IIT-JEE 2012

100 Pages·2011·2.21 MB·English

To fly, we have to ha ve resistance

Volume - 6 Issue - 12

June, 2011 (Monthly Magazine)
Editorial / Mailing O ffice :
112-B, Shakti Nagar, Kota (Raj.)

Tel. : [phone]
Editorial
e-mail : [email protected]

Editor :

Dear Students,
Pramod Maheshwari
[B.Tech. IIT-Delhi] Motivate Yourself
Cover Design One of the greatest virtues of human beings i s their ability to think and
act accordingly. The emergence of the techno savvy human from the
Satyanarayan Saini tree swinging ape has really been a long jou rney. This transition has

Layout taken a span of countless centuries and lots of thinking caps have been
involved. Inquisitiveness and aspiration to come out with
Rajaram Gocher
the best have been the pillars for man's quest for development.

Circulation & Advertisement Self-motivation is the sheer force, which pulled him apart and
distinguished him from his primitive ancestors.

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because of that creepy careless attitude which is slowly, but surely

entering into our mind. We easily forget the pains of yesterday to relish
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the joys of today. This is the only time in our life, when we can control
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written permission of the publisher our fate, by controlling our mind. So it is time to pull up our socks and
really motivate ourselves so that we can give our best shot in the future.
• All disputes are subject to the
Self-motivation is the need of the hour. Only we can control and restrict
exclusive jurisdiction of the Kota
Courts only. ourselves. It’s up to us, how we use our mental capabilities to the best
of our abilities.
Every effort has been made to avoid errors or Here are some Funda's for self-motivation. Don't just read them digest
omission in this publication. Inr spite of this, each one of them and apply them and I bet it will make a better YOU.
errors are possible. Any mistake, error or
• The ultimate motivator is defeat. Once you are defeated, you have
discrepancy noted may be brought to our
nowhere to go except the top.
notice which shall be taken care of in the
forthcoming edition, hence any suggestion is • Then only thing stopping you is yourself.
welcome. It is notified that neither the
• There is no guarantee that tomorrow will come. So do it today.
publisher nor the author or seller will be
responsible for any damage or loss of action to • Intentions don't count, but action's do.
any one, of any kind, in any manner, there from.
• Don't let who you are, stunt what you want to be.
Unit Price ` 20/- • Success is the greatest motivator.
• Your goals must be clear, but the guidelines must be flexible.
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With Best Wishes for Your Future.
Owned & Published by Pramod
Maheshwari, 112, Shakti Nagar, Yours truly
Dadabari, Kota & Printed by Naval
Maheshwari, Published & Printed at 112,
Shakti Nagar, Dadabari, Kota.

Editor : Pramod Maheshwari Pramod Maheshwari,
B.Tech., IIT Delhi

XtraEdge for IIT-JEE 1 JUNE 2011
Volume-6 Issue-12
CONTENTS
June, 2011 (Monthly Magazine)

INDEX PAGE

NEXT MONTHS ATTRACTIONS Regulars ..........

(cid:139) Much more IIT-JEE News. NEWS ARTICLE 3
(cid:139) Know IIT-JEE With 15 Best Questions of IIT-JEE • IIT-B launches 'clean' energy laboratory
(cid:139) Challenging Problems in Physics,, Chemistry & Maths • Tech tycoon Shiv Nadar to set up research-led
university in Greater Noida
(cid:139) Key Concepts & Problem Solving strategy for IIT-JEE.

(cid:139) Xtra Edge Test Series for JEE- 2012 & 2013 IITian ON THE PATH OF SUCCESS 5
Mr. Krishnamurthy Rengarajan

KNOW IIT-JEE 6
Previous IIT-JEE Question

Study Time........

DYNAMIC PHYSICS 13

S 8 -Challenging Problems [Set # 2]
S tudents’ Forum
Success Tips for the Months
Physics Fundamentals

• Electrostatics-2

• If you haven nothing else to do, look about • Newton's Law of motion

you and see if there is not something close
C ATALYSE CHEMISTRY 28
at hand that you can improve !

Key Concept
• He has achieved success who has worked
• Nomenclature & isomerism
well, laughed often, and loved much.
• Electro Chemistry

• You always pass failure on the way to Understanding : Inorganic Chemistry

success.

