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.
XI Science/Dashain-Tihar Homework Assignments
Trinity-1
English (002)
Magic of Words
Short Answer Questions:
1.
What do you think is the reason some people have recurring
dream?
2.
Why does the little old man close the door when he sees Kim?
3.
Write a paragraph describing the impact of the recurring dream
on Kim and the old man.
4.
How is the lost doll similar to Carmen?
5.
What makes you think that Evangeline is the reincarnated form of
Maria del Carmen?
6.
Write a paragraph describing Dr. Braun.
7.
Write a paragraph describing different physical things that
happened to Armando Gonzalez.
8.
Why does Gonzalez have to get into suspicious mood?
9.
Is the title 'The Loving Mother' appropriate? Elaborate your
answer.
10. Explain the paradoxical meaning of the child is the father of the
man.
Long Answer Questions:
1.
What similarities and differences do you find between the stories
'The Loving Mother' and 'The House Call'?
2.
What makes you think that 'Fear' is (not) different from other
supernatural stories?
3.
Write a short article for the newspaper on the topic of
4.
supernatural events.
What are the disadvantages of having plural children? Explain.
Meaning into Words
Short Answer Questions:
1.
Write a short description of your room explaining why you think
it is special for you.
2.
Write a paragraph about your plans for the future.
XI Science/Dashain-Tihar Homework Assignments
Trinity-2
3.
What good and bad things happen to a doctor? Use the passive
voice in your answer.
4.
Write about a small event in connection with a burglar breaking
into a house.
Long Answer Questions:
1.
Write an article describing your town as a tourist resort.
2.
Write an essay about the recent developments in your country.
Physics (110)
MECHANICS
Short Answer Questions:
1. Taking force, length and time as fundamental quantities, find the
dimensions of pressure and density.
2. What are the limitations of dimensional analysis?
3. Define the principle of homogeneity of dimensions.
4. Can a body have zero velocity and finite acceleration?
5. A ball is projected at an angle of projection 25 0, has certain
horizontal range. Is there any other angle of projection for the
same horizontal range? Explain.
6. What is unit vector? How do you obtain a unit vector from a given
vector?
7. What do you mean by resolution of a vector?
8. Distinguish between dot product and cross product of two
vectors.
9. Give the physical meaning of vector product.
10. Electric current has both magnitude and direction. Is it a vector?
Why or why not?


11. Two vectors P and Q act on a body making an angle , show by




diagram how P  Q and P  Q obtained? How would you obtain
 
QP?
12. If you drop a ball of certain mass from height h and at the same
instant another mass is thrown with velocity u, which will hit the
ground first?
XI Science/Dashain-Tihar Homework Assignments
Trinity-3
13. Can a body have a eastward velocity while experiencing
westward accelereation.
14. Define stress and strain with units.
15. In acatapult, when rubber is stretched and released, bullet gains
kinetic energy. From where does it gain K.E.?
Long Answer Questions:
1. What is triangle law of vector addition? Derive an expression for
resultant and directions of resultant using triangle law.
2. Young’s modulus of elasticity is 19 × 10 10N/m2. Express it in
dynes/cm2?
3. What do you mean by resolution of a vector? Find out rectangular
components of a given vector.
4. Show that the trajectory of a projectile fired from a height is
parabolic and also determine its time of height and the horizontal
range.
5. What is elastic limit? State and explain Hook’s law.
Numerical Problems:
1. Convert 1 kwh into cgs unit.
2. Check the correctness of following equations.
2GM
R
rhg
b. Surface tension (T) =
.
2cos
c. F = 6rv
r = radius
v = velocity
 = coefficient (Nsm-2)
Time period of a harmonic motion depends upon pressure P,
a.
3.
Escape velocity (v) =
density  and energy E of the system. Derive the relation between
them.
4.
Find the dimension of a, b and c in the following equations.
a.
a 

 P  2 V  b  RT
V 

Where, P = pressure
XI Science/Dashain-Tihar Homework Assignments
Trinity-4
V = Volume
T = Temperature
R = gas constant
b.
S = at + bt2 + ct3
Where, s = distance
t = time
5.
Sum of the magnitude of two vectors acting at a point is 18 units
and magnitude of their resultant is 12 units. If the resultant is at
90o with smaller vector, calculate the magnitude of two vectors.
6.


If a = 3î - 2ĵ + 5k̂ and b = 2î - ĵ - k̂ , find:

(i) | a |

(ii) | b |
(iii) â
(iv) b̂
 
 
(v) a . b (iv) a × b
(vii) Angle between them
7.

