Some change has happened in the syllabus for the isc 2010 12th exam for maths, compared to syllabus for last year. You can view the latest syllabus at cisce.org or in particular cisce.org/syllabus.jsp

The question papers of past years of the karnataka board +2 pre university course puc may be available at

pue.kar.nic.in or pue.kar.nic.in/questionbank.htm

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## Saturday, December 19, 2009

## Tuesday, December 15, 2009

### Usha bank

I recently read about how some commercial sex workers in Sonagachi in Calcutta, West Bengal , had set up a cooperative bank called Usha cooperative bank, with the help of an NGO called Durbar mahila samanwaya committee. The aim seems to be to reduce the influence of goons and moneylenders. It seems to be a success. There seems to be some idea of opening branches and going into some other business ventures.

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## Tuesday, December 8, 2009

### trivandrum to leepuram near kanyakumari

journey from trivandrum to leepuram near kanyakumari

Recently I went to visit someone in leepuram near kanyakumari.

We started out around 11am from trivandrum. The roads were not that crowded at that time.After the overpass over the railway line at nagercoil, the road divides into two. When we go to thirunelveli, we usually take the one on the left and the other one if we want to go into the town. But for going to kanyakumari, I think it is better to take the road on the right, especially if you are not conversant in Tamil, as there are boards all along the way in english and tamil.

Anyway we took the road along the left, went someway and asked some autodriver about the way. He pointed us the along the road that went straight through the town, along the bus stand and some market street, both of which were very congested at that time, and there were some unmarked bumps near some school or something.

After that you go along NH47 towards kanyakumari. The view on both sides is nice with paddy fields, coconut trees and small water bodies. I also noticed some fields with tapioca.

After going along NH47 for around 20 km we asked for directions at a wayside shop and the person gave directions to a road along the left which led us to some place called kottaram and vattakotai (circular fort) .There were some potholes on this road. From there leepuram was around 3 kms away towards the right from the junction.

(just before vattakotai some large scale construction on some highway or something seems to be going on)

For the return journey , after coming back to NH47, we just followed the boards on the traffic signals at the junctions. This time round we avoided coming through the inside of nagercoil. Just outside the town, there are roadside vendors selling tender coconuts and nongu sherbet (nongu is the fruit of panamaram a type of palm tree).

Nongu is a lot cheaper and fresher than one can get in trivandrum.

But on the return journey the road was a lot more congested, especially near martandam, the kaliyakkavila border, pappanamcode etc. and it took more than 1 hour to cover the last 25km.

Anyway I think the best time for this route would be in the early morning before 7am (very sparse traffic but the buses might come at you on the wrong side of the road when they are overtaking etc) or around 11am (light to medium traffic).

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Recently I went to visit someone in leepuram near kanyakumari.

We started out around 11am from trivandrum. The roads were not that crowded at that time.After the overpass over the railway line at nagercoil, the road divides into two. When we go to thirunelveli, we usually take the one on the left and the other one if we want to go into the town. But for going to kanyakumari, I think it is better to take the road on the right, especially if you are not conversant in Tamil, as there are boards all along the way in english and tamil.

Anyway we took the road along the left, went someway and asked some autodriver about the way. He pointed us the along the road that went straight through the town, along the bus stand and some market street, both of which were very congested at that time, and there were some unmarked bumps near some school or something.

After that you go along NH47 towards kanyakumari. The view on both sides is nice with paddy fields, coconut trees and small water bodies. I also noticed some fields with tapioca.

After going along NH47 for around 20 km we asked for directions at a wayside shop and the person gave directions to a road along the left which led us to some place called kottaram and vattakotai (circular fort) .There were some potholes on this road. From there leepuram was around 3 kms away towards the right from the junction.

(just before vattakotai some large scale construction on some highway or something seems to be going on)

For the return journey , after coming back to NH47, we just followed the boards on the traffic signals at the junctions. This time round we avoided coming through the inside of nagercoil. Just outside the town, there are roadside vendors selling tender coconuts and nongu sherbet (nongu is the fruit of panamaram a type of palm tree).

Nongu is a lot cheaper and fresher than one can get in trivandrum.

But on the return journey the road was a lot more congested, especially near martandam, the kaliyakkavila border, pappanamcode etc. and it took more than 1 hour to cover the last 25km.

Anyway I think the best time for this route would be in the early morning before 7am (very sparse traffic but the buses might come at you on the wrong side of the road when they are overtaking etc) or around 11am (light to medium traffic).

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## Friday, December 4, 2009

### geojit bnp paribas online investing

I used to prefer only bank recurring deposits and bank fixed deposits. But some years ago , when the stock market indices were close to their peak, I was drawn towards stocks. At that time mutual funds seemed to be a nice option.

As I was using State Bank of India, I started off with SBI mutual fund, I made some investment in SBI Taxgain, SBI muticap, SBI global, SBI multiplier 93 all of which were dividend option. At that time the NAV made some nice gains of about 20 to 25 % in around 7 to 8 months on paper and I got some dividend (but nowhere near the gains on paper) from the funds except for SBI global.

So in retrospect, I should have redeemed/sold the units (except for taxgain scheme which is locked for 3 years) at that time and pocketed the gains .

But since I was new to the concept of mututal funds I did not do anything, then the market indices crashed, there was recession in the US etc and the NAV declined by around 40% from the level when I bought the units of the funds.

After that some of the NAV's have recovered somewhat.

So I decided to learn how to invest directly in stocks instead of depending on others.

I looked around at the brokerage options available. There was Hedge equities opposite LIC buildings at Pattom, Capstocks also near pattom and also at east fort, Sharekhan on the road from spencers to bakery junction , geojit bnp paribas opposite smv school etc.