DICEY MATHS 36
• A journey of a thousand miles begins with
Mathematical Challenges
a single step.
Students’ Forum

• Your success will be largely determined by Key Concept

your ability to concentrates single- • Inverse Trigonometric Function

mindedly on one thing at a time. • Quadratic Equation

• Success is a journey, not a destination.
Test Time ..........

• Success comes in "Cans". Failure comes in

"Can't". XTRAEDGE TEST SERIES 46

• Success seems to be largely a matter of Class XII – IIT-JEE 2012 Paper
hanging on after others have let go. Class XI – IIT-JEE 2013 Paper

AIEEE- 2011 Examination Paper with Solution 61

XtraEdge for IIT-JEE 2 JUNE 2011
IIT-B launches ‘clean’ energy Tech tycoon Shiv Nadar to set up 300 students,” said Dr Nikhil Sinha,
laboratory research-led university in Greater the founding vice-chancellor of the
Noida University. Sinha has served as
Mumbai: The Indian Institute of
associate dean for academic affairs at
Technology-Bombay on Thursday Shiv Nadar, the founder chairman of
the University of Texas.
launched a laboratory, set up in major HCL Technologies, announced on

association with Applied Materials Monday that he would set up a research-
Nuclear plans get makeover
Inc, a global supplier for led multidisciplinary university at
manufacturing solutions for semi- Greater Noida, a satellite town of Delhi. SAFETY FIRST Independent
conductor and solar industries. The Shiv Nadar University, named after regulator, reviews by external
the IT billionaire, marks the experts on govt to-do list
The scope of the Applied Materials
germination of an idea that was
Chemistry Laboratory for Energy and Stunned by Fukushima and hit by
incubated five years ago in the mind of
Nanoelectronics (CLEAN) will unprecedented anti-nuclear protests
Nadar, who thought of the concept in
include developing materials that in Jaitapur, the government
his zest to make a creative difference in
could be used for electronic and announced a series of dramatic
India’s educational system.
renewable energy focused reforms to the country's nuclear
applications, such as next generation “The University will be endowment- review mechanism that are aimed at
solar cells. led, research-driven with rebuilding public confidence in
multidisciplinary and interdisciplinary India's ambitious nuclear
Under the first phase of collaboration,
approach,” Nadar told. The total programme.
Applied Materials supplied equipment
endowment would be R1,000 crore.
worth $7.5 million to IIT-B for a
Education is not a virgin territory for Soon, a one-shot cure for all
semiconductor fabrication facility.
IIT-B director Devang Khakhar said, Nadar. The Shiv Nadar Foundation runs cancers
the VidyaGyan School at Bulandshahar
“CLEAN will begin a new phase of
Universal Vaccine Uses Body’s
in Uttar Pradesh that aims at nurturing
the collaboration in areas related to
talent and leadership amongst the Own Defences To Stop All
renewable energy.”
highly gifted rural poor children. Tumours In Their Tracks
“This is a great example of the kind A visibly happy Nadar said with the
London: Coming soon. Universal
of university and corporate setting up of this University, he feels
cancer jab, say scientists who are
collaboration that is helping to the same excitement as was when HCL
developing the vaccine which they
advance technology by enabling was first formed in 1976. Nadar had
claim would stop all tumours in their
world-class research, innovation and already committed a 10% of his wealth
tracks. According to the scientists,
workforce development,” said Mike for philanthropic causes. His total
the jab is part of a new generation of
Splinter, chairman of the board of worth has been estimated at around
drugs that use the body’s own
Applied Materials. R15,000 crore.
defences to fight cancers like
The inauguration marked the renewal Nadar said an undergraduate student pancreatic, prostate and breast,
of its five-year relationship, during spends close to $150,000-$200,000 stopping tumours in their tracks. The
which it endowed the institute with seeking degrees on foreign shores and a jabs would hit the market in just two
$12 million as research grants. good chunk comes from North India. years’ time, say the scientists.
“At undergraduate levels one doesn’t
Officials said as part of the Indo-US get scholarships. The idea to create a Although vaccines usually prevent
collaboration in the sector, Applied world class University at Greater Noida disease, the Telo-Vac jab is designed
Materials will work with the was born out of this need.” as a treatment. Rather than attacking
Jawaharlal Nehru National Solar cancer cells, like many existing
Mission (JNNSM). “Our unique It will offer courses in engineering, drugs, it harnesses the power of the
collaboration will allow us to turn social sciences, natural sciences, immune system to fight the tumours,
material inventions into innovations,” schools of business and other they say. It works by encouraging the
said Omkaram Nalamasu, chief professional courses in due time. “We immune system to seek out and