Show that the vectors a = 3 î + 6 ĵ - 2 k̂ and 4 î - ĵ 3 k̂ are
perpendicular.
8.


  
Two vectors A & B are such that C = A + B and C2 = A2 + B2.
Find angle between them.
KINETICS
1.
A projectile is fired from ground level with a velocity of 500 m/s at
300 to horizontal. Find horizontal range, greatest vertical height.
What is the least speed with which it could be projected in order
to achieve same horizontal range?
2.
An object is dropped from the top of tower of height 156.8 m and
at the same time another object is thrown vertically upward with
velocity 78.1m/s from the foot of tower. When and where do the
objects meet?
3.
A baseball is thrown towards a player with an initial velocity
20ms-1 and 450 with the horizontal. At the moment ball is thrown,
the player is 50 m from the thrower. At what speed and in what
direction must he run to catch the ball at same height it was
released?
XI Science/Dashain-Tihar Homework Assignments
Trinity-5
HEAT
Short Answer Questions:
1.
2.
3.
4.
5.
6.
State zeroth law of thermodynamics.
What is thermal equilibrium?
Why water is not taken as thermometric substance?
If a plate having a hole of radius 1cm at 20 0C is heated up to 1000C.
What will be the radius of hole?
A hollow sphere and a solid sphere of equal radius are heated to
same temperature, what will happen to their new radius?
Why do frozen pipes brust in winter?
Long Answer Questions:
1.
2.
3.
Define linear and superficial expansions. Find an expression of
length and area of solids at temperature 00C in terms of their
values at 00C.
 
