# Engineering mathematics set 3

By | November 22, 2018

 Question 1
What is wrong with the proof? $$x^2=\underbrace{x+x+\cdots+x}_{(x\text{ times})}$$ $$\frac{d}{dx}x^2=\frac{d}{dx}[\underbrace{x+x+\cdots+x}_{(x\text{ times})}]$$ $$2x=1+1+\cdots+1=x$$ $$2=1$$
 A Proof is correct B One $x$ as a variable and the other $x$ as constant C Both A and B D None of the above
 Question 2
$\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=?$
 A $-\frac{1}{24}$ B $\frac{1}{24}$ C $\frac{1}{12}$ D $-\frac{1}{12}$
 Question 3
There are $16$ students who use either bicycles or tricycles. The total number of wheels is $38$. Find the number of students using bicycles.
 A 7 B 10 C 14 D 13
Question 3 Explanation:
If everybody had bicycles, there would be $16 \times 2 = 32$ wheels. There are actually $38$, so that's $6$ additional wheels. Each one must be on a different tricycle. So there are $6$ tricycles, and the other $10$ students have bicycles.
 Question 4
If you are a pretty good basketball player, and were betting on whether you could make.
1. I) 2 out of 4 baskets
1. II) 3 out of 6 baskets
which would you take?
 A I B II C III D Any of the above
Question 4 Explanation:

https://en.m.wikipedia.org/wiki/Law_of_large_numbersAccording to the law of large number ( ). the more events you consider the closer will be the outcome to the expected result. In your case the expected outcome depends on actuall ability of you and your opponents in basketball playing. so if you know that you are truely a better performer to your opponents you should choose 4/8. otherwise 2/4.

 Question 5
Imagine there are a 100 people in line to board a plane that seats 100. The first person in line realizes he lost his boarding pass so when he boards he decides to take a random seat instead. Every person that boards the plane after him will either take their "proper" seat, or if that seat is taken, a random seat instead. What is the probability that the last person that boards will end up in his/her proper seat?
 A 1/2 B 1/3 C 1/100 D None of the above
Question 5 Explanation:
The answer is that the probability that the last person ends in up in his proper seat is exactly $\frac{1}{2}$ The reasoning goes as follows: First observe that the fate of the last person is determined the moment either the first or the last seat is selected! This is because the last person will either get the first seat or the last seat. Any other seat will necessarily be taken by the time the last guy gets to 'choose'. Since at each choice step, the first or last is equally probable to be taken, the last person will get either the first or last with equal probability: $\frac{1}{2}$.
 Question 6
Which one is true about $n\geq2$
 A $n\geq2$ do not have perfect square B $n\geq2$ have many pefect square when $n>7865$ C If $n\geq2$, then $n!$ is not a perfect square. D None of the above
 Question 7
King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always tell the truth. One day, four servants met.
1. The blue one says, “Altogether, we have 28 legs.”
1. The green one says, “Altogether, we have 27 legs.”
1. The yellow one says, “Altogether, we have 26 legs.”
1. The red one says, “Altogether, we have 25 legs.”
What is the colour of the servant who tells the truth?
 A Green B Blue C Yellow D Red
Question 7 Explanation:
Since the four are disagreeing then $3$ must be lying. Since only octopuses with 7 legs lie then there must be $7\times3 = 21$ legs. That leaves the honest octopus with either $6$ or $8$ legs. So the total number of legs should either be $21+6= 27$ legs or $21+8=29$ legs. Since no one says that they have $29$ legs then only the Green octopus is saying the truth., p. Source
 Question 8
Which of the following is/are true?
 A $\ln{2}\leq(\dfrac{2}{5})^{\frac{2}{5}}$ B $\ln{2}\geq(\dfrac{2}{5})^{\frac{2}{5}}$ C $\ln{2}>(\dfrac{2}{5})^{\frac{2}{5}}$ D $\ln{2}<(\dfrac{2}{5})^{\frac{2}{5}}$
Question 8 Explanation:
$\left(2 \over 5\right)^{2/5} = 0.69314\color{#ff0000}{\Large 4}843155146\ldots\, , \qquad\qquad \ln\left(2\right) = 0.69314\color{#ff0000}{\Large 7}180559945\ldots$
 Question 9
A goat is tied to an external corner of a rectangular shed measuring 4 m by 6 m. If the goat’s rope is 8 m long, what is the total area, in square meters, in which the goat can graze?
 A 38.5 sq.m B 144 sq.m C 166.5 sq.m D 155 sq.m
Question 9 Explanation:
There are 9 questions to complete.