Instructions:
1. The homework assigned in different subjects is COMPULSORY.
2.
Students HAVE TO COMPLETE the given homework on a dayto-day basis except during the actual festival days. They would need
to write down the dates when they have actually done particular
assignments.
3. Students who don't complete their homework fully shall face strict
DISCIPLINARY ACTION.
4.
Parents/Guardians are requested to MONITOR the completion of
the given Homework during the vacation.
5.
The homework for the vacation should be done on a SEPARATE
COPY.
XII Science/Dashain-Tihar Homework Assignments
Trinity-1
English (004)
Heritage of Words
Short Answer Questions:
1.
How does the story 'About Love' differ from other love stories?
2.
Why does the speaker have to lament over his old age? (The
Lamentation of the old Pensioner)
3.
Are the problems we are facing now interrelated? How? (Two
Long Term Problems ---)
4.
Write a paragraph or two giving an account of the life of Karnali
people while pointing out the contrast between people of
Kathmandu and them.
5.
How is the poem 'Travelling Through the Dark' related to Ecology
and Change?
6.
Explain the word 'satire' in connection with 'A Story'.
7.
What images do you find in the poem ‘Grandmother’? Explain.
Long Answer Questions:
1. Make a comparative study of the narrators of the stories 'About
Love' and 'A Story' .
2.
How do the speakers of the poems 'Travelling through the Dark',
'The Lamentation of the old Pensioner' and 'Full Fathom ---' differ
in their attitudes?
Meanings into Words
1.
Imagine that you are a doctor. Write a couple of paragraphs
describing your experiences and achievements upto now.
2.
Write a paragraph about an occasion when you were very
frightened or about an occasion when something exciting
happened to you.
XII Science/Dashain-Tihar Homework Assignments
Trinity-2
3.
Write paragraphs describing your attitudes towards these people
(any three).
i) Beggars
ii) Policemen
iii) Doctors
iv) Politicians
v) Film stars
vi) Religious leaders
4.
Write your reactions to a cultural program you saw recently in
about 100 words.
5.
Imagine that you are a popular teacher or a TV personality.
Write a paragraph describing the duration of different activities
you did, you have been doing and will be doing.
6.
Report a conversation you remember in which someone accused
you of doing something.
XII Science/Dashain-Tihar Homework Assignments
Trinity-3
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XII Science/Dashain-Tihar Homework Assignments
Trinity-4
Physics (210)
ELECTRICITY
DC Circuits
Short answer questions
1. Define the term resistivity or specific resistance. What is its
unit?
2. What is the cause of resistance?
3. What do you mean by drift velocity of electrons?
4. A large number of electrons are present in metals. Why is
there no current in the absence of electric field across it?
5. On what factors resistance of a conductor depends?
6. Why do we use alloys like manganin, constantan or
nichrome to make standard resistance?
7. Why is an ammeter connected in series in an electric circuit?
8. Why do voltmeter always connected in parallel across a circuit
element?
9.
Can a potential difference across a battery be greater than its emf?
10. The element of a heater is very hot while the connecting wire
carrying the current are cold. Why?
11. When a motor car is started, its light becomes slightly dim. Why?
12. Differentiate between emf and terminal difference of a cell.
13. Why does the bulb glow instantly when it is switched on, even
though the drift velocity of the electron is very small? Explain.
14. Which one is correct statement: resistivity of a metal or resistance of
a metal ? Explain.
Long answer questions
1.
Define drift velocity of free electrons in metals. Obtain a relation for
current in terms of drift velocity.
2.
State ohm’s law. Show that the equivalent resistance of two
resistors connected in parallel is less than the individual resistor.
XII Science/Dashain-Tihar Homework Assignments
Trinity-5
3.
A number of resistors are joined in series. Calculate the combined
resistance.
4.
Deduce an expression for the heat developed in a wire by the
passage of an electric current.
5.
What do you mean by shunt? Describe its use in the conversion
of galvanometer into an ammeter.
6.
State and explain Joule’s laws of heating effect of electric current.
Discuss how they are verified experimentally.
Numericals
1. A wire having the diameter of 1.2mm and resistivity of 100X10 -8 Ωm
at 0oC is connected across a cell of emf 1.5 V and gives a current of
2.
10mA. Calculate the length of the wire.
[Ans: 216m]
A battery of emf 1.5 V has a terminal p.d of 1.25 V when a resistance
of 25 Ω is joined to it. Calculate the current flowing , the internal
resistance and terminal p.d when a resistance of 10Ω replaces 25Ω
resistor.
3.
*Ans: 0.05A, 5Ω, 1V+
What is the potential difference across 100Ω resistor in the circuit
given below?
4.
[Ans: 0.75V]
In the given circuit, calculate the potential difference between the
points B and D.
[Ans: 1.998V]
XII Science/Dashain-Tihar Homework Assignments
Trinity-6
5. The resistance of a conductor is 10Ω at 50 oC and 15Ω at 100o C.
Calculate its resistance at 0 oC?
6.
[Ans: 6.67Ω+
A galvanometer can bear maximum current of 25mA and has
resistance 5Ω. Find the suitable resistance to convert it into (i) a
voltmeter of range 0-2V (ii) an ammeter of range 0-10A.
7.
[Ans: 75Ω,0.0125Ω+
An electric bulb is marked 100W, 220V. If the supply voltage drops
to 110 V, what is the energy dissipated by the bulb in 10 minutes?
[Ans: 15000J]
8. Two bulbs rated 40W, 200v and 60W, 200V are joined in series and
supplied by a 200V mains. Find the power consumed by each bulb.
[Ans: 14.4 W, 9.6W]
Kirchhoff’s law
Short answer questions
1. State Kirchhoff’s laws of electric circuits.
2.
What is the principle used in potentiometer?
3.
A potentiometer is preferred than a voltmeter to measure the emf of
a cell. Why?
OR
We prefer a potentiometer to measure emf of a cell rather than a
voltmeter. Why?
Long answer questions
1.
State Kirchhoff’s laws of electric network and apply it to find the
balanced condition for a Wheatstone bridge.
2. Explain the principle of potentiometer and use it compare emf of
two cells and to determine the emf of a cell.
3. How will you use the principle of potentiometer to measure the
internal resistance of a cell?
XII Science/Dashain-Tihar Homework Assignments
Trinity-7
Numericals
1. In the adjacent circuit, find:
(i) The current in the resistor R
(ii) The resistance R
(iii) The unknown emf E
(iv) If the circuit is broken at P, what is the current in resistor R?
*Ans: 2A, 5Ω, 42V, 3.5A+
2. Figure below shows a network in which the currents I 1, I2 can be
found from Kirchhoff’ laws. From the first law the current in the 8Ω
wire is (I1 + I2 ), assuming I1, I2 are the currents through the cells.
