Autumn Break Homework for class XI
MATHS
1.)Find the domain and range of the following functions :
(i)√𝑥 − 3
(ii) √25 − 𝑥 2
2.)(i) If Ө+Φ=α and tanӨ=k tanΦ, prove that : sinα=
(ii)If α+β=γ and
𝑡𝑎𝑛𝛼
𝑡𝑎𝑛𝛽
=
𝑥
𝑦
𝑘+1
𝑘−1
sin(Ө − Φ).
𝑥−𝑦
, then prove that sin(α-β)=
𝑥+𝑦
𝑠𝑖𝑛𝛾 .
3.)Prove that:
𝜋
𝜋
𝜋
𝜋
𝑡𝑎𝑛𝑥 𝑡𝑎𝑛 (𝑥 + ) + tan (𝑥 + ) tan (𝑥 − ) + tan (𝑥 − ) 𝑡𝑎𝑛𝑥 = −3
3
3
3
3
4.)(i) If 𝑐𝑜𝑡𝑥 𝑐𝑜𝑡𝑦 = 2 , show that
cos(𝑥+𝑦)
cos(𝑥−𝑦)
(ii)If tan A = m.tan B, prove that
sin(𝐴−𝐵)
sin(𝐴+𝐵)
=
=
1
3
.
𝑚−1
𝑚+1
.
5.) Prove that:
(i)cos 4𝑥 = 1 − 8𝑐𝑜𝑠 2 𝑥 + 8𝑐𝑜𝑠 4 𝑥
(ii)sin 4𝑥 = 4 sin 𝑥 𝑥 𝑐𝑜𝑠 3 𝑥 − 4 𝑐𝑜𝑠𝑥 𝑠𝑖𝑛3 𝑥
(iii)sin 5𝑥 = 5 sin 𝑥 − 20𝑠𝑖𝑛3 𝑥 + 16𝑠𝑖𝑛5 𝑥
6.)Solve the following equations :
(i)√3 𝑐𝑜𝑠 𝑥 − sin 𝑥 = 1
(ii)tan x+sec x = √3
7.)In any triangle ABC , prove that :
𝑎2 − 𝑏2 /(𝑐𝑜𝑠 𝐴 + cos 𝐵) + 𝑏2 − 𝑐 2 /(cos 𝐵 + cos 𝐶) + 𝑐 2 − 𝑎2 /(cos 𝐶 + cos A ) = 0
8.) Prove , by mathematical induction , that 5n+1+4.6n when divided by 20 leaves
remainder 9 for all n ∈ 𝑁.
9.) Prove , by mathematical induction , that 8.7n+4n+2 is divisible by 24 but not 48 for
all n ∈ 𝑁.
10.)Find the square roots of the following complex number :
-5-12i
11.) Find the modulus of :
2+𝑖
4𝑖+(1+𝑖)2
.
12.) A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to
it. The resulting mixture is to be more than 4% but less than 6% boric acid . If we
have 640 litres of 8% solution , how many litres of 2% solution will have to be added?
13.)Solve the following system of linear inequalities graphically :
(i)x-2y<=2, -3x+2y<=3, 2x+3y<12, 2x+3y>=6.
(ii)x+y>=1, 3x+4y<12, x-2y<=2, x>=0, y>=0.
14.)Find the number of :
(i) combinations
(ii) permutations
Of four letters taken from the word EXAMINATION.
15.) Find the value of k so that the term independent of x in the expansion of
𝑘 10
(√𝑥 + 𝑥 2)
is 405.
1 𝑛
5
16.) If the fourth term in the expansion of (𝑎𝑥 + ) is , then find the value of a
𝑥
2
and n.
CHEMISTRY
CLASS XI AUTUMN BREAK HOME WORK 2013
1
Everyday three numricals from text book exercise.(thermodynamics,equilibrium and states of matter)
2
3
4
5
6
7
All solved examples of ncert.
Comman ion effect and its applications in salt analysis.
Limting reagent and the numericals based on it.
bond order,stability and magnetic properties of O2,N2+,O2-,Be2,F2,Ne2+
Expalination of the shapes of the given species on the basis of VSEPRT XeF4,PCl5,IF7,NH3,XeF2,H2O,SF6.