technology officer, Applied Materials. will start admissions from this destroy an enzyme called telomerase.
academic session itself and the total
Found at high levels in many cancer
intake this year would be around 200-
cells, telomerase effectively makes
XtraEdge for IIT-JEE 3 JUNE 2011
them fully immortal, allowing them to decrease auto emissions up to 90 has taken the first big leap towards
live on when healthy cells would percent when compared with translating his dream into reality by
die — easing the growth and spread of conventional combustion engines. securing the seat.
the tumour.
The engine has a rotor that's equipped He had already started the
In the largest trial of its kind in the with wave-like channels that trap and groundwork travelling daily from
UK, more than 1,000 men and women mix oxygen and fuel as the rotor spins. one dusty village to another on the
in the late stages of pancreatic cancer These central inlets are blocked off, state roadways bus to the hinterland
are either being given the vaccine building pressure within the chamber, of Sikar, presiding over small public
alongside their normal drugs or treated causing a shock wave that ignites the gatherings, explaining to the
as usual, the ‘Daily Mail’ reported. compressed air and fuel to transmit villagers the need for education and
energy. healthcare to alleviate their social
The results from the 53 hospitals
and economic status.
taking part will not be available until The Wave Disk Generator uses 60
next year but, anecdotally, some percent of its fuel for propulsion; Rohit now plans to take his work to a
patients credit their participation in the standard car engines use just 15 higher level after completing his
trial with giving them an extra year or percent. As a result, the generator is 3.5 IIM-A course.
two of life. times more fuel efficient than typical
An alumnus of the IIT-Kgp 2008
combustion engines.
John Neoptolemos, who is co- batch, Rohit was employed by a
ordinating the large-scale British trial, Researchers estimate the new model financial firm listed in Fortune 500
said: “When you have got pancreatic could shave almost 1,000 pounds off a companies. He called it quits a year
cancer, it is like a timebomb in car's weight currently taken up by later worn out by the daily rigours of
people.” Pancreatic cancer cells are conventional engine systems. explaining and devising business
normally invisible to the immune models.
Michigan State's team of engineers
system but the vaccine “spots” the
hope to have a car-sized 25-kilowatt Back home, the IITian, being from a
telomerase spilling out from them and
version of the prototype ready by the farming background and a strong
kickstarts the fight back.
end of the year. advocator of inclusive growth,
Dr Jay Sangjae Kim, the founder of ventured in social entrepreneurship.

GemVax, the Korean company IITian from Sikar leaves Fortune He joined as consultant of an NGO
developing the TeloVac vaccine, said: 500 company to take up rural Helplads.
“We s welfare Using his technical skill, Rohit
trongly believe this has the potential From a government school at a organised workshops on themes
to overcome the limits of other current nondescript village in Sikar district to ranging from the basics of a
cancer vaccines and become part of IIT-Kgp, this youngster has come a computer to robotics for village
the standard of care not only for long way. Born to a humble farmer's children. "I plan fund-raising
pancreatic cancer but for various other family, Rohit Garhwal now cherishes a activities along with developing
types of cancers.” dream of developing an international business models for small-time social
platform for the traditional agriculture entrepreneurs in this region," Rohit
New engine sends shock waves art & craft forms and agriculture and said.
through auto industry minimise the exodus of rural talent to
• Inspired by other IIM students
cities.
Prototype could potentially who have turned entrepreneurs,
decrease auto emissions up to 90 To achieve his dream, the 25-year-old he said he was determined to
has quit plush jobs at an MNC and an find a way to help the rural
percent Despite shifting into higher
NGO to study at the IIM-A. people. "I am very worried of
gear within the consumer's green
the migration of villagers to
conscience, hybrid vehicles are still "IIM-A offers incubation centre for
small towns and cities
tethered to the gas pump via a fuel- social ventures. Here, I will like to
abandoning their agricultural
thirsty 100-year-old invention: the construct a model of branding products
and traditional art and craft
internal combustion engine. made by villagers and taking them in
practices. I would like to use my
international markets," said Rohit, who
However, researchers at Michigan technical expertise and
has secured a seat in the most
State University have built a prototype management tools to create a
prestigious management school, the
gasoline engine that requires no self-reliant environment for
result of which was announced on
transmission, crankshaft, pistons, them," Rohit added.
Friday afternoon.
valves, fuel compression, cooling

