study

Questiom of TELECOMMUNICATION SYSTEMS (sem-5) -2009

noreply@blogger.com (abhilash thakur) — Mon, 29 Mar 2010 09:59:00 +0000

                               TELECOMMUNICATON SYSTEM
                             CS/B.tech(ECE)SEM-5/EC-501/209-10
1. Choose the correct Alternative.
(1) In modem uploading data rates always less then downloading data rates because
   (i) SNR (20db)is very low in communication channel.
   (ii) quantisation noise limits the channel data rates
   (iii) during uploading extra control bits are added with the data
   (iv) none of these.
(2) the voice signal BW is 4 KHz and the Nyquist sampling rate is 8 KHz and time multiplexed space swiching 30 channel is to be multiplexed. the TS is
   (i) 4.16 micro sec (ii) 8.33 micro sec. (iii)125 micro sec (iv) none of these
(3) MTTR means
   (i) Mean time to repair (ii) Maximum time to repair
   (ii) Most time to repair (iv) mean time to represent.
(4) Blocking probability is
    (i) call congestion (ii) time congestion (iii) both (i) and (ii). (iv)none of these
(5) GOS in india is
   (i)0.002 (ii) 0.02 (iii) 0.2 (iv) 2.
(6) ISDN B-channel carries data and service at
    (i) 16 kbps (ii) 32 kbps (iii) 64 kbps (iv) 1.544 Mbps
(7) Loudspeaker is an end instrument of
   (i)transmitter side (ii) receiver side (iii) both (iv) none of these
(8) CHILL is a
    (i) CCITT language (ii) IEEE language (iii) IEE language (iv) ANSI language.
(9) Attenuation can be reduced in subscriber loop by using
   (i) higher diameter in copper wire (ii) series of inductance in line
   (iii) lower diameter in copper wire (iv) serise of capacitance in line.
(10) SDL stands for
    (i) software description language (ii) specification derived language
    (iii) specification description language (iv) sofeware derive language.
(11) A subscriber makes 3 calls of 3 mints , 4 mints, and 2 mints duaration in one hour period Calculate the subscriber traffic in Erlangs.
   (i)0.15 E (ii) 0.2E (iii)0.5E (iv) 0.7 E
(12) In a Strowger system the high value of CCI indicates
   (i) good design (ii) poor design (iii) no impact on design (d) none of these
                       GROUP - B
Answer any three
2 (a) What do you mean by point to point communication ?
   (b) Explain the disadvantages of this system
   (c) If the number of node in point to point communication is 770 , find out the total number of links required for total connevtivity.
3. (a) Show the GOS = p b , explain the meaning of the symbol.
   (b) Over a 20 minute observation interval, 40 subscribers initiate calls. Total duration of the calls is 4800 sec . calculate the load offered to the network by the sescribers and the average subscriber traffic.
4. What is call completion rate (CCR) ? 10000 subscribers are connected to an exchange , if the exchange is designed to achieve a CCR of 0.8 when the busy hour calling rate is 4.8 , calculate BHCA of the exchange.
5. What is BORSCHT function ? Why is this important in electronics exchange.
6. How many type of transmission medi are used in telecommunication ? What are the advantages of twisted pair cable over parallel wire cable ? what is step index fiber and graded index fiber?
                    GROUP -C
Answer any there
7 (a) assuming simultaneously forward and backward wave propagation in a transmission line. Derive the follwing general equation for the line,
    V=V1cos hrd +I1Z0sinhrd,
    I= I1coshrd+I1/Z0 sinhrd,
   Where V and I are the voltage and current respectively at a distance from a load end of the transmission line having characteristic independence Z0 and propagation constant r. the load end voltage and current V1 and I1respectively.
(b) A loseless line has a characteristics impedance of 75 ohm and is terminated in a load of 300 ohms . find out the reflection cofficient and VSWR in the line.
(c) explain the principle of DTMF dialing.
8. (a) what ia ISDN? Explain the transmission channel in ISDN?
   (b) what are the drawbacks of ISDN? how does B-ISDN overcome from this?
(C) Write function grouping and reference point in ISDN.
9. (a) Explain centralized SPC and different modes of it.
(b) Explain distributed SPC and explain the different types of leve processing in it.
(c) In the load sharing configuration of centralised SPC MTBF =2000 hours and MTTR =4 hours calculate the unavailability for single and dual processor system.
(d) Explain time division space switching.
10. What is DTE and DCE? Explain how data communication takes place between DTE and DCE using RS @#@C serial interface. why is conventional telephone modem down stream data rate 56 kbps? A telephone line has a bandwidth of 3000 Hz and SNR is 34 Db calculate the data rate of this line.
11. Write short notes on any three of the following.
(A) Packet switching
(b) ISDN systems interface.
(c) Difference between circiut switch , packet swith and message swith
(d) Modems and standards
(e) facsimile transmission.

EKT Question of MECHANICAL ENGINEERING

noreply@blogger.com (abhilash thakur) — Sun, 28 Mar 2010 06:05:00 +0000

PART B-1 AE (M): MECHANICAL ENGINEERING
1. An impulse turbine
(A) Makes use of a draft tube
(B) Always operates submerged
(C) Converts the pressure head into velocity
head through the vanes
(D) Is most suited for low head installations
2. Power required to drive a centrifugal
pump is directly proportional to
(A) Diameter of its impeller
(B) Square of diameter of its impeller
(C) Cube of diameter of its impeller
(D) Fourth power of diameter of its
impeller
3. The locus of the common point on the
two meshing spur gears is known as
(A) Addendum circle
(B) Duodenum circle
(C) Pitch circle
(D) Base circle
4. When there is a reduction in amplitude
over every cycle of vibration then the body
is said to have
(A) Free vibration
(B) Forced vibration
(C) Damped vibration
(D) Natural vibration
5. For machining at high speed the tool
material should have
(A) Wear resistance
(B) Red hardness
(C) Toughness
(D) All of these
6. MIG welding is
(A) A gas welding process
(B) An electric resistance welding process
(C) A electric resistance welding process
(D) A forge welding process involving high
temperatures and low pressures
7. The ability of sand to permit the metal to
shrink when it solidifies is known is
(A) Plasticity (B) Permeability
(C) Collapsibility (D) Cohesiveness
8. Rivets are generally specified by
(A) Overall length
(B) Shank diameter
(C) Thickness of plates to be jointed
(D) Diameter of head
9. Which of the following is steady flow
compressor
(A) Reciprocating compressor
(B) Centrifugal compressor
(C) Voot blower
(D) Vane blower
10. A closed cycle gas turbine works on
(A) Carnot cycle (B) Rankine cycle
(C) Brayton cycle (D) Joule cycle
11. Thermal conductivity of solid metals
(A) Decreases with rise in temperature
(B) Does not vary with temperature
(C) Increases with rise in temperature
(D) Remains constant with rise in
temperature
12. During adiabatic saturation process, air
property which remains constant, is known
as
(A) Wet bulb temperature
(B) Dry bulb temperature
(C) Relative humidity
(D) Specific humidity
13. Bell-Coleman cycle as applied to
refrigeration operates
(A) On open air system
(B) On vapour compression system
(C) On vapour absorption system
(D) On none of these
14. The gears in which axes of the shaft
connected by them, intersect, are known as
(A) Spur gears (B) Bevel gears
(C) Spiral gears (D) Gear train
15. Shot peening
(A) Is done at re-crystallization temperature
(B) Changes the crystalline structure at
materials
(C) Improves the fatigue life of small parts
(D) Refines the grain structure
16. In a bomb calorimeter the heat released
by the fuel is absorbed by
(A) Atmospheric air
(B) Water
(C) Metal container
(D) Bomb, water and metal container
17. Nitriding is done
(A) On low carbon steels only
(B) To impart blue colour to steels
(C) To improve machinability
(D) To increase surface hardness
18. The extent of cold work that a metal can
withstand depends on
(A) Purity of metal
(B) Carbon percentage
(C) Ductility
(D) Room temperature
19. Which engine has the highest air fuel
ratio
(A) Petrol engine (B) Gas engine
(C) Diesel engine (D) Gas turbine
20. Annealing of steels is done to
(A) Remove internal stresses
(B) Produce soft core under hard surface
(C) Produce hard core under soft surface
(D) Introduce capacity to withstand shocks