Calculate I1 and I2 . Find also the terminal p.d of each cell and p.d
across the resistance.
[Ans: 0.61A, -0.09A, 96/23V, 96/23V, 96/23V]
XII Science/Dashain-Tihar Homework Assignments
Trinity-8
3. Determine the value of I1, I2 andI3
[Ans: 8A, 2A , 4A]
4.
The driver cell of a potentiometer has an emf of 2V and negligible
internal resistance . The potentiometer wire has a resistance of 3Ω.
Calculate the resistance needed in series with the wire if a p.d of
5mV is required across the whole wire. The wire is 100 cm long and
the balance length of 60 cm is obtained for a thermocouple of emf E.
What is the value of E?
5.
[Ans: 1197Ω, 3mV].
A 1Ω resistor is in series with an ammeter M in a circuit. The p.d
across the resistor is balanced by a length of 60 cm on a
potentiometer wire. A standard cell of emf 1.02V is balanced by a
length of 50 cm. If M reads 1.10A, what is the error in the reading?
[Ans: 0.124A]
6. In an experiment to measure the internal resistance of a cell by a
potentiometer, it is found that balance point is at a length of 2m
when the cell is shunted by a 5Ω resistance and at a length 3m when
the cell is
shunted
by 10Ω
resistance. Calculate the internal
resistance of the cell.
[Ans: 10Ω]
MODERN PHYSICS
Photons and photoelectric effect
Short answer questions
1. Which has more energy, a photons in the infrared or one in the ultra
violet? Give reasons.
2. Why alkali metals are suitable for photoelectric emission?
3. It is harder to remove a free electron from copper than from
sodium. Which metal has higher threshold wavelength?
XII Science/Dashain-Tihar Homework Assignments
Trinity-9
4.
5.
6.
What is threshold frequency?
What is meant by stopping potential?
Photoelectric emission is an instantaneous process but not a
spontaneous. Why?
7. If the intensity of incident radiation on a metal is doubled, what
happens to the kinetic energy of electrons emitted?
Long answer questions.
1. Write down Einstein's photoelectric equation and describe and
experiment to verify it.
2. State the laws of photoelectric effect. Describe Millikan’s
experiment to determine the value of Planck’s constant.
3. What is photoelectric effect? Derive Einstein photoelectric equation
and define various terms used in it.
Numerical Questions
1. In a photoelectric effect experiment, with light of a certain
frequency, it is found that a reverse potential difference of 1.5 V is
required to reduce the current to zero. Calculate the maximum
kinetic energy and the maximum speed of photoelectrons. If the
light used has wavelength 3650 A0, what is the work function of the
material? [h = 6.62 × 10 -34 Js, m = 9.1 × 10 -31 kg]
[Ans: 3.2 × 106J]
2. Light of two different frequencies with energies 1 eV and 2.5 eV
respectively successively illuminate a metal of work function 0.5
eV. Calculate the ratio of maximum speed of the emitted electrons.
[Ans: 1 : 2]
3. A radiation of wavelength 2000 A o falls on an aluminum surface
having work function of 4.2 eV. What is the kinetic energy in eV of
a) The fastest emitted photoelectrons
b) The slowest emitted photoelectrons
c) What is the stopping potential?
d) What is cut off wavelength for aluminum?
[h = 6.6 × 10 -34 Js]
[Ans: (a) 2 eV (b) 0 (c) 2V (d) 3000 A 0]
4. The maximum velocity of an electron ejected from a photoelectric
emitter when radiation falls on the later is found to be 2 × 10 6 m/sec.
Assuming that the specific charge of an electron to be 1.8 × 10 11
C/kg, find the stopping potential.
[Ans: 11.1 Volt]
5.
For calcium the value of work function is 1.35 electron volts.
a) What is the longest wavelength that can cause photoelectric
emission from a calcium surface?
XII Science/Dashain-Tihar Homework Assignments
Trinity-10
6.
7.
8.
b) What is the maximum velocity with which photoelectrons will
be emitted from a calcium surface illuminated with light of
wavelength 4 × 10 -7 m.
c) What potential difference will just prevent a current
passing through a calcium photocell illuminated with light of
wavelength 4× 10-7m? [Take e = 1.6 × 10 -19 C, m = 9 × 10-31 kg, h =
6.6 × 10-34 Js]
[Ans: a) 9.2 × 10 -7m b) 7.9 × 10 5 m/sec c) 1.74 V]
The photoelectric threshold wavelength of a tungsten surface is
272nm. Calculate the maximum kinetic energy of the electrons
ejected from this tungsten surface by ultraviolet radiation of
frequency 1.45 × 10 15 Hz. Express answer in eV.
[Ans: 1.4 eV]
When ultraviolet light with a wavelength of 254 nm falls upon a
clean copper surface, the stopping potential necessary to stop
emission of photoelectrons is 0.181 V.
a) What is the photoelectric threshold wavelength for this
copper surface?
b) What is the work function for this surface?
[Ans: a) 1.54 eV b)0 ]
In a photoelectric experiment, it was found that the stopping
potential decreases from 1.85 V to 0.82 V as the wavelength of the
incident light is varied from 300 nm to 400 nm. Calculate the value
of the Planck’s constant.
[Ans: 4.12 × 10-15 eVs]
QUANTIZATION OF ENERGY
Short Answer Questions
1. Explain why the spectrum of hydrogen atom has many lines
although a hydrogen atom contains only one electron?
2.
3.
How is the Paschen series originated in hydrogen spectra?
Differentiate between excitation and ionization potential.
4.
The total energy of an electron of an atom in an orbit is negative‛.
What does this negative energy indicate?
5. Which has more energy, a photon in the infrared or a photon in the
ultraviolet? Give reasons.
6.
What do you mean by excited state and excitation energy?
7.
What do you mean by uncertainty principle?
XII Science/Dashain-Tihar Homework Assignments
Trinity-11
8.
A photon and electron have got some de-Broglie wavelength.
Which has greater total energy? Explain.
9.
Differentiate between stimulated and spontaneous emission of
radiations.
Long Answer Questions
1. What are Bohr’s postulates of hydrogen atom? Derive an
expression for the radius of Bohr’s orbit.
2. Explain how Bohr modified the Rutherford model of an atom to
explain the radiation from atoms. (Only quantitative discussion is
required).
Numerical Questions
1. The excitation energy of hydrogen like ion in its 1 st excited state is
found to be 40.8 eV. Find the energy needed to remove the electron
2.
from an atom .
[Ans : 54.4 eV]
Calculate the size of hydrogen atom with an electron in the 1 st
excited state. Also calculate the velocity of this electron.
[Ans : 4.24 A o , 1.1 × 106 m/sec]
3. Total energy of an electron in the 1 st excited state of hydrogen atom is
–3.4 eV. Calculate the K.E and P.E of the electron in this state.
[Ans : Ep = - 6.8 eV, Ek = -3.4 eV]
4.
Calculate the wavelength of electron in hydrogen atom in its
5.
ground state. (Bohr’s radius = 0.53 A o )
[ Ans : 3.33 A o ]
Show that velocity of electron in ground state of hydrogen atom is
C
137
and hence calculate the frequency of the electron. (Bohr radius