Define,  and  and show that  = = .
2 3
A steel rod and a brass rod differ by 5cm in length at all
temperature. What are their lengths at 0oC?
(Linear expansivity of steel = 12 × 10 -6 oC-1,
Linear expansivity of brass = 18 × 10 -6 oC-1)
4.
A copper cylinder is initially 20 0C. At what temperature will its
volume be 0.15% larger than that at 200C?
Given,  = 17 × 10-6K-1)
OPTICS
Short Answer Questions:
1.
2.
3.
4.
5.
Distinguish between real and virtual images.
Why are the convex mirrors used in cars for rear view?
Can a convex mirror form real image?
State the law of Refraction.
What will be the shape of sky if you observe it from dip below the
surface of water?
Long Answer Questions:
1.
2.
Derive mirror formula for convex mirror.
Derive mirror formula for concave mirror. When the image
formed is virtual?
XI Science/Dashain-Tihar Homework Assignments
Trinity-6
3.
What is meant by lateral shift? Derive a relationship to show the
variation of lateral shift with incident angle for a ray passing
through rectangular glass slab.
Numerical problems
1.
2.
3.
A spherical concave shaving mirror has a radius of curvature of
25cm. What is the magnification produced when the face is 10cm
from the pole of the mirror.
A mirror forms an erect image 30cm from the object and twice its
height. Assuming the object to be real, determine whether the
mirror is convex or concave?
A meter scale is placed along the axis of convex mirror of focal
length 25cm, its nearer ends being at a distance of 50cm. Calculate
the size of image formed.
ELETROSTATICS
Short answer questions:
1.
2.
3.
4.
5.
Define one coulomb charge.
Explain the induction method to charge the body.
Can a charged body attract an uncharged body? explain.
When a body is charged by induction method. The source can be
used for infinite times. Explain.
Can a positively charged body attract another positively charged
body?
Long answer questions
1.
2.
3.
State coulomb law of electrostatics and find out the expression for
the force between two charges q1 and q2 at a distance x in a
medium having relative permittivity r.
Explain the method of charging a conductor negatively by the
induction method.
Write down the properties of charge.
XI Science/Dashain-Tihar Homework Assignments
Trinity-7
Chemistry (112)
1.
Distinguish between the following pairs with examples:
a) Minerals and ores
b) Flux and slag
c) Alloys and amalgams
d) Pyrometallurgy and electrometallurgy
2. Define the terms:
a) Gangue
b) Concentration of ore
3. What is the principle of froth floatation method for concentration?
4. Discuss the Aluminothermite process used in metallurgy.
5. Distinguish between:
a) Calcination and roasting
b) Gangue and slag
6. Why carbon reduction methods in not applied for the reduction of
oxides of the metals like Cr, Mn etc?
7. Write down the extraction of sodium metal by Down’s process.
8. Describe manufacture of sodium hydroxide by Castner Kellener’s
process.
9. Describe manufacture of sodium carbonate by Solvey Ammonia
Process.
10. Write down the limitations of Rutherford's atomic model.
11. What are emission spectra? What is Balmer series of hydrogen
spectrum?
12. What experimental evidence led Rutherford to conclude that (a)
the nucleus of an atom contains most of the atomic mass (b) the
nucleus of the atom is positively charged (c) the atom is mostly
empty.
13. Write postulates of Bohr's atomic model.
14. Describe the origin of hydrogen spectra on the basis of Bohr's
theory.
15. State and explain:
a. Paulis exclusion principle
b. Hund's rule
c. Aufbau principle
16. What are the limitations of chemical equation?
XI Science/Dashain-Tihar Homework Assignments
Trinity-8
17. What is chemical equation? Write essentials of chemical equation.
18. 35 gm of sucrose C12H22O11 are dissolved in 190 gm of water.
Calculate the number of oxygen atoms in the solution.
19. Calculate the mass of 120 cc of nitrogen molecule at NTP. How
many number of molecules are present in it.
20. Calculate the no. of moles of oxygen in one litre of air containing
19.5% oxygen by volume under standard condition.
21. What do you mean by limiting reactant?
Consider the following reaction:
CaCO3(S) + 2HCl(aq)  CaCl2(aq) + H2O(l) + CO2(g)
If 5 gm of pure CaCO3 is treated with 5 gm of HCl to produce
CaCl2, H2O and CO2.
a.
Find out limiting reactant.
b.
Calculate mass of CaCl2 formed.
c.
How many number of water molecules are produced?
d. Calculate the volume of CO2 produced at NTP.
22. a.
Calculate the mass of water having the same number of
hydrogen atom as are present in 32 gm of methane.
c.
[
How many number of oxygen molecules are present in 3L of
CO2 at STP ?
c.
[
Calculate the mass of one molecule of hydrogen.
23. Write the significance of
.
24. What volume of oxygen will be produced by heating 245 kg of
pure KClO3 at NTP?
25. Atomic weight of elements is in fractions. Explain.
26. Calculate the mass in gram of 1x1022 molecules of CuSO4.5H2O
(atomic weight of copper=63)
27. Define limiting reagent.
28. What will be the molecular weight of a gas; 11.2 litre of which at
NTP weighs 14 gram?
29. A chemical reaction was carried out by mixing 23 gm NaOH with
25.5 gm of H2SO4 to produce Na2SO4 and water.
i) Which one is limiting reagent?
ii) Calculate the mass of sodium sulphate produced.
XI Science/Dashain-Tihar Homework Assignments
Trinity-9
iii) How many moles of water are formed?
iv) Find the no. of molecules of unreacted reactant left over.
30. a. How much sulphuric acid containing 80% H2SO4 by weight is
needed for the production of 1000 kg of hydrochloric acid
containing 62% HCl by weight in the following reaction.
2NaCl (aq) + H2SO4 (aq)
Na2SO4 (aq)+2HCl
XI Science/Dashain-Tihar Homework Assignments
Trinity-10
[
Biology (114)
Botany
BIODIVERSITY
Very Short Answer Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Define binomial nomenclature with an example.
Write hierarchical system of classification.
Who is called as the father of taxonomy?
Give hierarchical classification of mustard.
What is taxonomic category?
How does Spirogyra get its name?
What do you mean by primordial utricle?
Define biodiversity.
What do you mean by floral diversity?
Define taxonomy and systematics.
What do you mean by identification and nomenclature?
Define the term species.
What is phylogeny?
Define species, genus, family, order, class and division.
Name the five kingdoms.
Mention the contributions of John Ray and Theophrastus.
Define Monera.
What do you mean by artificial classification?
Write the drawbacks of five kingdom system.
What are identification keys in taxonomy?
Short Answer Questions
1.
Give the shortcomings of two kingdom classification.
2.
