THE ASIAN SCHOOL, DEHRADUN
HOLIDAY HOMEWORK OF WINTER VACATION 2014-15 FOR CLASS XI
English: 1. Prepare a debate on the topic – “Computers cannot replace books’ . Write for/against the motion. The content should be 200 to 250
words.
2. In a group of four students, in a conversational or a dialogue format, discuss ways to attain world peace. You may consider the following
points. (World limit 200 to 250)
* Tolerance & Moral values
* Communal harmony & negotiations
* International peace talks
3. Give a brief understandings from the Long Reading Test ‘Up From Slavery’ on ‘The Dignity of work’, ‘The net of slavery’, ‘ The Relationship
between Blacks’ and Whites’ and ‘The Secret of Success’.
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Mathematics:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Find 18 th term of the A.P. 2, 3 2, 5 2,....
If the sequence < an> is an A.P., show that am + n + am – n = 2am
Which term of the A.P. 3, 8, 13,…. is 248?
Is 302 a term of the A.P. 3, 8, 13,…?
th
th
th
The 6 and 17 terms of an A.P. are 19 and 41 respectively, find the 40 term.
th
th
th
If 9 term an A.P. is zero, prove that its 29 term is double the 19 term.
th
th
The first and the last terms of an A.P. are a and ℓ respectively. Show that the sum of k term from the beginning and k term
from the end is a + ℓ.
a
a
2
If < an > is an A.P. such that 4  , find 6
a7 3
a8
Three numbers are in A.P. if the sum of these numbers be 27 and the product 648, find the numbers.
10.
Find the sum of the arithmetic progression 50,46,42, ...to 10 terms
11.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
12.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
13.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5 th terms.
14.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
15.
If S n= n 2 p and Sm = m2 p, m  n, in an A.P., prove that Sp= p 3.
16.
If 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
17.
If the 5th and 12th terms of an A.P. are 30 and 65 respectively, what is the sum of first 20 terms? S1be the sum of (2n + 1)
terms of an A.P. and S2 be the sum of its odd terms, then prove that S1:S2 = (2n + 1):(n + 1)
18.
Insert 4 A.M.s between 4 and 19.
19.
A man saves Rs 32 during the first year, Rs 36 in the second year and in this way he increases his savings by Rs 4 every year.
Find in what time his saving will beRs200.
20.
A man arranges to pay off a debt of Rs 3600 by 40 annual installments which form an arithmetic series. When 30 of the
installments are paid, he dies leaving one-third of the debt unpaid, find the value of the first installment.
Straight Lines
21.
What is the value of y so that the line through (3, y) & (2, 7) is parallel to the line through (–1, 4) and (0, 6).
22.
If A (– 2, 1), B (2, 3) and C (– 2, – 4) are three points, find the angle between BA and BC.
23.
Find the x and y intercepts of the following lines – (i) 2x + 3y = 6
(ii) 4x – 3y = 12
(iii) 7x + 8y + 13 = 0
24.
Find the perpendicular distance of the point (1, 0) from the line 3x + 2y – 1 = 0
25.
What are the points on x-axis whose perpendicular distance from the line 4x + 3y = 12 is 4?
26.
Find the distance between the parallel lines 3x – 4y + 9 = 0 and 6x – 8y – 15 = 0.
27.
Find the equation of a line with slope – 1 and cutting off an intercept of 4 units on negative direction of y – axis.
28.
Find the equation of a straight line cutting off an intercept – 1 from y – axis and being equally inclined to the axis.
29.
Find the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, – 5) and (1, 2).