a0 = 0.53 A o , Me = 9.1 × 10-31 kg, h = 6.62 × 10 -34 Js)
[Ans : f = 6.5 × 1015Hz]
6.
Calculate the de-Broglie wavelength associated with a neutron
moving with energy of 2eV. Mass of proton m p = 1.67 × 10-27 kg.
[Ans : 6.4 × 10-13m]
XII Science/Dashain-Tihar Homework Assignments
Trinity-12
7.
Ultraviolet light of wavelength 800 A o and 700 A o when allowed
to fall on hydrogen atom in its ground state is found to liberate
electrons with kinetic energy 1.8 eV and 4 eV respectively.
Calculate the value of Planck’s constant.
8.
[Ans : h = 6.57 × 10 -34Js]
Compute the de Broglie wavelength of a proton whose kinetic
energy is equal to the rest energy of an electron. [Given M p = 1836
M e]
[Ans : 4 × 10-14 A0]
X-RAYS
Short Answer Questions
1. In the production of x-ray, how will you control the penetrating
power of x-rays?
2.
What is the x-ray? Confirm with experiment the wave nature of xrays?
3.
4.
5.
Can aluminium be used as a target in x-ray tube? Explain .
Why is the production of x-rays called inverse photoelectric effect?
X-rays are not deflected by electric and magnetic fields. Why?
6.
How can the intensity of x-ray be controlled in a Coolidge tube?
7.
X-rays penetrate through the flesh but not through bones. Why?
8.
Distinguish between continuous and characteristics spectrum.
Long Answer Questions
1. What are x-rays? Confirm with experiment the wave nature of xrays.
2.
Derive Bragg’s law and explain how this law is used to determine
the crystal plane spacing.
3. X-ray diffraction has been very useful in determining the structure of
a crystalline substance. Use this concept to determine the
4.
distance between two planes.
Explain the origins of characteristics and continuous x-rays. Give
applications of x-rays briefly.
5. Write the properties of x-rays and also describe x-ray diffraction.
XII Science/Dashain-Tihar Homework Assignments
Trinity-13
Numerical Questions
1. Electrons are accelerated from rest through a potential difference of
10,000 volts in a Coolidge tube. Calculate the maximum energy and
minimum wavelength of x-radiation generated. [e = 1.6 × 10 -19 C, c=
3 × 108 m/sec, h = 6.625 × 10 -34 Js]
[Ans : 1.24 × 10-10m]
2. An x-ray tube is operated with an anode potential of 15kV and
anode current of 10mA. Calculate (i) the number of electrons hitting
the anode per second (ii) the rate of production of heat at the
anode.
3.
[Ans : 6.25 × 10 16 /sec, 150 W]
Electrons are accelerated from rest through potential difference of
10,000 volt in an x-ray tube. Calculate the wavelength of the
associated electrons wave and the minimum wavelength of the Xradiation generated.
4.
[Ans : 0.123 A0, 1.24 A0]
Knowing that the minimum x-ray wavelength produced by 40 KeV
electrons striking a target is 31.1 × 10 -12 m, determine the value of h.
5.
[Ans : 6.63 × 10-34 Js]
X-ray beam of wavelength 2.9 A is diffracted from plane of cubic
0
crystal. The 1st order diffraction is obtained at an angle 35 0. Calculate
6.
the spacing between the planes.
[Ans : 2.53 × 10-10 m]
An x-ray tube works at a d.c potential difference of 50kv. Only 0.4%
of the energy of the cathode rays is converted into x-radiation and
heat is generated in the target at a rate of 600W. Estimate (i) current
passed into the tube (ii) the velocity of the electrons striking the
target. [Me = 9.0 × 10-31 kg, e = - 1.6 × 10-19 C]
[Ans : (i) 0.012 A0 (ii) 1.33 × 108 m/sec]
7.
X-rays from a tube undergoes first order reflection at a glancing
angle of 120 from the face of calcite crystal. The grating space of the
calcite is 3.04 × 10 -8 cm. Calculate the wavelength of x-rays. At what
angle will the 3rd order reflection takes place from the crystal?
[Ans : 1.3 × 10 -10 m, 39.30]
XII Science/Dashain-Tihar Homework Assignments
Trinity-14
WAVE OPTICS
Nature and Propagation of Light
Short questions:
1. Differentiate between wavefront and wavelet?
2. Differentiate between plane wavefront and spherical wavefront.
3. What do you mean by dual nature of light?
Long questions:
1. Describe Michelson method of determining the speed of light with
the help of labelled diagram.
2. Explain Foucault’s method with diagram to determine the speed of
light.
3. State Huygen’s principle. Prove the laws of reflection of light on
the basis of Huygen’s principle.
4. Use Huygen’s principle to verify the laws of refraction of light on
the basis of wave theory.
Numerical Problems
1. The radius of curvature of the curved mirror is 20 meters and the
plane mirror is rotated at 20 rev/s. Calculate the angle in degrees
between a ray incidents on the plane mirror and then reflected
from it after the light has travelled the curved mirror and back to
the plane mirror. (c = 3 × 10 8 m/sec).
2. In Michelson’s rotating prism method, the distance between the
rotating prism and the distant mirror is 45 km. A minimum speed
of 416.7 rev/sec of the rotation of the prism is needed to view the
source in the same position as when the prism is at rest. Calculate
the speed of light.
3. In experiment with Foucault’s apparatus, the distance between the
rotating and the fixed mirror is 16 m, distance between the lens and
the rotating mirror is 6 m and distance between the source and lens
is 2 m . When the mirror is rotated at a speed of 356 rev per sec, the
image shifts by 0.7 mm. Calculate the speed of light.
Waves and Sound
Short answer questions
1.
What are mechanical and non-mechanical waves? Give some
examples.
XII Science/Dashain-Tihar Homework Assignments
Trinity-15
2.
Transverse waves are not produced in liquids and gases. Why?
3.
What is resonance and cause of resonance?
4.
Longitudinal waves are also called pressure waves. Why?
5.
Can we talk to each other on the surface of the moon? Or, if you are
walking on the moon surface, can you hear the cracking sound
behind you?
6.
Explain why soldiers are ordered to break steps while crossing a
bridge.
7.
What do you mean by resonance?
8.
Why are bells made of metal and not of wood?
9.
Is polarization possible for longitudinal waves? Why?
Long answer questions
1. Distinguish between progressive wave and stationary wave.
2. Derive an equation of a plane progressive wave in a medium.
Numerical Problems:
1. A plane progressive wave is represented by the equation y = 0.1 sin [
200πt - 20πx/17]
Where y is the displacement in millimeters, t is in seconds and x is
the distance from a fixed origin X in meters.
Find (i) the frequency of the wave (ii) its wavelength (iii) its speed
(iv) the phase difference between a point between a point of 0.25 m
from O and a point 1.10m from o(v) the equation of a wave with
double the amplitude and double the frequency but travelling
exactly in opposity direction. [ Ans: 100Hz, 1.7m, 170m/sec, π
radians, y= 0.2 sin ( 400πt + 40πx/17)]
2.
The equation y = a sin (ωt – kx) represents a plane wave travelling in
a medium along the X- direction , y being the displacement at the