Acid Base concept all three concepts with their examples and limitations.
PHYSICS
1. Why two holes are made to empty an oil tin?
2. Why mercury is used in barometer?
3. A tank with square base of area 1m2 is divided by a vertical partition in the middle. The bottom of
the partition has small hinged door of area 20 cm2. The tank is filled with water in one
compartment and an acid of relative density 1.7 in the other, both to a height of 4.0 m.
Compute the force necessary to keep the door closed.
( Ans. = 54.88N)
4. Why two boats moving in a parallel direction close to each other get attracted?
5. A big sized balloon of mass M is held stationary in air with the help of a small block of mass M/2
tied to it by a light string such that both float in midair. Describe the motion of the balloon and
the block when the string is cut. Support your answer with the calculation.
6. A balloon filled with Helium does not rise in air indefinitely but halts after certain height. Explain
why?
7. Describe various factors which affect the surface tension of the liquid.
8. State Hooke’s law of elasticity. Draw graph between stress and strain for a wire and explain its
various stages.
9. A liquid drop of diameter D breaks into 27 tiny drops. Find the resulting change in surface
energy. Take surface tension of the liquid as ‘S’.
10. In Millikan’s oil drop experiment, what is the terminal velocity of a drop of radius 2x10-5 m and
density 1.2x103 kg/m3. Take viscosity of air at the temperature of experiment to be 1.8x10-15
Nsm-2. How much is the viscous force on the drop at that speed? Neglect the buoyancy on the
drop due to viscosity.
(Ans. = 3.9413x10-10 N)
Computer Science
Q1. WAP that accept two numbers n and m and print nm.
Q2. WAP that accept a number and display whether number is prime number or not.
Q3. WAP that display first 10 odd numbers. ( with the help of loop).
Q4. WAP that display the following series.
1
5
9
13
17………….N
Q5 WAP that print every integer between 1 and n divisible by m. also report whether the number that is
divisible by m is even or odd.
HINDI
GEOGRAPHY XI
1. With the help of the diagram explain coriolis force, heat zone,pressure belt and
winds?
2. On the bases of maximum & minimum temperature from 15/10/12 to 25/10/12 draw a
bar diagram.Also find out the range of temperature during this period?
3. Explain the structure or layers of the atmosphere.
Also draw the diagram ?
4. Visit the costal area discuss about the climatic conditions and erosional / depositional
features found there ?
5. What is the significance of monsoons in agricultural system ?
6. Make the following on the outline map of india:
(i) s.w.monsoon
(iii) annual rainfall
(ii) n.e. monsoon
(iv) climatic regions
7. What are contours ? How will you represent the
contours ?
relief features with the help of
ECONOMICS
Make PPT or file on any one topic
1. Rural development
2. Human capital formation
3. Poverty
Questions
1.
2.
3.
4.
Write about animal husbandry and holiculture
What do you mean by organic forming
Write benefits of organic forming
Write about golden revolution.
Political Science
5. Write down about Indian parliament, Paste the picture and full
information about it’s both the houses. Composition of Lok Sabha and
Rajya Sabha.
6. Write down about the names of states where there is Bi-cameral
legislature. Show these states in Indian Political Map.
7. All this work should be done in a project file.
HISTORY
1) Make question bank & key points of nomadic empire & three orders.
2) Make map file from all chapters.
3) Revise chapters 1, 2, 3 & 4.
BUSINESS STUDIES
1. Describe the scope of Business process ousourcing with a pie diagramme.
2. What are the software and hardware risk in e-business transactions.
3. What is C2C commerce and explain with example referring from websites.
And name the websites.
4. Explain any one personal experience on online transactions.
5. Go to any company website and find out five e-business transactions. And
give the name of the website.
6. Write two examples for each principle of insurance.
7. Discuss VSAT services reffering the website.
8. Describe DTH services provided by different companies naming its service.
9. Describe the terms and conditions of health insurance.
ACCOUNTANCY
1. Do two practical questions on journalizing and post them into ledger accounts including one
from unit test II question paper
2. Solve the unit test question paper (II)
3. Do two practical question one in purchases book another in sales book and post the transaction
into ledger.