EKT Question of ELECTRONICS AND COMMUNICATIONS

noreply@blogger.com (abhilash thakur) — Sun, 28 Mar 2010 06:00:00 +0000

The model question paper only offers a broad overview and does not purport to represent either
the syllabus or the pattern of questions that would appear in the Engineering Knowledge Test
PART B-4 AE (L): ELECTRONICS AND COMMUNICATIONS
1. In a communication system, noise is
most likely to get into the system
(A) at the transmitter
(B) in the channel
(C) in the information source
(D) at the destination
2. When modulation frequency is doubled,
the modulation index is halved, and the
modulating voltage remains constant, the
modulation system is
(A) amplitude modulation
(B) phase modulation
(C) frequency modulation
(D) angle modulation
3. Impedance inversion may be obtained
with
(A) a short – circuited stub
(B) an open – circuited stub
(C) a quarter – wave line
(D) a half – wave line
4. HIGH frequency waves are
(A) observed by the F2 layer
(B) reflected by D layer
(C) capable of use for long-distance
communication on the moon
(D) affected by the solar cycle
5. Which one of the following terms does
not apply to the Yagi-uda array
(A) Good band width
(B) Parasitic elements
(C) Folded diploe
(D) High gain
6. A duplexer is used
(A) to couple two different antennae to a
transmitter without mutual interference
(B) to allow one antenna to be used for
reception or transmission without mutual
interference
(C) to prevent interference between two
antennae when they are connected to
receiver
(D) to increase the speed of the pulses in
pulsed radar
7. Indicate which of the following system is
digital
(A) Pulse – Position modulation
(B) Pulse – Code modulation
(C) Pulse – Width modulation
(D) Pulse – Frequency modulation
8. A forward error correcting code corrects
errors only
(A) requiring partial retransmission of the
signal
(B) requiring retransmission of entire signal
(C) using parity to correct to errors in all
cases
(D) requiring no part of the signal to be
transmitted
9. A typical signal strength received from a
geosynchronous communication satellite is
of the order of
(A) a few milli watts
(B) kilo watts (C) watts
(D) few pico watts
10. Telephone traffic is measured
(A) with echo cancellers
(B) by the relative congestion
(C) in terms of the grade of service
(D) in erlangs
11. Positive logic in a logic circuit is one in
which
(A) logic 0 and 1 are represented by 0 and
positive voltage respectively
(B) logic 0 and 1 are represented by
negative and positive voltages respectively
(C) logic 0 voltage level in higher than
logic 1 voltage level
(D) logic 0 voltage level is lower than logic
1 voltage level
12. A half-adder can be made from
(A) two NAND gates
(B) a NOT gate and an OR gate
(C) an AND gate and an OR gate
(D) an AND gate and an X-OR gate
13. Which of the following devices has its
characteristics very close to that of an ideal
current source.
(A) Field effect transistor
(B) Transistor in common bas mode
(C) Zener diode
(D) MOSFET
14. The main use of a common base
transistor amplifier is
(A) as voltage amplifier
(B) current amplifier
(C) for matching a high source impedance
to a low load impedance
(D) for rectification of a.c. signal
15. A class-B amplifier is biased
(A) Just at cut-off
(B) nearly twice cut-off
(C) at mid point of load line
(D) so that IB equals jut IC
16. If the peak transmitted power in a radar
system is increased by a factor of 16, the
maximum range will be increased by a
factor of
(A) 2 (B) 4 (C) 8 (D) 16
17. A high PRF will (indicate the false
statement)
(A) make the returned echoes easier to
distinguish from noise
(B) make target tracking easier with conical
scanning
(C) increase the maximum range
(D) have no effect of the range resolution
18. A solution to the “blind speed” problem
in a radar system is to
(A) change the Doppler frequency
(B) vary the PRF
(C) use mono pulse
(D) use MTI
19. The number of active picture elements
in a television image depends on
(A) fly back time
(B) CRT screen size
(C) received band width
(D) FB ratio of receiver antenna
20. In a colour TV, the three primary
colours are
(A) red, orange and blue
(B) red, blue and green
(C) red, green and yellow
(D) red, orange and green

Modal Question Paper for EKT General Engineering

noreply@blogger.com (abhilash thakur) — Sun, 28 Mar 2010 05:39:00 +0000

MODEL QUESTION PAPER
ENGINEERING KNOWLEDGE TEST (EKT)
Part A: General Engineering
1. The probability of hitting a target from
one gun 9/10, from another gun is 7/10. If
both gun are fired at the same time, the
probability of hitting the target is
(A) 2/20 (B) 63/100
(C) 16/20 (D) 63/20
2. If the three vectors a, b and c are
coplanar , then the missed product a x b. c
is
(A) Zero (B) Non-Zero
(C) Unity (D) Non of these
3. Limit sin x is
x→0 x
(A) not defined (B) 1
(c) zero (D) -1
4. The Laplace transform of sin23t is
(A) 18 (B) 18
S(S2+36) S2(S+36)
(C) 18 (B) 18
(S+36) (S+36)(S+4)
5. The function
x2 for x< 3
f(x)
2x+3 for x>3
(A) continuous over the entire number scale
(B) continuous at x=3 but discontinuous at
all other points
(C) discontinuous at x=3 but continuous at
all other points
(D) discontinuous everywhere
6. When a body hits an obstacle, the force
with which it hits the obstacle depends
upon its
(A) average velocity
(B) velocity at the instant of collision
(C) initial velocity
(D) all of these
7. The wavelength of visible light is of the
order of
(A) 1μm (B) 100 μm
(C) 1mm (D) 1 Å
8. Whenever a source of sound moves
towards an observer
(A) the frequency heard by the observer is
less than that of the source
(B) the frequency heard by the observer is
greater than that of the source
(C) the frequency heard by the observer is
unchanged
(D) the wavelength of sound heard is
greater than that of the sound emitted
9. Moving electric charges will interact
with
(A) electric field only
(B) magnetic field only
(C) both of these
(D) none of these
10. Gamma radiation is most similar to
(A) sound waves (B) X-ray
(C) Alpha particles (D) neutrons
11. The fundamental particle responsible
for keeping the nucleus together is
(A) meson (B) anti proton
(C) positron (D) muon
12. Air contains 21% oxygen by volume
and the rest nitrogen. If the barometer
pressure is 740 mm of Hg the partial
pressure of oxygen is close to
(A) 155 mm of Hg
(B) 310 mm of Hg
(C) 465 mm of Hg
(D) 162 mm of Hg
13. In the electrolytic cell
(A) electrical energy is converted into
chemical energy
(B) chemical energy is converted into
electrical energy
(C) mechanical energy is converted into
potential energy
(D) potential energy is converted into
kinetic energy
14. The force required to maintain a body at
constant speed in free space is equal to
(A) the mass of the body
(B) zero
(C) the weight of the body
(D) the force required to stop it
15. If the length of a spring is halved, the
spring constant becomes
(A) half (B) 1/4th
(C) double (D) four times
16. The coefficient of static friction
depends on
(A) the material of the bodies in contact
(B) the quality of surface finish of the
bodies
(C) the presence of foreign matter between
the surface
(D) all of these
17. The units of angular impulse in SI
system are
(A) Nms (B) Ns
(C) Nm/s (D) Ns/m
18. A particle is projected with a velocity
√4gR
3 ½ ½
(A) gR (B) gR
2 3
½ ½
(C) gR (D) 2gR
3
19. Stainless steel contains iron and
(A) Chromium and nickel
(B) Chromium and carbon
(C) Nickel and carbon
(D) Chromium and manganese
20. The property of material by which it
offers resistance to scratching or
indentation is called
(A) Brittleness
(B) Hardness
(C) Toughness
(D) Resilience
21. The failure of a material due to repeated
stressing is known as
(A) Creep
(B) Fracture
(C) Fatigue
(D) Brittle Fracture
22. The electric device which blocks DC
but allows AC is called
(A) Capacitor
(B) Inductor
(C) Amplifier
(D) Transducer
23. When a charge is moved from one point
to another in an electric field, the work
done is
(A) independent of the path
(B) zero along the direction of the field
(C) measured in Joules per metre
(D) measure in Volt per metre
24. A capacitor with lowest leakage is
(A) Paper (B) Ceramic
(C) Polyester (D) Mica
25. A zener diode operates
(A) In an extremely high forward bias
(B) In an extremely low reverse bias
(C) In an extremely low forward bias
(D) In a reverse bias higher than laid down
voltage
26. The specific gravity of a lead acid cell
is often used as a measure of its
(A) Rate of discharge
(B) Operating temperature
(C) State of charge
(D) Life expectancy
27. An uniformly distributed load is one
which
(A) Acts at a point on a beam
(B) Spreads uniformly over the whole
length of a beam
(C) Varies uniformly over the whole length
of a beam
(D) loads the beam from one end only
28. A steam engine device which keeps the
speed of the engine, all loads, constant is
known as
(A) Flywheel
(B) Eccentric
(C) Connecting rod
(D) Governor
29. The refrigerant hiving the lowest
freezing point is
(A) Ammonia
(B) Carbon dioxide
(C) Freon – 11
(D) Freon – 22
30. Heat and work are
(A) Path functions
(B) Properties of a substance
(C) Point functions
(D) Absolute units