systems or fluids. Their so-called Leaving behind the luxuries of an MNC
Wave Disk Generator could greatly job earned after receiving a degree in
improve the efficiency of gas-electric aerospace engineering from the most
hybrid automobiles and potentially sought after IIT at Kharagpur, Rohit
XtraEdge for IIT-JEE 4 JUNE 2011
SSuu cccceessss SSttoorryy

This article contains story/interviews of person s who succeed after graduation from different IITs

Mr. Krishnamurthy Rengarajan

IIT-B Gold M edallist

Knowledge is indeed wealth. Who better exemplifies it excellent. I made best of friends and thoroughly enjoyed
than Krishnamurthy Rengarajan, IIT-B gold medallist my college life.
(B Tech dual-degree course). Krishnamurthy's story is that I don't think I will ever get this experience anywhere else.
of hard work, sheer grit and determination.
On studies
His undying passion for learning and excellence has paid
Before joining IIT, I used to study for 7 to 8 hours daily.
off. Coming from a lower middle class background ,
After joining IIT, I used to spend about a couple of hours. I
Krishnamurthy has made his parents proud when he passed
did not go for anything coaching classes. I learnt through
with flying colours.
Brilliant Tutorial correspondence course and my
His father, who works as a typist at Bharatiya Vidya preparation began after I finished my 10th standard.
Bhavan is overwhelmed by his son's achievement.
Why IIT
Rengarajan, who hails from Tamil Nadu, came to Mumbai
28 years ago and settled down in a distant Mumbai suburb IIT is one of the premier institutes in India. I always
of Dombivli. Though the family went through a lot of wanted to get good higher education, so I opted for IIT.
hardships initially, he made sure that his children were My mantra for success
well educated.
There is no short cut to success. One has to work very
"My son always wanted to join the IIT. When people hard, put in a lot of effort, should have a problem-solving
asked him what if you don't get through the entrance mentality and a right approach to every problem.
examinations, he used to say, `there is no question of me
My parents always stood by me, their support has been
not clearing the test,'" says his proud father.
invaluable and am overwhelmed.
And, of course, he did top all the five years at IIT, a result
Advice to IIT aspirants
of sheer hard work and brilliance, says his mother, barely
Work hard. You have to spend a lot of time preparing as
able to control her excitement. "I am very happy for him,"
exams are getting more and more competitive. You must
says Radha Rengarajan. Krishnamurthy did his schooling
also have problem-solving skills.
at the Kidland School in Dombivli and pre-degree from V
G Vaze College at Mulund. His favourite subject being Next move
mathematics it was obvious that he would pursue a degree "I have been selected for the scholarship programme at
in engineering. Stanford University for a PhD in operations research. I
He won the Rakesh Mathur award of Rs 1 lakh (Rs would like to research on optimising computer networks
100,000) during his third year and other scholarships and operation systems.
throughout the four years. Will you come back to India?
Here's what Krishnamurthy had to say on his IIT I have been good in studies from my childhood. But
experience. preparation for JEE is altogether different from earlier
My IIT experience studies. It is all about conceptual clarity rather than
cramming. So I always focussed on concepts and
The five years I spent at IIT were the best in my life. I will
supplemented it with required no. of problems.
cherish each and every moment here. I loved everything
here: the professors are the best one can ever get, the My advice to all the IIT is aspirants out there is: Believe in
facilities to study and the extra-curricular activities are your capabilities and never under estimate yourself.

