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ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK 1.

ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

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Page 1: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

ENGLISH CORE (301)

CLASS: XII

HOLIDAY HOMEWORK

1.

Page 2: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her
Page 3: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her
Page 4: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

2.

Page 5: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

3. On the occasion of Vana Mahotsava Day , the Environment Club of Greenfield

Public

School , Gandhinagar is organizing a Tree Plantation Drive.As the Secretary of the Club ,

draft a notice in about 50 words to

Page 6: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

Announce the drive and give details like date , time , venue and occasion

Invite all the students to participate in it

Mention different activities that will be undertaken as part of the drive

Page 7: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

4. International Tobacco Control Programme is an organization that is working worldwide

to spread awareness about the hazards of tobacco use. Create a poster for the organization

highlighting the harmful effects of smoking and tobacco consumption in other forms.

Include a helpline number for quitting tobacco and a website address for more

information on quitting smoking / tobacco.

5. A poor accident victim needs financial help for surgery. As the President of a charity

organization that arranges financial help for such parents, draft a classified advertisement

to raise funds for the patient.

In your advertisement you should say

What the patient’s gender , age and financial conditions are

What kind of surgery he/ she needs and its total cost

How much money is needed and how donations can be made

What the organisation’s name and contact details are

6. Reckless driving on highways turns roads into death traps for pedestrians and motorists

alike. Write an article in about 200 words on the topic “Reckless Driving Thrills But

Kills.”

In your article you should

Give some examples of accidents on highways to prove they are not safe.

Discuss the causes and consequences of such accidents

Suggest some effective ways to ensure safety on highways.

7. Too much television is bad for children. Unfortunately, parents find it very hard to wean

their children away from the idiot box. Write an article for a local newspaper to :

Page 8: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

Discuss the hazards of viewing too much TV

Explain why it is difficult to wean children away from TV

Suggest what should be done to restrict TV viewing among children

8. The sports incharge of your school has asked you to make a speech on the value of games

and sports in life in the morning assembly. Draft a speech in about 200 words in which

you should:

Highlight the importance of games and sports as natural instinct of Man

List the benefits of games and sports

Urge young people to practice some sport or the other

9. In recent times there has been a sudden proliferation of tuition and coaching centres.Are

they relevant and useful? Are they a blot on our education system? What are your views?

Draft a speech in about 200 words to ;

Highlight the hardships students have to bear on account of tuitions

Discuss the causes of mushrooming f tuition and coaching centres

Suggest what should be done to curb this menace

10. Due to poor maintenance of the existing system of water supply, the common people of

your city have been hit hard .Write a letter to the Municipal Commissioner of your City

for a permanent solution to this problem. You are Ashutosh Rana , resident of 7/23

,Kunal Apartments ,Delhi.

In your letter you should :

Page 9: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

Introduce yourself and raise the issue of erratic water supply in the city

Describe how much the common and poor people have to suffer due to shortage of

water , while the rich and powerful enjoy unrestricted supply

Suggest some practical steps needed to effectively tackle the problem

Wind up with the hope that the problem will be resolved at the earliest

11. Read the following books and write the book reviews.

(a) A Suitable Boy by Vikram Seth.

(b) The Hungry Tide-Amitav Ghosh.

12. Solve the Unit Test.

13. Make a separate file for AIE. (Art Integrated Education) – Compose poems on

various

forms of dances of India.

All work to be done on A4 sheets and file them. The work should be submitted on

the

reopening Day.

“ASK YOURSELF, WHAT YOU ARE DOING TODAY IS GETTING YOU

CLOSER TO WHERE YOU WANT TO BE TOMORROW?”

Page 10: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055)

GENERAL INSTRUCTIONS:

Each student will prepare and submit his/her project report. Following essentials

are required to be fulfilled for its preparation and submission

The project should be handwritten in A4 Size Paper only one side.

The project should be presented in a neat folder.

The project report should be developed in the following sequence

Cover page should include the title of the Project, student information,

school and year.

List of contents.

Acknowledgements and preface. (Acknowledging the institution, the places

visited and the persons who have helped).

Introduction.

Topic with suitable heading.

Conclusion.

COMPREHENSIVE PROJECT

Page 11: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

Take a real life business situation and then: (Max. 25 Transactions

Include GST ‘compulsory’.

Pass Journal Entries

Prepare Ledger Accounts.

Make Trial Balance

Make financial statements i.e. Trading & Profit and Loss

Account and Balance Sheet.

