MILESTONE ACADEMY
CLASS – XII (Sci.)
VACATION HOME-WORK
----------------------------------------------------------------------------------------------------------------------------- ----ENGLISH
1. Write an article on „Make in India‟ in about 150-200 words
2. Write the summary of the novel which one you would like to read – Invisible Man/ Silas Marner
PHYSICS1. Statement of Gauss's theorem and its applications to find field due to infinitely long straight wire,
uniformly charged infinite plane sheet and uniformly charged thin spherical shell.
2. Equipotential surfaces, electrical potential energy of a system of two point charges
3. Capacitance of a parallel plate with and without dielectric medium between the plates, Spherical
capacitor and Cylinder capacitor
BIOLOGY1. Write down the various steps involved in pollen - germination and double fertilisation.
(Draw Diagram)
2. Briefly describe post-fertilisation changes in flowering plants.
EGIsometric projection (Chapter 1) from example 10 to 27 (NCERT Book)
CHEMISTRY1. Ch-2 Back Exercise (NCERT Book)
MATHS
Q1. Find the area of triangle, whose vertices are (2, 7), (1, 1) and (10, 8).
1 𝑎 𝑏+𝑐
Q2. Evaluate 1 𝑏 𝑐 + 𝑎
1 𝑐 𝑎+𝑏
1 2
Q3. If 𝐴 =
, show that 2𝐴 = 4|𝐴|
4 2
1 2 𝑥
Q4. Find 𝑥, if 1 1 1 is singular.
2 1 −1
2 −3
Q5. If 𝐴 =
, show that 𝐴2 − 6𝑎 + 17𝐼 = 0. Hence, find 𝐴−1 .
3 4
3 −2
Q6. If 𝐴 =
, then find the value of 𝜆, so that 𝐴2 = 𝜆𝐴 − 2𝐼. Hence, find 𝐴−1
3 4
1 −1 1
Q7. If 𝐴 = 2 −1 0 , then find 𝐴2 and show that 𝐴2 = 𝐴−1
1 0 0
2 −1 1
3 1 −1
Q8. If 𝐴 = −1 2 −1 and 𝐵 = 1 3 1 , then find the product AB and use this result to solve the
1 −1 2
−1 1 3
following system of linear equations :
2𝑥 − 𝑦 + 𝑧 = −1
−𝑥 + 2𝑦 − 𝑧 = 4
and 𝑥 − 𝑦 + 2𝑧 = −3
Q9. The sum of three numbers is 6. If we multiply third number by 3 and add second number to it, we get
11. By adding first and third numbers, we get double of the second number. Represent it algebraically
and find the numbers using matrix method.
Q10. Using matrices, solve the following system of equations:
𝑥 − 𝑦 + 2𝑧 = 7, 3𝑥 + 4𝑦 − 5𝑧 = −5, and 2𝑥 − 𝑦 + 3𝑧 = 12
1
Q11. If 𝐴 = −1
1
2
1
−3
1
1 , then find 𝐴−1 and hence solve the system of equations
1
𝑥 + 2𝑦 + 𝑧 = 4, −𝑥 + 𝑦 + 𝑧 = 0 and 𝑥 − 3𝑦 + 𝑧 = 4
Q12. A diet is to contain 30 units of vitamin A, 40 units of vitamin B and 20 units of vitamin C. three
types of foods F1, F2 and F3 are available. 1 unit of food F1 contains at 3 units of vitamin A, 2 units
of vitamin B and 1 unit of vitamin C. 1 unit of food F2 contains at 1 unit of vitamin A, 2 units of
vitamin B and 1 unit of vitamin C. 1 unit of food F3 contains 5 units of vitamin A, 3 units of vitamin B
and 2 units of vitamin C. Represent the above situation algebraically and find the diet contains each
types of food by using matrix method. Why a proper diet is required for us?
Q13. A merchant plans to sell three types of personal computers – a palmtop model, a portable model and a
desktop model that will cost Rs 8000/-, Rs 10500/- and 10000/- respectively. He makes the survey of
two persons, one person estimates that the total monthly demand of computers will be 70 units and the
other person says that palmtop model type computers will be demanded 30 units and total units
required is 273 units. If a dealer wants to invest Rs 7 lakh on it. Represent the above situation
algebraically and find each type of unit sales. How can we use computer in student life and which is
the best computer model for students?
Q14. If 𝑓 𝑥 is an invertiable function, find the inverse of 𝑓 𝑥 =
3𝑥−2
5
Q15. Let 𝑓: 𝑅 → 𝑅 be defined as 𝑓 𝑥 = 10𝑥 + 7 find the function 𝑔: 𝑅 → 𝑅 such that 𝑔𝑜𝑓 = 𝑓𝑜𝑔 = 𝐼𝑅
Q16. Show that the relation R on the set R of real numbers, defined as 𝑅 = { 𝑎, 𝑏 : 𝑎 ≤ 𝑏2 } is neither
reflexive nor symmetric nor transitive.
Q17. If the function 𝑓: 1, ∞ → [1, ∞] defined by 𝑓(𝑥) = 2𝑥
𝑥−1
is invertible find , 𝑓 −1 (𝑥).
Q18. Consider 𝑓: 𝑅+→ [−5, ∞] given by 𝑓 𝑥 = 9𝑥 2 + 6𝑥 − 5. Show that 𝑓 is invertible and
𝑓 −1 𝑦 =
𝑦 +6−1
3
𝑎 +𝑏,𝑖𝑓 𝑎 +𝑏<6
Q19. A binary operation * on set [0, 1, 2, 3, 4, 5] is defined as 𝑎 ∗ 𝑏 = 𝑎 +𝑏 −6 𝑖𝑓 𝑎 +𝑏≥6 Show that the
zero is the identity for this operation and each element ′𝑎′ of the set is invertible with 6 − 𝑎, being
the inverse of ′𝑎′.