After talking to the persons in the various offices and spending some time reading reviews on the internet, I decided to go to geojit. They asked for money in cash(not cheque) for the application form. I filled up the form/booklet and had to affix my signature at around 20 or more places in that booklet. So you should be prepared to spend at least one hour and read everything before signing up. You also might need to give an email id since they send the contract notes by email if you are using online trading

I went in for the online option. I initially had some problem with the login password , password for the encrypted pdf file which contained the login password etc ( they mention a particular version of adobe which did not work on windows 98 and the older version of adobe did not seem to handle the encryption properly, so I had to use another pdf reader ) . Anyway after that initial hiccup , there does not seem to be any problem.

I paid the initial investment amount by cheque (There is online transfer option from some banks). It took 2 or 3 days for the amount to be available in my account.

One thing to remember is that there seems to be a minimum transaction limit of Rs.1000/- and a minimum brokerage of around Rs.20/- per transaction.

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As I was using State Bank of India, I started off with SBI mutual fund, I made some investment in SBI Taxgain, SBI muticap, SBI global, SBI multiplier 93 all of which were dividend option. At that time the NAV made some nice gains of about 20 to 25 % in around 7 to 8 months on paper and I got some dividend (but nowhere near the gains on paper) from the funds except for SBI global.

So in retrospect, I should have redeemed/sold the units (except for taxgain scheme which is locked for 3 years) at that time and pocketed the gains .

But since I was new to the concept of mututal funds I did not do anything, then the market indices crashed, there was recession in the US etc and the NAV declined by around 40% from the level when I bought the units of the funds.

After that some of the NAV's have recovered somewhat.

So I decided to learn how to invest directly in stocks instead of depending on others.

I looked around at the brokerage options available. There was Hedge equities opposite LIC buildings at Pattom, Capstocks also near pattom and also at east fort, Sharekhan on the road from spencers to bakery junction , geojit bnp paribas opposite smv school etc.

After talking to the persons in the various offices and spending some time reading reviews on the internet, I decided to go to geojit. They asked for money in cash(not cheque) for the application form. I filled up the form/booklet and had to affix my signature at around 20 or more places in that booklet. So you should be prepared to spend at least one hour and read everything before signing up. You also might need to give an email id since they send the contract notes by email if you are using online trading

I went in for the online option. I initially had some problem with the login password , password for the encrypted pdf file which contained the login password etc ( they mention a particular version of adobe which did not work on windows 98 and the older version of adobe did not seem to handle the encryption properly, so I had to use another pdf reader ) . Anyway after that initial hiccup , there does not seem to be any problem.

I paid the initial investment amount by cheque (There is online transfer option from some banks). It took 2 or 3 days for the amount to be available in my account.

One thing to remember is that there seems to be a minimum transaction limit of Rs.1000/- and a minimum brokerage of around Rs.20/- per transaction.

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## Tuesday, November 10, 2009

### Is google buying admob

google might be trying to buy admob. Admob is related to advertisement on mobile phones.This might tie up nicely with the adsense for mobile program.

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## Monday, November 9, 2009

### advertising with google adsense

Trying to increase your revenue from the web

Google adsense is highly useful for sites with lot of searchable content(keywords).

The wide range of advertisers is very useful.

Your website will have to get approved for using google adsense.

The advertisements are pay per click type and are usually relevent to the content of the web page.

There are other options like adbrite, yahoo , clicksor, chitika etc

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Google adsense is highly useful for sites with lot of searchable content(keywords).

The wide range of advertisers is very useful.

Your website will have to get approved for using google adsense.

The advertisements are pay per click type and are usually relevent to the content of the web page.

There are other options like adbrite, yahoo , clicksor, chitika etc

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## Wednesday, November 4, 2009

### Triangular distribution

Triangular distribution

pdf f(x) , mean and variance of the triangular distribution are given below

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pdf f(x) , mean and variance of the triangular distribution are given below

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## Friday, October 23, 2009

### word problem 5

The area of a right angle triangle is 63 sq.cm. The length of the base of the triangle is 5 cm. more than the altitute of the triangle. Find the length of the altitute of the triangle.

let the length of the altitute be x cm.

therefore length of the base is ( x + 5) cm.

area of the right angled triangle is (1/2) * base * altitude = (1/2)(x)( x + 5 )

but given that area = 63

therefore

(1/2)(x)( x + 5 ) = 63

or x(x+5) = 126

or

x ² + 5x - 126 = 0

solving

x ² + 14x -9x - 126 = 0

x( x +14 ) - 9( x + 14 ) = 0

( x - 9 ) ( x + 14 ) = 0

x = 9 or x = -14

ignoring negative value for x

x = 9 cm

therefore length of the altitude = 9 cm.

other word problems with some explanation

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let the length of the altitute be x cm.

therefore length of the base is ( x + 5) cm.

area of the right angled triangle is (1/2) * base * altitude = (1/2)(x)( x + 5 )

but given that area = 63

therefore

(1/2)(x)( x + 5 ) = 63

or x(x+5) = 126

or

x ² + 5x - 126 = 0

solving

x ² + 14x -9x - 126 = 0

x( x +14 ) - 9( x + 14 ) = 0

( x - 9 ) ( x + 14 ) = 0

x = 9 or x = -14

ignoring negative value for x

x = 9 cm

therefore length of the altitude = 9 cm.

other word problems with some explanation

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### word problem4

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number is equal to 3 less than four times the original number. What is the original number?

let digit in unit's place be x and that in ten's place of the original number be y

original number = 10y + x

given

x + y = 7 ----------(i) (sum of digits)

after the digits are reversed, the new number is 10x + y

given that new number = 4*(original number ) -3

therefore ( 10 x +y) = 4*(10y + x ) - 3

or 10x + y = 40y + 4x - 3

or 6x -39 y = -3 ----------(ii)

system is

x + y = 7 ----------(i)