point x at time t. if a= 10 -7m,ω= 6.6X103rad/sec and k= 20m-1, calculate
(i) speed of the wave (ii) maximum speed of the particles of the
medium due to wave.
3.
[Ans: 330m/sec, 6.6X10 4m/sec]
A stone is dropped into a well and a splash is heard after 2.6 second.
Calculate the depth of the well. ( velocity of sound = 334m/sec)
XII Science/Dashain-Tihar Homework Assignments
[Ans: 30.73m]
Trinity-16
4.
A man stationed between two parallel cliffs fires a gun. He hears the
first echo after 3 seconds and next after 5 seconds. What is the
distance between two cliffs. (velocity of sound in air =350m/sec)
[Ans: 1400m]
5.
A directional loudspeaker aims a sound wave of frequency 200Hz at
a wall. At what distances from the wall would you stand and hear
no sound at all?
* Ans: 0.43m, 1.29m, 2.15m,…..+
Chapter 2
Short answer questions
1. Explain why the velocity of sound in solids is greater than that in
gases, though the density of solid is greater than that of gases.
2.
Velocity of sound increases on a cloudy day. Why?
3.
Why sound made at a distance can be heard distinctly at night than
at day time?
4.
What do you mean by ultrasonics and infrasonics?
5.
Does the velocity of gas depend on the atomicity of the gas?
Long answer questions.
1.
State Newton’s formula for the velocity of sound in gases. What
correction was done by Laplace on it?
2.
Explain why and how Laplace corrected the Newton’s formula for
the velocity of sound in air.
3. Discuss the effect of change in pressure, density of the medium and
temperature on the velocity of sound in air.
4. Derive an expression for the velocity of sound in a medium by
dimensional method.
Numerical
1. Find the wavelengths of a wave in air of sound of frequency 256Hz
at 0oC and 71oC , if the velocity of sound through air at 16 oC is
340m/sec. [Ans: 1.29m, 1.444m]
XII Science/Dashain-Tihar Homework Assignments
Trinity-17
2.
Calculate speed in air saturated with water vapour at 27 oC. It is
given that atmospheric pressure is 750 mm of mercury, SVF.P of
water at 270C is 25mm of Hg and velocity of sound at S.T.P is
331m/sec. [Ans: 349.18m/sec]
3. If the velocity of sound in air at 3o 0C is 350m/sec, calculate the ratio
of the molar heat capacities of air. (density of air at 0 0C is 1.29
kg/m3) [ Ans: 1.42]
4.
Compute the speed of sound in helium at S.T.P. 9(γ=1.66, M=4gm,
R=8.31Jmol -1K-1) [ Ans: 970.3m/sec]
5.
The thunder accompanying a lightening is heard 3 second later than
the flash when the temperature of the air is 27 0C. How far away is
the storm? (velocity of sound in air at 0 A o C= 332m/sec)
[Ans: 1044m]
XII Science/Dashain-Tihar Homework Assignments
Trinity-18
Chapter 3
1.
2.
3.
The frequency of fundamental note of an open organ pipe is double
than for closed pipe of same length. Why?
Why is an end correction necessary for an organ pipe?
Note produced by an open organ pipe is sweeter than that
produced in a closed organ pipe. Explain.
4.
Two organ pipes of same length open at both ends produce sound
of different frequencies if their radii are different, why?
5.
Why does resonance not occur in the resonance tube when the first
6.
length of resonance from a tuning fork is made exactly three times?
When we start filling an empty bucket with water, the pitch of
sound produced goes on changing . Why?
7. The frequency of organ pipe changes with temperature? Does it
increase with temperature?
Long Answer Questions
1. What do you mean by a stationary wave? Discuss the possible
modes of vibration of air column in (i) open pipe (ii) closed pipe
2. What is resonance? Describe an experiment giving the necessary
theory by which the speed of sound in air may be determined
using resonance air column method
3. Derive an expression for the velocity of transverse wave along a
stretched string.
4. Discuss possible modes of vibration of stretched string.
5. State the laws of transverse vibration of strings. Give the methods
of verifying the laws of transverse vibration.
XII Science/Dashain-Tihar Homework Assignments
Trinity-19
Chemistry (212)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Define the following terms:
Normality, Molarity, Normal Solution, Molar Solution, End point,
Equivalent point, Titration error, Normality factor
Is the molarity of solution always equal to the normality? If not why?
How many moles of H+ ions are contained in 500 ml of 0.5 M H2SO4?
Find the equivalent weight of H3PO4 in the reaction.
Ca(OH)2 + H3PO4 → CaHPO4 + 2H2O
2.65 gm of Na2CO3 is dissolved in 100 ml. Calculate the Molarity of
the solution.
What are the requisites for a substance to be a primary standard?
N
N
N
10 c.c. of HCl, 30 c.c. of
HNO3 and 60 c.c. of H2SO4 are mixed
2
10
5
together. Calculate the Normality of the mixture.
A sample of Na2CO3 weighing 0.53 gm is added to 100 c.c of 1N (f =
0.1) H2SO4, will the resulting solution be acidic, basic or neutral?
100 ml of 0.1 M HCl is mixed with 50 ml of 0.1 M KOH. Calculate the
concentration of acid in terms of gm/litre in the resulting solution.
Define Normality equation. Derive the relation between normality
and molarity.
Ostwald's dilution law.
Write short notes on Arrhenius concept of acid and base.
Write short notes on Bronsted-Lowery concept of acid and base.
Write short notes on Lewis concept of acid and base.
Define common ion effect, solubility product and solubility product
principle. Write the application of solubility product and common
ion effect.
Extraction of copper from copper pyrites.
Chemistry of white vitriol and zinc white.
Chemistry of blue vitriol.
Laboratory preparation of Chloroform and its chemical properties.
General methods of preparation of haloalkane.
How would you distinguish primary, secondary and tertiary alcohol
by Victor-Meyer method?
Give general methods of preparation of alcohol.
XII Science/Dashain-Tihar Homework Assignments
Trinity-20
Biology (214)
Botany
Physiology
Very Short Answer Questions:
1.
2.
3.
4.
5.
6.
7.
Where does oxygen comes from during photosynthesis?
What are Absorption and Action spectra?
What is photophosphorylation?
Define Guttation.
What is hydathode?
Define osmotic pressure.
Define incipient plasmolysis.
Short Answer Questions:
1. Write down various factors affecting transpiration.
2. Describe cohesion-tension theory.
3. Write a short note on plant cell as osmotic system.
4. Write the differences between PS I & PS II of photosynthesis.
Long Answer Questions:
1.
Describe light reaction.
Genetics
Very short questions
1. Define cistron and recon.
2.
What is clone?
3.
Write the function of mRNA, tRNA and rRNA.
4.
What is okazaki fragment.
5.
Define codon and anti-codon.
6.
Define exon and intron.
7.
Write the ratio of Mendel’s monohybrid and dihybrid crosses.
8.
Define genotype and phenotype.
9. What is incomplete dominance?
XII Science/Dashain-Tihar Homework Assignments
Trinity-21
Short questions
1.
Explain the structure of tRNA with diagram.