EKT (Engineering Knowledge Test) exam scheme

noreply@blogger.com (abhilash thakur) — Sun, 28 Mar 2010 05:35:00 +0000

Engineering Knowledge Test is a common test aimed at testing the Basic Engineering knowledge of the candidates applied for
Aeronautical Engineering Courses. EKT has two parts, namely
Part A - General Engineering: 40 Questions Duration: 1 Hour
Part B - Specialist Paper for each Engineering discipline: 35 Questions
Engineering Knowledge Test is pitched at pre-final to final year engineering level. The test consists of two parts viz General Engineering
and Specialist subjects for the two streams of Technical Branches i.e Aeronautical Engineering (Electronics) and Aeronautical
Engineering (Mechanical).
The specialised papers are in Mechanical Engineering, Aeronautical engineering, Electronics and Communication engineering, Electrical
and Instrumentation engineering and Computer Engineering.
The questions are objective type in nature and duration of test is approximately one hour. It is mandatory for the candidates to pass in
both General and Specialist papers to qualify for AFSB interview.

syllabi for General Aptitude for Gate 2010

noreply@blogger.com (abhilash thakur) — Thu, 17 Sep 2009 17:29:00 +0000

Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.

Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data interpretation.

Gate-2010 (New rule)

noreply@blogger.com (abhilash thakur) — Thu, 17 Sep 2009 17:14:00 +0000

IN Gate 2010 some new things is added . some of them are as follows:-
1. Biotechnology (BT) has been introduced as an independent paper from GATE 2010.
2.Common Component of General Aptitude (GA) introduced in GATE 2010: Each GATE paper shall have a common General Aptitude (GA) component carrying 15 marks from GATE 2010.
3. Q.56 to Q.60 : From General Aptitude (GA) will carry one mark each (sub-total 5 marks).1/3 marks will be deducted for each wrong answer.Q.61 to Q.65 : From GA will carry two marks each (sub-total 10 marks).2/3 mark will be deducted for each wrong answer.
4. All the papers bearing the codes AE, AG, BT, CE, CH, CS, EC, EE, IN, ME, MN, MT, PI and TF will contain few questions on Engineering Mathematics carrying 15 marks.
5.GATE 2010 score is valid for TWO YEARS from the date of announcement of the GATE 2010 results
6.

History of cricket

noreply@blogger.com (abhilash thakur) — Fri, 28 Aug 2009 19:38:00 +0000

एक नए शोध में दावा किया गया है कि क्रिकेट मूल रूप से ब्रिटेन का खेल नहीं है बल्कि उत्तर बेल्जियम के अप्रवासियों के जरिए इंग्लैंड लाया गया है। एक कविता जिसके बारे में कहा जाता है कि यह 1533
में लिखी गई थी, उसकी खोज से ये बात सामने आई है कि ये खेल फ्लैंडर्स में शुरू हुआ था।

ऑस्ट्रेलियन नैशनल यूनिवर्सिटी के पॉल काम्पलेक्स के अनुसार जॉन स्केलटन की रचनाओं में फ्लेमी बुनकरों को 'किंग ऑफ क्रिकेटर्स' कहा गया है। इस खोज ने पुराने तथ्य को चुनौती दी है जिसके अनुसार ये मान लिया गया था कि क्रिकेट का खेल अंग्रेज बच्चों के खेलकूद से निकला है। इंग्लैंड में इसका पहला निश्चित उल्लेख 16वीं शताब्दी में मिलता है जब चर्च से भाग कर खेलने वालों पर जुर्माना लगाया गया था।

इस देश में जनसाधारण के इस खेल को पब्लिक स्कूल, ऑक्सफर्ड और कैम्ब्रिज जैसी यूनिवर्सिटियों में अगली शताब्दी में शामिल कर लिया गया। पहले क्रिकेट क्लब की स्थापना हैम्बेलडन में 1760 में हुई और सुप्रसिद्ध मेरिलेबॉन क्रिकेट क्लब (एमसीसी)की स्थापना 1787 में हुई।

लेकिन जर्मन शोधकर्ता और उनके ऑस्ट्रेलियाई सहयोगी कैम्पबेल ने कहा है कि इस खोज से ये साबित होता है कि कुछ भी हो यह विशिष्ट ब्रितानी खेल ब्रितानी नहीं है। कैम्पबेल ने 16वीं शताब्दी की एक रचना 'द दमेज ऑफ इपोक्रिसी' में क्रिकेट का एक उल्लेख ढूंढ निकाला है। इस रचना को अंग्रेजी के कवि स्केलटन से जोड़ा जाता है और इसमें फ्लेमी बुनकरों का जिक्र मिलता है जो दक्षिण-पूर्वी इंग्लैंड में जा बसे थे। उन्हें 'किंग ऑफ क्रिकेट' यानी क्रिकेट का बादशाह कहा गया है। इसमें विकेट का भी जिक्र है। आपको यह सोच कर हैरानी होगी कि बेल्जियम क्रिकेट नहीं खेलता है।

ISRO elctronics syllabus

noreply@blogger.com (abhilash thakur) — Sun, 19 Jul 2009 10:32:00 +0000

* Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices.
* Solution methods: nodal and mesh analysis.
* Network theorems: superposition, Thevenin and Norton’s maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis simple RLC circuits, Solution of network equations using Laplace transform; frequency domain analysis of RLC circuits.
* 2-port network parameters: driving point and transfer functions. State equations for networks.
* Electronic Devices: Energy bands in silicon, intrinsic and extrinsic silicon.
* Carrier transport in silicon: diffusion current, drift current, mobility, resistivity. Generation and recombination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-I-n and avalanche photo diode, LASERs. Device technology: integrated circuits fabrication process, oxidation, diffusion, ion implanation, photolithography, n-tub, p-tub and twin-tub CMOS process.
* Analog Circuits: Equivalent circuits (large and small-signal) of diodes, BJTs, JFETs, and MOSFETs. Simple diode circuits, clipping, clamping, recitifier. Biasing and bias stability of transistor and FET amplifiers.
* Amplifiers: single-and multi-stage, differential, operational, feedback and power. Analysis of amplifiers; frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits. Power supplies.
* Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinational circuits: arithmetic circuits, code converters, multiplexers and decoders.
* Sequential circuits: latches and flip-flops, counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories.
* Microprocessor(8085): architecture, programming, memory and I/O interfacing.
* Signals and Systems: Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier seris, continuous-time and discrete-time Fourier Transform, z-transform. Sampling theorems. Linear Time-Invariant (LTI) Systems: definitions and properties; casuality, stability, impulse response, convoilution, poles and zeros frequency response, group delay, phase delay. Signal transmission through LTI systems.
* Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density.
* Controls Systems: Basic control system components; block diagrammatic description, reduction of block diagrams. Open loop and closed loop (feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady state analysis of LTI control systems and frequency response.
* Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion, Bode and Nyquist plots.
* Control system compensators: elements of lead and lag compensation, elements of Proporational-Integral-Derivative(PID) control. State variable representation and solution of state equation of LTI control systems.
* Communications: Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superheterodyne receivers; elements of hardware, realizations of analog communication systems; signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions.
* Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), delta modulation (DM); digital modulation schemes-amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwith consideration and probability of error calculations for these schemes.
* Electromagnetics: Elements of vector calculus: divergence and curl; Gauss’ and Stokes’ theorems, Maxwell’s equations: differential and integral forms. Wave equation, Poynting vector.
* Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth.
* Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; pulse excitation.
* Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations.
* Antennas: Dipole antennas; antenna arrays; radiation pattern; reciprocity theorem, antenna gain.