6x - 39 y = -3 ----------(ii)

solving

eliminating x

6x + 6y = 42----------(i)

6x - 39 y = -3 ----------(ii)

subtracting

45 y = 45 or y =1

substituting x + 1 = 7 or x = 6

therefore

x = 6 , y = 1

original number = 16

other word problems with some explanation

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let digit in unit's place be x and that in ten's place of the original number be y

original number = 10y + x

given

x + y = 7 ----------(i) (sum of digits)

after the digits are reversed, the new number is 10x + y

given that new number = 4*(original number ) -3

therefore ( 10 x +y) = 4*(10y + x ) - 3

or 10x + y = 40y + 4x - 3

or 6x -39 y = -3 ----------(ii)

system is

x + y = 7 ----------(i)

6x - 39 y = -3 ----------(ii)

solving

eliminating x

6x + 6y = 42----------(i)

6x - 39 y = -3 ----------(ii)

subtracting

45 y = 45 or y =1

substituting x + 1 = 7 or x = 6

therefore

x = 6 , y = 1

original number = 16

other word problems with some explanation

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### collection of word problems

collection of word problems

The area of a right angle triangle is 63 sq.cm. The length of the base of the triangle is 5 cm. more than the altitute of the triangle. Find the length of the altitute of the triangle. solution

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number is equal to 3 less than four times the original number. What is the original number? solution

A man has 10 paise and 25 paise coins in his purse. The man has a total of 60 coins which amount to Rs.8.25.How many 10 paise and 25 paise coins does the man have in his purse? solution

The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 . If each of them saves Rs.200/- per month, find their monthly incomes. solution

X can do a piece of work in 2 hours, while Y can do the same piece of work in 4 hours.What is the time taken if X and Y do the work together? solution

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The area of a right angle triangle is 63 sq.cm. The length of the base of the triangle is 5 cm. more than the altitute of the triangle. Find the length of the altitute of the triangle. solution

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number is equal to 3 less than four times the original number. What is the original number? solution

A man has 10 paise and 25 paise coins in his purse. The man has a total of 60 coins which amount to Rs.8.25.How many 10 paise and 25 paise coins does the man have in his purse? solution

The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 . If each of them saves Rs.200/- per month, find their monthly incomes. solution

X can do a piece of work in 2 hours, while Y can do the same piece of work in 4 hours.What is the time taken if X and Y do the work together? solution

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### word problem2

A man has 10 paise and 25 paise coins in his purse. The man has a total of 60 coins which amount to Rs. 8.25.

How many 10 paise and 25 paise coins does the man have in his purse?

let the man have x 10ps. coins and y 25ps coins in his purse.

x + y = 60 (number of coins)

10x + 25y = 825 (value in paise)

solving x = 45 , y = 15

other word problems with some explanation

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How many 10 paise and 25 paise coins does the man have in his purse?

let the man have x 10ps. coins and y 25ps coins in his purse.

x + y = 60 (number of coins)

10x + 25y = 825 (value in paise)

solving x = 45 , y = 15

other word problems with some explanation

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### word problems

The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 . If each of them saves Rs.200/- per month, find their monthly incomes.

let their monthly incomes be 9x and 7x respectively

let their monthly expenditures be 4y and 3y respectively

therefore ( income - expenditure = saving )

9x - 4y = 200 -------------(i)

7x - 3y = 200 -------------(ii)

solving

(eliminating y)

27x -12y = 600 --------------(i)*3

28x -12y = 800 --------------(ii)*4

subtracting x = 200

monthly incomes be 9x and 7x respectively

therefore monthly incomes be 9*200 and 7*200 respectively

monthly incomes be 1800 and 1400 respectively

other word problems with some explanation

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let their monthly incomes be 9x and 7x respectively

let their monthly expenditures be 4y and 3y respectively

therefore ( income - expenditure = saving )

9x - 4y = 200 -------------(i)

7x - 3y = 200 -------------(ii)

solving

(eliminating y)

27x -12y = 600 --------------(i)*3

28x -12y = 800 --------------(ii)*4

subtracting x = 200

monthly incomes be 9x and 7x respectively

therefore monthly incomes be 9*200 and 7*200 respectively

monthly incomes be 1800 and 1400 respectively

other word problems with some explanation

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### uses of graph in solving equations

uses of graph in solving equations

solve (x^2)- 2x - 8 = 0 by graphing

solving a quadratic equation by graphing

graphical solution of system of two simultaneous linear equations in two unknowns

solve graphically 3x-7y+10=0 , 2x-y+3=0 graphical solution

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solve (x^2)- 2x - 8 = 0 by graphing

solving a quadratic equation by graphing

graphical solution of system of two simultaneous linear equations in two unknowns

solve graphically 3x-7y+10=0 , 2x-y+3=0 graphical solution

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## Friday, October 16, 2009

### linear approximation for (sin x) /x

linear approximation for (sin x) /x about x=pi/4

taylor series (truncated) with the first two terms has been used

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taylor series (truncated) with the first two terms has been used

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## Thursday, October 15, 2009

