Friday, September 26, 2008

Math Queries

Hello Students
Enter your doubts and queries below by clicking at 'comments' below.
I will try to solve them as soon as possible.

Dr. Pragati jain

Click here to Download a complete Mathematics Equations and formulae reference.


shreyans said...

Hello Madam !
Please solve my Query

Q) What will be the nature of


Dr. Pragati Jain said...

Dear Shreyans

This is a general equation ,which represents a circle. The standard form of this Equation is

Comparing your equatiion with this standard form , you will get center = (-g,-f)=(-7/4,-9/4)
and radius = sqrt(g2+f2-c)=5/(2sqrt(2))

shreyans said...

Thank You Madam !

Awanish said...

Mam what is the genral and better solution for transportation problem by which we can reverse check our answer

sandeep said...

Respected Madam,
I have problem in dual simplex method.

Dj said...

Hello Mam A Very Good Morning to you, im very glad to visit your blog it will surely help the students and any other person facing problems and need a speedy solution to their problem, and if i'll have any sort of problem in mathematics i'll let u know!!!
Dhawal Joshi

chetan said...

A Very Good morning to you mam,this is very useful blog and nicely designed in keeping mind the problems we face in day-today life specially in mathematics.

I hope that it is useful today and it will be very usefull for us in oue examination time.As such i dont have any query right now mam but i will definitely post my queries if i will have any.One more thing mam,I heartly feel that one who is devoted by heart can only make such efforts and u have made it.

Thank You mam.

mit said...

Hello Mam, A Very Good Morning to you,this is best blog i have seen ever.this is very interactive blog for the this students can directly intrect with faculty.

Thank you mam for this kind of facility which is provided by you.
Thank you mam

Sanju Mahawar said...


My question is

"What is i to the Power of i" ?

I mean to say i is called iota and its value is root of (-1) so how?

And second thing,

If I write z = a + bi,

so please tell me the value of power of i



avinassh tiwari said...

Good Morning madam,this is most interactive site ,i have no queries ,but if i will have any query ,i will ask it to u.

it will be helpful for us whether we will be studying in sims or will be placed at some company.

thanks madam

Rattle Snk said...

It had been really always a point of despair for a student, when he/she is solving problems and at some point, math's fear overshadow a student's confidence and sometimes it is very difficult to ask someone for solution,specially when chronological factors are there. So this sort of blog where one can not only get his problems solved also can discuss about the queries or the other ways to approach a single problem.
Hopefully many of us will get advantage of this...............

Shashank Jain said...

Its realy nice to have a blog about mathematics problem by my favorite teacher....thank you mam.

If i will have any query then i will post here...

thank you mam


Shashank jain

Dr. Pragati Jain said...


The most ideal method to find the general solution of transportation problems is Vogels Approximation method.

Dr. Pragati Jain said...


Please point out clearly that in which step you are having problem while solving Dual Simplex Method.

Saloni said...

Hello Madam !
got to know about ur blog from shreyans...

It's really nice..
As of now I have no doubts but I would post them later

sanjay said...

hello madam

my problem is:

there are 3 circle of radii 72cm,49cm and the 3rd radii isn't given .these three circles lie on the same tangent.Find the area of the smallest circle.

richa d/o sanjay

PRATeeK said...

Hello Madam,

I face a difficulty to solve the n th
root of a number. Is there any short trick for that?

aayush said...

show that the f(x)defined by f(x)=|x|+|x-1|is derievable at x=0 and x=1

rahul jain said...

hello mam !

Is step input function countinous
at x=0 ?

if f(x)= 1 for x>0,
0 for x<=0

aditya said...

hello mam
my question is
find the no. of all integer sided isosceles obtuse angled triangle with perimeter 2008.

benu said...

A wheel of outer radius 10 cm inner radius 5 cm takes 10 revolution why the distance coverd by both the outer and inner wheel is not same ?Can you pls. clear this querry

Vicky said...

Hello Madam,
My name is vicky. I have applied to some universities in UK for MBA.One of those university has asked me to take Test which is having two section Numeric reasoning and verbal reasoning.
I am facing problem in numeric reasoning where pattern of questions is a bit different and little bit similar to GMAT questions.I have solve those questions with the help of Facts and figures presented in statistical tables.can u plz guide me how can solve that kinda a questions.i m sending you a link where sample question are there.

Dr. Pragati Jain said...