Disclaimer: We do not take any responsibility of the accuracy of the information provided on this site. You are requested to verify and confirm the final details from the concerned company or department.

books for IES

noreply@blogger.com (abhilash thakur) — Mon, 15 Jun 2009 16:49:00 +0000

Recommended Books for IES
Books for IES Electronic and Telecommunications Engineering
- Network Analysis: Van Valkenburg
- Network and Systems: D. Roy Choudhary
- Integrated Electronics: Jacob Milman & C. Halkias, Millman & Grabel
- Integrated Circuits: K.R. Botkar
- Op. Amps & Linear Integrated Circuit: Gayakwad
- Digital Logic & Computer Design: Moris Mano
- Signals and System: Oppehum, Willsky & Nacob
- Automatic Control System: Benjamin C. Kuo
- Control System Engineering: Nagrath & Gopal
- Principle of Communication System: Taub & Schilling
- Communication System: A. Bruu Carlson
- Electromagnetic Waves & Radiating Systems: Jardon & Balmain, JD Kraus

Books for IES Electrical Engineering
- Network Analysis: Van Valkenburg
- Electromagnetic: Willain H. Hayt
- Electrical Machinery: PS Bhimra
- Electrical Machines: Nagrath & Kothari
- Power System Engineering: Nagrath & Kothari
- Electric Power Systems: CL Wadhwa
- Automatic Control System: Benjamin C. Kuo
- Control System Engineering: Nagrath & Gopal
- Electrical & Electronic Measurement and Instrumentation: AK Sawhney
- Integrated Electronics: Milman & Halkias, Millma & Grobel
- Digital Logic & Computer Design: Morris Mano
- Power Electronics: PS Bhimra

Books for IES Civil Engineering
- Strength of Materials: Gere & Temoshenko, B C Punamia
- Structural Analysis: Negi, S Ramamurtham, C K Vang
- Concrete Structures: Punamia & Jain, H J Shah
- Steel Structures: Duggal
- Soil Mechanics & Foundation Engineering: Ranjan & Rao, Venkat Ramaiha, S K Garg
- Fluid Mechanics and Hydraulics: Modi & Seth, R K Bansal, Subramanyam
- Hydrology: Subramanyam
- Irrigation: S K Garg
- Highway Engineering: Khanna & Jasto, Kadiyali

Books for IES Mechanical Engineering
- Enginnering Thermodynamics: PK Nag
- IC Engine: ML Mathur and RP Sharma
- Gas Turbine and Propulsive Systems: PR Khajuria & SP Dubey
- Fluid Mechanics: Modi & Seth, RK Bansal
- Compressible Flow: SM Yahya
- Heat and Mass Transfer: JP Hollman, RC Sachdeva
- Refrigeration and Air Conditioning: CP Arora, Domkundwar
- Fluid Machinery: Jagdish Lal, RK Bansal
- Theory of Machines: RS Khurmi, Malik & Ghosh
- Mechanical Vibration: Grover
- Machine Design: Shigley, VB Bhandari
- Material Science: WD Callister, IP Singh
- Production Engineering: Kalpkjian Schmid, Amitabh Ghosh & AK Malik
- Industrial Engineering: O P Khanna, Buffa & Sarin
- Operations Research: Kanti Swarup
- Strength of Materials: Gere & Timoshenko, BC unamia, Sadhu Singh

GATE syllabus of EE

noreply@blogger.com (abhilash thakur) — Sat, 13 Jun 2009 14:44:00 +0000

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory: Fourier transform, Laplace transform, Z-transform.

ELECTRICAL ENGINEERING

Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources, Thevenin's, Norton's and Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions; Ampere's and Biot-Savart's laws; inductance; dielectrics; capacitance.

Signals and Systems: Representation of continuous and discrete-time signals; shifting and scaling operations; linear, time-invariant and causal systems; Fourier series representation of continuous periodic signals; sampling theorem; Fourier, Laplace and Z transforms.

Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; auto-transformer; energy conversion principles; DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications; servo and stepper motors.

Power Systems: Basic power generation concepts; transmission line models and performance; cable performance, insulation; corona and radio interference; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of over-current, differential and distance protection; solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion; HVDC transmission and FACTS concepts.

Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Niquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; state space model; state transition matrix, controllability and observability.

Electrical and Electronic Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; instrument transformers; digital voltmeters and multimeters; phase, time and frequency measurement; Q-meters; oscilloscopes; potentiometric recorders; error analysis.

Analog and Digital Electronics: Characteristics of diodes, BJT, FET; amplifiers - biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers - characteristics and applications; simple active filters; VCOs and timers; combinational and sequential logic circuits; multiplexer; Schmitt trigger; multi-vibrators; sample and hold circuits; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing.

Power Electronics and Drives: Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters - fully controlled and half controlled; principles of choppers and inverters; basis concepts of adjustable speed dc and ac drives.

Microelectronic & optoelectronic quastion of 2007 ,4th sem ECE ,WBUT

noreply@blogger.com (abhilash thakur) — Fri, 12 Jun 2009 12:36:00 +0000

Microelectronic and optoelectronic 2007 ,wbut 4th semester
GROUP-B
2. Derive the one dimensional continuity equation for minority carriers in generation recombination process, under low injection condition.Gn, GP, Rn and Rp are generation and recombination rates for electron/hole.
3. What is population inversion in laser? What is external quantum efficiency in a semiconductor laser? What is the optical feedback and oscillation by which the amplified coherent emission is obtained?
4. An n-type semiconductor at thermal equilibrium(T=300K) has a linear variation in doping concentration given by Nd(x)=1016-1919x, 0≤x≤1µm.Determine induced electric field. (volt equivalent temperature at room temperature =0.02V)
5. Discuss the principle of operation of vertical power BJT.
6. With energy band diagram describe schottky junction barrier formation . Describe its operation under external bias.
GROUP-C
7. (a) What is SCR? point out its major uses.
(b0 By using two transistor analog, briefly describe the operation of two terminal scr.
(c) Is it possible to observe the purpose of SCR by connecting two transistors? Explain.
(d) How does the presence of third terminal control the I-V response of SCR? Explain with system diagram.
8. (a) Sketch the ideal energy band diagram of a metal-semiconductor junction in which Фm<фs. Explin why this is an ohmic contact.
(b) Discuss how 2D-electorn gas is formed ain semiconductor heterojuction.
(c) the schottky barrier of a Si schottky junction is фBN=0.59v,the effective Richardson is A=111A/K2-cm2 and the crosssection area is a=10-4cm2
for T=100k, calculate
(i) Ideal reverse saturation current
(ii) The diode current for V (applied)=0.30V.
9. (a) Illustrate the basic process flow in micromanaging? What do you mean by optical lithography?
(b) What do you mean by plasma etching?
(c) Explain one non-lithographic microfabrication technology.
10. (a) What is the advantage of optical fibre over the copper wire system ?
(b) What is the difference between step index and graded index fibres?
(c) Distinguish between non-radiative and radiative recombination processes in a semiconductor .Express the internal quantum efficiency in terms of the life times of the process.
(d) Asilican optical fiber has a core refractive index of 1.5 and the cladding refractive index of 1.450 . calculate
(i) the critical angle for the core cladding interface.
(ii) the acceptance angle in air for fiber .
(iii) the nimerical aperture (NA) of the fiber.
11. Write short note on any three of the following
(a) Solar cell
(b) semiconductor laser
(c) Insulated bipolar junction transistor
(d) P-I-N photodiode
(e) O.E.I.C.