### implicit differentiation to find second derivative

if sqrt(x) + sqrt(y) = 1 find y"

differentiate the given expression w.r.t.x and do not forget to add dy/dx when differentiating

y w.r.t.x simplify and extract the value of dy/dx

differentiate that again w.r.t.x and do not forget to add dy/dx when differentiating

y w.r.t.x , use the earlier value for dy/dx for substitution

other questions

if √(xy) = x - 2y, find dy/dx ---------------->( implicit differentiation )

if xy + y^2 =1 , find dy/dx ---------------- implicit differentiation

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differentiate the given expression w.r.t.x and do not forget to add dy/dx when differentiating

y w.r.t.x simplify and extract the value of dy/dx

differentiate that again w.r.t.x and do not forget to add dy/dx when differentiating

y w.r.t.x , use the earlier value for dy/dx for substitution

other questions

if √(xy) = x - 2y, find dy/dx ---------------->( implicit differentiation )

if xy + y^2 =1 , find dy/dx ---------------- implicit differentiation

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index of math problems

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## Tuesday, October 13, 2009

### if (A-B) = pi/4 show that (1+tanA)(1+tanB) = 2tanA

if (A-B) = pi/4 show that (1+tanA)(1+tanB) = 2tanA

make it into A = B + (pi/4)

take tan on both sides, apply tan(A+B) identity

simplify and extract tanA

add tanA to both sides and then factorise

trigonometry identities

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make it into A = B + (pi/4)

take tan on both sides, apply tan(A+B) identity

simplify and extract tanA

add tanA to both sides and then factorise

trigonometry identities

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## Thursday, October 8, 2009

### geometric distribution

geometric distribution

proof of memory less property of geometric distribution ----------memory less property of geometric distribution

proof of memory less property of geometric distribution ----------memory less property of geometric distribution

## Wednesday, October 7, 2009

### Binomial distribution

Binomial distribution

pdf (probability distribution function ) of the binomial distribution is

Mean of the binomial distribution = np

Variance of the binomial distribution = npq

mgf (moment generating function of the binomial distribution) is [q + p (e^t) ] ^n

derivation of mean and variance of binomial distribution :derivation of mean and variance of binomial distribution

derivation of mgf of binomial distribution and deduction of mean and variance from the mgf:

mgf of the binomial distribution

derivation of mode of binomial distribution : mode of binomial distribution

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pdf (probability distribution function ) of the binomial distribution is

Mean of the binomial distribution = np

Variance of the binomial distribution = npq

mgf (moment generating function of the binomial distribution) is [q + p (e^t) ] ^n

derivation of mean and variance of binomial distribution :derivation of mean and variance of binomial distribution

derivation of mgf of binomial distribution and deduction of mean and variance from the mgf:

mgf of the binomial distribution

derivation of mode of binomial distribution : mode of binomial distribution

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## Monday, September 21, 2009

### journey from trivandrum to karaikudi

journey from trivandrum to karaikudi

The route was along

Trivandrum - Martandam - Nagercoil - Thirunelveli -Madurai - Melur - Karaikudi

around 400 km. NH 47 and then NH 7

The road from Trivandrum to Nagercoil was the worst in terms of congestion and it took around 2 hours. There was also a small strip of road at Martandam near the bridge which was full of potholes (This could be avoided by taking a side road ).

After that there was a 4-lane road (2-lanes each for either direction) for most of the route to Madurai, which bypassed most of the small towns. But there is some construction going on at some parts of the road. So there is diversion at some parts

and you might also see some vehicles, (some of which are part of the road works ) coming at you from the opposite direction in your lane due to these diversions.

There was also some construction work near Thirunelveli which caused some traffic block for around 20 minutes.

Earlier you would buy sweets like thenkuzhal(the sweet, not the murukku) , aluva etc at thirunelveli. You could buy small cucumbers, pomegranite at various small towns, but most of these are not possible on the new 4-lane road unless you went out of the way along the exit to visit those towns. You could go to the new bus stand at Thirunelveli and buy the sweets from the shops inside the bus stand.

Earlier it was a headache to go through Madurai due to the traffic, but now there is a bypass [ There is a right angle turn towards the right with a (unmarked ?)bump leading to the bypass ] There is a toll of Rs. 35 /-(depending on where you are going) and around four toll gates where you have to show your receipt. There is also some traffic on the bypass since it is connected to the city at some points.

After that the journey is along the 4-lane road for some more distance. You can bypass Melur and take the cut for Karaikudi from the 4-lane road if you know the correct cut [ a vendor of tender coconuts on the roadside told me about that in terms of the approximate distance km ]

After that the road is the usual 2-lane(1-lane each for either direction)with some tamarind trees on the sides.

There is a lot more traffic in Karaikudi. Traffic signals have been installed. A traffic warden shouts at people who have not parked properly through a public address system. Road dividers have come up on the main road.

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The route was along

Trivandrum - Martandam - Nagercoil - Thirunelveli -Madurai - Melur - Karaikudi

around 400 km. NH 47 and then NH 7

The road from Trivandrum to Nagercoil was the worst in terms of congestion and it took around 2 hours. There was also a small strip of road at Martandam near the bridge which was full of potholes (This could be avoided by taking a side road ).

After that there was a 4-lane road (2-lanes each for either direction) for most of the route to Madurai, which bypassed most of the small towns. But there is some construction going on at some parts of the road. So there is diversion at some parts

and you might also see some vehicles, (some of which are part of the road works ) coming at you from the opposite direction in your lane due to these diversions.

There was also some construction work near Thirunelveli which caused some traffic block for around 20 minutes.

Earlier you would buy sweets like thenkuzhal(the sweet, not the murukku) , aluva etc at thirunelveli. You could buy small cucumbers, pomegranite at various small towns, but most of these are not possible on the new 4-lane road unless you went out of the way along the exit to visit those towns. You could go to the new bus stand at Thirunelveli and buy the sweets from the shops inside the bus stand.

Earlier it was a headache to go through Madurai due to the traffic, but now there is a bypass [ There is a right angle turn towards the right with a (unmarked ?)bump leading to the bypass ] There is a toll of Rs. 35 /-(depending on where you are going) and around four toll gates where you have to show your receipt. There is also some traffic on the bypass since it is connected to the city at some points.

