Question

Mathematics Quiz #2 :

Get ready.

Total Questions :10

Marks for correct answer : 4
Marks for wrong answer : -1

The first who answers will be awarded with +4.
The second who answers with a short hint of the soln will also be awarded +4.

Only 2 answers will be considered.

Are you guys ready?

Answer 1

Why the change of rules?

Answer 2

It was required. :)

Answer 3

2 minutes more. Then we will have the quiz started.

Have any questions?

Answer 4

Yes. What is the answer to the ultimate question of life, the universe, and everything?

Answer 5

42 :D

Answer 6

Lol , only related to quiz :D

Answer 7

@Zarkon @Mertsj @jim_thompson5910 @dumbcow @ganeshie8 [Test ur skills now :) ]

Answer 8

Here comes first question. Good Luck all

Let \(a_1 , a_2 , ... ,a _{10} \) be in AP and \(h_1 , h_2 , ... , h_{10} \) be in HP If \(a_1 = h_1 = 2\) and \(a_{10} = h_{10} = 3 \) then \(a_4 h_7 = ?\)

Answer 9

6.48? lol

Answer 10

@chris00 : -1

Answer 11

o well.

Answer 12

HP : Harmonic Progression
GP : Geometric Progression
AP : Arithmetic Progression

Answer 13

Wouldnt it be 6?

Answer 14

totally did not know that...haha

Answer 15

@johnweldon1993 : +4

One more chance left guys. But now provide soln

Answer 16

(Provide hint) not soln...

Answer 17

on top of it john! haah

Answer 18

Come on friends ! Its not that difficult ;)

Answer 19

Should we move on for next question ?

Answer 20

2 minutes more !

Answer 21

Time up !!!

Answer 22

OK So here is the next question (Very very easy):

If H is the harmonic mean between P and Q , then the value of (H / P) + (H / Q) is

(in terms of P and Q)

Answer 23

You will get 5 minutes for this question. Time starts now

Answer 24

PQ/P+Q

Answer 25

Surre

Answer 26

@chris00 : -1

Answer 27

i got no clue if the questions are similar. haha i'm out.

Answer 28

@SharpEdge I need answer. Whats your answer ?

@oldrin.bataku Same for u

Answer 29

2

Answer 30

@chris00 No problem. Keep trying

Answer 31

@terenzreignz +4

Answer 32

good work

Answer 33

2 minutes more

Answer 34

Solution is needed when you have posted the answer :)

Answer 35

$$H=2/(1/P+1/Q)=2PQ/(P+Q)\\H/P=2Q/(P+Q)\\H/Q=2P/(P+Q)\\H/P+H/Q=2(P+Q)/(P+Q)=2$$

Answer 36

@oldrin.bataku +4

Answer 37

@SharpEdge +4 (your sol. was correct)

Answer 38

Time up !

Next question:
Another easy one :

If the sum of the series 2, 5, 8, 11, …… is 60100, then n is

Answer 39

You have got 8 minutes

Answer 40

Good work @SharpEdge +4

Answer 41

lol does that mean he gets +8?

Answer 42

How gracing. It's (apparently) an arithmetic progression so
\[\Large 60100 = \frac{n(a_1+a_n)}{2}=\frac{n(2+3(n-1))}{2}\]

Answer 43

Clearly \(a_n=3n-1\) so:$$S_n=\frac{n(2+3n-1)}2=60100\\3n^2+n-120200=0\\n=200 $$

Answer 44

@oldrin.bataku , @terenzreignz +4

Answer 45

200, but it'd be redundant, as already mentioned :( oh well moving on :D

Answer 46

Now wait for points table

Answer 47

haha fail ^

Answer 48

LOL jk

Answer 49

Aren't you basically stealing attention from all the other posts? :-p now they'll never get answered!

Answer 50

hush @oldrin.bataku you'll expose @mathslover 's grand plan!!!!

haha jk

Answer 51

@terenzreignz +8
@SharpEdge +8
@oldrin.bataku +8
@johnweldon1993 +4
@chris00 -2

Answer 52

just u wait guys

Answer 53

haha is that a sympathy medal?

Answer 54

My Teamwork score went up a point.

Answer 55

Next question : If the equation : \(x^4 - 4x^3 + ax^2 + bx + 1 =0\) has four positive roots, then (a,b) = ?

Answer 56

Are they distinct roots?

Answer 57

Not given.

Answer 58

(-2,4)

Answer 59

just a ping

Answer 60

@chris00 , No :(

-1

Answer 61

(6,-4)

Answer 62

@chris00 : +4

@SharpEdge : -1 :(

Answer 63

BOOM

Answer 64

One more chance left... Any one?

Answer 65

$$x_1x_2x_3x_4=1\\x_1x_2x_3+x_2x_3x_4+x_1x_3x_4+x_1x_2x_4=b\\x_1x_2+x_2x_3+x_1x_3+x_2x_4+x_3x_4+x_1x_4=a\\x_1+x_2+x_3+x_4=4$$So clearly we have \(x_1=x_2=x_3=x_4=1\) yielding \(b=4\) and \(a=6\) yielding \((6,-4)\)

Answer 66

Here it comes... @oldrin.bataku +4

Answer 67

\((6,4)\)*

Answer 68

sorry wrote it wrong I believe

Answer 69

@oldrin.bataku ? 6,4 or 6,-4 ?

Answer 70

ERG it should be \((6,-4)\)

Answer 71

i kept flipping the signs when writing

Answer 72

Ok. @oldrin.bataku : -1 and @SharpEdge : -1 @chris: +3

Answer 73

@SharpEdge y so competitive? LOL

Answer 74

Hmm... @oldrin.bataku : 2 and @SharpEdge : 2

because ur hints were right...

Answer 75

hahahaha

Answer 76

@mathslover your point system is so indecisive XD

Answer 77

lol but thy were good

Answer 78

$$x_1x_2x_3x_4=1\\x_1x_2x_3+x_2x_3x_4+x_1x_3x_4+x_1x_2x_4=-b\\x_1x_2+x_2x_3+x_1x_3+x_2x_4+x_3x_4+x_1x_4=a\\x_1+x_2+x_3+x_4=4$$We clearly see \(x_i=1\) and thus \(b=-4,a=6\) so \((6,-4)\)

Answer 79

I can't neglect their work...

Answer 80

If you say so...

Answer 81

Support a bit guys... you all have some chances left. 6 quest. left

Answer 82

COMING BACK FROM THE DEAD!

Answer 83

Points table :

@oldrin.bataku : 10
@SharpEdge : 10
@terenzreignz : 8
@chris00 : 1

Answer 84

Oh and @johnweldon1993 : 4

Answer 85

Find the maximum and minimum values of f(x) = x^2 - 5x + 6

[Question no. 5]

Answer 86

No maximum
-1/4 min

Answer 87

No maximum but a minimum \((5/2,-1/4)\)

Answer 88

we can do this by differentiating f(x) HINT

Answer 89

@terenzreignz : + 4
@oldrin.bataku yes at x = 5/2 it is -1/4

+4 for u too

Answer 90

$$f'(x)=2x-5\\2x=5\\x=5/2\\f(5/2)=25/4-25/2+6=-1/4$$

Answer 91

and finding stationary points

Answer 92

Points table :

@oldrin.bataku : 14
@terenzreignz : 12
@SharpEdge : 10
@johnweldon1993 : +4
@chris00 : 1

Answer 93

Be ready for next quest.