What are the advantages of five kingdom system over two
kingdom system?
3.
Give the concept of binomial system of nomenclature.
4.
Write a short note on scope of biodiversity.
5.
What are the advantages of classification?
6.
Compare artificial, natural and phylogenetic classifications.
XI Science/Dashain-Tihar Homework Assignments
Trinity-11
Long Answer Question
1.
Describe conjugation in Spirogyra.
CELL BIOLOGY
Very Short Answer Questions:
1.
Define cell
2.
What is cyclosis or protoplasmic streaming?
3.
What is cellular totipotency?
4.
Why middle is middle lamella called cementing layer?
5.
What is extrinsic information?
6.
What are plasmodesmata?
7.
Define lignified cell.
8.
What are the different layers of cell wall?
9.
Why cell is called unit of life?
10. What are cell inclusions?
11. Why Protoplasm is called physical basis of life?
12. What is sub cellular membrane?
13. Define cellular pool.
Short Answer Questions:
1.
2.
3.
4.
5.
What is prokaryotic cell? Describe its characters.
Explain cell theory.
Explain the flow of energy through cell.
What is prokaryotic cell? Describe its characters.
Explain the experimental evidence of totipotency.
Long Answer Question
1.
Describe the structure and function of cell wall and mitochondria.
XI Science/Dashain-Tihar Homework Assignments
Trinity-12
Zoology
Very Short Answer Questions:
1.
What is Biology? Who coined the term 'Biology'?
2.
Mention the roles of Theophrastus and Robert Hooke in the
development of Biology.
3.
What do the following deals about?
Embryology, Palaeobiology, Morphology, Ichthyology,
Ornithology, Ecology, Mycology, Epidemiology and Taxonomy.
4.
Define the given terms:
Life, Growth, Excretion, Osmoregulation, Metabolism and
Homeostasis
5.
How does nutrition in plants and animals differ?
6.
How is Biology related with Geography and Geology?
7.
Give one example each of poilikothermic and Homeothermic
animals.
8.
Mention two important features of Amphibians.
9.
What are Amniotes and Anamniotes?
10. Give one example each from Hemichordata, Cephalochordata and
Urochordata.
11. Define Notochord.
12. What type of cells form the Notochord?
Short Answer Questions:
1.
"Biology is the science of exceptions'. Justify the statement with
examples from different aspects.
2.
How is Biology related with Chemistry?
3.
Mention the application of biological knowledge on agriculture,
industry and health.
4.
How is Biology dependent on Physics?
5.
Write the characteristics of Phylum chordata.
6.
Write the characters of cyclostomata.
7.
Differentiate between Chondrichthyes and Osteichthyes.
XI Science/Dashain-Tihar Homework Assignments
Trinity-13
8.
Differentiate between Protochordata and Euchordata.
9.
List the characters which help the bird in aerial adaptations.
Very Short Answer Questions:
1.
2.
3.
4.
5.
6.
Who coined the term 'Protista'? What is its literal meaning?
What types of organisms belong to Kingdom Protista?
What are Dinoflagellates?
Define the term Bio-luminescence with example.
Name any two photosynthetic protists.
What do you mean by mixotrophic nutrition? Write with
examples.
7. How do diatoms differ with Euglenodis?
8. Protozoans are called acellular rather than unicellular, why?
9. Who coined the term 'Protozoa' and who studied them first?
10. What do you mean by monomorphic and dimorphic nuclei?
11. Define the terms syngamy and conjugation.
12. How do Rhizopods reproduce?
13. Which protozoan parasite causes malignant malaria?
14. Give a labeled diagram of Paramecium.
15. Who discovered Plasmodium as malarial parasite and who
identified Anopheles mosquito as its primary host?
16. Write in short about distribution of Plasmodium.
17. What do you mean by digenetic lifecycle?
18. Why is Anopheles female mosquito considered as primary host of
Plasmodium?
19. How is Plasmodium inoculated in human body?
20. Which stage of Plasmodium is infective?
21. Plasmodium belongs to class Sporozoa, why?
Short Answer Questions:
1. Classify the Protists on the basis of mode of nutrition.
2. What are pseudopodia? Mention the types of pseudopodia with
examples.
3. Write in short about habit/habitant, distribution & structure of
Paramecium.
4. Write short note on teeth of frog.
XI Science/Dashain-Tihar Homework Assignments
Trinity-14
Long Answer Question:
1.
2.
Mention important features of protozoans and classify them upto
classes with their characteristics and examples.
Describe alimentary of canal of frog & earthworm.
ORIGIN & EVOLUTION OF LIFE
Very Short Answer Questions:
1. Define life.
2. Define homeostasis.
3. What is abiogenesis?
4. What was Louis Pasteur's view regarding origin of life?
5. Mention the view of Aristotle about Evolution.
6. Define Ylem.
7. What is primitive atompsphere?
8. What do you mean by primordial soup?
9. Who verified Oparin-Haldane theory experimentally?
10. Name the sources of energy on primitive earth for the synthesis of
life.
11. What was the source of energy in Miller-Urey experiment?
12. Name the gases filled in the gas chamber to recreate the conditions
of primitive earth.
13. What is the view of special creation theory about the origin of life?
14. Define coacervates.
15. Name the first cell like structure and mention the probable time of
its origin in the Earth.
16. Name the first oxygenic photoautotroph and mention the
probable time period of its origin.
17. What were the end products of Miller Urey's experiment?
18. Write the conclusion of Miller Urey's experiment.
19. Define evolution.
20. Define Divergence
XI Science/Dashain-Tihar Homework Assignments
Trinity-15
Short Answer Questions:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Mention the characteristic features of living organism.
Write in brief about Spontaneous generation theory.
Describe Redi's experiment.
Explain Pastur's experiment.
Write in brief about origin of Earth.
How were the coacervates formed? Explain.
Discuss Oparin-Haldane theory in brief.
"New life cannot originate today" Explain.
What were the conditions prevailing on primitive earth?
List out the possible steps by which the complex organic
molecules are synthesized from simple inorganic substances.
11. Describe Miller and Urey's experiment.
12. Differentiate between inorganic and organic evolution.
13. What are the differences between convergent and divergent
evolution?
XI Science/Dashain-Tihar Homework Assignments
Trinity-16
Mathematics (116)
LIMIT
Short Questions:
1.
Find limiting value of following functions:
a.
b.
c.
d.
e.
f.
2.
3x - 2x+a
2(x – a)
lim
x→a
3a – x – x + a
4(x – a)
lim
x→a
lim
x→∞
( x–a–
lim
x→1
lim
x→∞
lim
bx
2x – 3 – x2
(x – 1)
x( x–
x–
x→2
x – a)
8 – x2
x2 + 12 – 4
Prove that:
a.
9
 1
 2
Lim
 3