After that the journey is along the 4-lane road for some more distance. You can bypass Melur and take the cut for Karaikudi from the 4-lane road if you know the correct cut [ a vendor of tender coconuts on the roadside told me about that in terms of the approximate distance km ]

After that the road is the usual 2-lane(1-lane each for either direction)with some tamarind trees on the sides.

There is a lot more traffic in Karaikudi. Traffic signals have been installed. A traffic warden shouts at people who have not parked properly through a public address system. Road dividers have come up on the main road.

-----------------------------------------------------------

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------------------------------------------------------------

index of math problems

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Labels:
4-lane,
bypass,
google maps,
Karaikudi,
Madurai,
Melur,
Nagercoil,
NH 47,
NH 7,
photo,
route,
Thirunelveli,
Trivandrum - Martandam

## Tuesday, September 8, 2009

### finance

There seems to be a type of people who live on credit. They buy the latest items like the newest model cars, tv' s etc and do not care if they are not able to afford the items. They would just charge it to their cards or take out a new loan. This was not common in India in the 70's . But with the advent of liberalisation and entry of foreign banks, this type of people are becoming common in india, especially among those in the IT field.

Till the recent recession in the USA and the corresponding slowdown in India, banks were competing with each other in issuing credit cards. Some people would just use a credit card to waste money on the latest and costliest stuff and would then just go about paying the minimum possible on their credit card debt per month.Some people do not even understand that even a single mistake on their part or a late/ missed payment might sometimes just blow up the interest rates on their credit card debt. They sometimes fail to understand that there is no such thing as a free lunch with regard to credit card companies.

Some of the younger generation seem to have forgotten the value of frugality and the concept of living within their means.

When you use credit cards , you do not have the same feeling / care as when you count out currency notes. Also some credit card companies entice you with offers of cash back offers, free gifts etc if you buy a lot of items using your credit card. All of this sometimes leads to overspending.

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Till the recent recession in the USA and the corresponding slowdown in India, banks were competing with each other in issuing credit cards. Some people would just use a credit card to waste money on the latest and costliest stuff and would then just go about paying the minimum possible on their credit card debt per month.Some people do not even understand that even a single mistake on their part or a late/ missed payment might sometimes just blow up the interest rates on their credit card debt. They sometimes fail to understand that there is no such thing as a free lunch with regard to credit card companies.

Some of the younger generation seem to have forgotten the value of frugality and the concept of living within their means.

When you use credit cards , you do not have the same feeling / care as when you count out currency notes. Also some credit card companies entice you with offers of cash back offers, free gifts etc if you buy a lot of items using your credit card. All of this sometimes leads to overspending.

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index of math problems

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## Monday, August 3, 2009

### collection of problems in integration, differentiation, areas, volumes, trigonometry, matrices, limits

Calculus

problems on integration ------------------------ integration

problems on application of integration like

area, volume, arc length etc ------------------------integration application

problems on differential equations ------differential equation

problems on differentiation------------------------ differentiation

problems on limits ------------------limits

problems on matrices --------------matrices

problems on trigonometry ------trigonometry

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problems on integration ------------------------ integration

problems on application of integration like

area, volume, arc length etc ------------------------integration application

problems on differential equations ------differential equation

problems on differentiation------------------------ differentiation

problems on limits ------------------limits

problems on matrices --------------matrices

problems on trigonometry ------trigonometry

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## Wednesday, July 29, 2009

### cars, bikes etc in india

some links to websites with information / review on used cars, new cars , bike review in india,like maruti 800, maruti alto, ambassador, hyundai santro, cielo, tata nano, tata indica, karizma, bajaj pulsar, ford fiesta, honda city etc

Interesting information on bikes seems to be available at bikeadvice.in

The website seems to be in the form of a blog . Information on carburetor tuning, engine oils etc is available. review/information on some bikes from yamaha , karizma, suzuki , honda , bajaj pulsar etc seem to be available

Another website with review on cars bikes / two wheelers etc is gaadi.com.

Information on price of new cars, as well as of used cars seems to be available.

some other websites with information on new and used cars are

automobileindia.com

cardekho.com

carazoo.com

carwale.com

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.

Interesting information on bikes seems to be available at bikeadvice.in

The website seems to be in the form of a blog . Information on carburetor tuning, engine oils etc is available. review/information on some bikes from yamaha , karizma, suzuki , honda , bajaj pulsar etc seem to be available

Another website with review on cars bikes / two wheelers etc is gaadi.com.

Information on price of new cars, as well as of used cars seems to be available.

some other websites with information on new and used cars are

automobileindia.com

cardekho.com

carazoo.com

carwale.com

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.

### finding area using green's theorem

The area enclosed by a plane curve C can be evaluated using the following integral

for the proof refer the following page

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for the proof refer the following page

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## Sunday, July 19, 2009

### hair oil

In Kerala, people used to use plain coconut oil heated/treated with hibiscus or some other spices as hair oil.

Some of the women had very long hair. But then they started to cut down the length of their hair just like males.

So I think their concept of use of hair oil also has changed with time.

But now you can buy varieties of hair oil, perfumed etc in bottles, small pouches etc. with attributes like non greasy, non sticky, stops hair loss, adds vitality to your hair, gets rid of dandruff, herbal hair oil, almond drops hair oil, amla hair oil, leaves hair soft, silky and shiny etc.

But I do not know what is the difference between the old hair oil and the new fangled ones except the cost and ease of buying and using .

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Some of the women had very long hair. But then they started to cut down the length of their hair just like males.

So I think their concept of use of hair oil also has changed with time.