@ prateek

There's no such short trick.
visit : for higher roots.

Dr. Pragati Jain said...

@ Rahul
unit step function, is a discontinuous function whose value is zero for negative argument and one for positive argument. It seldom matters what value is used for H(0), since H is mostly used as a distribution.

Dr. Pragati Jain said...

@ aditya

let x be length of 2 equal sides and y the length of the 3rd with x,y integers.
so we have
2x+y=2008 x>0 y>0
if it is obtuse then y is longest
let t be angle across from y
we have
now if t>90 then cos(t)<0 so we have
2x^2< y^2
but 2x+y=2008 so y=2008-2x
now we also have
so there are 588-502+1=87 such triangles.

jeetu said...

Hello Madam !
my Query is
while adding ten two digit numbers the digits ofone of the numbers were interchanged. As the result sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of that original number is ten less than the number. what is the product of the digits of that number?

Vishal said...

what is the equation for the point A(2,3)& B(2,-2)?What is the slope ,Distance???

sunil said...

Hello Madam!
Please tell us how to calculate h.c.f.

Dr. Pragati Jain said...

@ vishal

Equation of the line is

slope= infinity
distance= 5

Dr. Pragati Jain said...

@ sunil

Factorization Method:
Express each one of the numbers as product of prime factors.
The product of least powers of common prime factors gives HCF.

Greatest Common Measure of 36, 90, 72.

Step1: Express the numbers as product of prime factors.
36 = 22 × 32
90 = 2 × 5 × 32
72 = 23 × 32

Step2: Take the prime numbers with least power and is present in all sets.
2 and 3 are the prime number common to all given numbers.

The least power of 2 in the set is - 2
The least power of 3 in the set is - 32

Step3: Product of the numbers taken.
32 × 2 = 9 × 2 = 18

So 18 is the H.C.F (Highest Common Factor) of the numbers.

krutika said...

hello mam
q. lim(x-0)xcosx+sinx/x2+tanx

kush said...

hello madam ....

can u plz tell me dat r u comfortable in solving problem business mathematics (b.coM)

plz reply..

by e-mail.......

i shall very thankful of u?///

Dr. Pragati Jain said...

@ aayush

the function f(x)=|x|+|x-1|
is continous,but not derivable
at 0 and 1.

Dr. Pragati Jain said...

@ kush

Though it is not my field of specialisation , I will try my best to answer ur queries.

Dr. Pragati Jain said...

@ Vicky

well this book might help you

download it and prepare well

Best of luck !

R K Gupta said...

I,parent of shalini gupta send my best wishes for developing such useful blogspot for the students for the right and useful direction in math.

Dr. Pragati Jain said...

@ R. K. Gupta

Dear Parent

Thank you for your good wishes.I shall try my level best to solve students' mathematical problems.

Dr. Pragati Jain said...

@ Krutika

By using property of limit
lim x→0 ( f(x)+g(x))= lim x→0 f(x)+ lim x→0 g(x)
lim x→0 xcosx+ lim x→0 sinx/x2+ lim x→0 tanx
=0+ lim x→0 (cosx/2x)+0
= lim x→0 (-sinx/2)=0
use L-Hospital rule for the middle term.
L-Hospital rule is used for cases that reduce to an undeterminable condition of zero/zero in the limit or if the limit is infinity , then
lim x→0 (f(x)/g(x))
=lim x→0(f'(x)/g'(x))

PRATeeK said...

hello mam,

on solving

i am getting

which is not correct.

please help me how to solve this.

Dr. Pragati Jain said...


Taking log both sides
=(a+1+2x)log {(a+x)/(1+x)}
=( a+1+2x) {log(a+x)-log(1+x)}
{1/f(x)}f’(x)=2{log(a+x)-log(1+x)} +( a+1+2x){(1/(a+x)) – (1/(1+x))}
Put x=0 and f(0)= a^(a+1) and using log 1= 0
f’(0)= 2a^(a+1)log a + a^a{(1-a)^2}

abhishek daniel said...

mam can u tell me question related to enggineering...........

krutika said...

Thank you mam

chirag said...

good evening ma'am

plz clear my doubt

Q. INTEGRATE tan-1x.1/x

PRATeeK said...

thanks mam...

how did u get this idea to create a blog?

its really a nice way to help the students.

chirag said...



Dr. Pragati Jain said...

