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Maths >> Algebra >> Sequence and Series Others

The sum of three positive real numbers x, y and z is 9. If the largest positive difference between any 2 of the 3 numbers is 5 and these 3 numbers are in arithmetic progression then the product of these 3 numbers will be what .please tell me.

Asked By: S.NANDHINI
is this question helpfull: 10 2 read solutions ( 1 ) | submit your answer
Joshi sir comment

let the numbers are a-d, a, a+d

then according to the given condition    a-d+a+a+d = 9   so  3a = 9   so a = 3

and [a+d]-[a-d] = 5   so 2d = 5 so d =5/2

now solve 

Maths >> Calculus >> Limit Continuity and Differentiability Others

 

 

 

 

Importance High!!!!!!!!!!!!!!!!!

 

Dear Sir / Madam

 

Myself Rajeev Shrivastava, I am putting a signs series in front of you which based on numbers from 01 to 100. Actually I want to know that what reason of behind Approx equability of signs is 

(++), (+-), (--) & (-+) at end of the month or year between the below mentioned.

 

Let's define a kind of mapping:
0↔1
2↔3
4↔5
6↔7
8↔9

(+) means: an Even number
(-) means: an Odd number

I simply say: for any EO (+-) it exists an OE (-+) which is paired to.
And that's true since each E is mapped to a O and vice versa (1 to 1 relation where "f(f(x))=x" ) !
E.g.: 29 ↔ 83

There is 25 numbers in the EO (+-) group, so 25 in OE (+-).
There is 25 numbers in the EE (++) group, so 25 in OO (--).

Picking a number at random between 01 and 100 inclusive is choosing equitably in EO, OE, EE or OO group. (25% for each)

 

So, I really need of your help to solve a puzzle please. I just am trying to make you understand what type of solution I need:

 

There are some results for your review:

MONTH

DATE

DAY

FIRST_SERIES

SECOND_SERIES

FIRST_SERIES

SECOND_SERIES

APR

1

SUN

+

-

-

+

+-

-+

APR

2

MON

+

+

-

+

++

-+

APR

3

TUE

+

-

+

-

+-

+-

APR

4

WED

+

+

+

+

++

++

APR

5

THU

-

+

-

+

-+

-+

APR

6

FRI

+

+

+

-

++

+-

APR

7

SAT

+

-

-

+

+-

-+

APR

8

SUN

-

+

+

-

-+

+-

APR

9

MON

-

+

-

+

-+

-+

APR

10

TUE

+

+

+

+

++

++

APR

11

WED

+

+

-

-

++

--

APR

12

THU

-

+

-

-

-+

--

APR

13

FRI

+

+

+

+

++

++

APR

14

SAT

+

-

+

-

+-

+-

APR

15

SUN

+

-

+

-

+-

+-

APR

16

MON

-

-

+

+

--

++

APR

17

TUE

-

-

+

+

--

++

APR

18

WED

 

 

 

 

 

 

APR

19

 THU

 

 

 

 

 

 

APR

20

 FRI

 

 

 

 

 

 

APR

21

 SAT

 

 

 

 

 

 

APR

22

 

 

 

 

 

 

 

APR

23

 

 

 

 

 

 

 

 

  (Complete sheets for the year 2011 and 2012 are attached with this mail)

 

You can see that there are two times falls in a day of pair make by even (+) and odd (-) signs, i.e. (++), (+-), (--) & (-+) as above said.

The total of pair combination signs become approx equal to each other at the end of the month or year (every year- so, I am sending you attachment to go through the year’s result).

By this analysis:

1-     I want to know that what is the relation between current falling signs and past fell signs.

2-     How can I come to know, what type of combination of sign would be any particular date or day.

3-     As you can seen on 22nd and 23rd April’2012 I don’t know what combination of sign is.

4-     There is surety that there is some relation between current First fall of combination of signs and past fall or First fall of combination of signs and Second fall of combination of signs.

 

Please help me to how come to know what type of fall may be for next day by reviewing past or first combination of signs. So reply or elaborate me with an example.

 

 I would be very grateful to you till entire life.

 

Regards

 

RAJEEV SHRIVASTAVA

 

 

 

Importance High!!!!!!!!!!!!!!!!!