But now you can buy varieties of hair oil, perfumed etc in bottles, small pouches etc. with attributes like non greasy, non sticky, stops hair loss, adds vitality to your hair, gets rid of dandruff, herbal hair oil, almond drops hair oil, amla hair oil, leaves hair soft, silky and shiny etc.

But I do not know what is the difference between the old hair oil and the new fangled ones except the cost and ease of buying and using .

-----------------------------------------------------------

please leave your comments below

------------------------------------------------------------

index of math problems

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## Thursday, July 16, 2009

### some silly things

Is it possible to lose a lot of weight in a single week through exercise ?

Does the cockroach have a bizarre odour

Why do some clothes smell mouldy even after they are washed ?

Is practicing hard for football worth it ?

How does a shy boy talk to a girl he has just met in class ?

Why do people try so hard to participate in the auction of bsnl vanity cellphone numbers ?

Is buying a used car better than buying a new car even if you have ready cash for the new car?

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Does the cockroach have a bizarre odour

Why do some clothes smell mouldy even after they are washed ?

Is practicing hard for football worth it ?

How does a shy boy talk to a girl he has just met in class ?

Why do people try so hard to participate in the auction of bsnl vanity cellphone numbers ?

Is buying a used car better than buying a new car even if you have ready cash for the new car?

-----------------------------------------------------------

please leave your comments below

------------------------------------------------------------

index of math problems

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

## Tuesday, July 14, 2009

### mobile cell phones vs landline

In the old days, the only telecom company in India was BSNL, the government controlled entity.

There was no mobile network. Only landlines were present. Getting a telephone connection was a long process. You applied for a connection and waited for something like months before you got a telephone alloted to you.

But now with the arrival of cell phone companies , getting a phone connection is a lot easier. You just go to a phone shop (or even some other general stores) with a passport size photo and copies of identification documents like voter id etc, and you can buy a sim card which is usually activated then itself on receipt of the identification documents by the shop keeper.

some of the networks in kerala are idea ( earlier bpl mobile or escotel ? ) , bsnl cellone, airtel, tata indicom

ideacellular.com

bsnl.co.in

airtel.in

tataindicom.com

There have been problems with call congestion on certain networks during peak usage hours. There are also complaints about billing on post paid services of some service providers. There are also some problems with unwanted promotional messages, advertisement calls etc.

In kerala mobile phones have become very common place. Even people earning very little money like casual labourers , auto drivers etc use mobile phones (usually cheap mobile handsets with black and white display) to keep in touch with their clientele.

Some college students carry around two or three mobile phones. Students seem to be searching for the latest and hottest mobile phones. Sometimes this kind of mobile phone usage seems to develop into something like an addiction. There was even an incident when some student committed suicide apparently because his parents enforced some ban on his cell phone usage.

There also have been safety concerns on the use of mobile phones by very young children.

Some governments have banned the use of cell phones in schools and some universities like anna university in tamilnadu have banned the use of camera phones in engineering colleges during class hours.

Using a mobilephone while driving is very dangerous since the reaction time may be slower.

Some of the qualities to look for in a mobile phone seem to be ruggedness ,durability, memory, camera quality in case of a phone with camera, texting ease, should fit easily in ones pocket etc.

-----------------------------------------------------------

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------------------------------------------------------------

index of math problems

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

There was no mobile network. Only landlines were present. Getting a telephone connection was a long process. You applied for a connection and waited for something like months before you got a telephone alloted to you.

But now with the arrival of cell phone companies , getting a phone connection is a lot easier. You just go to a phone shop (or even some other general stores) with a passport size photo and copies of identification documents like voter id etc, and you can buy a sim card which is usually activated then itself on receipt of the identification documents by the shop keeper.

some of the networks in kerala are idea ( earlier bpl mobile or escotel ? ) , bsnl cellone, airtel, tata indicom

ideacellular.com

bsnl.co.in

airtel.in

tataindicom.com

There have been problems with call congestion on certain networks during peak usage hours. There are also complaints about billing on post paid services of some service providers. There are also some problems with unwanted promotional messages, advertisement calls etc.

In kerala mobile phones have become very common place. Even people earning very little money like casual labourers , auto drivers etc use mobile phones (usually cheap mobile handsets with black and white display) to keep in touch with their clientele.

Some college students carry around two or three mobile phones. Students seem to be searching for the latest and hottest mobile phones. Sometimes this kind of mobile phone usage seems to develop into something like an addiction. There was even an incident when some student committed suicide apparently because his parents enforced some ban on his cell phone usage.

There also have been safety concerns on the use of mobile phones by very young children.

Some governments have banned the use of cell phones in schools and some universities like anna university in tamilnadu have banned the use of camera phones in engineering colleges during class hours.

Using a mobilephone while driving is very dangerous since the reaction time may be slower.

Some of the qualities to look for in a mobile phone seem to be ruggedness ,durability, memory, camera quality in case of a phone with camera, texting ease, should fit easily in ones pocket etc.

-----------------------------------------------------------

please leave your comments below

------------------------------------------------------------

index of math problems

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

Labels:
airtel,
bsnl,
cell phone,
cellone,
idea cellular,
landline,
mobile,
review,
tata indicom

## Monday, July 13, 2009

### digital cameras

In the old days you had cameras which used film, It was very costly to develop the film and print it out. The capacity was also small.

Nowadays there are digital cameras where the capacity can be expanded using memory cards. You can review the photos on the screen or on a computer, use software to make the photos prettier and print them out on special photo paper (slightly more expensive than ordinary paper)

some of the common brands are jvc , kodak, epson, canon , hitachi, nikon, panasonic, philips, sony, benq etc

jvc.com

digitalcameras.kodak.com

usa.canon.com

benq.com/products/digicam

I use a simple kodak camera, and sometimes wish that i had bought one which can be fitted with extra lens for taking photos of objects a little far away.