WBUT question of Analog communication 2007

noreply@blogger.com (abhilash thakur) — Fri, 05 Jun 2009 08:28:00 +0000

2007
ANALOG COMMUNICATION
GROUP-B
2 (A) Define amplitude modulation and modulation index. Use a sketch of sinusoidally modulated AM waveform to help to explain the definition.
(b) Derive the expression between the output power of an AM transmitter and the depth of modulation.
3. What is angle modulation ? Justify that frequency modulation is an angle modulation.
4. drive the expression of single to noise ratio of DSB-SC system.
5.(A)What do you mean by FDM? when it is used?
(b) What is Carson's rile?
6. The equation for an FM wave is
S(t)=10sin(5.7×108t + 5sin12×103t)
Calculate:
(a) carrier frequency
(b) modulating frquency
(c) frequency deviation
(d) modulation index
(e) power dissipated in 100 ohm
GROUP-C
7.(a) What is the concept behind NBFM ? Drive its equation.
(b) Explain how FM can be generated using VCO.
(c) Discuss about the roles of pre-emphasis and de-emphasis circuit in FM
broadcasting.
8.(a) Draw the block diagram for generation and detection of PCM system.
(b) What is quantization? Find signal to quantization noise ratio for PCM system.
(c) A signal is sampled at Nyquist rate of 8 kHz and is quantized using 8 bit uniform quantizer. Assuming SNRq for a sinusoidal signal, calculate bit rate, SNRq and BW.
9 (a) State and prove parseval's power theorem.
(b) Describe with a block diagram the principle of operation of a square low modulator generating DSB-SC.
(c) Explain the advantages and disadvantages of modulation.
10 (a) Draw the block diagram of a superheterodyne receiver and explain its working principle .
(b) Explain the operation of balanced modulator.
11 Write short notes on any three of the following :
(a) Entropy and its properties
(b) QCM
(c) termal noise
(d) power spectral density function
(e) pulse coded modulation

Question of WBUT Analog circuit of 2008 4th sem ECE

noreply@blogger.com (abhilash thakur) — Tue, 02 Jun 2009 06:12:00 +0000

hi my friends form 3rd june B.TECH exam of WBUT is start ,so i going to post the Question paper of 2008 of ECE 4th sem .i try to post the question paper before exam.so today i am posting the question of anlog circuit of 4th sem because the frist exam is analog circuit on 4th june.
the Question is as follows(objective question are not given)
QUESTION of 2008
GROUP-B
2. Draw and explain half wave rectifier.
3. compare between class A,class B,and class AB amplifier.
4. what is the advantages and disadvantages of feedback in amplifier?What are the type of feedback required for (i) voltage amplifier (ii) current amplifier?
5. Draw and explain the operation of Hartley oscillator.
6. What is clipper?with help of circuit diagram and wave forms,describe the operation of a positive and negative clipper.
GROUP-C
7 (a) Draw and explain briefly the circuit of single stage current series feedback amplifier . Mention effect of negative feedback on gain and bandwidth.(b) Write down the barkhausen criterion for sinusoidal oscillation.Obtain expression for output frequency and condition to sustain oscillation of a RC phase shift oscillator.
(c) What are the advantages of differential amplifier?
8 (a) a numerical problem form op-amp.
(b) Write down the criteria of good instrumentation amplifier. Draw the circuit of an instrumentation amplifier using a transducer bridge and explain its operation.
(C) Realize multiplier using logarithmic amplifier. Mention application of analog multiplier.
9 (a) Draw the circuit and explain voltage to current converter (Grounded load) .
(B)Explain the Op-Amp integrator circuit .
(c) What is voltage follower ?
10. (a) what is function of voltage regulator ?
(b) Give and explain the important parts of series regulated power supply using discrete component.
(c) Draw the function diagram of 723 regulator.
11.Write short notes on any three of the follwing.
(A) Push pull amplifier
(B) Wein bridge oscillator
(C) Bridge rectifier
(D) clamping circuit
(e) Logarithmic amplifier.
this is question of 2008
bast of luck for sem.

ouestion for WBUT upcoming exam 4th sem ECE

noreply@blogger.com (abhilash thakur) — Fri, 22 May 2009 11:05:00 +0000

Analog Electronics & Circuits
EC-401
Time:3 Hours TotalMarks-70

Group-A

Answer any ten questions 10 x 1= 10

1.i) In a full wave rectifier if the input frequency is 50 Hz then frequency at the output of the filter is
(a) 50 Hz (b)75 Hz (c) 75 Hz (d) 0 Hz

ii) To obtain high input and output impedance the type of the feedback amplifier is (a)Voltage series (b) Current series (c) Voltage shunt (d) Current shunt

iii) An OP-AMP has gain bandwidth product of 1 MHz and a voltage gain of 20 dB .Then the -3dB bandwidth of the OP-AMP will be
(a) 50 kHz (b) 100 kHz (c) 1000/17 (d) 1000/7.07

iv) Wide range of high purity sine wave can be generated by
(a) RC-phase shift oscillator (b) Crystal oscillator (c) Wein bridge oscillator d) Hartley oscillator

v) The slew rate of an OP-AMP is 0.5V/μs.The maximum frequency of a sinusoidal input of 2Vrms that can be handled without excessive distortion is
(a) 3 kHz (b) 30 kHz (c) 200 kHz (d) 2 MHz

vi) In order to generate a square waveform from a sinusoidal input signal the choice of the circuit is
(a) Schmitt trigger (b) Clipper and amplifier (c) Monostable Multivibrator (d) Both a and c

vii) An increase in the ambient temperature means that maximum power rating of the transistor
(a) will increase (b) will decrease (c) may increase or decrease (d) may increase or remain the same.

viii) The threshold voltage of an n channel enhancement mode MOSFET is 0.5 ,when the device is biased at a gate voltage of 3V,pinch of will be occur at a drain voltage of
(a) 1.5 V (b) 2.5 V (c) 3.5 V (d) 4.5 V

ix) Stability factor (S) for a fixed bias circuit is given by
(a) 1+β (b) 1-β (c) 1/β (d) β-1

x) For maximum unclipped output from a CE amplifier , the Q point should be
(a) at the centre of the DC load line.(b) at the centre of the AC load line (c) at the centre of the collector current (d)none of these.

xi) A CB amplifier has re =6 ohm, RL =600 ohm and α= 0.98.Voltage gain is
(a) 100 (b) 588 (c) 98 (d) 6

xii) For high frequency response of a transistor amplifier suitable model to use is
(a) Lattice network (b) Hybrid-π (c) T-network (d) Kelvin network

xiii) The period of oscillation of a symmetrical multivibrator depends upon the discharging time constant and is roughly given by
(a) T=1.4RC (b) T=RC/14 (c) T=1.4 √(RC) (d) T= √(1.4) RC

Group-B

Answer any three questions 3 x 5= 15

2. a) Define the term thermal resistance for a power transistor.
b) A Ge transistor has thermal resistance of its junction as 0.33oC/mW and the ambient temperature is 28 oC.Calculate : (i) maximum power dissipation that can be allowed without heat sink, and (ii) ) maximum power dissipation that can be allowed if a heat sink is used,which reduces the thermal resistance of the transistor to 0.09 oC/mW.
2+3=5
3.Draw the Ebers-Moll model of an npn transistor and find out the expression of the transistor terminal currents.
2+3=5
4.An amplifier has a gain A= 60 dB and output impedance of 12 K. It is required to reduce the output impedance to 500 ohm. Calculate the negative feedback required.
5
5.Find out the expression of the stability factor for a voltage divider biased amplifier.
5
6.a)What will be the shape of the output for the following circuit

b) Find out the expression of ripple factor for a half wave rectifier.
2+3=5

Group-C

Answer any three questions 3 x 15= 45

7.a) What are the differences between voltage and power amplifiers ? Why heat sink is used ?
b) Find out the expression of collector efficiency of a class-A amplifier.
c) An crystal has equivalent series inductance L= 3 H and series capacitance C=0.05 Pf and mounting capacitance Cm=10 pF. Calculate the series and parallel resonant frequencies for the crystal.
(4+2)+4+5=15
8.a)Draw a circuit of differential amplifier with an active load connection.
b)What are the advantages of differential amplifier ?
c)Find out the transconductance of the above amplifier.
d) Explain with diagram the operating principle of 555 timer. 3+2+4+6=15
9. a) Draw the circuit of an instrumentation amplifier and find out the expression of Vo.
b) What will be the transfer function of the following circuit. What type of filter it is ?

c) What are the applications of tuned amplifiers ?(2+4)(6+1)+2=15
10.a)Draw the I-V characteristics of a CE configuration transistor
b) What do you mean by early-effect.
c) Show that a transistor can be used as an inverter.
d) Analyze the transistor amplifier (shown below in the figure)using small signal equivalent circuit. Given β = 100.
2+1+4+8=15
11. Write short notes on any of the three from the following given below:
3x5=15
a) Photodiode
b) Wein bridge oscillator.
c) Bistable multivibrator.
d) Enhancement type MOSFET.
e) Schmitt trigger.
i am not able to post the corresponding figure of some question.
this is a question set for upcoming exam of WBUT .