30.
Find the equation of the straight line which passes through the point (– 5, 4) and is such that the portion intercepted between the axis is
divided by the point in the ratio 1 : 2.
0
31.
Find the equation of the line which is at a distance 3 from the origin and the perpendicular from the origin to the line makes an angle of 30
with the positive direction of the x – axis.
32.
The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 1500 with the positive direction of y – axis. Find
the equation of the line.
33.
Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle
α with x – axis such that sin α =
34.
35.
36.
37.
38.
39.
40.
41.
1
.
3
Find the equations of a line passing through (2, – 3) and inclined at an angle of 135 0 with the positive direction of x – axis.
Find the equation of the perpendicular bisector of the line segment joining the points A (2, 3) and B (6, – 5).
Find the equations of the medians of the triangle ABC whose vertices are A(2, 5), B(– 4, 9) and C (– 2, – 1).
0
A straight line is drawn through the point P (2, 3) and is inclined at an angle of 30 with the x – axis. Find the coordinates of two points on
it at a distance 4 from P on either side of P.
Find the distance of the point (3, 5) from the line2x + 3y = 14 measured parallel to a line having slope 1/2
0
Find the equations of the two straight liens through (7, 9) and making an angle of 60 with the line x – 3 y – 2 3 = 0
Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenuse 3x + 4y = 4 and the opposite vertex
is the point (2, 2).
Two sides of an isosceles triangle are given by the equations 7x – y + 3 = 0 and x + y – 3 = 0 and its third side passes through the point (1, –
10). Determine the equation of the third side.
42.
Show that the lines x – y – 6 = 0, 4x – 3y – 20 = 0 and 6x + 5y + 8 = 0 are concurrent. Also find their common point of intersection.
43.
Reduce the lines 3x – 4y + 4 = 0 and 4x–3y+12= 0 to the normal form and hence determine which line is nearer to the origin.
Conic Section
44.
Find the equations of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x -4y = 1.
45.
Find the equation of the circle concentric with the circle x2 + y2 - 6x + 12y + 15 = 0 and double of its area.
46.
Find the equation of the circle with x + y - 4x - 6y - 3 = 0 and which touches the y-axis.
47.
If the equation of the two diameters of a circle are x – y = 5 and 2x + y = 4 and the radius of the circle is 5, find the equation of the
2
2
circle.
48.
2
2
2
The circle (x – a) + (y – a) = a is rolled on the y-axis in the positive direction through one complete revolution. Find the equation of
the circle in its new – position.
49.
A circle of the radius 2 lies in the first quadrant and touches both the axes. Find the equation of the circle with centre at (6, 5) and
touching the above circle externally.
50.
Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x-4y+3=0. Also find the length of its latusrectum.
51.
For the parabola y2 = 4px find the extremities of a double ordinate of length 8 p. Prove that the lines form the vertex to its extremities
are at right angles.
52.
2
Find the area of the triangle formed by the lines joining the vertex of the parabola x = 12y to the ends of its latus rectum.
Trigonometry
2
2
53.
Prove that (sec A sec B + tan A tan B) – (sec A tan B + tan A sec B) = 1
54.
Prove that (1 + tantan)2 + (tan - tan)2 = sec2 sec2
55.
If sin =
56.
57.
58.
12
and  lies in the second quadrant, find the value of sec + tan
13
3
1