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Nowadays there are digital cameras where the capacity can be expanded using memory cards. You can review the photos on the screen or on a computer, use software to make the photos prettier and print them out on special photo paper (slightly more expensive than ordinary paper)

some of the common brands are jvc , kodak, epson, canon , hitachi, nikon, panasonic, philips, sony, benq etc

jvc.com

digitalcameras.kodak.com

usa.canon.com

benq.com/products/digicam

I use a simple kodak camera, and sometimes wish that i had bought one which can be fitted with extra lens for taking photos of objects a little far away.

-----------------------------------------------------------

please leave your comments below

------------------------------------------------------------

index of math problems

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### conditional identities in trigonometry

conditional identities in trigonometry are usually based on A,B, C being angles of a triangle or A + B +C = Ï€

examples

If A + B + C = Ï€ , show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)

explanation of If A + B + C = Ï€ , show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)

If A+B+C=Ï€, prove that: sinA+sinB+sinC = cot(A/2).cot(B/2) [sinA+sinB-sinC]

explanation

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examples

If A + B + C = Ï€ , show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)

explanation of If A + B + C = Ï€ , show that cosA + cosB + cos C = 1 + 4 sin(A/2)sin(B/2)sin(C/2)

If A+B+C=Ï€, prove that: sinA+sinB+sinC = cot(A/2).cot(B/2) [sinA+sinB-sinC]

explanation

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## Sunday, July 12, 2009

### radius of curvature

find the radius of curvature of y = exp(-x) at x =1

y' = -exp(-x)

y" = exp(-x)

at x = 1

y' = -exp(-1)= -1 /e

y" = exp(-1) = 1/e

radius of curvature = { [ 1 + (y')² ] ^(3/2) } / y"

radius of curvature = { [e² + 1] ^(3/2) } / e²

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y' = -exp(-x)

y" = exp(-x)

at x = 1

y' = -exp(-1)= -1 /e

y" = exp(-1) = 1/e

radius of curvature = { [ 1 + (y')² ] ^(3/2) } / y"

radius of curvature = { [e² + 1] ^(3/2) } / e²

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## Saturday, July 11, 2009

### gensets

In the old days for marriages rececptions, they would keep petromax lamps on hand in case the current went out.

Later on they started renting out generators which usually ran on kerosene or petrol , usually starts up on petrol and runs on kerosene, and were very noisy. The starting up of the generator was also quite hard with having to pull a cord to turn the flywheel? .

But now a days you can see generators in most shops due to the worsening power situation with power cuts and so on. Most of them are self starting as in they will start when you turn the key

In some of the big offices / banks you can see big generators which are of the size of a small room with huge mufflers to cut down on the sound. Even the small generators now are relatively silent when compared to the old ones.

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Later on they started renting out generators which usually ran on kerosene or petrol , usually starts up on petrol and runs on kerosene, and were very noisy. The starting up of the generator was also quite hard with having to pull a cord to turn the flywheel? .

But now a days you can see generators in most shops due to the worsening power situation with power cuts and so on. Most of them are self starting as in they will start when you turn the key

In some of the big offices / banks you can see big generators which are of the size of a small room with huge mufflers to cut down on the sound. Even the small generators now are relatively silent when compared to the old ones.

-----------------------------------------------------------

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index of math problems

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## Friday, July 10, 2009

### microwave oven

Recently we have been looking around for a microwave oven since there have been many advertisements for microwave ovens from LG, Samsung, IFB whirlpool etc. After looking around it seems that the microwave oven from bajaj is pretty good considering its cost of around Rs. 5000/- . We mainly use the oven to heat up food like puffs etc bought from the bakery and sometimes rarely to bake cake.

Only after buying the microwave oven did we notice that it is not good to put metal vessels inside the microwave oven . Even some types of glass vessels cannot be used in the microwave oven.

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Only after buying the microwave oven did we notice that it is not good to put metal vessels inside the microwave oven . Even some types of glass vessels cannot be used in the microwave oven.

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Labels:
bajaj,
cake,
IFB whirlpool,
LG,
microwave oven,
puffs,
Samsung

### pressure cooker

In Kerala, pressure cookers are usually used to cook idili, rice, meat, vegetables for sambar etc.

In our house we recently bought a new prestige pressure cooker. The older one also was a prestige pressure cooker which was around for a very long time .

Spare parts seem to be readily available. The only thing that has been replaced from time to time is the gasket. Here we take the old gasket to a shop in Chalai near east fort, and the shopkeeper gives a new gasket by comparing the size with the old one.

Other brands commonly available seem to be Hawkins, Premier pressure cooker etc

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In our house we recently bought a new prestige pressure cooker. The older one also was a prestige pressure cooker which was around for a very long time .

Spare parts seem to be readily available. The only thing that has been replaced from time to time is the gasket. Here we take the old gasket to a shop in Chalai near east fort, and the shopkeeper gives a new gasket by comparing the size with the old one.

Other brands commonly available seem to be Hawkins, Premier pressure cooker etc

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please leave your comments below

------------------------------------------------------------

index of math problems

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

## Wednesday, July 8, 2009

### cable vs dth service

We had been using cable tv from asianet for many years. Initially it was for one tv and the cost was around Rs.180/- which was later increased to around 200 rupees.

They had introduced a set top box and digital service. But we did not change over to that.

Then we asked them for an extra connection for another tv which increased the charge to around 285 rupees. The only problem was that now and then some of the english channels like star world,some sports channels etc would just disappear for some months .

Then the age of dth channels came around with doordarshan dth service ddinews.gov.in, dish tv dishtv.in , tata sky tatasky.com airtel dth airtel.in, suntv dth sundirect.in etc.