2.
Differentiate
between
continuous
and
discontinuous
variation.
3.
Write the characteristics of genetic code.
4.
Differentiate between lytic and lysogenic life cycle of virus.
5.
What is codominance? Explain with suitable example.
Long questions
1.
Explain the mechanism of semi-conservative method of DNA
replication.
2.
Describe Mendel’s laws of inheritance.
Zoology
Very Short Answer Questions:
1.
Define tissue.
2.
Name the membrane on which epithelium rests.
3.
Where is transitional epithelium found?
4.
Name any two structures, which bear pavement epithelium.
5.
Mention the basic functions of epithelial tissues.
6.
Which parts of the body have keratinized epithelium?
7.
Which type of epithelium lines blood vessels and alveoli of lungs?
8.
Name the cells that secrete heparin and histamine.
9.
What is the role of keratinized stratified epithelium of skin?
10. Name tissues that connect bones with bone and muscle.
11. Give the location of germinal epithelium.
12. Give proper terms for endoplasmic reticulum of the muscle fibre.
13. Where is Z-line present?
14. Name the proteins found in A-band and I-band.
15. Name the tissue whose cells divide throughout the life.
16. Which tissue stores the fat?
17. In which tissue, the matrix is fluidy and fibre free?
18. Name the protein found in yellow and white fibres.
19. How does white adipocyte differ from brown adipocyte?
XII Science/Dashain-Tihar Homework Assignments
Trinity-22
20. Name the anticoagulant found in the blood vessels.
21. Give the location of brush bordered columnar epithelium.
22. What is the structural and functional unit of muscle fibre?
23. Define digestion.
24. Name two protein digesting enzymes.
25. Name two carbohydrates digesting enzymes.
26. Name the sphincters present between pharynx and oesophagus.
27. Name the sphincters present between oesophangus ans stomach.
28. Name the sphincter present between Small Intestine and Large
Intestine.
29. Name the sphincters present between common bile duct and
pancreatic duct.
30. Name the ducts present in parotid, sub-mandibular and sublingular glands.
31. Name causative agent of typhoid fever.
32. Where are the semi-lunar valve located?
33. Where are the Tricuspid and Bicuspid valves located?
34. What is deamination?
35. Define Emulsificaiton.
36. Name two commonly cultivated species of fish in Nepal.
37. What do you mean by amniocentesis?
38. Define pre-natal period.
39. How is the sex determined by using amniocentesis?
40. Define pre-natal diseases.
41. What do you mean by test tube baby?
42. Define IVF.
43. Who is surrogate mother?
44. Define immune-suppressant.
45. What do you mean by non-self organ?
46. Mention two limitations of organ transplantation.
47. What is antibiotic?
48. Name the first antibiotic produced commercially.
49. What is immunity?
XII Science/Dashain-Tihar Homework Assignments
Trinity-23
50. Differentiate between active immunity and passive immunity.
Short Answer Questions:
1.
Write about the mode of action of antibiotics.
2.
Mention four common vaccines and their uses in the treatment of
diseases.
3.
Mention the methods by which the transplanted organ is made
accepted by reciepient.
4.
Compare advantaged and disadvantages of test tube baby.
5.
Describe the process of amniocentesis.
6.
Explain the structure of striated muscles fibre.
7.
Give an account of areolar tissue.
8.
How striated muscle differs from unstriated muscle?
9.
Explain various types of cells and fibres present in areolar tissue.
10. Give an account of adipose tissue.
11. Explain squamous epithelium.
12. What are multicellular glands? Describe their types.
13. List the functions of connective tissue.
14. Differentiate between spongy and compact bones.
15. Discuss the various types of simple epithelium.
16. Describe double circulation.
17. Describe the mechanism of Protein digestion in human.
18. List the functions of Liver.
19. Describe the histological structure of stomach.
20. Describe the structure of Liver.
21. Describe the structure of Pancreas.
22. Mention the functions of Saliva.
23. Draw the Internal Structure of human heart.
24. What does the following glands or gland cell secretes?
a. Oxyntic cell
d. Argentaffin cell
b. Zymogenic cell
e. Crypts of Lieberkuhn
c. Paneth cell
f. Brunner's Gland
XII Science/Dashain-Tihar Homework Assignments
Trinity-24
Long Answer questions:
1.
2.
Describe the causes & symptoms of the following:
a.
Cancer
b.
Ascariasis
c.
Typhoid
d. Tuberculosis
e.
AIDS
Give an account of fish farming.
XII Science/Dashain-Tihar Homework Assignments
Trinity-25
Basic Mathematics (216)
PERMUTATIONS
1.
A coin is tossed three times, how many possible outcomes are
there?
2.
How many 3 digit numbers can be formed without using the
digit 0 , 5 , 6 , 9 when the repetition of digits is not allowed?
3.
If 3 persons enter a bus in which there are 10 vacant seats, in how
many ways can they take their seats?
4.
There are 8 letter boxes in a post office. In how many ways can a
man post 4 distinct letters?
5.
Find the number of arrangement that can be made out of the
letters of word 'MISSISSIPPI'.
6.
In how many ways can 6 persons be seated
a.
In a row
b.
At a round table
7.
In how many ways can eight different coloured beads be made
8.
From the digits 1,2,3,4,5,6,7,8, how many 4 digits even numbers
into a bracelet?
can be formed when the repetition of digits is allowed?
9.
In how many ways can 4 Art students and 4 science students be
arranged in a circular table if
a.
They may sit any where
b.
They sit alternately
10. In how many ways can the letters of the word "CALCULUS" be
arranged so that two C's do not come together.
11. How many words can be formed from the letters of the word
"ENGLISH"? How many of these do not begin with E ? How
many of these begin with E and do not end with H?
12. How many numbers of 4 different digits can be formed from the
digits 4 , 5 , 6, 7 , 8 ? How many of these numbers are dividable
by 5 ? How many of these are not dividable by 5?
XII Management/Dashain-Tihar Homework Assignments
Trinity-26
COMBINATIONS
9
1. Find the value of r, if
C 2 r = 9 C 3r1 .
2. A bag contains 5 red balls. How many ways can select at most 3
balls.
3. In an examination paper there are 10 questions. In how many
ways can an examinee choose 8 questions in all if two questions
are compulsory?
4. A bag contains 8 white balls and 5 blue balls. In how many ways
can 5 white balls and 3 blue balls be drawn.
5. A man has 15 friends of whom 10 are relatives. In how many ways
can he invite 8 guests such that 5 of them may be relatives?
6. A committee of 5 is to be selected from among 6 boys and 5 girls.
Determine the number of ways of selecting the committee if it is
to consist of at least 1 boy and 1 girl.
BINOMIAL THEOREM
1. Find the general term in the expansions of
 2 1
2. Find the 7th term in the expansion of  x  
x

