poem: childhood

BRAIN INTERNATIONAL SCHOOL

POEM: CHILDHOOD

Q1 What is the poet‟s feelings towards his childhood?

Q2 How did the poet conclude that heaven and hell are two imaginary places?

Q3. How does the poet expose man and present him in true colours?

CHAPTER: SILK ROAD

Q 4. How does the author describe the atmosphere and sky when they were leaving Ravu?

Q5. Describe the qualities of Tibetan mastiffs as described by the author.

Q6. Why did the travellers stop at the tyre repair shop at Hor?

Q7. What steps did the travellers take to negoitiate the snow on the road during the shortcut

they took to reach Hor? (120-150 words)

CHAPTER : DISCOVERING TUT : THE SAGA CONTINUES Q8. Howard Carter ran into trouble when he finally reached the mummy. Why?

Q9. How was the mummy detached by Carter?

Q10.What snag did the million dollar scanner develop? How was the defect corrected?

CHAPTER : THE AILING PLANET Q11. What do you mean by the Era of Responsibility?

Q12. What happens when the productivity of the principal biological system gets impaired?

POEM : THE LABURNUM TOP Q13. What values do you learn from the goldfinch in the poem „ The Laburnum Top‟?

Q14. “ Then sleek as a lizard and alert and abrupt, she enters the thickness‟. Explain the given

line.

CHAPTER : THE ADDRESS

Q15. Describe Mrs. Dorlings

Q16. “ I was absolutely not interested in all that stored stuff.” Who was not interested and

why?

Q17. What is the significance of the title „ The Address‟.

WRITING SKILLS :

Q18. You are Advait/Akriti , resident of C-42, Vikaspuri. Write a letter of complaint to the

Sanitary Inspector of the Municipal Corporation, requesting him to take necessary steps about

the miserable condition of your locality.

Q19. You are Aakarshan/Aditi . Media has a strong hold on society. Write a speech in 120-

150 words on how media influences public opinion to be delivered in the school assembly.

TERM II CLASS XI 2020-21

SUBJECT: ENGLISH REVISION SHEET

Q20. Read the following passage carefully.

An era, a culture is eventually determined by its news. What is missed out by those who track the news of that time is lost forever. We know nothing about Shakespeare’s contemporaries even though some of them may have been better playwrights. We know nothing about those who came in with Babar, or around the same time, to loot India and stayed back as rulers. Or the many soldiers of fortune who landed here during the time of the East India Company. We know of a few and, apart from avid historians, no one knows who led the Portuguese, Dutch or French into India or ran their empires here till they were dismantled. Why is that? Simple. The media of that time, known as historians, did not mention them. We who consume news today see it as a fleeting experience. We observe a powerful image on TV, are moved by its impact or repelled by its horror, and move on. We read a headline today and can’t even recall it tomorrow. Current news always drives out the old (often with ruthless cunning) and It’s only when the media goes back in time to recall a particular (7 story that we suddenly remember that, yes, there was something called HDW or Bofors that once shook up the entire nation and held it in thrall for a decade. We are suddenly reminded that Congress treasurer LN Mishra was mysteriously killed in a bomb blast on a train and no one ever knew who killed him or where his secret millions vanished. Since I’m a journalist I can tell you many such stories. There are others too, full of stories. But, like news, the stories die with them. History only remembers what it chooses to, or what is indelibly stamped on its pages. The rest is occasionally recalled as gossip. But is it gossip? Or is it truth that we are trying to forget so that we can move on and make space in our hearts and minds for more recent news? Our memory, collective as well as individual, has limited storage and however many data cards we may insert, there’s simply too much to absorb and retain. The information surge that hits us every morning is so i large, so intimidating that we remember only a tiny fraction of it. It’s that fraction which actually scares us by the possibility of impacting our lives. The gap between news and entertainment was always sacrosanct. News was about facts. Entertainment was about imagination, ergo fiction. To see them occupy the same media platforms today is scary for those like me who have spent a lifetime pursuing facts in the search for news. Even the dividing line has blurred. What we once shunned as preposterous lies slip in so casually today into our news menu. It’s no one’s fault. It’s just that the fault lines have shifted. News has become just another consumable, another platform to commercially (and cynically) exploit. No, don’t blame our journalists and media owners. They are only following a global model that, for better or for worse, is making our times an entirely forgettable chapter of history.

On the basis of your reading of the passage, make notes and write a summary in 80 words.