2 
x 3  x  3
x  3x  3
b.
 x2  9
3  1
Lim 2



x 3 x  9
x  3  2

Long Questions:
1.
Prove that Lim
Sin
 1 where

2.
Prove that Lim
xn  an
 na n 1 for different cases.
x a
3.
Find the limiting value of followings:
Cosx  Cosy
a. Lim
x y
xy
0
x a

is measure in radian.
XI Science/Dashain-Tihar Homework Assignments
Trinity-17
b.
c.
d.
e.
Lim
x y
Cotx  Coty
xy
x sin    sin x
x 
x tan    tan x
Lim
x 
x 
cos   sin 
Lim
 

4
4
Lim
x 
f.
Lim
g.
Lim
x 1
x  2  x2
2x  2  2x 2
sin x  sin a
x a
x a
a 1
x
x
h.
Lim
i.
Lim
j.
Lim
k.
l.
m.
x 0
1  Sec
 0
2
e 2x  1
( x  0)
x 0
2x
Sin x0
lim
x
x 0
lim Sin
x 0
lim
x→0
1
|x|
xSin
1
x
CONTINUITY
Short questions:
1. In what condition does a function exist?
2. What do you mean by continuity of a function at a point?
3. Evaluate the following limit if exists.
a. Lim x  2
x 2
XI Science/Dashain-Tihar Homework Assignments
Trinity-18
b.
Lim
c.
Lim
d.
x3
1
x3
x
x
x 1
Lim
x 1 x  1
x0
Long questions:
1. Test continuity or discontinuity at a given points.
a.
f(x) = x2 at x = 4
b.
f(x) = 3x2 – 2x + 4 at x = 1
1
at x = 0
2x
1
d. f(x) =
at x  2
x2
1
f(x) =
at x = 3
x3
c.
e.
f(x) =
f.
f(x) =
g.
f(x) =
x 2  16
at x = 4
x4
x2
at x = 2
x2
h. Show that the function continuous at x = 0 x = 1, f(x) =
 x

 x
2  x

i.
if
if
if
Discuss the continuity of the functions at the point specified.
x sin(1 / x )
ii) f(x) = 
0

i) f(x) = |x| at x = 0
x  2
iii) f(x) = 
 4
j.
x0 

0  x  1
x  1 
if
if
if
if
x  0
 at x  0
x  0
x  2
 at x  2
x  2
Show that the function
 sin 2 ax

f(x) =  x 2
 1

if
x0
if
x0
is discontinuous at x = 0. Redefine the
function in such a way that it becomes continuous at x = 0.
XI Science/Dashain-Tihar Homework Assignments
Trinity-19
k.
Find the value of k for which the following functions are
continuous at the indicated point.
1  x 2