 

Dear Sir / Madam

 

Myself Rajeev Shrivastava, I am putting a signs series in front of you which based on numbers from 01 to 100. Actually I want to know that what reason of behind Approx equability of signs is 

(++), (+-), (--) & (-+) at end of the month or year between the below mentioned.

 

Let's define a kind of mapping:
0↔1
2↔3
4↔5
6↔7
8↔9

(+) means: an Even number
(-) means: an Odd number

I simply say: for any EO (+-) it exists an OE (-+) which is paired to.
And that's true since each E is mapped to a O and vice versa (1 to 1 relation where "f(f(x))=x" ) !
E.g.: 29 ↔ 83

There is 25 numbers in the EO (+-) group, so 25 in OE (+-).
There is 25 numbers in the EE (++) group, so 25 in OO (--).

Picking a number at random between 01 and 100 inclusive is choosing equitably in EO, OE, EE or OO group. (25% for each)

 

So, I really need of your help to solve a puzzle please. I just am trying to make you understand what type of solution I need:

 

There are some results for your review:

MONTH

DATE

DAY

FIRST_SERIES

SECOND_SERIES

FIRST_SERIES

SECOND_SERIES

APR

1

SUN

+

-

-

+

+-

-+

APR

2

MON

+

+

-

+

++

-+

APR

3

TUE

+

-

+

-

+-

+-

APR

4

WED

+

+

+

+

++

++

APR

5

THU

-

+

-

+

-+

-+

APR

6

FRI

+

+

+

-

++

+-

APR

7

SAT

+

-

-

+

+-

-+

APR

8

SUN

-

+

+

-

-+

+-

APR

9

MON

-

+

-

+

-+

-+

APR

10

TUE

+

+

+

+

++

++

APR

11

WED

+

+

-

-

++

--

APR

12

THU

-

+

-

-

-+

--

APR

13

FRI

+

+

+

+

++

++

APR

14

SAT

+

-

+

-

+-

+-

APR

15

SUN

+

-

+

-

+-

+-

APR

16

MON

-

-

+

+

--

++

APR

17

TUE

-

-

+

+

--

++

APR

18

WED

 

 

 

 

 

 

APR

19

 THU

 

 

 

 

 

 

APR

20

 FRI

 

 

 

 

 

 

APR

21

 SAT

 

 

 

 

 

 

APR

22

 

 

 

 

 

 

 

APR

23

 

 

 

 

 

 

 

 

  (Complete sheets for the year 2011 and 2012 are attached with this mail)

 

You can see that there are two times falls in a day of pair make by even (+) and odd (-) signs, i.e. (++), (+-), (--) & (-+) as above said.

The total of pair combination signs become approx equal to each other at the end of the month or year (every year- so, I am sending you attachment to go through the year’s result).

By this analysis:

1-     I want to know that what is the relation between current falling signs and past fell signs.

2-     How can I come to know, what type of combination of sign would be any particular date or day.

3-     As you can seen on 22nd and 23rd April’2012 I don’t know what combination of sign is.

4-     There is surety that there is some relation between current First fall of combination of signs and past fall or First fall of combination of signs and Second fall of combination of signs.

 

Please help me to how come to know what type of fall may be for next day by reviewing past or first combination of signs. So reply or elaborate me with an example.

 

 I would be very grateful to you till entire life.

 

Regards

 

RAJEEV SHRIVASTAVA

 
Asked By: RAJEEV SHRIVASTAVA
is this question helpfull: 8 1 read solutions ( 1 ) | submit your answer
Joshi sir comment

If you are making the sequence on the basis of dates then you should take signs accordingly then you can make this sequence for many years

for example if you take 23 june then first sign series will be +-, + for even number and - for odd number , now as conversion rule as you gave in your explanation 23 will be converted to 32 so second series will be -+

similarly you can make it for any date 

for example 29 december first series will be +- and its conversion is 38 so next series will be -+

if you are thinking something else then explain your question correctly 

Maths >> Calculus >> Differential Equations IIT JEE

how to find differential eqn. of all conics whose axes coincide with coordinate axes??   tell me the eqn. of tht. conic

Asked By: SHALINI SINGH
is this question helpfull: 10 4 submit your answer
Joshi sir comment

Parabola   eq.  y2 = 4ax ,

on differentiating this eq. with respect to x we get 2y(dy/dx) = 4a                        

on taking this value of 4a in eq. y2= 4ax we will get the differential eq. of parabola.

similarly for ellipse    x2/a2  +   y2/b2  =   1

on differentiaing this eq. twice we will get two additional eq. 

by solving these eq. get an eq. free from a and b, this will be the differential eq. of the ellipse.

similarly for hyperbola

 

 

 

Maths >> Trigonometry >> General Trigonometry IIT JEE

Which of the following angles are co-terminal angles: 480  ,   -240  or 600

how can we get it which is co-terminal and what does co-terminal means?????

