INTERSECTION MATHS QUIZ CLASS XI

The answer to the cyborg shooters problem is as follows:

You are A, 1/3 accuracy
B is 1/2 accurate
C is always accurate
x X y = x shoots at y
As A, you can either:
1) shoot at B
2) shoot at C
3) shoot at the ground (deliberately miss).
1) a X b
if you hit (1/3 of the time), you lose, and C fires next and takes you out
otherwise (2/3 of the time) b X c as C is B's biggest threat. 1/2 the time B takes out C, which leaves a X b to resolve. 1/2 the time B misses, C kills B, and you have 1/3 chance to take out C before he takes you out.
First, a X b (with C out of the picture) is
1/3 + 2/3 * 1/2 * 1/3 + 2/3 * 1/2 * 2/3 * 1/2 * 1/3 + ...
= 1/3 + (1/3)^n * 1/3
= 1/3 + 1/6 = 1/2
So a X b (with C there) is
2/3 * 1/2 * 1/2 + 2/3 * 1/2 * 1/3 = 10/36 chance of winning
2) a X c
if you hit C, B shoots are you, 1/2 the time you survive and it boils down to the a X b (C out of picture) calculated above.
if you miss C, B shoots at C, 1/2 the time hits and it boils down to a X b above. 1/2 the time B misses, C takes B out, and you have 1/3 chance to take C out.
So a X c is
1/3 * 1/2 * 1/2 + 2/3 * 1/2 * 1/2 + 2/3 * 1/2 * 1/3
= 1/12 + 1/6 + 1/9 = 13/36 chance of winning
This makes sense, relatively, as you best hope is to take out the most accurate shooter.
3) option 3, you skip your turn by firing into the ground.
b X c, 1/2 the time B hits and it becomes a X b calculated above. The other 1/2, C takes out B and you have 1/3 chance to take out C.
So, A miss on purpose is
1/2 * 1/2 + 1/2 * 1/3 = 1/4 + 1/6 = 15/36 chance of winning.
So your best option, at 15/36 = 41.7% of winning, is to miss your first shot on purpose!!

TRICKS FOR EASIER AND FASTER CALCULATIONS

ABHINAV VERMA PRESENTS TO YOU THE FOLLOWING TRICKS OF THE TRADE WHICH WILL DEFINITELY HELP YOU IN THE FUTURE



1.To find the square of a two digit no.

Example 32²

STEPS

1) First find the square of the digit at units place

2² = 4

32² = ____4

2) Find the product of the digit at units place, digit at tens place and the index and add the carry on(if there)

3*2*2 = 12

32² = ____24

here 1 is the carry on

3) now find the square of 3 and add the carry on

3² + 1 = 10
32² = 1024 (answer)

2.To find the cube of a two digit number

Example: 24³

Step 1
First we will find the cube of units place (that is 4 in this case)
4³=64
24³=___4 (we will write only 4 and will take 6 as a carry on)



Step2
Now we will find the product of both the digits, the no. and the index and will add
the carry on
So we will multiply (2*4*3*24)+6
(2*4*3*24)+6=582
24³=__824(here we will write only two digits i.e. 82 and will
take 5 as a carry on)



Step3
Now we will find the cube of digit at tens place and will add the carry on

Here we will find the cube of 2 and will add 5 which was the carry on obtained from
previous result)
2³+5=8+5=13

24³=13824 (answer)


3. To find the square of the three digit number

Example 246²

STEPS

1) To find the square of 6

6² = 36
We will write 6 and take 3 as carry on

246²= _____6

2) Now we will find the product of digit at tens place, the digit at units place and the index and we will add the carry on .
So, here we will multiply (4*6*2) + 3 = 51

246² = _____16
here we will take 5 as a carry on

3) Now we will find the square of 24 and add the [digit at hundreds place *(digit at unit place *index)] i.e.(2*(6*2)
and then add the carry on

24² + 2*12 + 5 = 605
246² = 60516 (answer)



4. To find the square of a number which has 6 in the units place

Example 96²

Steps
1.First we will find the square of digits in the units place i.e.6
6²=36
and we will write only 6 and will take 3 as a carry on
therefore 96²=___6 (take 3 as carry on)

2. Now we will multiply the digit at tens place with the index and will add the carry on.
(9*2)+3=21
here we will write only 1 and will take 2 as carry on
therefore 96²=__16 (take 2 as carry on)

3.Now we will find the product of the no.at tens place with the next no.
i.e in this case we will multiply 9*10(here 9 is the no. and 10 is the next no.) and we will add 2
9*10+2=92
96²=9216 (answer)




5. To find the square of a no. which has 8 in the units place


Example 482

1.first we will find the square of a digit in the units place i.e. we will find the square of 8.
82 =64 here we will write 4 and will take 6 as a carry on.
482=____4(here 6 is the carry on)

2.now we will multiply the digit at ten’s place with 6 and will add the carry on.
So here we will multiply 4 with 6 and will add 6.
(4*6)+6=30 here we will write 0 and will take 3 as a carry on.
482=__04

3.now we will multiply the digit at tens place with next no. so here we will multiply 4 with 5 and then we will add the carry on that is 3 in this case.
(4*5)+3=23

482=2304(answer)

MADE BY :

ABHINAV VERMA

Finals Maths Quiz Class 11 Important Information

So this post will help all the qualifying teams to better prepare for the quiz on Friday, the 9th of Feb 2007.
It is recommended that this post is read thoroughly and all further preparation is done accordingly. Believe me, the Quiz will not be easy .

