Download Holiday Homework for Class XI

GITA CONVENT SCHOOL, FARIDABAD
(AN ISO 9001:2008 CERTIFIED)
HOLIDAYS
HOMEWORK
CLASS-XI
Dear Students,
Vacation is a time when you connect with your friends, family members and
relatives. So, all of you
“FIX A GOAL AND STRIVE HARD EACH DAY TO ACHIEVE IT!”
Here are few tips for you to follow –
1. Inculcate good manners – 4 magic words `Please, Thank you, Excuse me,
Sorry’ – Use them and see the difference.
2. Help your mother to keep the house clean. Do small household jobs like
dusting, watering the plants, laying dinner table and so on.
3. Go out for morning walk, talk about things you see around.
4. Listen stories from family members and try to narrate them.
5. Inculcate the feeling of empathy, affection and tolerance.
6. Cultivate sportsmanship by playing various indoor and outdoor games.
7. Last but not the least –
‘Always speak in English with your family members and friends.’
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ENGLISH
1. Poetry adds music and colour to our life. Emotions are unleashed and we are transported to a
beautiful world of rainbow colours. Collect five poems each under the heading of human
emotions, nature and humour and design a book titled ‘A book of poems’ add images to
explain the theme of poem. Paste picture of poet as well. Prepare a suitable cover page.
(Use A4 sheets)
2. Make a book review of Canterville Ghost.
3. Cut 5 Articles, 5 Reports and 5 Letters to the Editor from the newspaper. Paste on A4 size
sheet and write main points about each of them. (4 to 5 points)
4. Enrich your Vocabulary write 50 words and give their substitute words on A4 size sheet.
MATHEMATICS
Trigonometry
1. If
+
= a2 – b2 and
–
= 0 then show that
(ax)2/3 + (by)2/3 = (a2 – b2)2/3
2. Evaluate: cosec 480 + cosec 960 + cosec 1920 + cosec 3840
3. If
=
then prove that ABC is either isosceles or right angled triangle.
4. Solve: sin8 x + cos8 x =
5. Solve: cos 3x cos3 x + sin 3x sin3 x = 0
6. If the equation sin4 x – 2 cos2 x + a2 = 0 is solvable for x € R. Find the range of a.
7. Find the number of solution of the equation
= x2 –
x+4
8. If sin A + cos A = m and sin3 A + cos3 A = n then obtain the equation in terms of m and n.
9. Find the value of log tan 10 + log tan 20 + log tan 30 + ……… + log tan 890
10. Find the minimum and maximum value of sin6 θ + cos6 θ
11. Prove that 5 cos θ + 3 cos
12. If
=
=
+ 3 lies in [–4, 10]
then evaluate x + y + z
13. Prove that cosec x + cosec 2x + cosec 4x = cot – cot 4x.
14. Solve: tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ.
15. Solve: 2 sin2 x + sin2 2x = 2.
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16. Solve: 4 sin x sin 2x sin 4x = sin 3x.
sin x – cos x = a has no solution.
17. Find the set values of a for which the equation
18. Find the general solution of tan 5θ = cot 2θ.
19. How many solutions does 3 cos x + 4 sin x = 6 have?
20. How many values of x in the interval [0, 5 ] satisfy the equation 3 sin2 x – 7 sin x + 2 = 0
21. If sin α + sin β = a and cos α + cos β = b prove that
cos (α – β) =
i)
ii)
tan
α
β
=±
22. If α and β are distinct roots of a cos θ + b sin θ = c prove that sin (α + β) =
23. If sin α + sin β = a and cos α + cos β = b show that
cos (α + β) =
i)
ii)
sin (α + β) =
24. If α and β are the solutions of equation a tan θ + b sec θ = c then show that
tan (α + β) =
25. If α and β are the solutions of a cos θ + b sin θ = c then show that
i)
cos (α + β) =
ii)
cos (α – β) =
26. If cos θ =
prove that tan =
27. If cos θ =
prove that tan = ±
28. If cos θ = cos α cos β prove that tan
29. If tan =
tan
tan
= tan2
prove that cos θ =
30. Prove that tan α + 2 tan 2α + 4 tan 4α + 8 cot 8α = cot α
31. If tan
= tan3
prove that sin θ =
32. Prove that cos A cos 2A cos 22A cos 23A …… cos 2n–1A =
33. Prove that sin
sin
sin
sin
sin
sin
sin
=
34. If α and β are two different values of θ lying between 0 and 2π which satisfy the
equation 6 cos θ + 8 sin θ = 9 find the value of sin (α + β)
35. Prove that cot θ cot 2θ + cot 2θ cot 3θ + 2 = cot θ (cot θ – cot 3θ)
36. If cos (α + β) sin (γ + δ) = cos (α – β) sin (γ – δ)
37. If 2 tan β + cot β = tan α prove that cot β = 2 tan (α – β)
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38. If sin B = 3 sin (2A + B) prove that 2 tan A + tan (A + B) = 0
39. If cos (α – β) + cos (β – γ) + cos (γ – α) =
then prove that
cot α + cot β + cot γ = sin α + sin β + sin γ
40. Evaluate: sin2 A + sin2
+ sin2
41. Solve: sec – tan x =
42. Prove that cos3 x + cos3 (120 + x) + cos3 (240 + x) = cos 3x
43. Prove that sin 100 sin 500 sin 600 sin 700 =
44. Find in degrees and radians the angle subtended between the hour hand and the minute hand
of a clock at half past three.