XtraEdge for IIT-JEE 5 JUNE 2011
KNOW IIT-JEE

By Previous Exam Questions

⇒ acceleration of the system is zero.
PHYSICS
(ii) Taking equilibrium of B into consideration
2mg  1 2mg
1. Block A of mass m and block B of mass 2m are Since, > µBNB µBNB = × 
2  3 2 
placed on a fixed triangular wedge by means of a
∴ The difference of this force is provided by the
massless, in extensible string and a frictionless
force of tension
pulley as shown in figure. The wedge is inclined at
2mg 1 2mg 2 2mg 2 2mg
45º to the horizontal on both sides. The coefficient T = – = × =
of friction between block A and the wedge is 2/3 2 3 2 3 2 3
and that between block B and the wedge is 1/3. If 2 2mg
(iii) T = in upwards direction; weight
the system A and B is released from rest, find
3
[IIT-1997]
mg
component in downward direction.
2
A B mg
Since T >
2
m 2m
45º 45º ∴ The frictional force will act in downward

direction
(i) the acceleration of A,
(ii) tension in the string, and mg 2 2 mg 4–3 mg
f = T – = mg – = mg =
(ii) the magnitude and direction of the force of 2 3 2 3 2 2
friction acting on A
2. A uniform thin rod of mass M and length L is standing
2 1 vertically along the y-axis on a smooth horizontal
Sol. µ = ; µ =
AW BW
3 3 surface, with its lower end at the origin(0, 0). A slight
disturbance at t = 0 causes the lower end to slip on the
smooth surface along the positive x-axis, and the rod
A T T B starts falling. [IIT-1993]
N N (i) What is the path followed by the centre of mass of
A B
the rod during its fall?
mg mg 2mg 2mg (ii) Find the equation of the trajectory of a point on the
2 mg 2 2 2mg 2 rod located at a distance r from the lower end. What
45º 45º is the shaper of the path of this point?

Sol. (i) Let the position of the rod at any instant be as
Diagram shows the various forces acting on the
shown in the figure at any instant. Let the end point
masses and their resolution in the direction of
of the rod have dimensions(x, 0) and (0, y) and rod
motion.
making an angle θ with the x-axis as shown in the
Let us consider the two masses to be a system. The
figure.
forces trying to move the system, such that A moves

upwards and B moves downwards
(0,y) B
2mg mg mg
= – = L/2
2 2 2
C
The forces trying to stop this motion (maximum N
L/2
frictional force)
= fA + fB = µA NA + µB NB θ A
2 mg 1 2mg 4 mg O M (x, 0)
= × + × =
3 2 3 2 3 2 ∆CBN is similar to ∆ABO
Since the stopping force is more therefore the mass CN AO CN x
∴ = ⇒ =
system will not move. CB AB L/2 L
XtraEdge for IIT-JEE 6 JUNE 2011
⇒ CN = L/2 Sol. The mass B is moving in a circular path centred at
Also ∆ACM is similar to ∆ABO A. The centripetal force (mlω2) F'. Therefore a force
CM BO CM y F' acts on a (the hinge) which is equal to mlω2. The
∴ = ⇒ =
same is the case for mass C. Therefore the net force
CA BA L/2 2
in the hinge is
∴ The co-ordinates of C (centre of mass) are
F = F'2+F'2+2F'F'cos60º
x y net
 , 
2 2 1
Also x2 + y2 = L2 [in ∆ABO] using pythagorous Fnet = 2F'2+2F'2×2F'2×2 = 3F'= 3 mlω2
theorem] y
2 2 2
x y L
∴   +  =   A X
2 2 2 F' 60º
F'
L
⇒ Motion of c.m. is a circular path of radius F
2 l net l
and the centre of the circle is at origin.
(ii) Let us consider a point P(x, y) at a distance r
from A and q be the inclination of rod AB with x- B C
l
axis at any arbitraty instant of time t. (b) The force F acting on B will provide a torque to
x the system. This torque is
cos θ = (In ∆BPN)
L–r l 3
F × = Iα
y 2
sin θ = (in ∆APM)
r
But cos2θ + sin2θ = 1 F × 3l = (2ml2)α
2
2 2
⇒  x  + y = 1 ⇒ a = 3 F
L–R r  4 ml