i) f(x) =  k
1  2x

for
for
 x 2  2x

ii) f(x) =  x  2

 k
l.
x  2

x  2at x  2
x  2

for
for
for
x  3
 at x  3
x  3
Find the point of discontinuity of the following functions.
i) f(x) =
x 1
x 1
iii) f(x) =
ii) f(x) =
3x  1
x  5x 2  6 x
3
x 1
( x  2)( x  3)
DERIVATIVE
1.
Give the geometrical and physical meaning of the derivative.
2.
Using definition, find the derivatives of the followings:
i) x5
vi)
x.
ii) xn
x
iii) ax + b
1 x
vii)
1
2x  3
xi.
viii) x 
1 x2
xii.
iv) x2 – 2
ix)
x
3x  5
x
v) x3 – 4x
1
x 1
xiii.
ax  b
x
SETS AND REAL NUMBERS
Short questions:
 N}, B = {-2} Then show that A 
1.
If A = {x:x2 = 4, x
B
2.
Write the power set of the set {a, b, c, d}. Verify that this set
contains 24 subsets (or elements).
3.
If A = {x:x = 2n-1, n
 6, n  N}, B = {x:x = 3n + 1, n  3, n  N}
then, find:
a.
A B
XI Science/Dashain-Tihar Homework Assignments
Trinity-20
4.
5.
b.
A B
c.
A B
Prove that:
a.
A  B B A
b.
AA 
Rewrite the following without using absolute value sign
2 x  3  2.
6.
Define absolute values of a real number prove that.
a.
xy  x  y
b.
x  y  x  y and hence verify if x = -3 and y = 4
7.
Find x and y if (2x – 3, 4) = (4x, y + 5)
8.
Using the axioms of real numbers, if a > b and c > 0 then show that
a b

c c
9.
If X = {Squares}, Y = {Rectangles}, Find (X  Y)
10. In a town of 50,000 populations, 28,000 read Rising Nepal and
5,000 read Kathmandu post. If 1000 Person read both of two news,
how many read neither Rising Nepal nor Kathmandu post?
11. Define the following with suitable examples.
a.
Intersection of two sets.
b.
Union of two sets
c.
complement of a set
d. Symmetric difference of two sets.
Also show the examples in Venn- diagram.
12. Define absolute value of a real number.
13. Rewrite with absolute value sign for:
a.
-4 < x < 12
b.
-11 < x < 6
c.
1  x  
1
3
XI Science/Dashain-Tihar Homework Assignments
Trinity-21
Long questions:
1.
2.
If U = {x:1  X  10, X  N}, A = {x:x<8, x  N}
B= {x:x  6, x  N}; verify that:
a.
AB BA
b.
AB AB
c.
AB AB
Let A = [-2, 4] and B = (2, 5]; compute
a.
AB
b.
AB
c.A – B
d. B – A
3.
If A, B and C are subsets of the universal set U, then prove that:
a.
A  (B  C)  (A  B)  (A  C)
b.
A  (B  C)  (A  B)  (A  C)
c.
A  (B  C)  (A  B)  (C  A)
d.
A  (B  C)  (A  B)  (A  C)
e.
( AB)  (A  B)  (A  C)
f.
i. A  B  A  B
ii. A  B  A  B
iii. A  B  B  A
iv. A  B  B  A
4.
5.
Solve the followings:
a.
2x  7  4
b.
x 9
c.
3x  7  5
In a class, 30 students read physics, 32 read chemistry and 32
mathematics. If 16 read physics and chemistry, 16 reads
chemistry and mathematics, 14 read physics and mathematics
and 6 read all subjects. Find how many students read.
XI Science/Dashain-Tihar Homework Assignments
Trinity-22
a.
At least one subject
b.
Exactly one subject
c.
Physics Only
d. Exactly two subjects
e.
6.
At most two subjects
If n(U) = 360, n(A) = 240, n(B) = 160; Find:
a.
The maximum value of n(A  B)
b.
the maximum value of n(A  B)
c.
the minimum value of n(A  B)
d. the minimum value of n(A  B)
LOGIC
1.
Define Bi-Conditional of a compound statement and construct its
truth table.
2.
Show that disjunction of any statement and its negation is
tautology.
3.
4.
For any simple statement p, q and r. Verify the followings:
a.
pq  pp
b.
p  (q  r)  (p  q)  r
c.
p  (q  r)  (p  q)  (p  r)
d.
~ (p  q) ~ p  ~ q
e.
~ (p  q) ~ p  ~ q
If p, q, r are simple statement and q is false then construct the
truth table for [(p ~ q) ~ r]
COMPLEX NUMBERS
1.
Express each of the following as a single order pair.
i. (1, 0)50
ii. (0, 1)200
2.
Prove that: i50 + i60 + i51 + i53 = 0
3.
Solve the equation x2 + 9 = 0
XI Science/Dashain-Tihar Homework Assignments
Trinity-23
4.
Prove that
–3
–3 = -3
5.
Simplify
6.
If Z1 = 3–2i and Z2 = 4-3i Find,
1 1 1 1
- + i i 2 i3 i 4
i. z1-1
ii. z2-1
iii.
z1
z2
x  iy 
1 i
prove that x2 + y2 =1
1i
7.
If
8.
If x + iy =
9.
Find the square roots of 5 + 12i.
U  iv
prove that x2 + y2 = 1
U  iv
10. Find the square roots of
( 2 ,36)
.
( 2 ,3)
11. Change (1  3i) into the polar form.
12. Change x + iy into polar form.
13. State De’moivre’s theorem and prove it.
14. Using De’moivre’s theorem evaluate:
a.
(1 – i)8
b.
i12
c.
(–1 +
3 i )6
15. Using De’moivre’s theorem find cube roots of –1.
16. Solve: a) Z4 = 1 b) Z6 = 1
SEQUENCE AND SERIES
1.
Prove that x, y, z are in A.P., G.P. or H.P. according as
xy x
x
x