45. Prove that: sin2 B = sin2 A + sin2 (A – B) – 2sin A cos B sin (A – B)
46. If cos (θ + 2α) = m cos θ then show that cot α =
47. Prove that:
tan (θ + α)
=
48. Prove that: cos α + cos β + cos γ + cos (α + β + γ) = 4 cos
cos
cos
49. Find the value x > 0 for which tan (x0 + 100) = tan (x0 + 50) tan x0 tan (x0 – 50)
50. If sin 2A = λ sin 2B prove that
=
51. If A + B + C = 1800 prove that tan tan + tan tan + tan tan = 1
52. If tan x. tan y = a and x + y = obtain the quadratic equation having roots tan x and tan y.
53. If tan x = 2 tan y prove that
54. Prove that
=3
= tan
55. Simplify
56. If sin A = ½ (x + ) prove that sin 3A + ½ (x3 +
)=0
57. If cos θ = ½ (x + ) prove that
i)
cos 2θ = ½ (x2 +
)
ii) cos 3θ = ½ (x3 +
)
58. If α + β – γ = π and sin2 α + sin2 β + sin2 γ = λ sin α sin β sin γ find the value of λ
59. If a sin θ = b sin
60. If
=
= c sin
prove that tan
evaluate ab + bc + ca
tan
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=m
Complex Number
1. If Z is a purely imaginary number and lies on the positive direction of y axis then what is
argument of Z?
2. If |Z| = 4 and Arg (Z) =
then write Z in x + iy form.
3. Convert the complex number –3
4. If
+3
into polar form.
= 1 show that Z is a real number.
5. If Z1, Z2 are complex members such that
=1
6. If x = –1 + I then find the value of x4 + 4x3 + 4x2 + 2
7. Solve 2Z = |Z| + 2i.
8. For any two complex number Z1 and Z2 prove the following:
a) | Z1 + Z2|2 + | Z1 – Z2|2 = 2 (|Z1|2 + | Z2|2)
b) | aZ1 + bZ2|2 + | bZ1 – aZ2|2 = (a2 + b2) (|Z1|2 + | Z2|2)
c) For any complex no. Z show (Z – 1) ( – 1) = |z – 1|2
9. If Z = 2 – 3i then show that Z2 – 4Z + 13 = 0 hence find the value of 4Z3 – 3Z2 + 2Z + 170
10. If Z is a complex number and iZ3 + Z2 – Z + i = 0 then prove that |Z| = 1
11. Convert the following complex numbers into polar form:
a)
b)
c)
d)
12. Find the square root of the following complex numbers:
a) –3 – 4i
b) 5 – 12i
c) –1 + 2
e) 8 – 15 I
f) –15 – 8i
g) – i
i) 7 – 30
i
j) 4 – 4
i
d) 4 + 4
i
h) –8 – 6i
i
13. Find the least positive integral value of n for which
14. Convert the complex number 3 (cos
is a real number.
– i sin ) into polar form.
15. If Z is a complex number such that |Z| = 1 prove that
is purely imaginary. What
will be your conclusion if Z = 1?
16. If |Z1| = |Z2| = |Z3| = …….. = |Zn| = 1 prove that |Z1 + Z2 + Z3 + …… + Zn|.
17. Solve the equation Z2 + |Z| = 0 where Z is a complex number.
18. Find all non zero complex numbers Z satisfying
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= i Z2.
19. Find the real value of θ for which the complex number
is purely real.
20. If π < θ < 2 π and Z = 1 + cos θ + i sin θ then write the value of |Z|
21. Find x and y if
22. Show that
+
+
=i
=
Principle of mathematical induction
Using principle of mathematical induction show the following:
1. 10n + 3.4n +2 + 5 is divisible by 9 for all n € N.