BOOKS for IES ece student

noreply@blogger.com (abhilash thakur) — Tue, 12 May 2009 17:26:00 +0000

1. Electronic Devices and Circuits & Analog Electronics--

(i)Integrated electronics : Analog and Digital Circuit and system by Jacob Millman & Christos C. Halkias

(ii)Microelectronic Circuits by Sedra & Smith

(iii)Electronic Devices and Circuits by J.B. Gupta

(iv)OP Amp and linear Integrated Circuit by Ramakant A. Gayakwad

(v)Solid State electronic devices by Streetman and Banerjee

(vi)Semiconductor devices by S.M.Sze
2. Communication System

(i)Communication System by Simon Haykins

(ii)An introduction to Analog and Digital Communication by Simon Haykins

(iii)Communication System : Analog and Digital by Singh and Sapre

(iv)Modern Digital and Analog Communication System by B.P. Lathi

(v)Electronic Communication System by Kennedyand Davis

3.Signal and System by Oppenheim and Willsky
4. Optical Fiber Communication by Senior
5. Satellite Communications by Pratt and Bostian
6. Monochrome and colour by R.R. Gulati
7. Control System

(i)Control System Engg. by I.G. Nagrath & M. Gopal

(ii)Automatic Control System by B.C. Kuo

(iii)Linear Control System by B.S. Manke
8. Electro Magnetic Theory

(i)Elements of Engineering Electromagnetics by N. N. Rao

(ii)Elements of Electromagnetics by Sadiku

(iii)Engineering Electromagnetics by W.H.Hayt

(iv)Antenna and Wave Propagation by K.D. Prasad

9. Digital Electronics

(i)Digital Design by M. Morris Mano

(ii)Digital Systems by Tocci & Widmer

(iii)Modern Digital Electronics by R. P. Jain
10.
Computer Engg.

(i)Microprocessor Architecture, Programming & Application by Ramesh S. Gaonkar

(ii)Computer Organization and Structure byStalling
11. Microwave Engg.
(i)Microwave Devices and Circuits by Liao

(ii)Microwave Engineering by Sanjeev Gupta

(iii)Microwave Engineering by Pozar
12. Network Theory

(i)Networks and Systems by D. Roy Chaudhary

(ii)Engineering Circuit Analysis by Hayt
13. Electrical Engineering Material by S.P. Seth
14. Measurement and Instrumentation

(i)Electrical & Electronic Measurement and Instrumentation by A. K. Sahney

(ii)Electronic Instrumentation by H. S. Kalsi

EXAMINATION PATTERN

noreply@blogger.com (abhilash thakur) — Tue, 12 May 2009 16:39:00 +0000

hi dear friends welcome once again
now a days i am little bit busy due to my upcoming semester examination
the even semester examination of WBUT will be start form first week of JUNE due to which i am busy ,All of you know how hard syllabus for engineering course . it like impossible to complete the whole syllabus in 6 months.
Teachers and students both are active just before examination,( before one month of exam). teaches give assignment and practical work just before examination. Every day write 20-30 pages of assignment ,lab copy ,after that if you able to menages time go through your big and boring course book, which so weighted if any one hit you by that book properly you do not able to work for some day.
this is time of examination for all engineering college and universities ,so i talk about study pattern of this universities, i the student come here after completing their 12th ,with some dream ,all the principle which read upto class 12th ,is try to apply in real life with the help of lab.they though this is a place where they show their creativity and do some thing different but due to bad educational police of Indian government this is not happen.
Engineering is a course in which the main focus of study is practical knowledge . but Indian government want to student become clerk rather than engineer . there is a need to change the pattern of educational system .
What you think about it and what kind of changes you want in educational system of India . say your idea .
I am waiting for your valuable comment on this impotent topic because this is matter of India development

Study for IIT

noreply@blogger.com (abhilash thakur) — Sat, 09 May 2009 05:46:00 +0000

hi guys today i am share my experience with you .on topic of how to get high rank in IIT jEE.
ITT JEE is the most popular engineering entrance exam in india ,All the student want to do their B.tech degree for iit . The stander of exam is high and question patter is good and design in such a manner that is able to check the basic understanding of subject matter. so no need to take tension .
All of you know the number of student sitting for this examination is very high and sit are limited ,appor 500000 student are sit for exam and only 7000 sit in all iit institute .so first i clear you one thing about number of student.do not take tension about high number of student. more then 50% student sit in exam only for see how the exam is held ,they only fulfill the desire of their parent to sit in iit ,they are to sit for not for admition in iit .now half of rest are low level student ,they have no ability to rank in iit .so real fight for rank only for 1/4th student.
this is a grate exam and all want to success ., so there is high capitation for rank.
for good rank there are neet to a grate plan
today i say about math
first you see the syllabus of iit . For syllabus see my article syllabus of iit mathematics. now you analyze yourself ,which topic is strong and which one is weak.first thing is, you see which topic is most important means form which topic maximum number of question is asked in JEE . For IIT quadratic equation.inequality ,function,limit ,differentiation ,differential equation,circle,conic section ,this is the most important topic .appox 80% of problem come for thic topic.
First you read entire syllabus and after that you concentrated on important topic , because in IIT question are come in such a way that all topic connected to each other ,i.e. for solve one problem need to concept of different topics.
the cut off of iit is very low in math paper so there is no need solve all the problem ,because for one wrong answer your 1/3 mark of a right answer is reduce . so solve only those problem on which you have confidence .
bast of luck for your upcoming exam.

MOSFET

noreply@blogger.com (abhilash thakur) — Sat, 09 May 2009 04:41:00 +0000

A Power MOSFET is a specific type of Metal Oxide Semiconductor Field-Effect Transistor (MOSFET) designed to handle large amounts of power. Compared to the other power semiconductor devices (IGBT, Thyristor...), its main advantages are high commutation speed and good efficiency at low voltages. It shares with the IGBT an isolated gate that makes it easy to drive.
It was made possible by the evolution of the CMOS technology, developed for manufacturing Integrated circuits in the late 1970s. The power MOSFET shares its operating principle with its low-power counterpart, the lateral MOSFET.
The power MOSFET is the most widely used low-voltage (i.e. less than 200 V) switch. It can be found in most power supplies, DC to DC converters, and low voltage motor controllers.
Several structures had been explored at the beginning of the 1980s, when the first Power MOSFETs were introduced. However, most of them have been abandoned (at least until recently) in favour of the Vertical Diffused MOS (VDMOS) structure (also called Double-Diffused MOS or simply DMOS).
The cross section of a VDMOS (see figure 1) shows the "verticality" of the device: It can be seen that the source electrode is placed over the drain, resulting in a current mainly vertical when the transistor is in the on-state. The "diffusion" in VDMOS refers to the manufacturing process: the P wells (see figure 1) are obtained by a diffusion process (actually a double diffusion process to get the P and N+ regions, hence the name double diffused).
Power MOSFETs have a different structure than the lateral MOSFET: as with all power devices, their structure is vertical and not planar. In a planar structure, the current and breakdown voltage ratings are both functions of the channel dimensions (respectively width and length of the channel), resulting in inefficient use of the "silicon estate". With a vertical structure, the voltage rating of the transistor is a function of the doping and thickness of the N epitaxial layer (see cross section), while the current rating is a function of the channel width. This makes possible for the transistor to sustain both high blocking voltage and high current within a compact piece of silicon.
It is worth noting that power MOSFETs with lateral structure exist. They are mainly used in high-end audio amplifiers. Their advantage is a better behaviour in the saturated region (corresponding to the linear region of a bipolar transistor) than the vertical MOSFETs. Vertical MOSFETs are designed for switching applications, so they are only used in On or Off states.
On-state resistance
When the power MOSFET is in the on-state (see MOSFET for a discussion on operation modes), it exhibits a resistive behaviour between the drain and source terminals. It can be seen in figure 2 that this resistance (called RDSon for "drain to source resistance in on-state") is the sum of many elementary contributions:
* RS is the source resistance. It represents all resistances between the source terminal of the package to the channel of the MOSFET: resistance of the wire bonds, of the source metallisation, and of the N+ wells;
* Rch. This is the channel resistance. It is directly proportional to the channel width, and for a given die size, to the channel density. The channel resistance is one of the main contributors to the RDSon of low-voltage MOSFETs, and intensive work has been carried out to reduce their cell size in order to increase the channel density;
* Ra is the access resistance. It represents the resistance of the epitaxial zone directly under the gate electrode, where the direction of the current changes from horizontal (in the channel) to vertical (to the drain contact);
* RJFET is the detrimental effect of the cell size reduction mentioned above: the P implantations (see figure 1) form the gates of a parasitic JFET transistor that tend to reduce the width of the current flow;
* Rn is the resistance of the epitaxial layer. As the role of this layer is to sustain the blocking voltage, Rn is directly related to the voltage rating of the device. A high voltage MOSFET requires a thick, low-doped layer (i.e. highly resistive), whereas a low-voltage transistor only requires a thin layer with a higher doping level (i.e. less resistive). As a result, Rn is the main factor responsible for the resistance of high-voltage MOSFETs;
* RD is the equivalent of RS for the drain. It represents the resistance of the transistor substrate (note that the cross section in figure 1 is not at scale, the bottom N+ layer is actually the thickest) and of the package connections.
Breakdown voltage/on-state resistance trade-off
Fig. 3: The RDSon of the MOSFETs increase with their Voltage rating.