All the very best

HOLIDAY ACTIVITY – CLASS 12

BUSINESS STUDIES

TOPIC: “A STUDY ON THE APPLICATION OF HENRY FAYOL’S PRINCIPLES OF MANAGEMENT WITH SPECIAL REFERENCE TO ‘NAME OF YOUR ORGANISATION’”.

Principles of Management

The students are required to visit any one of the following:

1. A departmental store. 2. An Industrial unit. 3. A fast food outlet. 4. Any other organization approved by the teacher.

Page 12: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

They are required to observe the application of the general Principles of management advocated by Fayol.

Fayol’s principles

1. Division of work. 2. Unity of command. 3. Unity of direction. 4. Scalar chain 5. Espirit de corps 6. Fair remuneration to all. 7. Order. 8. Equity. 9. Discipline 10. Subordination of individual interest to general interest. 11. Initiative. 12. Centralization and Decentralization. 13. Stability of tenure.

Following essentials are required to be fulfilled for its preparation and submission.

Page 13: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

1. The total length of the project will be of 25 to 30 pages.

2. The project should be handwritten.

3. The project should be presented in a neat folder.

4. The project report should be developed in the following sequence-

Cover page should include the title of the Project, student information, school and year.

List of contents.

Acknowledgements and preface (acknowledging the institution, the place visited and the persons who have helped).

Introduction.

Topic with suitable heading.

Planning and activities done during the project, if any.

Observations and findings of

Conclusions (summarized suggestions or findings, future scope of study).

Photographs (if any).

Appendix (attach the questionnaire)

Page 14: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

HOLIDAY ACTIVITY – CLASS 12

ECONOMICS

Project work on the Topic you chosed.

Following essentials are required to be fulfilled for its preparation and submission.

1. The total length of the project will be of 25 to 30 pages.

2. The project should be handwritten.

3. The project should be presented in a neat folder.

4. The project report should be developed in the following sequence

Cover page should include the title of the Project, student information,

school and year.

List of contents.

Introduction.

Topic with suitable heading.

Photographs (if any).

Conclusions (summarized suggestions or findings, future scope of study).

Bibliography

Page 15: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

HOLIDAY HOMEWORK

CLASS XII

INFORMATICS PRACTICES(065)

I.MySQL Basic SELECT statement - Exercises

Based on the table

Employee(EMPLOYEE_ID,FIRST_NAME,LAST_NAME,EMAIL,PHONE_NUMBER,

HIRE_DATE,JOB_ID, SALARY , COMMISSION_PCT ,MANAGER_ID ,

DEPARTMENT_ID )

1.Write a query to display the names (first_name, last_name) using alias name

“First Name", "Last Name"

2. Write a query to get unique department ID from employee table.

3. Write a query to get all employee details from the employee table order by first

name, descending.

4. Write a query to get the names (first_name, last_name), salary, PF of all the

employees (PF is calculated as 15% of salary).

5. Write a query to get the employee ID, names (first_name, last_name), salary

in ascending order of salary.

6. Write a query to get the total salaries payable to employees

7. Write a query to get the maximum and minimum salary from employees table.

8. Write a query to get the average salary and number of employees in the

employees table.

Page 16: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

9. Write a query to get the number of employees working with the company.

10. Write a query to get the number of jobs available in the employees table

II Exercises MySQL Restricting and Sorting data

Based on the table

Employee(EMPLOYEE_ID,FIRST_NAME,LAST_NAME,EMAIL,PHONE_NUMBER,

HIRE_DATE,JOB_ID, SALARY , COMMISSION_PCT ,MANAGER_ID ,

DEPARTMENT_ID )

1.Write a query to display the name (first_name, last_name) and salary for all

employees whose salary is not in the range $10,000 through $15,000

2. Write a query to display the name (first_name, last_name) and department ID

of all employees in departments 30 or 100 in ascending order.

3. Write a query to display the name (first_name, last_name) and salary for all

employees whose salary is not in the range $10,000 through $15,000 and are in

department 30 or 100

Page 17: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

4. Write a query to display the name (first_name, last_name) and hire date for all

employees who were hired in 1987.

5. Write a query to display the first_name of all employees who have both "b" and

"c" in their first name.

6. Write a query to display the last name, job, and salary for all employees whose

job is that of a Programmer or a Shipping Clerk, and whose salary is not equal to

$4,500, $10,000, or $15,000.

7. Write a query to display the last name of employees whose names have

exactly 6 characters.