b
a
  
b
a


2n 1
10
2 
 2
3. Find the term independent of x in expansion of  x  3 
x 

1 
 2

4. Find the coefficient of x in the expansion of  3x 
3x 

15
9
6
1

5. Find the middle terms in the expansion of  x  
x

16
2n 1
6.
x a
Find the middle term in the expansion of   
x
a
7.
If the successive coefficients in the expansion of (1 + x)n are 28 , 56
and 70, find n.
XII Management/Dashain-Tihar Homework Assignments
Trinity-27
8.
Show that the middle term of the expansion of
1 x 2n
is
1.3.5.......... .( 2n  1) n n
2 x
n!
9.
If 1  x n  C0  C1x  C 2 x 2  ..... C n x n , prove that
2n!
C 0 2  C12  C 2 2  ......... C n 2 
(n!) 2
10. Sum to infinity of the following series ,
1
1  2 1  2  22

 .....
2!
3!
11. Prove that ,
1
1
1
1


 .....  log e 3
2
4
3.2
5.2
7.2 6
VECTOR
1.
Find the unit vector along 3a  5b where a = (7, 9) and b = (2, 6).
2.
Find a if b = (5, 7) and a - b =(12, 4)
3.
Define collinear and coplanar vectors.
4.
If a and b be two given vectors, then every vector r in the plane
parallel to a and b can uniquely be represented as the sum of
5.
two vectors parallel to a and b .
Define linearly dependent and independent vectors.
6.
If the position vectors of M and N are 3i  j  3k and
4i  2 j  k respectively, find MN and determine its direction
cosines.
7.
The position vectors of the points P, Q, R, S are i  j  k ,
2i  5 j , 3i  2 j  3k , i  6 j  k . Prove that the lines PQ and
8.
RS parallel and find the ratio of their lengths.
Show that three points A, B and C with position vectors
i  2 j  3k , 2 i  3 j  4k ,  7 j  10k respectively are collinear.
XII Management/Dashain-Tihar Homework Assignments
Trinity-28
9.
Show that the following vectors are coplanar a  2b  3c,
 2a  3b  4c,  b  2c .
10. If ABCD is a quadrilateral, show that AB  AD  CB  CD  4PQ
where p and Q are the middle points of AC and BD respectively.
11. If a = (3, -1, -4), b = (-2, 4, -3) and c = (-5, 7, 1), Find:
a.
a  2b  c
ii.
a  2b  c
iii. a unit vector along the direction of a  2b  c
iv. the direction cosines of the line represented by the vector
a  2b  c
12. Find (a  b) and a  b when
i.
a  i  7 j and b  2i  3 j .
ii.
a  4 i  j  2k and b  3i  k .
iii. a  i  7 j  3k and b  2i  3 j  k .
13.
a.
If a   3i  4 j  7k and b  6i  2 j  3k then find a  b
Verify that a and b both are perpendicular to a  b.
b.
Find the unit vectors perpendicular to both a and b .
If
i.
a  i  2 j  3k and b  2i  3 j  5k .
ii. a  2 i  2 j  k and b  4i  j  3k .
c.
Find a vector of magnitude 6 which is perpendicular to both
the vector a  4 i  j  3k and b  2i  j  2k .
d.
Find a vector of magnitude 5 units, perpendicular to each of
(a  b) and (a  b) , where a  i  j  k and b  i  2 j  2k .
14. a.
Find the area of parallelogram whose adjacent sides are
represented by the vectors 3 i  j  2k and i  3 j  4k .
b.
Find the area of the triangle whose two adjacent sides are
determined by the vectors.
i.
 2 i  5 j and i  2 j
ii.
i  j  k and  2i  3 j  k
XII Management/Dashain-Tihar Homework Assignments
Trinity-29
15. a.
Find the area of the parallelogram whose diagonals are
represented by the vectors
i.
d1  2 i  j  k and d 2  3i  4 j  k
ii. d1  i  3 j  2k and d 2  i  2 j
b.
Show that the points whose position vectors are
2 i  j  3k, 4i  3 j  k and 3i  j  2k are collinear.
16. Using vector method, find the area of ∆ABC, whose vertices are
i. A(3, -1, 2), B(1, -1, -3) and C(4, -3, 1)
ii. A(1, -1, 2), B(2, 1, -1) and C(3, -1, 2)
17. a.
b.
If a  b  c  0, Prove that: a  b  b  c  c  a
Prove that the points A, B, C with position vector a, b, c are
collinear if and only if (b  c)  (c  a )  (a  b)  0
18. a.
b.
If a  2, b  5 and a  b  8 Find a  b
If a  3, b 
2
3
and a  b is a unit vector, find the angle
between a and b
c.
If a . b = a . c , a  b = a  c and a  0 , then prove that b  c
19. Prove by vector method
i.
Sin(A+B) = SinACosB + CosASinB
ii. Sin(A-B)= SinACosB – CosASinB
SinA SinB SinC