or
or
respectively.
yz x
y
z
XI Science/Dashain-Tihar Homework Assignments
Trinity-24
1
1
( x  y), y and ( x  z) be in H.P., Show that x, y, z are in G.P.
2
2
2.
If
3.
If G is the geometric mean between a and b, show that
1
1
1
 2
 2
2
2
G a
G b
G
2
4.
If H be the harmonic mean between a and b, prove that
1
1
1 1

 
Ha H b a b
5.
If a, b, c be in A.P., b, c, d in G.P. and c, d, e in H.P., prove that a,
c, e are in G.P.
6.
The A.M. between two numbers exceeds their G.M. by 2 and the
G.M. exceeds the H.M. by 1.6. Find the numbers.
7.
If ax = by = cz and a, b, c are in G.P., prove that x, y, z are in H.P.
8.
If one G.M. ‘G’ and two A.M.’s p and q are inserted between two
given positive numbers, prove that G2 = (2p – q) (2q – p)
9.
If a, b, c are in H.P., prove that
i)
bc
ca
ab
are in H.P.
,
,
bc ca a b
ii) 2a – b, b, 2c – b are in G.P.
iii) a(b + c), b(c + a), c(a + b) are in A.P.
10. Find nth term and sum upto nth terms of followings:
a. 1.3 + 2.4 + 3.5 + …………..
b. 2 + 6 + 12 + 20 + ………….
c. 1.3 + 3.5 + 5.7 + …………..
d. 1 + (1 + 3) + (1 + 3 + 5) + …………….
e. 3.12 + 4.22 + 5.32 + ……………
f. 12.2 + 22.3 + 32.4 + …………….
11. Find nth term and sum upto nth term of followings
a. 2 + 6 + 12 + 20 + ………….
b. 3 + 7 + 13 + 21 + ………….
c. 1 + 3 + 6 + 10 + …………….
d. 1 + 3+ 7+ 15 + ……………..
XI Science/Dashain-Tihar Homework Assignments
Trinity-25
e.
5 + 7 + 13 + 31 + 85 + …………….
12. Find nth term and sum upto nth terms of followings
a. 1 +
2 3
4


 ........
2 22 23
4
5
7 10

 .........
52 53
3
2
5
4
b. 1  
7
8
c. 1     .......... ..
d.
1 2 3 4
  
 .......... .
2 4 8 16
e.
2 6 10 14



 .......... .....
5 52 53 54
f. 1 + 2a + 3a2 + 4a3 + …………
13. Find sum upto nth term of
a. 2 + 22 + 222 + ……………
b. 0.3 + 0.33 + 0.333 + ………………
c. 0.7 + 0.77 + 0.777+ …………….
14. Find sum upto infinity of
2
2
a. 1  
3
4