Asked By: AMBUJ SINGLA
is this question helpfull: 1 1 submit your answer
Joshi sir comment

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.  For example 30°, –330° and 390° are all coterminal.

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 360° if the angle is measured in degrees or 2π if the angle is measured in radians.

 

480 and -240 are co terminal angles because 480-360 = 120 and -240+360 = 120

Maths >> Trigonometry >> General Trigonometry IIT JEE

is there any need to know or learn the proof pf formulas of trigo

 

Asked By: AMBUJ SINGLA
is this question helpfull: 2 0 submit your answer
Joshi sir comment

No, For making a good command in trigonometry, only implementation is a need. But for your knowledge you can proof these results

Maths >> Algebra >> Set Theory and Relations IIT JEE

number of real  values of x satisfying 2log2(x+7x+1)+log2(x+1x-1)=1  is

Asked By: SHUBHAM VED
is this question helpfull: 2 1 read solutions ( 1 ) | submit your answer
Joshi sir comment

given eq. can be written as log2 [(x+7)/(x+1)]2 + log2 [(x+1)/(x-1)] = 1

or log2 [(x+7)2(x+1)/(x+1)2(x-1)] = 1

or log2 [(x+7)2/(x2-1)] = 1

or (x+7)2/(x2-1) = 2

or x2 + 14x +49 = 2x2 - 2

or x2-14x -51 = 0

or x = -3, 17

since at x = -3 first part will become negative inside root so it will not be a root.

so only 1 root

Maths >> Algebra >> Permutation and Combination IIT JEE

If the letters of the word are arranged as in dictionary, find the rank of the word INDIA.

Asked By: UMESH
is this question helpfull: 4 5 submit your answer
Joshi sir comment

On arranging the letters in ascending order we will get

A D I I N

total no of words = 5*4*3*2*1/2*1 = 60

rank = (60/5)*2 + (24/4)*3 + (6/3)*1 + (2/2)*1 + 1 = 24+18+2+1+1 = 46

here 60/5 means total words/ total letters and 2 is here because in INDIA, I is first letters and this comes at 3rd and 4th place in ascending order arrangement so total letters before it are 2. similarly 24 stands for total words after removing I from the spelling of INDIA and etc 

Maths >> Algebra >> Equation and Enequalities Others

4[3t+17]=10

Asked By: GLADNESS
is this question helpfull: 2 0 submit your answer
Joshi sir comment

let [ ] is greatest integer function

so 4[3t+17] = 10

or [3t+17] = 2.5

since greatest integer function can not be non integral so no t is possible.

 

now if [ ] is a normal bracket

then 3t+17 = 2.5 or 3t = -14.5 or t =-14.5/3 = -145/30 = -29/6

Maths >> Vector and 3-D >> Plane Others

Is area always a vector quantity or it can be a vector quantity?

Asked By: AMIT DAS
is this question helpfull: 3 1 submit your answer
Joshi sir comment

generally it is scalar but in the measurement of flux through a surface it is considered a vector perpendicular to the surface with same magnitude 

Maths >> Algebra >> Set Theory and Relations IIT JEE

The number of solutions of :  4x²-4x+2 = sin² y   &     x²+y² ≤ 3    are ?    (please solve it graphically i am getting one solution by using graph but the answer is 2)

Asked By: AMIT DAS
is this question helpfull: 3 2 submit your answer
Joshi sir comment

Given eq. can be written as (2x-1)2 + 1 = sin2y

and max. of siny is 1 so only possible value of x = 1/2

and possible values of y = ±nπ/2  where n is odd integer

but by drawing the circle of 2nd eq. we find that only y = ±π/2 are possible values so answer will be 2

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