iii.
a
b
C
20. If a  i  j  k and b  j  k , find a vector c such that
a  c  b and a . c  3
21. a.
Show that the vector area of the triangle with its vertices
having position vectors a . b . c is 1 (a  b  b  c  c  a )
2
b. Prove by vector method that the equation of the line which
x y
makes intercepts a and b on the axes of x and y is a  b  1.
22. Find the Scalar (dot) product of the following vectors.
a. (2, 3) and (1, -2)
b. (1, 2, -3) and (-1, 2, 1)
XII Management/Dashain-Tihar Homework Assignments
Trinity-30
c. 3 i  2 j  k and i  3 j  2k
23. Let a) a  (1, 2, 3) and b  (1, 0, 2)
b) a  i  2 j  2k and b  2i3 j  2k
Find,
i. the cosines of the angle between the vector
a and b
ii. the angle between a and b
iii. the projection of a on b
24. Define Scalar product of two vectors and interpret it geometrically.
25. Find the value of m where the following pairs of vector
a.
(m, 2, 5) and (-2, 1, 2)
b.
 7 i  m j  8k and 2mi  2m j  3k
26.
Prove the following
a.
a .b  a . b
b.
ab  a  b
27. a. If a  i  j  2k and b  3i  2 j  k , find the value of
(a  3b) . (2a  b)
b. If a and b are vectors such that a  2, b  3 and a . b  4 , find
a b .
c. If a, b, c be three vectors such that a  b  c  0 and
a  3, b  5, c  7 find the angle between a and b .
d. If a  5, b  4, c  3 and each is perpendicular to the sum of
the other two. Find a  b  c
e. If a, b, c are unit vectors such that a  b  c  0 then find the
value of a . b  b . c  c . a
XII Management/Dashain-Tihar Homework Assignments
Trinity-31
28. a. Let a and b be two non Zero vectors. Prove that
a b  a b  a b
b. Prove that (a . b) 2  (a  b) 2  a 2 b 2
c. If a, b, c are three mutually perpendicular vectors of the same
magnitude, prove that (a  b  c) is equally inclined to the
vectors a, b, and c
29. Prove by vector method.
a. i.
a= bCosc + cCosB
ii.
c = aCosB + bCosA
b. i.
a2 = b2 + c2 – 2bcCosA
ii.
b2 = a2 + c2 – 2acCosB
c. i.
Cos(A+B) = CosACosB – SinASinB
ii.
Cos(A-B) = CosACosB + SinASinB
^
30. If
^
a and b are two vectors of unit length and  is the angle
1

a  b  sin
2
2
Find the angel between the two diagonals of a cube.
If a line makes angles α, β, γ and δ with the four diagonals of
4
cube, show that Cos2α +Cos2β +Cos2γ + cos2δ =
3
In right angle triangle ABC, right angled at A, D is middle
point of BC then show that
i.
AB2 + AC2 = BC2
ii. AD = DC = DB
If AC and BD are the diagonals of a parallelogram ABCD
show that
i. AC2 + BD2 = 2(AB2 + AD2)
between them, show that
31. a.
b.
32. a.
b.
33. a.
b.
c.
ii. AC2 – BD2 = 4 AB.AD
Prove that the diagonals of a rhombus bisect each other at
right angles.
Prove that the mid-points of the sides of a quadrilateral form a
parallelogram.
Prove that the angle in the semi circle is a right angle.
XII Management/Dashain-Tihar Homework Assignments
Trinity-32
d.
prove that a parallelogram whose diagonals are equal is a
rectangle.
e. If two medians of a triangle are equal prove that it is a
rectangle.
f.
Show that the median to the base of an isosceles
triangle is perpendicular to the base
DERIVATIVE
1.
2.
Find the limit of:
1
a. f ( x ) 
at x = 0 if exists.
1
1 e x
1
b. f ( x )  sin at x= 0 if exists
x
1
c. f ( x )  x sin at x=0
x
a x  bx
d. Evaluate: lim
x 0
x
e Sinx  1
e. Evaluate: lim
x 0
x
Test the continuity of the following functions:
x
, x0

a. f (x)   x
, x0
 1
b.
Show that the function f(x) defined by
i.
 sin ax . sin bx
for x  0

f ( x)  
x2
for x  0

1

ii.
f(x) =
3.
a.
b.
c.
Sin 2 ax
x2
for
x0
1
for
x=0
is discontinuous at x=0, unless ab=1.
Find the differential coefficient of SinxX.
dy
If xy = ex-y then find
dx
dy
If y = x sinx then find
.
dx
XII Management/Dashain-Tihar Homework Assignments
Trinity-33

1  cos x  sin x 
tan  cos x  sin x 



-1
e. Differentiate 2tan (tan h x/2) w.r.t. 'x'.
f. Differentiate log sin h x/a w.r.t. 'x'.
g. Differentiate (sin h x/a + cos h x/a) nx w. r. t. 'x'.
a. The edge of a cube increases from 10cm to 10.025cm. Find
the approximate increments in the volume and the surface
area of the cube. Also, find the actual increments and
percentage error in the approximation.
b.
Find the points on the curve where the tangents are parallel
to the x-axis.
i. y = x3 – 3x2 – 1
ii. 4y = x4 – 8x3
c.
Find the equation of the tangent and normal to x2 + 3xy + y2 =
5 at (1, 1)
d.
Find the angle of intersection of the curves y = x2 and x= y2.
e.
Show that the equation of the tangent to the curve
d
dx
d. Find
4.
y
x2 y2
x

 1 is

2
a b
a 2 b2
f.
Show that the curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 cut
orthogonally.
Long questions:
1.
Find from first principles, the derivative of:
b.
etanx
c.
e cos
2
x
d. ax
e.
log(secx2)
f.
sec-1x
g.
log cos-1x
x2
h. 2
i. log xx
XII Management/Dashain-Tihar Homework Assignments
Trinity-34
2.
3.
Find the derivatives of :
a.
(sinx)Cosx+ (Cosx)sinx
b.
Find
c.
If Siny = xSin(a+y), Prove that
a.
Find, from first principles, the derivative of f(x) = e cosx at x=0.
b.
1
 2
x cos
If f(x) = 
x
0

x x2  a2 a2
dy

log( x  x 2  a 2 )
if y 
2
2
dx
for
for
dy sin 2 (a  y )