Q20. Prove that the relation R in the set 𝐴 = {5, 6, 7, 8, 9} given by 𝑅 =
𝑎, 𝑏 : |𝑎 − 𝑏| is divisible by 2,
is an equivalence relations.
2
4𝑥+3
Q21. Show that the function 𝑓 in 𝐴 = 𝑅 − 3 difined as 𝑓 𝑥 = 6𝑥−4 is one one and onto. Hence find 𝑓 −1 .
Q22. If 𝐴 = [3, 4, 7, 9] and 𝐵 = [6, 7, 8, 9, 12] and R is the relation “ is a factor of from” A to B, find R.
Q21. Prove that the function 𝑓 ∶ 𝑁 → 𝑁, defined by 𝑓 𝑥 = 𝑥 2 + 𝑥 + 1 is one – one but not onto .
Q22. Find the value of 𝑆𝑖𝑛
𝜋
3
1
− sin−1 − 2
Q23. Write the value of 𝑆𝑖𝑛 2 sin−1
3
5
Q24. Prove that 2 tan−1
1
Q25. Prove that 𝐶𝑜𝑡 −1
1+𝑠𝑖𝑛𝑥 + 1−𝑠𝑖𝑛𝑥
Q26. Prove that : tan−1
2
+ tan−1
1
31
= sin−1 25
7
1+𝑠𝑖𝑛𝑥 − 1−𝑠𝑖𝑛𝑥
1+𝑥− 1−𝑥
1+𝑥+ 1−𝑥
𝜋
=
𝑥
2
1
= 4 − 2 cos −1 𝑥
Q27. Simplify :
tan−1
3 sin 2𝛼
1
+ tan−1 𝑡𝑎𝑛𝛼
5 + 3𝑐𝑜𝑠2𝛼
4
2
Q28. If 𝑦 = cot −1 ( 𝑐𝑜𝑠 𝑥) − tan−1
Q29. Prove that tan
𝜋
4
1
𝑐𝑜𝑠𝑥 then prove that 𝑠𝑖𝑛𝑦 = tan2
𝑎
+ 2 cos −1 𝑏 + tan
Q30. Prove that : tan−1
𝑐𝑜𝑠𝑥
1+𝑠𝑖𝑛𝑥
𝜋
𝜋
4
1
𝑎
− 2 cos −1 𝑏 =
𝑥
2
2𝑏
𝑎
𝑥
=4 −2
Q31. If 𝑡𝑎𝑏−1 𝑎 + tan−1 𝑏 + tan−1 𝑐 = 𝜋 prove that 𝑎 + 𝑏 + 𝑐 = 𝑎𝑏𝑐
𝛼
𝜋
2
4
Q32. Show that 2 tan−1 tan . tan
−
𝛽
2
= tan−1
𝑠𝑖𝑛𝛼 .𝑐𝑜𝑠𝛽
𝑐𝑜𝑠𝛼 +𝑠𝑖𝑛𝛽
Physical Education
Chapter – Xth Psychology and Sports
1. What is ethics and sports anxiety?
2. What are the stages of growth in the development of a child?
3. Explain any two techniques to manage stress.
4. Explain goal setting as a technique of motivation in brief.
5. What are the development characteristics of childhood?
6. Adolescence is the age of stress and strain. Explain.
7. How can you manage anxiety in sports?
8. Discuss the problems of adolescence and their sports managements.
9. Define :- (a) intrinsic and extrinsic motiration
(b) sports personality and stress
(c) body image
Chapter – XIth Training in Sports
1. What are pace races training method.
2. Define cardiovascular endurance, interval training method, isometric, isotonic, isokinetic exercise.
3. Suggest different ways to improve reaction ability of a player.
4. Briefly explain the advantages of fartlek training.
5. Define flexibility and explain the methods of flexibility development.
6. Discuss any two methods of endurance development.
7. Define speed. Explain the methods of speed development with the help of example.
8. Define the term strength. Draw eight stations circuit training programme for upper body strength.
9. Weight training is one of the oldest methods for development of strength. What are its advantages and
disadvantages?
10. Dynamic strength is divided into three parts. Write in brief about each.
11. Which test would you suggest for your father to test lower body flexibility?
12. Explain the cognitive aspect of stress. Suggest any three techniques briefly to over come stress.
Chapter 1st Sports Envionment
1. Define environment and sports environment
2. What is the meaning of a positive and social sports environment?
3. Explain the role of sports spectators for improving positive sports environment and proper sports environment.
4. Elucidate the role of individual in the improvement of sports environment for health promotion.
5. Play grounds are essential for creating sports environment. Justify your answer.
6. What are the five essential elements of positive sports environment and individual in improving sports
environment.
7. Give any six reasons of law participation of women in sports and games.
8. Comment on the role of spectators and media in creating a positive sports environment.
9. Distinguish between hostile and favourable spectators.
10. Prepare a project report on the topic given to each student individually.
PUBLIC SPEAKING-.
Record and write the conversation between you and the travel agent for a complete package
(food, lodging, sight view, transport, etc.) a complete trip planned for summer vacation.
For Eg. :- Written Conversation
Child :- Sir please brief about the tour packages for different cities.
Agent :- Well ! Just come down to our office and I will give you all the details.
LIFE SKILL- Think of situations where you can “give” yourself to others, gifts which money cannot buy –
such as kindness, thoughtfulness, courtesy, consideration, good nature, courage, tolerance, appreciation.
Do not make up stories. Talk about a genuine act - do not boast. Write the incident and your experience
of situations where you had given yourself.
----------------------------------------------------------------------------------------------------------------------------- ----------