@ chirag
Dear, check ur query, otherwise
For ∫tan^ -1x/x dx
Put tan^-1x=t, 1/(1+x^2)dx=dt and x= tant

= 2∫t cosec2tdt

Now integrating by parts , ans will be

2{-tan^-1t/2.log (cosec2t+cot2t)

Dr. Pragati Jain said...

@ Abhishek
Yes, u can ask Eng. Math.

Dr. Pragati Jain said...

@ Prateek

I just wanted to do something innovative to help students.That's why I created this special blog for you people.

sanket said...

hello mam!

Dr. Pragati Jain said...


seca(1-sina)(seca + tan a)
=(seca-tana)(seca + tana)
=sec^2a - tan^2a

gurashish said...

evaluate tan65/cot25

Dr. Pragati Jain said...



amit said...

my :9406883562.

thanking you
with regards :

Dr. Pragati Jain said...


Dear Amit

I know the syllabus of B.C.A V Sem.It covers Abstract algebra, Linear algebra and Discrete Maths.
If u have any difficulty , then u can communicate me through this blog.

isha said...

hi mam isha here...
really a nice blog...!!! glad to visit it..!!!!!

Aniket said...

Hello mam can you solve this question for me.


Dr. Pragati Jain said...

@ Aniket

You have written only a function..
What's th query ?

Dr. Pragati Jain said...

@ Dear Aniket
You didn't mention in your question, what has to be found out? :(

If you want to integrate the function within the limits (0,2l), your ans. will be e^2l-1.

fake86 said...

nidhi sachdeva:- good morning mam

give an example of ring which is artinian but not noetherian... and explain it

poorwa said...

hello ma'am
can you please solve this que.
*evaluate lim x tends to y (x^y-y^x)/(x^x-y^y)

Pranjal said...

Hello mam,
Please solve my questions.
I m a 10th class student...

Q)Find the coordinates of the circumcentre of a triangle whose vertices are A(4,6), B(0,4) and C(6,2). Also, find its circumradius.

Q)The mid-points of the sides of a triangle are (3,4), (4,6) and (5,7). Find the coordinates of the vertices of the triangle.



Dr. Pragati Jain said...

@ Pranjal

Ans-1 The circumcentre is the centre of the circumcircle which passes through the vertices A, B, C of the triangle.
Let the circumcentre be P(x, y), then
PA = PB = PC (circumradius)
x2- 8x + 16 + y2- 12y + 36 = x2 + y2 - 8y + 16

x2- 8x + 16 + y2- 12y + 36 = x2-12x + 36 + y2- 4y + 4

Subtracting (2) from (1), we have

5y = 15
y = 3

Substituting y=3 in (1), we get

2x + 3 = 9
2x = 6
x = 3

Circumcentre P = (3, 3)

Circumradius = PA =PB =PC = sqt 10


Let the coordinates of three vertices are (x1,y1), (x2,y2),

Now (x1+x2)/2=4
Similarly y1+y2=12

On solving these equations, we get
(2,3), (6,9) and (4,5).

Pranjal said...

Thank you mam.....

pranshu said...

Hello ma'am!
pls. solve foll. query.
Q:-Two vessels A and B contain mixtures of spirit and water. A mixture of 3 parts from A and 2 parts from B is found to contain 29% of spirit and a mixture of 1 part from A and 9 parts from B is found to contain 34% of spirit. Find the %age of spirit in A and B respectively

Dr. Pragati Jain said...

@ Pranshu
For 100 lit.
x% of 3/5 x 100 + y% of 2/5 x 100
= 29% of 100
so 3x/5 + 2y/5 = 29 ---(1
x/10 + 9y/10 = 34 ---(2

Solving above two equations
x = 25% & y = 35%

shreyans said...

Can You Help Me with GRE Maths !

Dr. Pragati Jain said...

@ Shreyans
Yes ! Just post your queries here !

rishi said...


Dr. Pragati Jain said...

@ rishabh
In a recent survey, readers indicated that the hardest thing about math was learning the formulae. To improve this skill, following points are useful to reduce Math Phobia
•Read Ahead
•Know the meaning
•Keep a list of symbols
•Absorb the formulas via different channels
•Use memory techniques
•Know why
•Deal with cramps right away
•Stay in training

Akriti said...

Find the length of the tangent of the circle x^2 + y^2 - 2x -2y +4 = 0 drawn from the point (2,3).