8. Write a query to display the last name of employees having 'e' as the third

character

9. Write a query to display the jobs/designations available in the employees table

10. Write a query to display the name (first_name, last_name), salary and PF

(15% of salary) of all employees.

III.Aggregate Functions and Group by

Based on the table

Employee(EMPLOYEE_ID,FIRST_NAME,LAST_NAME,EMAIL,PHONE_NUMBER,

HIRE_DATE,JOB_ID, SALARY , COMMISSION_PCT ,MANAGER_ID ,

DEPARTMENT_ID )

1.Write a query to list the number of jobs available in the employees table

2. Write a query to get the minimum salary from employees table

Page 18: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

3. Write a query to get the maximum salary of an employee working as a

Programmer

4. Write a query to get the minimum salary from employees table.

5. Write a query to get the average salary and number of employees working the

department 90.

6. Write a query to get the number of employees with the same job.

7. Write a query to get the highest, lowest, sum, and average salary of all

employees

8. Write a query to get the difference between the highest and lowest salaries.

9. Write a query to find the manager ID and the salary of the lowest-paid

employee for that manager.

10. Write a query to get the department ID and the total salary payable in each

department.

IV.MySQL Subquery

Page 19: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

Based on the below tables

1.Employee(EMPLOYEE_ID,FIRST_NAME,LAST_NAME,EMAIL,PHONE_NUMBER,

HIRE_DATE,JOB_ID, SALARY , COMMISSION_PCT ,MANAGER_ID ,

DEPARTMENT_ID )

2.DEPARTMENT(DEPARTMENT_ID ,DEPARTMENT_NAME , MANAGER_ID ,

LOCATION_ID )

3.LOCATION(LOCATION_ID STREET_ADDRESS, POSTAL_CODE, CITY,

STATE_PROVINCE, COUNTRY_ID)

1.Write a query to find the name (first_name, last_name) and the salary of the

employees who have a higher salary than the employee whose last_name='Bull'.

2. Write a query to find the name (first_name, last_name) of all employees who

works in the IT department.

3. Write a query to find the name (first_name, last_name) of the employees who

have a manager and worked in a USA based department.

4. Write a query to find the name (first_name, last_name) of the employees who

are managers.

5. Write a query to find the name (first_name, last_name), and salary of the

employees whose salary is greater than the average salary.

6. Write a query to find the name (first_name, last_name), and salary of the

employees whose salary is equal to the minimum salary for their job grade

7. Write a query to find the name (first_name, last_name), and salary of the

employees who earns more than the average salary and works in any of the IT

Page 20: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

departments.

8. Write a query to find the name (first_name, last_name), and salary of the

employees who earns more than the earning of Mr. Bell.

9. Write a query to find the name (first_name, last_name), and salary of the

employees who earn the same salary as the minimum salary for all departments.

10. Write a query to find the name (first_name, last_name), and salary of the

employees whose salary is greater than the average salary of all departments

Holiday’s Assignment

2020-2021

Class XII Mathematics Relations and Functions

1. Let f: RR be defined as f(x) = 10x + 7. Find the function g: R R such that gof = fog = IR

2. Let f: W W be defined as f(n) = n – 1, if n is odd and f(n) = n + 1, if n is even. Show that f is

invertible. Find the inverse of f. Here, W is the set of all whole numbers.

3. Show that the function f:R{ x 𝜖 R: -1 < x < 1} defined by f(x) = , x 𝜖 R is one-one and +||

Page 21: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

onto function.

4. Show that the function f : R R given by f(x) = x3 is injective.

5. Give an example of two functions f: NN and g: N N such that gof is onto but f is not

onto.

6. Given a non-empty set X. Consider P(X), which is the set of all subset of X. Defined the

relation R in P(x) as follows: For subsets A and B in P(X), ARB if and only if A⊂B. Is R an

equivalence relation on P(X)? Justify your answer.

