NAVY CHILDREN SCHOOL, GOA Session 2018-2019

Class XII - Science

Summer Vacation Assignment

Date of submission: 14.06.2018

SNO SUBJECTS ASSIGNMENT

1

ENGLISH

Read the novel ‘The Invisible Man’ laying stress on the new and unfamiliar vocabulary and also focusing on characterization.

2

PHYSICS

1. Completion of Investigatory Project.

2. Study the Wavelength/Frequency range of

Electromagnetic Spectrum. (Chapter 8 – EM Waves)

3. Read Chapter 15 - ‘Communication’

4. Journal work to be completed as per the given instructions

5. Revise chapter 1 and 2 for a class test

3 CHEMISTRY

1.Ch11- Q11.13 to 11.21 2.Study Ch 2, 5,10,11 for class test 3.Complete lab journal as instructed Homework to be done in the chemistry note book.

4 BIOLOGY

1. Journal completion. 2. Solution of exercise questions of Ch - 2 to 4 3. Study first unit. 4. Class test on Ch 3 and 4 on 14/06/18 Homework to be done in the assignment note book.

5 PSYCHOLOGY Case Study on any one psychological disorder using methods like Observations, Interviews, Questionnaires, etc. Homework to be done in the Psychology note book.

6 PHYSICAL EDUCATION

1. Write on a game of your choice in the journal. 2. Report on Commonwealth Games (To be done on A4 size papers.)

7 COMPUTER SCIENCE 1. Journal to be completed 2. Solve the questions shared on google group

( To be done in classwork notebook )

8

MATHS

1. Given a square matrix of order 3, such that =15, find . 2. Find the value of k, if area of triangle with vertices (k,0), (4,0)

and (0,2) is 4 square units.

3. If A is a square matrix such that =5; Write the value of .

4. Find the maximum value of

5. For what values of x, y, z, w is the matrix A =

a

skew symmetric matrix? 6. If A is a skew symmetric matrix of order 3, then prove that det

A = 0

7. If A =

and I is the identity matrix of order 2, then

show that A2 = 4A – 3I. Hence find A-1.

8. For what values of the following system of equations does not have a unique solution:

x + y + z = 6

4x + 3x + 2y – 4z = -5

9. Find the matrix A such that

A =

10. Using properties of determinants, prove that

= x3

11. Using properties of determinants, solve for x:

= 0.

12. If A =

, show that AT A-1 =

13. Consider f: R+ [ - 5 , ) given by f(x) = 9x2 + 6x - 5 . Show that f is invertible, Also find f-1.

14. If A =

then prove that An =

,

n N 15. Using properties of determinants, prove that:

=

(a - b) (b -c) (c- a) (a+b+c) (a2 +b2 + c2)

16. Let A = {1,2,3,…..9 } and R be the relation in A x A defined by

(a, b) R (c, d) if a+d = b+c for (a, b), (c, d) in A x A, prove that R is an equivalence relation, Also obtain the equivalence class [(2, 5)].

17. If a+b+c 0 and

= 0, then using properties of

determinants, prove that a=b=c 18. Using properties of determinants solve the following for x:

= 0

19. Express the following matrix as the sum of a symmetric and skew symmetric matrix, and verify your result:

20. A diet is to contain at least 80 units of vitamin A and 100 units

of minerals. Two foods F1 and F2 are available. Food F1 costs Rs.4 per unit and food F2 costs Rs.6 per unit. One unit of food F1 contains 3 units of Vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of Vitamin A and 3 units of minerals. Formulate this as a linear programming problem. Find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

21. Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs. X each, Rs. Y each and Rs. Z each for the three respective values to 3, 2, 1 students respectively with a total award money of Rs.1600. School B wants to spend Rs.2300 to award its 4, 1, 3 students on the respective values ( by giving the same award money to the three values as before ). If the total amount of award for one prize on each value is Rs.900, Using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.

22. (a) Show that the relation R : A A, where A = NXN defined by (a,b) R (c,d) iff

a + d = b + c for all (a, b), (c, d) NxN is an equivalence relation.

(b) If f(x) =

, ( x 5/4 ) show that f{f(x)} is an identity

function. 23. By using elementary transformations, find the inverse of the

matrix

24. A person has 30 units and 17 units of labour and capital

respectively, which he can use to produce two types of goods X and Y. To produce one unit of X, 2 units of labour and 3 units of capital are required. Similarly 3 units of labour and 1 unit of capital are required to produce one unit of Y. If X and Y are priced at Rs.100 and Rs.120 per unit respectively, how should the producer use his resources to maximise the total revenue? Solve the problem graphically.

25. Check if the relation R in the set R given by R = { (a, b) :

a b3 } is reflexive , symmetric or transitive. Give reason. NOTE: Homework to be done on foolscap papers.