2. 11n +2 + 122n +1 is divisible by 133.
3. 72n + 23n–3 . 3n –1 is divisible by 25.
4. n (n +1) (n + 2) is divisible by 6.
5. (32n – 1) is divisible by 2n +2
6.
is a positive integer.
7. 5n + 1 + 4.6n when divided by 20 leaves reminder 9
8. 8.7n + 4n+2 is divisible by 24
9. 3n > n
10. x2n –1 – 1 is divisible by x – 1
11. n3 + (n + 1)3 + (n + 2)3 is multiple of 9.
BIOLOGY
A. Survey for investigatory project on any one of the following Topic:1. Respiratory disorder because of occupation like coal mines, Flour mills
2. Sources of air pollution in your city, effect & Control
3. Mission Clean Faridabad, green Faridabad.
B. Completion of Practical Record.
C. Poster on the topic(anyone)
1. Biodiversity
2. Ecosystem(Terrestrial/Aquatic)
3. Inflorescence
4. Compound leaves
D. Draw life cycles of Moss, Fern, Pinus, any angiosperm to explain alternation of generations
E. MCQ (Plant Kingdom)
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PHYSICS
1.
Do all the derivation and formulas of chapter 2, 3, 4 (till last date) in a separate notebook.
2.
Also solve five numericals on each formula in the separate notebook.
3.
The numericals should be different for each student.
CHEMISTRY
1.
Prepare the samples of the following at home:
a) Invisible Ink
b) Natural Mosquito repellent
c) Liquid Detergent
2.
Prepare a project report on SLIME?
3.
What is the chemistry behind “Green Fire”.
4.
Prepare HOT ICE and describe its preparation process.
FASHION STUDIES
1.
Make a project on Hippie era 1960.
OR
Make a project on Punk Fashion 1980.
2.
Make a folder of fabric swatches. Collect variety of fabric.
a)
b)
c)
d)
e)
Natural and Synthetic
Dyed
Printed
Embroidered
Woven, knitted, felts, nowoven.
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FINE ARTS
1.
What is colour? How many types of colours are there?
2.
Answer the following in one or two sentences.
a) Wavelength of different colour
b) Vanishing Point
3.
What is Principle of Arts?
4.
Write an essay on types of Limbs of Art?
5.
Discuss some important effects of Linen.
6.
Give the wavelength and warmness of all seven colour so light.
7.
What is Art? Define it with examples.
8.
What is an effect of forms?
9.
Answer the followings:-
a)
How many types of Art are there?
b) What is Fine Art and what are differences between Fine Arts and Commercial Art?
10.
Write an essay on ‘A Roaring Animal of Bhim Bethaka’.
11.
Write an essay on the Indus Valley Givilization Art.
12.
Write short not on Budhistava Head of Gandhara School.
13.
Write a short not of the following:a) Ware (Jar)
b) Mother Goddess
d) Wizard’s Dance
e) Jain Tirathankar
g) Seated Budh
14.
Write an essay on Ajanta Painting? Give five main features?
Drawing —
a) Two Painting Composition.
b) Two Nature and object Drawing.
COMPUTER SCIENCE
1.
c) Male Torso
f) Lion Capital
Create a Website on Dream Weaver software for Topic
o Hobbies
o My Holidays Trip
o Childhood
o Mobile Technology
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HOLIDAY HOME-WORK
CLASS XI – E



Read an English newspaper daily and write down five important headlines of each day
with their respective summaries. The summary should not exceed 20-30 words. Maintain
a notebook for this, the size of the notebook should not be more than 100 pages.
Make a poster for the classroom (on a chart paper), which highlights the importance of
English and also explains the importance of an all English environment in the school.
Define the various types of advertisements which are:
 Product service advertisements
 Classified advertisements
 Public service advertisements
 Industrial advertisements
 Corporate advertisements
Support your answer with newspaper and magazine cuttings of each type of
advertisements. Give at least two examples for each.
Make a scrap book for this.

Write biography (100-120 words) and the famous speeches of the following eminent
personalities:
 Martin Luther King
 Nelson Mandela
 Indira Gandhi
 Mahatma Gandhi
 Swami Vivekanada
Make a scrap book for this.

Prepare a presentation on various forms of govt.
 Aristocracy
 Monarchy
 Dictatorship
 Democracy
The presentation should contain proper example of the country following these systems.
The presentation should be handwritten and in the form of file.
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