7. Find the number of all onto functions from the set {1,2,3...n} to itself.

8. Let S = {a,b,c} and T = { 1,2,3}. Find F-1 of the following functions F from S to T, if it exists.

i) F = { (a,3), (b,2), (c,1)} ii) F = {(a,2), (b,1),(c,1)}

9. Let A = { -1, 0 , 1, 2}, B = { -4, -2, 0 ,2 } and f, g : A B be the function defined by f(x) = x2 – x, 1 x 𝜖 A, and g(x) = 2 |− -1, x 𝜖 A. Are f and g equal? Justify your answer. | 2 10. Functions f, g : R R are defined respectively, by f(x) = x2 +3x + 1, g(x) = 2x – 3, find

i) Fog ii) gof iii) fof iv) gog

Inverse Trigonometric Functions

Prove the following Functions

1. cos -1 4 + cos -1 12 = cos -1 33 51365 2. sin -1 8 + sin -1 3 = tan -1 77 17536 3. cos -1 12 + sin -1 3 = sin -1 56 13565 4. tan -1 63 = sin -1 5 + cos -1 3 16135 5. tan -1 1 + tan -1 1 + tan -1 1 + tan -1 1 = 𝜋 57384 1+𝑖+ 1−𝑖𝜋 √√

Page 22: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

6. cot -1 ()= , x 𝜖 (0,) 1+𝑖− 1−𝑖24 √√ 1+− 1−1 √√ -1 7. tan -1 ()= - cos x 1+− 1−22 √√ 𝜋91922 8. 9 - sin -1 = sin -1 √ 84343 −1 9. tan -1 1 = = tan -1x, (x>0) 1+2 5𝜋13𝜋 10. Find the value of tan -1(tan ) + cos -1(cos) 66

Page 23: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

Matrices

1−11 1. If A = [, B = [ and (A+B)2 = A2+B2, then find the value of a and b. ]] 2−1−1 2−1 5225 2. If A = [, B = [ and B = [ and a matrix D such that CD – AB = 0. ]]] 34 7438 2−1−1−8 3. Find matrix A such that [A = [. ]] 101−2 −34922 123−7−8−9 4. Find the matrix X so that X[ = [. ]] 456246 30−1 5. Obtain the inverse of the following matrix, using elementary operations: A = [ ] 230 041 2−11 6. For the matrix A = [, show that A2 – 5A + 4I = 0. Hence, find A-1. ] −12−1 1−12 7. A trust caring for handicapped children gets Rs. 30,000 every month from its donors. The

trust spends half of the funds received for medical and educational care of the children and

for that it charges 2% of the spent amount from them and deposits the balance amount in a

private bank to get the money multiplied so that in future the trust goes on functioning

regularly. What percent of interest should the trust get from the bank to get a total of Rs.

1,800 every month? Use matrix method, to find the rate of interest. 34 −121

Page 24: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

8. If AT = [ and B = [, then find AT – BT. ]] −12 123 01 01−2 9. For what value of x, is the matrix A = [ a skew symmetric matrix? ] −103 −30 1 3470 10. If 2[+[ = [, find (x-y). ]]] 5105 01 Determinants

1. Using properties of determinants, prove the 22 + 22 following:|=4a2b2c2 | + 22 + ++2 2. Using properties of determinants, prove that | = | ++2 ++2 2(a+b+c)3. 2 − 22 2 3. Show that |= 4 2 | − 2 − 1+11 4. Prove without expanding that | = abc + ab + bc +ca = abc (1 + | 11+1 111+ 111111 ++) or (1 + ++) is a factor of determinant.

Page 25: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

3−1112−2 5. If A-1 = [ and B = [, find (AB)-1 ]] −156−5−130 5−220−21 6. If A is a 3 x 3 invertible matrix, then what will be the value of k if det(A-1) = (det A )k.

3−1 −52 7. If |A| = 3 and A-1 = [], then write the adj A. 33 1−1022−4 8. Given A = [ and B = [ verify that BA = 6I, use the result to solve ]] 234−42−4 0122−15 the system of linear equations x – y = 3, 2x + 3y +4z =17, y +2z = 7.

1−12−201 9. Use product [to solve the system of equations x+3z =90, -x +2y ][] 02−392−3 3−2461−2 – 2z = 4, 2x – 3y +4z = -3.

10. 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.

Continuity and Differentiability

Differentiate given problems w.r.t. x

−1 1. 2 , -2 < x < 2. 2+7 √ 𝑙𝑔 2. (𝑔)

3. x +xa + ax + aa , for some fixed a > 0 and x > 0. 2 −3 4. 2+ (−3), for x>3.

2 5. Find , if y = sin -1x + sin -1√1− , -1 ≤ x ≤ 1.

Page 26: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

3 2 2 𝑑 [1+ ()] 6. If ( x – a)2+ (y –b)2 = c2 , for some c > 0, prove that 𝑑 is a constant independent of a 2 𝑑 2 𝑑 and b.