Done with the Maths,
Now the Quiz!

• There will be 6 rounds, and a Surprise Round if time permits.
• Rounds will be General, Rapid Fire, Visuals, Problem Solving, etc.
• The questions will consist of topics like General Maths Trivia, Personalities, Elementary Mathematical terms and concepts, Mental maths etc.
• There is no need to as such spend time in practicing maths questions for the quiz. It is better if you research out as much as you can on the above mentioned topics.
• Thinking logically on the spot will help.
• All 6 rounds will be passable , except Rapid Fire, so there are lots of opportunities to gain points.
• The Quiz will be made as interactive and interesting as possible.
  
• Have fun and All the best.

P.S.- David Hilbert was an amazing mathematician.

MATHS QUIZ CLASS XI SOLUTIONS

MATHS QUIZ CLASS XI

SOLUTIONS

1. First which almost all have attempted correctly had no logic except that you had to fill 1 and 8 in the center boxes and the rest follows. Note that in the solution given below order of the set of nos can interchange: (7182);[(64)(35)]

4 6
7 1 8 2
3 5

2. This was plain application of G.P The point to note is that the horizontal displacement is NOT being asked here. Also note that the ball travels 1m once but after that every other distance twice(while going up and while coming down)

D = 1 + 2 ( 1/3 + 1/9 + 1/27 + ..............∞)

= 1 + 2[(1/3) / (1 – 1/3)]

= 1 + 1

=2 meters

An interesting but non-mathematical problem.The catch is that as the water level rises, the ship also automatically rises and with it rises the ladder. Hence the max no of rungs submerged under water at any point is 3

4. The amount of wine in water is the same as the amount of water in wine.

There are two almost similar approaches to this question. I will be writing both: Let the volume of the cup is 1 cup, and the volume of each bucket is 10 cups. Clunking our way through this (and you don't really need to pay attention here), we see that after the first transfer the proportion of wine to total mixture in the water bucket is 1/11. Thus, on the return trip, the proportion of water to total mixture in the cup is 10/11. After dumping it in the wine bucket we get back to the original volume of 10 cups. The proportion of water to total mixture is

     (amount of water in wine bucket)/(total volume in wine bucket) =(10/11)/10  = 1/11

Well, what do you know. This is the same proportion as wine to total mixture in the
water bucket. Since both buckets are back to the same, original volumes, the amount
of wine in the water bucket is exactly the as the amount of water in the wine
bucket. 

Assume that each glass contained 100 units of liquid and that the spoon held 10 units. The spoon first removes 10 units of water, so the water glass contains 90 units of water, and the wine glass contains 100 units of wine and 10 units of water.

With 110 units in the wine glass, the spoon will remove 1/11 of each liquid in that glass. Thus it will transfer to the water glass 9 1/11 units of wine and 10/11 units of water. The water glass will then contain 90 10/11 units of water and 9 1/11 units of wine, and the wine glass will contain 90 10/11 units of wine and 9 1/11 units of water.

5. let xi (where I=1 ,2,…….,10) be the last digit of the 10 numbers not divisible by 10.

1<= xi <= 9

we have to now prove that x1+x2+x3+…..+x10 = 10k

By multinomial series method

LHS = (x^0 +x +x^2 +x^3 + ……+x^9) (x^0 +x +x^2 +x^3 + ……+x^9)…….. (x^0 +x +x^2 +x^3 + ……+x^9) (x^0 +x +x^2 +x^3 + ……+x^9) 10 times

==(x^0 +x +x^2 +x^3 + ……+x^9)^10

We require a coefficient of x^10 or x^10k in (x^0 +x +x^2 +x^3 + ……+x^9)^10

(x^0 +x +x^2 +x^3 + ……+x^9)^10

==[[1(1 – x^10)/(1-x)]]^10

=={[1- x^10]^10}{[1-x]^(-10)}

Now in the above series we can always find a coefficient of x^10 or x^10k

6. We first line them up and ask first (n-1) persons to divide the object into 1/n parts each.The last person cannot divide and we have n parts.Then the “choosing” of the part follows the reverse order i.e. the last person chooses first and then the second-last and so on. The first person virtually has no option but to take away the left piece.The first person does not choose and the last person does not cut!

7. A = 3(area of sector describing 30 degrees) – 2(area of equilateral triangle)

= 3(π/6) – 2(root3 / 4) since radius of circle = length of side of triangle = 1 unit

= π/2 - root3 / 2= 0 .705 sq.units

8 . f(32)=f(16+16)=f(16*16)=f(256)=37656

f(68)=f(64+4)=f(64*4)=f(256)=f(32)=37656