dx
sin a
x0
x0
.
DERIVATIVES AND ITS APPLICATIONS :
1.
State L'Hospital Rule and use it to evaluate the limit of :
i.
lim
x 0
x  sin x
x3
ii.
lim
x 0
xe x  log(x  1)
x2
iii.
lim
x 0
1  3x  1  3x
x
iv.
lim
x 0
e x  e  x  2Cosx
Sin 2 x
v.
lim
x 0
x  SinxCosx
x3
vi.
lim
x 0
(e x  1)Tanx
x2
Sec7 x
lim
x  Sec5x
Tan5x
viii. lim
x  Tan2x
vii.
ix.
lim
x 
log Sinx
Cotx
XII Management/Dashain-Tihar Homework Assignments
Trinity-35
x.
xi.
Tan5x
lim
x  Tanx
ex
x  x 4
lim
xii.
lim (Sinx) ln x
x 0 
xiii. lim x x
x 0
2. State Rolle's theorem. Interpret it geometrically. Further, verify the
Rolle's theorem for the functions:
i. f(x) = (x – 1)(x – 2)(x – 3) in [1, 3]
ii. f(x) = Cos2x in [- , ]
iii. f(x) = 25  x in [-5 , 5]
Using Rolle's Theorem, find a point on each of the following
functions where the tangent is parallel to x-axis.
i. f(x) = Sin2x in [-/2 , /2]
ii. f(x) = 6x – x2 in [ 0 , ]
State Lagrange's mean value theorem. Interpret it geometrically.
Further, verify the lagrange's MVT for the functions :
i. f(x) = x3 + x2 – 6x in [-1 , 4]
2
3.
4.
ii. f(x) = x  4 in [2 , 4]
iii. f(x) = ex in [0 , 1]
Using Lagrange's MVT, find the point on the curve (i) f(x) = x(x-2),
the tangent at which is parallel to the chord joining the points (1 , -1)
and (4 , 8).
2
5.
Group ‘C’
Solution of Non linear equations.
1.
Find the root of the equation x3 – 4x – 9 = 0 correct to three decimal
places by using bisection method.
2.
Find the positive roots of the equation x3 – 3x+ 1.06 = 0, by method of
bisection, correct to three decimal places.
3.
Compute one positive root of 2x – 3 sin x – 5 = 0 by bisection
method, correct to three significant figures.
XII Management/Dashain-Tihar Homework Assignments
Trinity-36
Use method of bisection
4. Compute one root of x + log10x – 2 = 0 correct to two decimal places
which lies between 1 and 2.
5.
Compute one root sinx = 10 (x – 1) correct to three significant figures.
6.
Compute the root of log10x = cosx correct to two decimal places.
Newton-Raphson’s method
1. Apply Newton’s method to find the real root of x3 + x – 1 = 0.
2.
Find the positive root of the equation x = 2sinx.
3.
The equation 3 tan3x = 3x + 1 is found to have a root near x = 0.9, x
being in radians.
4.
Find a positive root of x2 + 2x – 2 = 0, by Newton-Raphson method,
correct to six decimal figures.
5.
Compute the positive root of x3 – x – 0.1 = 0, by Newton-Raphson
method correct to six decimal figures.
System of linear equations
Using Gaussian elimination method test the consistency of the
followings.
1. 3x + y = 7
2. 4x – 2y = 6
3. 2x – 7y = 5
x – 4y = – 2
6x + y = – 3
8x + y = –9
4.
4x – y + 2z = 15
5.
–x + 2y + 3z = 5
5x – 7y + 9z = 8
7.
2x – 3y – 5z = 11
5x + 2y – 7z = – 12
–4x + 3y + z = 5
8.
x+y+z=7
x + 2y –3z = 16
x + 3y + 4z = 22
10.
3x + y + 2z = 3
2x – 3y – z = –3
x – 2y + z = 4
x–y–z=–2
x + 4z = 6
y – 2z = 1
9.
6.
3x – 5x = –7
3x + 5y = 3
3z – 3y = 2
x+y+z=6
x + 2y + 3z = 14
-x + y – z = –2
XII Management/Dashain-Tihar Homework Assignments
Trinity-37
11. Is the following system of equations diagonally dominant?
i)
10x + y + z = 6
ii)
10x – y – z = 13
x + 10y + z = 6
x + 10y + z = 36
x + y + 10z = 6
–x + y + 10z = 35
12. Solve the following system of the equation using Gauss- Seidel
method if it converses.
2x + y + z = 4,
x + 2y + z = 4,
x + y + 2z = 4
13. 2yx + 6y – z = 85, 6x + 15y + 2z = 72, x + y + 54z = 110
14. x + 10y + z = 6, 10x + y + z = 6, x + y + 10z = 6
15. 5x + 2y +z = 12, x + 4y + 2z = 15, x + 2y + 5z = 20
Numerical integration
1
1.
Evaluate
x
3
dx by trapezoidal rule.
0
1
2.
Evaluate
 ( 4 x – 3x
2
) dx taking 10 intervals by Trapezoidal rule.
0
3.
Given that e0 = 1, e1 = 2.72, e2 = 7.39, e3 = 20.09, e4 = 54.60, find an
4
approximation value of
e
x
dx by Trapezoidal rule.
0
1
4.
Evaluate

1  x 3 dx by (i) Simpson’s rule and (ii) Trapezoidal rule,
0
taking six interval correct to two decimal places.

2
5.
Evaluate

sin x dx taking x = 6, correct to four significant figures by
0
(i) Simpson’s one-third rule and ii) Trapezoidal rule.
2

dx
taking 4 subintervals, correct to five decimal places i)
x
6.
Evaluate
7.
Simplson’s one third rule ii) Trapezoidal rule
Compute by Simpson’s one-third rule, the integral
1
1
 x (1  x)dx correct to three places of decimal, taking step length
2
0
equal to 0.2.
XII Management/Dashain-Tihar Homework Assignments
Trinity-38
1
8.
Evaluate
 sin x
2
dx by i) Trapezoidal rule and ii) Simpson’s one -
0
third rule, correct to four decimal taking x = 10.
3
9.
Calculate approximate value of
 sin x
4
dx by using i) Trapezoidal
3
rule and ii) Simpson’s rule, taking n = 6.
Linear Programming Problems
Use simplex method for the followings.
1.
Maximize P = 15x1 + 10x2, Objective function
subject to
2.
x1, x2  0 Nonnegative constraints
Maximize P = 30x1 + x2, Objective function
Subject to
3.
2x 1  x 2  10
 Problems constraints
x 1  3x 2  10 
2x 1  x 2  10
 Problems constraints
x 1  3x 2  10 
x1, x2  0, Nonnegative constraints
Maximize P = 30x1 + 40x2, Objective function
2x 1  x 2  10

Subject to x 1  2x 2  7  Problems constraints
x 1  2x 2  12
4.
x1, x2  0, Nonnegative constraints
Maximize P = 2x1 + 3x2, Objective function
 2x 1  x 2  2

Subject to  x 1  x 2  5  Problems constraints

x2  6

5.
x1, x2  0, Nonnegative constraints
Maximize : z = x + y
Subject to : x + y  3
2x + 3y  18
x6
x, y  0

XII Management/Dashain-Tihar Homework Assignments
Trinity-39