When in the OFF-state, the power MOSFET is equivalent to a PIN diode (constituted by the P + diffusion, the N- epitaxial layer and the N+ substrate). When this highly non-symmetrical structure is reverse-biased, the space-charge region extends principally on the light-doped side, i.e over the N- layer. This means that this layer has to withstand most of the MOSFET's OFF-state drain-to-source voltage.

However, when the MOSFET is in the ON-state, this N- layer has no function. Furthermore, as it is a lightly-doped region, its intrinsic resistivity is non-negligible and adds to the MOSFET's ON-state Drain-to-Source Resistance (RDSon).
Two main parameters govern both the breakdown voltage and the RDSon of the transistor: the doping level and the thickness of the N- epitaxial layer. The thicker the layer and the lower its doping level, the higher the breakdown voltage. On the contrary, the thinner the layer and the higher the doping level, the lower the RDSon (and therefore the lower the conduction losses of the MOSFET). Therefore, it can be seen that there is a trade-off in the design of a MOSFET, between its voltage rating and its ON-state resistance. This is demonstrated by the plot in
Body diode
It can be seen in figure 1 that the source metallization connects both the N+ and P implantations, although the operating principle of the MOSFET only requires the source to be connected to the N+ zone. However, if it were, this would result in a floating P zone between the N-doped source and drain, which is equivalent to a NPN transistor with a non-connected base. Under certain conditions (under high drain current, when the on-state drain to source voltage is in the order of some volts), this parasitic NPN transistor would be triggered, making the MOSFET uncontrollable. The connection of the P implantation to the source metallization shorts the base of the parasitic transistor to its emitter (the source of the MOSFET) and thus prevents spurious latching.

This solution, however, creates a diode between the drain (cathode) and the source (anode) of the MOSFET, making it able to block current in only one direction.
Switching Operation
Location of the intrinsic capacitances of a power MOSFET.

Because of their unipolar nature, the power MOSFET can switch at very high speed. Indeed, there is no need to remove minority carriers as with bipolar devices.

The only intrinsic limitation in commutation speed is due to the internal capacitances of the MOSFET (see figure 4). These capacitances must be charged or discharged when the transistor switches. This can be a relatively slow process because the current that flows through the gate capacitances is limited by the external driver circuit. This circuit will actually dictate the commutation speed of the transistor (assuming the power circuit has sufficiently low inductance).
Capacitances

In the MOSFETs datasheets, the capacitances are often named Ciss (input capacitance, drain and source terminal shorted), Coss (output capacitance, gate and source shorted), and Crss (reverse capacitance, gate and source shorted). The relationship between these capacitances and those described below is:

\begin{matrix} C_{iss} & = & C_{GS}+C_{GD}\\ C_{oss} & = & C_{GD}+C_{DS}\\ C_{rss} & = & C_{GD} \end{matrix}

Where CGS, CGD and CDS are respectively the gate-to-source, gate-to-drain and drain-to-source capacitances (see below). Manufacturers prefer to quote Ciss, Coss and Crss because they can be directly measured on the transistor. However, as CGS, CGD and CDS are closer to the physical meaning, they will be used in the remaining of this article.

[edit] Gate to source capacitance

The CGS capacitance is constituted by the parallel connection of CoxN+, CoxP and Coxm (see figure 4). As the N+ and P regions are highly doped, the two former capacitances can be considered as constant. Coxm is the capacitance between the (polysilicon) gate and the (metal) source electrode, so it is also constant. Therefore, it is common practice to consider CGS as a constant capacitance, i.e its value does not depend on the transistor state.

[edit] Gate to drain capacitance

The CGD capacitance can be seen as the connection in series of two elementary capacitances. The first one is the oxide capacitance (CoxD), constituted by the gate electrode, the silicon dioxide and the top of the N epitaxial layer. It has a constant value. The second capacitance (CCDj) is caused by the extension of the space-charge zone when the MOSFET is in off-state (see the section Blocking Voltage). Therefore, it is dependent upon the drain to source voltage. From this, the value of CGD is:

C_{GD}=\frac{C_{oxD}\times C_{GDj}\left(V_{GD}\right)}{C_{oxD}+ C_{GDj}\left(V_{GD}\right)}

The width of the space-charge region is given by [1]

w_{GDj}=\sqrt{\frac{2\epsilon_{Si}V_{GD}}{qN}}

where εSi is the permittivity of the Silicon, q is the electron charge, and N is the doping level. The value of CGDj can be approximated using the expression of the plane capacitor:

Where AGD is the surface area of the gate-drain overlap. Therefore, it comes:

It can be seen that CGDj (and thus CGD) is a capacitance which value is dependent upon the gate to drain voltage. As this voltage increases, the capacitance decreases. When the MOSFET is in on-state, CGDj is shunted, so the gate to drain capacitance remains equal to CoxD, a constant value.

Drain to source capacitance

As the source metallization overlaps the P-wells (see figure 1), the drain and source terminals are separated by a P-N junction. Therefore, CDS is the junction capacitance. This is a non-linear capacitance, and its value can be calculated using the same equation as for CGDj
Other dynamic elements
Equivalent circuit of a power MOSFET, including the dynamic elements (capacitors, inductors), the parasitic resistors, the body diode.

Packaging inductances

To operate, the MOSFET must be connected to the external circuit, most of the time using wire bonding (although alternative techniques are investigated). These connection exhibit a parasitic inductance, which is in no way specific to the MOSFET technology, but has important effects because of its high commutation speed. Parasitic inductances tend to maintain their current constant and generate overvoltage during the transistor turn off, resulting in increasing commutation losses.

A parasitic inductance can be associated with each terminal of the MOSFET. They have different effects:

* the gate inductance has little influence (assuming it is lower than some hundreds of nanohenrys), because the current gradients on the gate are relatively slow. In some cases, however, the gate inductance and the input capacitance of the transistor can constitute an oscillator. This must be avoided as it results in very high commutation losses (up to the destruction of the device). On a typical design, parasitic inductances are kept low enough to prevent this phenomenon;
* the drain inductance tends to reduce the drain voltage when the MOSFET turns on, so it reduces turn on losses. However, as it creates an overvoltage during turn-off, it increases turn-off losses;
* the source parasitic inductance has the same behaviour as the drain inductance, plus a feedback effect that makes commutation last longer, thus increasing commutation losses.
o at the beginning of a fast turn-on, due to the source inductance, the voltage at the source (on the die) will be able to jump up as well as the gate voltage; the internal VGS voltage will remain low for a longer time, therefore delaying turn-on.
o at the beginning of a fast turn-off, as current through the source inductance decreases sharply, the resulting voltage across it goes negative (with respect to the lead outside the package) raising the internal VGS voltage, keeping the MOSFET on, and therefore delaying turn-off.

Limits of operation

Gate oxide breakdown

The gate oxide is very thin (100 nm or less), so it can only sustain a limited voltage. In the datasheets, manufacturers often state a maximum gate to source voltage, around 20 V, and exceeding this limit can result in destruction of the component. Furthermore, a high gate to source voltage reduces significantly the lifetime of the MOSFET, with little to no advantage on RDSon reduction.

Maximum drain to source voltage

Power MOSFETS have a maximum specified drain to source voltage, beyond which breakdown may occur. Exceeding the breakdown voltage causes the device to turn on, potentially damaging it and other circuit elements due to excessive power dissipation.