We opted for tata sky in addition to the cable service .

We selected the package which consisted of most of the south indian channels, sports channels , english movie channels, music channels etc. In those days there were also radio channels from all india radio on tata sky.

But after a few days the radio channels just disappeared from tata sky.

Then one by one most of the sports channels and some other channels started to be moved into other packages for which the subscriber had to pay extra money. Most of the repackaging of sports channels would happen when there was some cricket match or series likely to be watched by indians.

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They had introduced a set top box and digital service. But we did not change over to that.

Then we asked them for an extra connection for another tv which increased the charge to around 285 rupees. The only problem was that now and then some of the english channels like star world,some sports channels etc would just disappear for some months .

Then the age of dth channels came around with doordarshan dth service ddinews.gov.in, dish tv dishtv.in , tata sky tatasky.com airtel dth airtel.in, suntv dth sundirect.in etc.

We opted for tata sky in addition to the cable service .

We selected the package which consisted of most of the south indian channels, sports channels , english movie channels, music channels etc. In those days there were also radio channels from all india radio on tata sky.

But after a few days the radio channels just disappeared from tata sky.

Then one by one most of the sports channels and some other channels started to be moved into other packages for which the subscriber had to pay extra money. Most of the repackaging of sports channels would happen when there was some cricket match or series likely to be watched by indians.

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### driving test in trivandrum, kerala

Before taking the driving test you have to get a learner's license.For that you had to to take an objective test on the computer in the RT office. The questions that are asked correspond to important trafic signs, traffic rules etc. Books are available that contain model questions (usually in malayalam). But I was able to find an online version of the model questions in english.

After passing the test you are given a date after several weeks to appear for the driving test which consisted of taking a H test (driving the car in a particular pattern between iron stakes arranged in the shape of an H ; you go forward along one of the vertical lines of the H from bottom to top , then reverse to the middle , go in reverse along the centre horizontal line of the H , and then to the opposite bottom of the other vertical line of the H in reverse , then forward to the top of that vertical line , then reverse to the middle of the vertical line, then in reverse along the central horizontal line of the H and then in reverse along the first vertical line to the starting point. )and a short driving test on the road to test the gear shifting and hand signals.

My father taught me driving in his old petrol ambassador car (amby). But before going for the driving test, father advised me to take the test in a maruti 800 which is smaller and hence might make it easier to take the H test.

So we went to a driving school. The maruti 800 had the gear lever on the floor as opposed to the gear lever on the steering column of the ambassador I practiced on.

So we paid the driving school for a couple of hours of driving practice on the road and for practice of the H test using the Maruti 800.

The teachers at the driving school were very helpful. For those who had trouble taking the H test smoothly, they gave some pointers like stopping and taking the 90 degree turns based on sighting the iron stakes at certain points relative to the car's rear window quarter glass etc.

They also raise/adjust the fuel flow to the engine during idling for the test so that the engine does not shut down frequently in the hands of the amateur drivers.

Anyway the whole exercise was fun. I got the receipt of passing the driving test, but had to wait some days for the actual license since there was some problem with the printing machine in the RT office at that time

More details on the eligibility conditions , forms and documents , fee , requirements for renewal , international drivers licence etc is available at the kerala motor vehicle department website

keralamvd.gov.in .

The following diagram may have errors

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After passing the test you are given a date after several weeks to appear for the driving test which consisted of taking a H test (driving the car in a particular pattern between iron stakes arranged in the shape of an H ; you go forward along one of the vertical lines of the H from bottom to top , then reverse to the middle , go in reverse along the centre horizontal line of the H , and then to the opposite bottom of the other vertical line of the H in reverse , then forward to the top of that vertical line , then reverse to the middle of the vertical line, then in reverse along the central horizontal line of the H and then in reverse along the first vertical line to the starting point. )and a short driving test on the road to test the gear shifting and hand signals.

My father taught me driving in his old petrol ambassador car (amby). But before going for the driving test, father advised me to take the test in a maruti 800 which is smaller and hence might make it easier to take the H test.

So we went to a driving school. The maruti 800 had the gear lever on the floor as opposed to the gear lever on the steering column of the ambassador I practiced on.

So we paid the driving school for a couple of hours of driving practice on the road and for practice of the H test using the Maruti 800.

The teachers at the driving school were very helpful. For those who had trouble taking the H test smoothly, they gave some pointers like stopping and taking the 90 degree turns based on sighting the iron stakes at certain points relative to the car's rear window quarter glass etc.

They also raise/adjust the fuel flow to the engine during idling for the test so that the engine does not shut down frequently in the hands of the amateur drivers.

Anyway the whole exercise was fun. I got the receipt of passing the driving test, but had to wait some days for the actual license since there was some problem with the printing machine in the RT office at that time

More details on the eligibility conditions , forms and documents , fee , requirements for renewal , international drivers licence etc is available at the kerala motor vehicle department website

keralamvd.gov.in .

The following diagram may have errors

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## Tuesday, July 7, 2009

### problem on trapezoidal rule

evaluate integral of sinx from 0 to pi using trapezoidal rule with n=10

take a=0 b = pi, h = (b-a)/n = pi/10

break up the interval 0 to pi into subintervals of length h = pi/10

evaluate y = sinx at the endpointsformulae

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take a=0 b = pi, h = (b-a)/n = pi/10

break up the interval 0 to pi into subintervals of length h = pi/10

evaluate y = sinx at the endpointsformulae

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## Monday, July 6, 2009

### answers

1. b

2. c

3. a

4. a

5. b

back to questions 1 to 5

explanation

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2. c

3. a

4. a

5. b

back to questions 1 to 5

explanation

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### practice questions for various entrance exams

Answers and some explanation

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