7. Using mathematical induction prove that () = n x n-1 for all positive integers n.

8. Does there exist a function which is continuous every where but not differentiable at exactly

two points ? justify your answer. 2 9. If x = a ( cost + t sint) and y = a ( sin t – t cos t), find . mention the domain in which it is 2 valid. () 𝑖−. 10. (𝑠−𝑠)

APPLICATION OF DERIVATIVES

1. The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3

cm/s. How fast is the area decreasing when the two equal sides are equal to the base?

2. Find the equation of the normal to the curve y2 = 4x at the point (1,2).

3. Show that the normal at any point 𝜃 to the curve x = a cos 𝜃 + a 𝜃 sin , y = a sin 𝜃 - a 𝜃 cos 𝜃

is at a constant distance from the origin.

Page 27: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

22 4. Find the maximum area of an isosceles triangle inscribed in the ellipse + = 1, with its 22 vertex at one end of the major axis.

5. A tank with rectangular base and rectangular sides, open at the top is to be constructed so

that its depth is 2 m and volume is 8 m3. If building of tank costs Rs. 70 per sq metre for the

base and Rs. 45 per sq metre for sides. What is the cost of least expensive tank? 6. Fin the points at which the function f given by f(x) = (x -2)4(x+1)3 has

a) Local maxima b) local minima iii) point of inflexion

7. Find the absolute maximum and minimum values of the function f given by f(x) = cos2x + sin

x, x 𝜖 [0, 𝜋].

8. Show that the altitude of the right circular cone of maximum volume that can be inscribed in

a sphere of radius r is 4 . 3 9. A window is in the form of a rectangle surmounted by a semi-circle opening. The perimeter

of the window is 10 m. Find the dimension of the window to admit maximum light through

the whole opening. og 10. Show that the function given by f(x) = l has maximum at x = e.

VECTOR ALGEBRA

1. Find a vector of magnitude 5 units and parallel to the resultant of the vectors a = 2 + 2 -

and b = - 2+

2. Show that the points A(1,-2, -8), B (5, 0, -2) and C (11, 3, 7) are collinear and find the ratio in

which B divides AC.

3. The two adjacent sides of a parallelogram are 2 - 4 + 5 and - 2- 3 . Find the unit vector

parallel to its diagonal. Also, find its area.

Page 28: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

4. If a, b, c are mutually perpendicular vectors of equal magnitudes, show that the vector (a + b

+c) is equally inclined to a, b and c.

5. Prove that (a+b) . (a + b)= |a|2 + |b|2, if and only if a, b are perpendicular, given a≠0, b ≠0.

6. The scalar product of the vector + + with a unit vector along the sum of vectors 2 + 4-5

and 𝜆 + 2+3 is equal to one. Find the value of λ

7. Let a = + 4+2 , b =3 - 2+7 and c =2 - +4 . Find a vector d which is perpendicular to

both a and b and c . d = 15.

8. Find the position vector of point R which divides the line joining two points P(2a + b) and Q(a

- 3b) externally in the ratio 1: 2. Also, show that P is the middle point of the line segment RQ.

9. If a = b + c, then is it true that |a|= |b| + |c| ? justify your answer.

10. A girl walks 4 km towards west then, she walks 3 km in a direction 30° east of north and

stops. Determine the girl’s displacement from her initial point of departure.

Note: Study all the Exemplar and Exercise sums of all the chapters that are covered.

ALL the Best

INTEGRATED INDIAN SCHOOL, KUWAIT 2020-2021

HOLIDAY ASSIGNMENT CLASS-XII

SUBJECT: PHYSICAL EDUCATION (Code No. 048)

1. Fitness Tests Administration for all items.

2. Procedure for Asanas, Benefits and Contraindications for any

Page 29: ENGLISH CORE (301) CLASS: XII HOLIDAY HOMEWORK · 2020. 6. 4. · CLASS-XII A HOLIDAY ASSIGNMENT ACCOUNTANCY (055) GENERAL INSTRUCTIONS: Each student will prepare and submit his/her

two Asanas for each lifestyle disease.

3. Procedure for administering senior citizen Fitness Test for 5

elderly family members.

4. Any one game of your choice out of the list below. Labeled

diagram of field and Equipment (Rules, Terminologies and

Skills)-Print out.

(Basketball / Football / Kabaddi / Kho-Kho / Volleyball /

Handball / Hockey / Cricket / Bocce / Unified Basketball for CWSN

(Children With Special Needs – Divyang ) .