Maximum drain current

The drain current must generally stay below a certain specified value (maximum continuous drain current). It can reach higher values for very short durations of time (maximum pulsed drain current, sometimes specified for various pulse durations). The drain current is limited by heating due to resistive losses in internal components such as bond wires, and other phenomena such as electromigration in the metal layer.
Maximum temperature

The junction temperature of the MOSFET must stay under a specified maximum value for the device to function reliably. How high above ambient temperature this is, is given by the power dissipation times thermal resistance. The junction-to-case thermal resistance is intrinsic to the device; the case-to-ambient thermal resistance sss can be lowered as much as practical by using an appropriately sized heatsi Safe operating area

The safe operating area defines the combined ranges of drain current and drain to source voltage the power MOSFET is able to handle without damage. It is represented graphically as an area in the plane defined by these two parameters. Both drain current and drain to source voltage must stay below their respective maximum values, but their product must also stay below the maximum power dissipation the device is able to handle. Thus the device cannot be operated at both its specified maximum drain current and maximum drain to source voltage. [2]

myself

noreply@blogger.com (abhilash thakur) — Fri, 08 May 2009 07:44:00 +0000

gate syllabus of electronic &communication

noreply@blogger.com (abhilash thakur) — Thu, 07 May 2009 05:30:00 +0000

GATE Syllabus for Electronics and Communication Engineering - EC

ENGINEERING MATHEMATICS

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.
Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory: Fourier transform, Laplace transform, Z-transform.

ELECTRONICS AND COMMUNICATION ENGINEERING

Networks: Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parameters: driving point and transfer functions. State equations for networks.

Electronic Devices: Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current, drift current, mobility, and resistivity. Generation and recombination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-I-n and avalanche photo diode, Basics of LASERs. Device technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.

Analog Circuits: Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplifiers. Amplifiers: single-and multi-stage, differential and operational, feedback, and power. Frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits, 555 Timers. Power supplies.

Digital circuits: Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-flops, counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories. Microprocessor(8085): architecture, programming, memory and I/O interfacing.

Signals and Systems: Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transmission through LTI systems.

Control Systems: Basic control system components; block diagrammatic description, reduction of block diagrams. Open loop and closed loop (feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady state analysis of LTI control systems and frequency response. Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion, Bode and Nyquist plots. Control system compensators: elements of lead and lag compensation, elements of Proportional-Integral-Derivative (PID) control. State variable representation and solution of state equation of LTI control systems.

Communications: Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density. Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superheterodyne receivers; elements of hardware, realizations of analog communication systems; signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions. Fundamentals of information theory and channel capacity theorem. Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration and probability of error calculations for these schemes. Basics of TDMA, FDMA and CDMA and GSM.

Electromagnetics: Elements of vector calculus: divergence and curl; Gauss and Stokes theorems, Maxwell's equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; S parameters, pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Basics of propagation in dielectric waveguide and optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.

book for iit jee

noreply@blogger.com (abhilash thakur) — Wed, 06 May 2009 09:32:00 +0000

Books For IIT
I suggest following books for IIT JEE preparation:

Physics
MECHANICS
Physics by H.C. Verma
Problems in physics by I.E. Irodov
Resnick and Halliday
ELECRICITY AND MAGNETISM
Resnick and Halliday
Circuits devices and systems by R.J. Smith
Problems in physics by I.E. Irodov
OPTICS
Physics by H.C. Verma
MODERN PHYSICS
Physics by H.C. Verma
Problems in Physics by I.E. Irodov
HEAT AND WAVES
Physics by H.C. Verma
Resnick and Halliday

Chemistry
ORGANIC CHEMISTRY
Morrison & Boyd
Solutions to Morrison Boyd
Reaction mechanism in Organic Chemistry by Parmar ∓ Chawla
INORGANIC CHEMISTRY
NCERT Inorganic Chemistry
Concise Inorganic Chemistry by J.D. Lee
IIT Chemistry by O.P. Aggarwal
GENERAL CHEMISTRY
J.D. Lee
O.P. Aggarwal
R.C.Mukerjee
physical and inorganic chemistry by O.P.tandan
For numerical problem R.C.mukharjee
Maths
ALGEBRA
High school mathematics by Hall and Knight
IIT Maths by M.L. Khanna
CALCULUS and; ANALYTIC GEOMETRY
G.N.Berman
Calculus and analytic geometry by Thomas and Finney
Coordinate geometry by Loney
IIT Maths by M.L. Khanna
I.A.Maron
VECTORS
IIT Maths by M.L. Khanna
plane trigonomatic by Loney
All book of arihant pablication

Eligibility criteria for IIT

noreply@blogger.com (abhilash thakur) — Wed, 06 May 2009 09:27:00 +0000

Eligibility Criteria

Minimum Academic Qualification

The minimum academic qualification for admission through JEE is a pass grade in the final examination of 10+2 system or its equivalent, referred to as the Qualifying Examination in this brochure. In case the relevant qualifying examination is not a public examination, the candidate must have passed at least one public (Board or Pre-University) examination at an earlier level. Those appearing in 10+2 final or equivalent examination in 2005 may also appear in JEE-2005 (Screening Test and Main Examination) for consideration of provisional admission. Those who will be appearing in the qualifying examination in 2006 or later are not eligible to apply. All provisional admissions will stand cancelled if the proof of having passed the qualifying examination (10+2 or its equivalent) is not submitted to the Institute concerned by September 30, 2005.

All admissions will be subject to verification of facts from the original certificates/documents of the candidates. If an applicant is found ineligible at a later date even after admission to an Institute, his/her admission will be cancelled. The decision of the Joint Admissions Board regarding the eligibility of any applicant shall be final.

The list of qualifying examinations is given below:
The final examination of the 10+2 system, conducted by any recognized Central/State Board, such as Central Board of Secondary Education, New Delhi; Council for Indian School Certificate Examination, New Delhi; etc.
Intermediate or two-year Pre-University Examination conducted by a recognized Board/ University.
Final Examination of the two-year course of the Joint Services Wing of the National Defence Academy.
General Certificate Education (GCE) Examination (London/Cambridge/Sri Lanka) at the Advanced (A) level.
High School Certificate Examination of the Cambridge University.
Any Public School/Board/University Examination in India or in foreign countries recognized by the Association of Indian Universities as equivalent to 10+2 system.
H.S.C. Vocational Examination.
Senior Secondary School Examination conducted by the National Open School with a minimum of five subjects.
3 or 4-year Diploma recognized by AICTE or a State Board of Technical Education.

Date of Birth

Only those candidates whose date of birth falls on or after October 01, 1980 are eligible for JEE-2005. However, in the case of SC, ST and PD candidates, upper age limit is relaxed by 5 years, i.e., SC, ST and PD candidates who were born on or after October 01, 1975 are eligible. Only the date of birth as recorded in your High School/first Board/Pre-University Certificate will be taken as authentic. Candidates must produce this certificate in original as a proof of their age at the time of counselling, failing which they will be disqualified.

Physical Fitness

All qualified candidates will have to submit a Physical Fitness certificate from a Registered Medical Practitioner in a prescribed format that will be made available to them at an appropriate time. They will be admitted only if they are physically fit for pursuing a course of study at the participating Institutes.

Special Requirements for Mining Engineering and Mining Machinery Courses

Candidates opting for these courses should make sure that they are free from colour blindness. They will be required to submit a certificate from a Registered Medical Practitioner to this effect at the time of counselling. The standard of visual acuity with or without glasses will be adhered strictly for candidates seeking admission in Mining as per DGMS Circular 14 of 1972. Persons with one-eyed vision are not permitted to work underground. Candidates with above limitations are not allowed to opt for admission to Mining Engineering or Mining Machinery Engineering.

Women Candidates for Mining Courses

Section 46(1) of the Mines Act, 1952 states that ''No woman shall, notwithstanding anything contained in any other law, be employed (a) in any part of a mine which is below ground, (b) in any mine above ground except between the hours 6 a.m. and 7 p.m.''. The programmes of Mining Engineering and Mining Machinery at ISM Dhanbad do not admit women candidates, whereas, IIT Kharagpur and IT-BHU Varanasi have no such restriction.

Eligibility to Appear in the Main Examination

Candidates who qualify in the Screening Test of JEE-2005 shall be allowed to appear in the Main Examination

Eligibility criteria for IIT

noreply@blogger.com (abhilash thakur) — Wed, 06 May 2009 09:27:00 +0000

IIT mathematics syllabus

noreply@blogger.com (abhilash thakur) — Wed, 06 May 2009 08:50:00 +0000

IIT JEE 2009 - Mathematics Syllabus

Algebra: Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties.

Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.

Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.

Trigonometry: Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).

Analytical geometry:

Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.

Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord.

Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.

Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.

Locus Problems.

Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.

Differential calculus: Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus: Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations