarrow \infty }\frac{\sin x}{x}$
$\lim_{x\rightarrow 0} \frac{x^{x}-1}{x}$