J.K.G. INTERNATIONAL SCHOOLINDIRAPURAM

Class- XII ASummer Vacation Home Assignment

Session 2017-18Physics:-

1. Revision of chapters done in the class for UT’spreparation.

2. Do following projects and make a project report of thesame.a. To study various factors on which the internal

resistance/emf of a cell depends. (Roll no 1-9)b. To design an appropriate logic gate combination for a

given truth table. (Roll no 10-18).c. To estimate the charge induced on each one of two

identical Styrofoam (orpith) balls suspended in avertical plane by making use of coulomb’s law. (Roll no19-27).

d. To study earth’s magnetic field using tangentgalvanometer. (Roll no 28-36).

e. To investigate the dependence of angle of deviationon the angle of incidence using a hollow prism filledone by one with different transparent fluids. (Rollno-37-45).

Biology:-1. Prepare for UT-1 Examination.2. Make a investigatory project on the related topics.3. Complete your practical work in your record file.

Chemistry:-1. Prepare investigatory project for board exam. Topics

given in lab manual.2. Prepare UT 1 syllabus.3. Do numerical practice of solid state and solution.

English:-1. Revise all the syllabus given for Unit Test 1.2. Read the novel ‘The Invisible Man.’3. Write an article on the topic-‘Should we buy things

because they are advertised?’

Information Practices:-1. Complete Practical file of JAVA, SQL, HTML2. Learn Ch-1,8,9,10 for UT-1.3. Learn the syntax of all the SQL queries.4. Learn key points of summary of the syllabus covered.

Commercial Art:-Practical Work:

1. Colour Wheel2. Composition Daily Life Scenes Five Sheets3. Greeting Card4. Book Cover Designing5. Educational Poster

Physical Education:-1. Learn 10 Yoga postures and practice them and prepare afile about their benefits with photograph of that posture.

2. Visit any nearby hospital or dietician and prepare a dietchat according to your health.

Math:-

1. Evaluate i) sin(3sin 0.4) ii) sin(2 sin 0.8)2. Prove that sin (cos(sin ))+cos (sin(cos ))=3. Evaluate tan( cos √ )

4. Express each of the following in the simplest form:

1) tan ( ) 2) sin (√ ) 3) tan4)tan ( )

5. Prove that

1) sin +cos +tan =π

2) tan (√ √√ √ )= +3) tan (√ √√ √ )= + cos4) tan( + cos )+ tan( - cos )=

5) 2tan +sec √ +2tan =

6) tan + tan +tan +tan =

7) If a>b>c>0 prove that cot ( )+ cot ( ) + cot ( )=π

8) If y=cot ( cos )) − tan ( cos ) prove that siny=tan2x/2

9) If cos +cos =ß prove that -2xycos ß+ =sin 2ß

10) If cos +cos + cos = then prove that x2+y2+z2+2xyz=1

11). For what value of x the matrix A=1 −2 31 2 1x 2 −3

12). If =1 2 33 1 21 0 3 Find the value of A.(Adj.A) without finding Adj.A

13). A matrix A of order 3X3, has determinant 4. Find the value of I3AI

14). Find the number of all possible matrices of order 2 with each entry 5,2,or 1

15). If A is an invertible matrix of order 2 with determinant 5, then findIA I

16). Let A be non singular matrix of order 3X3 with IAI=7 Find Iadj AI.

17). If A=[1 2]B= 1 2 34 5 6 then find order of(AB)

18). If A=3 9 01 8 −27 5 4 B=

4 0 27 1 42 2 6 Verify 3(A+B)=3A+3B

19). Find the matrix X for which 1 −43 −2 X= −16 67 220). If A =

1 −2 02 1 30 −2 1 find A-1, Solve the system of Linear Equations x-

2y=10, 2x+y+3z=8, -2y+z=7.

21). Determine the product−4 4 4−7 1 35 −3 −1 1 −1 11 −2 −22 1 3 and use it to solve the

system of equations

x-y+z=4, x-2y-2z=9, 2x+y+3z=1

22). Find the inverse of the following matrices by using ERT

i)2 −1 31 2 43 1 1 ) 2 −1 3−5 3 1−3 2 3 iii)

1 1 23 1 12 3 123). Ram purchases 3 pens, 2 bags and 1 instrument box and pays Rs. 41. From thesame shop, Shyam purchases 2 pens, 1 bag and 2 instrument boxes and pays Rs 29,while Ankur purchases 2 pens, 2 bag and 2 instrument boxes and pays Rs 44.Translate the problem into a system of equations. Solve them by matrix method andhence find the cost of one pen, one bag and one instrument box.

24). Without Expanding Evaluate :91 92 9394 95 9697 98 99

25). Without Expanding Prove that+++ =0

26). Prove that: =abc(a-b)(b-c)(c-a)

27). Prove that :+ + ++ + ++ + + =2

28). Prove that :− − 2 22 − − 22 2 − − =( + + )

29). Prove that :( + ) ( + ) ( + ) =2abc( + + )

30). Prove that :1 + +1 + +1 + + =(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)

31). Prove that:1 1 + 1 + +2 3 + 2 1 + 3 + 23 6 + 3 1 + 6 + 3 =1

32). Kellogg is a new cereal formed of a mixture of bran and rice that contains atleast 88 gms. Of protein and at least 36 milligrams of iron. Knowing that brancontains 80 gms of protein and 40 milligrams of iron per kilogram, and thatrice contains 100 gms of protein and 30 milligrams of iron per kilogram. Findthe minimum cost of producing this new cereal if bran costs Rs. 5 per kilogramand rice costs Rs. 4 per kilogram.

33). A diet for a sick person must contain at least 4000 units of vitamins, 50 unitsof minerals and 1400 units of calories. Two foods A and B are available at acost of Rs. 4 and Rs. 3 per unit respectively. If one unit of A contains 200units of vitamins, 1 unit of minerals and 40 units of calories and one unit offood B contains 100 units of vitamins, 2 units of minerals and 40 units ofcalories, Find what combination of foods should be used to have at least cost?

34). A housewife wishes to mix up two kinds of foods X and Y in such a way thatmixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8units of vitamin C. The vitamin contents of 1 kg of food Y are given in thefollowing table :

Food Vitamin A Vitamin B Vitamin CX 1 2 3Y 2 2 1

35). A company has factories located at each of the two places P and Q. Fromthese locations, a certain commodity is delivered to each of the three depotsat A,B and C. The weekly requirements of depots are respectively 7,6 and 4units of the commodity while the weekly production capacities of the factoriesat P and Q are respectively 9 and 8 units. The cost of transportation per unitis given in the table:

To

From From

Cost (in Rs.)

A B C

P 16 10 15

Q 10 12 10