The total force acting on the system along x-
3. Three particles A, B and C, each of mass m, are
direction is F + (F )
connected to each other by three massless rigid rods to net x
This force is responsible for giving an acceleration
form a rigid, equilateral triangular body of side l. This a to the system.
x
body is placed on a horizontal frictioness table

(x-y plane) and is hinged to it at the point A so that it
can move without friction about the vertical axis
3
through A (see figure). The body is set into rotational c.m l
2
motion on the table about A with a constant angular
velocity ω.
F
[IIT-2002]
Therefore
y
F + (F ) = 3m (a ) c.m.
net x x
A x F 3 F l F
= 3m Q ax = αr = × =
4m 4 ml 3 4
ω
3F
=
4
→
F F
∴ (F ) = –
net x
B C 4
l
(a) Find the magnitude of the horizontal force (Fnet)y remains the same as before = 3 mlω2.
exerted by the hinge on the body.
4. Two fixed equal, positive charges, each of magnitude
(b) At time T, when the side BC is parallel to the
5 × 10–5 coul. are located at points A and B separated
x-axis, a force F is applied on B along BC (as
by a distance of 5 m. An equal and opposite charge
shown). Obtain the x-component and the
moves towards them along the line COD, the
y-component of the force exerted by the hinge on
perpendicular bisector of the line AB. [IIT-1985]
the body, immediately after time. T.
XtraEdge for IIT-JEE 7 JUNE 2011
A +q 5. A circular ring of radius R with uniform positive
charge density λ per unit length is located in the y-z
plane with its centre at the origin O, A particle of mass
– q
O m and positive charge q is projected from the point
D C
P(R 3, 0,0) on the positive x-axis directly towards
O, with an initial speed v. Find the smallest (non-
B +q zero) value of the speed v such that the particle does

not return to P. [IIT-1993]
The moving charge, when it reaches the point C at a
Sol. Let the particle be at a distance x from the origin at a
distance of 4 m from O, has a kinetic energy of 4
point P at any instant. The electric field at P due to
joules. Calculate the distance of the farthest point D
charge on the circular ring is
which the negative charge will reach before returning
Y
towards C.
Sol. Total energy of the system of three charges when the
charge – q is at C
= P.E + K.E. q v A
X
Kq×q K(q)(–q) Kq(–q) x P ( 3R,0,0)
= + + +4 ...(i)
 
 6 5 5 
+q Z
x2+32 A 1 2πRλx
5m E = from P to X
4πε (R2+x2)3/2
3m 0
D x 3m 4m C ∴ Force acting on q at P
–q
F = qE
B 5m
x2+32 Small amount of work done in moving the particle
+q toward O for an infinitsinally small distance dx

dW = Fdx
Final energy of the system of three charges when – q
is at D and momentarily at rest = P.E. + K.E. 1 2πRλxqdx
=
Kq×q Kq(–q) Kq(–q)  4πε0 (R2+x2)3/2
=  + + 
The total work done
 6 x2+32 x2+32 
0
2πRλq xdx
Kq×q 2Kq(–q) W = ∫ ...(i)
= = ...(ii) 4πε (R2+x2)3/2
6 x2+32 0 3R
0
By the principle of conservation of energy from (i) xdx
Now, ∫
and (ii) we get (R2+x2)3/2
3R
kq×q 2kq(–q) kq×q 2kq(–q)
+ = 4 = + Let R2 + x2 = t
6 5 6 x2+32
∴ 2xdx = dt
1 1  dt
2 = kq2  –  ⇒ xdx =
5 x2+32  2
dt 1 2  1
2 1 1 ∴ ∫ = –  = –
= – 2t3/2 2 t t
9×109×5×10–5×5×10–5 5 x2+32
0
 1 
20 1 1 = – 
= –
9×5×5 5 x2+32  R2+x2  3R
1 1 4 9–4 5 1 1 1 1 1 1
= – = = = = – + = – + = –
x2+32 5 45 45 45 9 R R2+3R2 R 2R 2R
∴ x2 + 9 = 91 ∴ x + 8.48 m Substituting in (i) we get
2πRλq 1 λq
W = × =
4πε 2R 4ε
0 0
XtraEdge for IIT-JEE 8 JUNE 2011