TERM-II CLASS-XI 2020-21

SUBJECT: ECONOMICS REVISION SHEET

MICROECONOMICS

UNIT 1 INTRODUCTION

1. Distinguish between microeconomics and macroeconomics. Give example.

2. Why does an economic problem arise? Explain the problem of 'How to Produce'?

3. Explain the problem of 'What to Produce' with the help of an example.

4. 'For whom to produce' is a central problem of an economy. Explain.

5. State three differences between normative economic analysis and positive economic analysis.

6. Write any three differences between Market Economy and Centrally Planned Economy.

7. What is PP Frontier? Explain it with the help of an imaginary schedule and diagram.

8. Show the following situation with PPF

(a) Fuller utilisation of resources

(b) Growth of resources.

(c) Under utilisation of resources.

9. Why is PPC called opportunity cost curve?

10. Define opportunity cost and explain it with the help of an example.

11. Explain PPF is (a) down ward sloping. (b) concave to the point of origin.

UNIT 2 CONSUMER'S BEHAVIOUR & THEORY OF DEMAND

1.What happens to total expenditure on a commodity when its price falls and its demand is price

elastic?

2. Why does total utility increases at diminishing rate due to continuous increase in units of a

good Consumed?

3. Due to decrease in price of pen why does the demand of ink increase?

4. When does budget line shift leftwards?

5 Under what situation does the slope of changed budget line be flatter?

6. What change should take place in price of the combination of two goods so that the slope of

budget line becomes steeper?

7. What will be the behaviour of total utility when marginal utility curve lies below X-axis?

8. What are the reasons behind Law of demand? State any two.

9.Explain the law of diminishing marginal utility with the help of a utility schedule.

10. Explain consumers equilibrium with utility approach when consumer is consuming one good.

11. What do you mean by budget line? What are the reasons of change in budget line?

12. Explain the relationship between total utility and marginal utility with the help of schedule.

13. What changes will take place in total utility when –

(a) Marginal utility curve has above X–axis.

(b) Marginal utility curve touches X–axis

(c) Marginal utility curve lies below X–axis.

14. State two features of indifference curve.

15. Why does two indifference curves do not touch each other?

16. Under what situations there will be parallel shift in budget line?

17. Explain the effect of a rise in the prices of ‘related goods’ on the demand for a good X.

18. Why does demand of a normal good increases due to increase in consumer’s income?

19. “If a product price increases, a family’s spreading on the product has to increase”. Defend or

refute.

20. State elasticity of demand of followings (a) Luxurious goods (b) Goods of alternate use (c)

Necessity goods.

21. Distinguish between expansion of demand and increase in demand with the help of diagram.

22. What do you mean by marginal rate of substitutions? Explain with the help of a numerical

example.

23. Measure Price Elasticity of Demand on the following points of a straight line demand curve :

(a) Centre point of the demand curve.

(b) Demand curve intercepting y-axis

(c) Demand curve intercepting x-axis.

24. Explain negative relationship between price and demand.

25. What will be the impact on demand if, elasticity of demand is same : (a) fall in price of good

‘X’ by 5% (b) increase in price of good ‘Y’ by 15%

UNIT 3 PRODUCTION BEHAVIOUR AND SUPPLY

1.Why is total variable cost curve parallel to total cost curve.

2. Why does average fixed cost falls with increase in output?

3. Why is total fixed cost curve parallel to ox-axis.

4. Under which situation MR will fall when an additional quantity of a good is sold?

5. What behaviour of per unit price will cause the equality of average and marginal revenue.

6. If two supply curves intersect, which one has the higher price elasticity?

7. Give one differences between law of supply and price elasticity of supply.

8. What is the price elasticity of supply associated when the supply curve passing through to

intersect to x-axis?

9. Why does a producer moves downward along a supply curve due to decrease in price of

commodity?

10. What is the price elasticity of supply associated when a supply curve passing on 40° angle

through the origin?

11. When does the supply curve shifted to rightward while price remains constant why the

supply increases due to increase in price?

12. What effect does an increase in price of competitive good on the supply of a commodity?

13. How does the imposition of a unit tax affect the supply curve of a firm?

UNIT4 - MARKET

1. Explain the characteristics of monopolistic competition.

2. Explain the following features of perfect competition. (i) Large number of firms or Sellers and

Buyers (ii) Homogeneous Product.

3. What will be the effect on equilibrium price due to change in supply if (i) demand is perfectly

inelastic (ii) demand is perfectly elastic

5. Explain equilibrium price. How is it determined? 6. Explain how change in price of a

substitute commodity would affect market equilibrium of the commodity X.