Anu said...

hi mam,
i would like to know how to find the radius of curvature of x3+y3=3axy at the point (0,0).

Anu said...

what is i to the power i?

shruti said...

please help with this question: a2 +2b=7
find the value of a2+b2+c2

Desert Sheikh said...


Shivam said...

Hello ma'm my query is-
find an equation of right circular cylinder whose radius is r and axis the line x-a/l = y-b/m = z-c/n.
l,m,n being dir ratios.

lokesh sharma said...

Dear mam,
My problem is on integration, which i can't publish through comments with the help of keyboard. Therefore, I am mailing you my problem.
Plz solve it as soon as possible.
Its urgent for me.

lokesh sharma said...

Dear mam,
My query is on integration, given as follows:-

∫[a/(sin^4 y - a^2 sin^2 y)] dy
Where, a is constant, y is variable.

lokesh sharma said...

Dear mam, my problem is on integration, which is given as follows:-

∫ a/√(sin^4 θ-a^2 sin^2 θ) dθ

Plz solve this as soon as possible.
Its urgent for me..........

Shantanu Tiwari said...

The angle in one regular polygon is to that in another as 3:2 and the number of sides in first is twice that in the second.Determine the number of sides of two polygons.

Devansh Shah said...

1, 3, 6, 10, 15,....5151. Find the average of 101 numbers?

Quickly reply ...

Rizwan Iqbal said...

Q) Devise a test for whether a point is inside a convex polygon based on the idea that a polygon can be described by a set of intersecting lines in a single plane?

pallavi aggarwal said...

what is the area of a rectilinear fiqure with dimentions 42,54,64,59ft?

pallavi aggarwal said...

what is the area of a rectilinear fiqure with dimentions 42,54,64,59ft?

Parvathy Subhash said...


A & B hold a property in the ratio 50:50. If A wishes to buy B s share of the property @ a price of 55 crore and pays only 25 crore upfront how much portion of B s property still belongs to B for the unpaid 30 crore

nova hu said...

what is the exact solution of this (5-6)-5=?
iam saying -6 but some one says +5 which is correct how plese tell me

nova hu said...

what is the exact solution of this (5-6)-5=?
iam saying -6 but some one says +5 which is correct how plese tell me

Nitesh Thakur said...

24 men can do 10 hours daily .they can do a work in 90 days.if 45 men can do 8 hours daily then in how many days they can do half of that work??



venkat said...

Dear Madam,

how can i calculate the variance of y function
Y = ∑Di + ∑Dj
where i = 0 to i = n
j = 0 to j = n-l

i, j represents the time period
n,l are constants
also it can be assumed that D varies between a & b (both a, b are constants)

Divyanshu Singh said...

Dear madam

In a parallelogram ABC,|AB| = a, |AD| = b and |AC| = c, then DA.AB
has the value?
Here AB, AD,AC, DA, and AB are all vectors.


A father is 24 years old than his daughter in 4 years. The father will be 3 years old as his daughter. Find the present age of the father and daughte

Khushi Kaushal said...

Can someone help me in the following question:
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial : x^4 + 1 ; x - 1.


(A) If Rs 5000 is deposited every month @ 8 % interest..then what is the Net amount after 5 years. How to make a formula for this ?

(B) What I s the rate of interest if on depositing Rs 5000 every month for 5 years , the net amount acrued is Rs 5 lakh ? How to make a formula to calculate this ?

venkat said...

Total amount at the end of 5 years = (EMI/i) *( (1+i)^n - 1 )
= (5000/.66%) * ((1+.66%)^60 - 1)
= 3,67,384

EMI = monthly deposit
i = interest rate per month
ensure every thing is in months i.e interest rate is (8/12) or 0.66% per month
and tenure is 60 months

B) you can use the same formula of A.
since, i is raised to power n, it is difficult to resolve with calculator.
you can work with hit and trail of applying different interest rates (greater than 8% in this case).


Sin theta -cos theta-1 divided by sin theta+cos theta-1=1 divided by sec theta-tan theta.prove it.

vaibhav srivastava said...

Prove That:-
1+cos 56+cos 58+cos 66=4 cos28 cos 29 sin 33

Sweety Rustagi said...


Sweety Rustagi said...


Unknown said...

there are 9 boxes and 100 stones...distribute stones in all boxes..using only even nunberss...and also we cant use 0&1

Pardeep Chhabra said...