3
, find the value of 8tan  5 sec
, tan = and       
5
2
2
2
12
4


If sin A =
and sin B = , where < A < and 0 < B < , find the following:
(i) sin (A + B)
13
5
2
2
3
9
3
If tan A = , cos B =
, where < A <
and
4
41
2

0 < B < , find tan (A + B).
2
If sin =
59.
Prove that
sin A  sinB
A B
 A B
 tan 
 cot 

sin A  sinB
 2 
 2 
60.
Prove that
cos A  cos B
 A B
 A B
 cot 
 cot  2 
cos B  cos A
2




61.
62.
63.
64.
65.
(ii) cos (A + B)
sin2
 tan
1 cos2
2  2  2cos 4   2 cos 

2
4
7 1
cos cos cos 
15
15
15
15 16
sin3Acos4A  sinAcos2A
 tan2A
Prove that
sin4AsinA  cos6AcosA
Prove that
cos
If tan A + tan B = a and cot A + cot B = b, prove that: cot (A + B) =
1 1
 .
a b
Physics: Topics : Make a model on anyone of the followings :
i) Circular Motion
ii) Moment of Inertia iii) Elasticity
iv) Surface tension
v) Satellites
vi) Simple Harmonic Motion
vii) Doppler’s Effect
viii) Second law of thermodynamics
ix) Kinetic theory of gases
x) Gravitation
Learning Objectives : History, Methodology, Circuit, Block Diagram, Basic Components used for making the model, Advantages of Project,
Applications and future work.
Source that can be used :
1. Science Magazines
2. Internet
3. Reference Books
Creteria for Evalution : * Aims & Objectives (1), * Methodology (2) , * Resources & Material used (2), * Working Procedure & Circuit/
Block diagram (2), * Analysis & summary (2) , *Bibliography (1)
Note : The total length of the Project Report should not be more than 15 written pages.
Chemistry : Assignment on the preparation of following compounds :
A)
1. Compound of Sodium
2. Washing Soda Na2CO3.10H2O Solvay process.
3. NaHCO3 Baking Soda
4. CaO Quicklime
5. Plaster of Paris
6. Manufacture of Cement – Composition and Setting
7. Boron
8. Borax Na2B4O7. 10H2O (Preparation, properties and uses)
9. H3BO3 – Orthoboric acid
10. Diborane B2H6 (Structure)
11. Silicone : Orthosilicatie , Pyrosilicate, Cyclic, Zeolites
B) Assignment covering the following aspects.
Environmental Pollution : sources, sinks and effects of : Gaseous pollutants : CO,
Content of CO,
CO2, NO,
Sulphur Oxides,
Chlorine
Smog : Classical and photochemical smog, Industrial air pollution, Dissolved Oxygen in H2O, Biological oxygen demand, Green Chemistry
Exercise Questions :
C) Seminar Presentation on GREEN CHEMISTRY.
Evaluation Criteria :
1. Preparation of compounds.
2. Structure
3. Chemical Properties and reactions
4. Applications
5. Viva
Note : Innovativeness & Timely submission carry higher weight age.
Bio : They say ‘Curiosity Kills the Cat’ but this statement does not hold true for the most lively subject of science i.e. Biology.
Prepare an PPT (Power Point Presentation) and brief synopsis on the topic allotted to you from the followings.
Topics : i) Air Pollution & its control
ii) Stone Cancer-Acid Rain
iii) Natural Gas
iv) Sacred Grooves v) Radioactive and e-waste
vi) Algal bloom – a menace.
vii) DNA finger printing & its application
viii) Cloning : is human cloning ethical
ix) Bio remediation
x) The BT Boom
xi) Indian Contribution to Biology
Details of the PPT and Synopsis file :
Index
No of Slides Content
Introduction
1
Introduce the topic
Objective
1
Aim of your study (2-3 points)
Body
4
In-depth study with descriptions and examples
Relevant pictures
3
Preventive Measures
2
At least 4 preventive measure
Conclusion
1
What you have learnt from this study
Bibliography
1
Quote all the source, material used: books/ websites

Refer to the following sites for further information on how to carry out an investigatory project with model.

www.1000 science fair projects.com

www.biology mad.com

www.fact monster.com

www.synbioproject.org.
Computer : 1. Make an application to store the names of 10 students in a double dimension array, 10 marks of them in separate float array. The
corresponding index number of each array will represent the record of each child. Make two functions :
st nd
rd
i) To display the marks of children along with their names whose rank is 1 2 and 3 .
ii) To display all names with marks alphabetically.
2. Develop a small game in C++ using random function.
History : Topic : Evolution of Social Hierarchies based on different Criteria : occupation, language, wealth, education. Compare medieval France with
Mesopotamia and the Roman Empire.
Objective : To analyse the impact of social hierarchies in medieral period
Geography : Prepare a project report on any of the topics given below. i) Malpa landslide
ii) Orissa Cyclones iii) Bhuj/ Latur Earthquake
Objective : To make the students aware of the National Disasters & learn about ‘DISASTER MANAGEMENT’.