 .......... ...
22 23
b. 1  3x  5x 2  7 x 3  .......... ...
c. 1 – 5a + 9a2 – 13a3 + …………….
15. State principle of mathematical induction and using it show
a. n(n + 1) is an even number
b. n(3n + 1) is divisible by 2
c. n(2n + 1) (2n – 1) is multiple of 3
d. n(n + 1) (2n + 1) is divisible by 6
e. n(n + 1) (n + 2) is multiple of 6
f. xn – yn is divisible by x – y
g. 23n –1 is divisible by 7
16. Using the principle of mathematical induction, show the
following statement for all natural numbers (n):
XI Science/Dashain-Tihar Homework Assignments
Trinity-26
a. 2 + 4 + 6 + … + 2n = n(n + 1)
b. 12 + 32 + 52 + … + (2n – 1)2 =
c. 13 + 23 + 33 + … + n3 =
n( 2n  1)( 2n  1)
3
n 2 ( n  1) 2
4
17. Applying the principle of mathematical induction, show the
following statement for all natural numbers (n):
a. 1.2 + 2.3 + 3.4 + … + n.(n + 1) =
1
n( n  1)(n  2)
3
b.
1
1
1
1
n


 .......... ... 

1.2 2.3 3.4
n( n  1) n  1
c.
1 1 1
1
1
   ....  n  1  n
2 4 8
2
2
d. 2 + 22 + 23 + … + 2n = 2(2n – 1)
XI Science/Dashain-Tihar Homework Assignments
Trinity-27
Computer Science (130)
1.
2.
3.
Write short notes on:
a. Napier's bone
b. Electromechinical computer
c. Pascaline
d. Howard Aiken
e. Analytical engine
f. Mark – I
g. Bio Chips
h. History of Computer in Nepal
i. Limitations of Computer
j. Super Computer
k. Artificial Intelligence
l. IBM Company
m. AT Computers
n. Binary Number System
o. Binary addition
p. Complement method of binary subtraction
q. Application Packages
Calculate these:
a. (813)10 = (?)2
m. (79.97)10 = (?)2
b. (875)10 = (?)8
n. (604.406)10 = (?)8
c. (956)10 = (?)16
o. (295.592)10 = (?)16
d. (101101)2 = (?)10
p. (101111.1011)2 = (?)10
e. (3456)8 = (?)10
q. 3456.65)8 = (?)10
f. (BCDE)16 = (?)10
r. (A6D9.A9)16 = (?)10
g. (1101101101)2 = (?)8
s. (11011.10111)2 = (?)8
h. (14325)8 = (?)2
t. (1011011011.101101)2 = (?)16
i. (101101101)2 = (?)16
u. (567.765)8 = (?)2
j. (B8C9F)16 = (?)2
v. (765.567)8 = (?)16
k. (4753)8 = (?)16
w. (1234.432)16 = (?)2
l. (B9E7F)16 = (?)8
x. (432.123)16 = (?)8
Calculate these:
a.
(1011011)2 + (101101)2
b.
(101111)2 + (10110)2
XI Science/Dashain-Tihar Homework Assignments
Trinity-28
c.
(11010)2 – (1011)2 [Using 1's complement method]
d. (10110)2 – (110)2 [Using 2' complement method]
e.
(110)2 – (1011)2 [Using 1's complement method]
f.
(1011)2 – (11001)2 [Using 2's complement method]
g.
(101101)2 × (111)2
h. 11011011÷111
i.
(7890)10 – (789)10 [Using 9's complement]
j.
(789)10 - (7890)10 [Using 9's complement]
k.
(689)10 – (123)10 [Using 10's complement]
l.
(567)10 – (8973)10 [Using 10's complement]
4.
Define commutative law. State and verify Demorgan's theorem.
5.
Construct truth table and draw the graphical symbol for NOT
gate.
6.
Define Boolean algebra, Boolean Function and duality principal.
7.
Differentiate between OR gate and AND gate with truth table,
symbol.
8.
Differentiate between NOR gate and NAND gate with truth table
symbol.
9.
Differentiate between X-OR gate X-NOR gate with truth table,
symbol.
10. Define logic gate, Venn diagram and universal gate.
11. Draw a logic circuit for the following:
a.
xyz' + xyz + x'y
b.
xy(y + y'z) + x'z
12. Simplify the following Boolean Expression.
a.
xy + xy' + x'y + x'y'
b.
(ab'c' + ab'c + abc + ab'c) (a+b)

XI Science/Dashain-Tihar Homework Assignments
Trinity-29