The area of a semicircular region is 308 cm2. Then its perimeter will:

44 cm
72 cm
28 cm
36 cm

Pardeep Chhabra said...

the sum of integers from 1 to 100 that are divisible by 2 or 5 is


Hanumanth Rao said...

I have a simple question. My son is in class 3, I was trying to explain him division. I gave an example of 6÷2 that if he has 6 chocolate and if he distributes to 2. Then he asked about 0÷2, to which I replied if u don't have any you can't give any so answer is 0.
Next is 5÷0, his logic is he has 5 and he doesn't have to distribute to any so it should be 5. I studied it is undefined/infinite, How do I explain him.

shubham raturi said...

The maximum of the areas of the isosceles triangles with base on the
positive x-axis and which lie below the curve y = e^-􀀀x is:

Hyderabad home Tutions said...

Hello,Goodday,this is best blog i have seen ever.this is very interactive blog for the this students can directly intract with faculty.

For tutions all over india contact:+91 7036810501.

Unknown said...

what is integration of root x by underoot x cube- a cube

Unknown said...

How can cumulative frequency polygon can be a polygon ?

kamala kannan said...

Hello madam. I have a doubt regarding transversal lines. Can you explain the formation of all angles when there are two intersecting transversals?

Chetan Maheshwari said...

There are five subjects namely A(40), B(50), C(60), D(80) and E(70) and one student scored 28, 31, 40, 64 and 35 in the respective subjects. The marks shown in parentheses are their total marks of the respective subjects.
Now, what would be the percentage of marks obtained by the student?
If, i go by direct method, i.e. marks obtained/total marks X 100 then
(28 + 31 + 40 + 64 + 35) X 100/(40 + 50 + 60 + 80 + 70) = 19800/300 = 66.00%
If, i go by converting each and every subject equivalent to 100 marks then
28 becomes 70; 31 becomes 62; 40 becomes 66.66; 64 becomes 80 and 35 becomes 50 and grand total 300 becomes 500
now percentage with the same formula would be
(70 + 62 + 66.66 + 80 + 50) X 100/500 = 32866/500 = 65.73%
My doubt is why this happens?

venkat said...

@chetan Maheshwari,

in the first method, the subject with higher score gets higher weight-age whereas in the second method, all the subjects have equal weightage

Bhabatosh Pagal said...

sir what will be the answer?

Bhabatosh Pagal said...

sir what will be the answer?


My birth day is in january.what would be a sufficient number of questions with YES/NO answers that will enable one to find my birth date..?
Options are 6,5,3 or 2

Dharmendra Yadav said...

Mam plzz solve this question- A mason can build a tank in 12Hours.after working for 6 hour,he took the help of a boy and finished the work in another 5 hours .the time that the boy will take alone to complete the work is a)30hrs b)45hrs c)60hrs d)64hrs

Unknown said...

Pipe a takes 60min to fill a tank, b takes 75min to fill that same tank. An outlet c also there. a,b,c collectively take 50min to fill same tank. What time is taken by c alone to fill that tank?

Unknown said...

12 unique colours. How many unique 2 colour combinations will there be?

Unknown said...
This comment has been removed by the author.
katrina dragonfaces said...

And no double colours, so no red and red

katrina dragonfaces said...

It's ok. Got it. 132. Assuming 2 positions a and b. Can have red a and green b but also green a and red b.

sushil tiwari said...

Evaluate √5+2√6

sushil tiwari said...

I want to know it full solution

arya Patel said...

If cos -225° = x than what value of x is ?

trapti said...

Please can you helpe how to identify in statement sums whether it is multiplication or division sum. What is the texhnique.

Unknown said...

Two machine selling prise is 240000
One profit 20%
One loss 18 %
Overall profit / loss is
A) 4000 gain
B) 4000 loss
C) 6000 gain
D) 6000 loss

Shivani Jaat said...

Hello mam
Can u solve my question please
The area of a rectangular field is 3584m and its length is 64 m. A boy runs around the field at the rate of 6km/h. How long will take to go 5 times around it??

amitha rao said...

The mean of 5 numbers is 50, out of which mean of 4 numbers is 46. Find the 5th number?

amitha rao said...

The mean of 5 numbers is 50, out of which mean of 4 numbers is 46. Find the 5th number?

amitha rao said...

The mean of 5 numbers is 50, out of which mean of 4 numbers is 46. Find the 5th number?

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