6. How are equilibrium price and quantity affected when demand and supply curve move in

opposite direction?

7. There is simultaneous change in demand and supply of a commodity and equilibrium price

will increase. Explain with the help of diagram.

8. There is simultaneous decrease in demand and supply of a commodity, when it result in (i) no

change in equilibrium price (ii) a fall in equilibrium price.

STATISTICS

UNIT -1 INTRODUCTION

1) Mention the two senses in which statistics is defined.

2) People are engaged in two types of activities in their day to day life. State these activities.

3) State any two functions of statistics.

4) Following examples relate to which data?

a) Intelligence of individuals

b) Tastes and preferences of individuals

5) Why should statistical data be collected in a systematic manner?

UNIT 2 COLLECTION OF DATA

1) What kind of data is collected by NSSO.

2) What is statistical investigation?

3) Which data should be used by an investigator if there is a limited time

frame?

4) Name two agencies at the national level which collect, process and tabulate

the statistical data.

5) Ayaan wants to collect information from respondents residing in Gujarat, Maharashtra and Madhya

Pradesh. Name any two methods of data

collection which can be used by him effectively.

UNIT 3 ORGANISATION AND CLASSIFICATION OF DATA)

I. Answer the following (1 mark)

1) What do you understand by organization of data?

2) What do you understand by ‘attribute’.

3) Which two values are used for calculating mid value?

4) Class mid-values of a frequency distribution of marks (in statistics) of students

of class XI are given as 46, 53 and 60. What will be the size of the class?

a) 5 b) 7 c) 10 d) 15

5) Give two objectives of an ideal classification of data.

UNIT- 4 ( PRESENTATION OF DATA)

I. Answer the following (1 Mark)

1) Write the names of main parts of a table.

2) Which type of diagram will be used to show two or more characteristics of

the data?

3) Which bar diagram is known as simple bar diagram?

4) Name the form of presentation to which the following example relates.

40% of India’s population lives below the poverty line and top 20%

population commands 70% of the national income.

II. Answer the following (3/4 Marks)

1) Briefly explain any four factors which should be kept in mind while

preparing a table.

2) Rice yield per hectare is given below. Show the data diagrammatically.

Year 1999-2000 2000- 2001 2201-2002 2002-2003 2003-2004 2004-2005 2005-2006

Yield 668 1013 1123 1235 1336 1552 1482

4) Differentiate between frequency polygon and frequency curve.

5) Construct a frequency polygon with histogram for the following data.

UNIT 5 MEASURES OF CENTRAL TENDENCY

(TOPIC – ARITHMETIC MEAN)


1) Mr. Ram has annual income of ₹10,00,000 while Mr. Raj has annual income

of ₹70,00,000. Their average income has been computed at ₹40,00,000 per

annum. Do you think average income is a good representation of their

actual annual income?

2) Name the two types of Arithmetic Mean.

3) “Calculation of arithmetic mean for an inclusive frequency distribution is

the same as in case of exclusive frequency distribution”. The given

statement is

a) True b) false c) partly true d) none

4) Give the formula of calculating arithmetic mean for ungrouped data.

TOPIC – MEDIAN AND QUARTILES

I. Answer the following ( 1 Mark)

1) The median value of a series is 22. The last value of the series is changed

from 40 to 75. Will the value of median be affected?

2) Which quartile is equal to median?

3) Give the formula for calculating median in continuous frequency

distribution.

4) Which average distributes the series into 100 equal parts?

5) Median can be graphically computed

a) By preparing ‘less than’ ogive

b) By preparing ‘more than’ ogive

c) By preparing ‘less than’ and ‘more than’ ogives

d) All of the above

4) Calculate the value of median, first quartile and third quartile from the

following data.

Marks Number of students

30-35 14

35-40 16

40-45 18

45-50 23

50-55 18

55-60 8

60-65 3

UNIT 6 MEASURES OF DISPERSION

TOPIC – STANDARD DEVIATION


1) What is the algebraic sum of deviations from mean?

2) Why is standard deviation computed from mean?

3) While calculating standard deviation, the deviations, as compared from mean are

squared. Why?

4) Greater the value of standard deviation, _____ is the consistency of data

a) Lesser b) greater c) constant d) none

II. Answer the following (3/4 Marks)

1) State two merits and two demerits of standard deviation.

2) Give four differences between mean deviation and standard deviation.

3) Find out mean and standard deviation of the marks obtained by 10 students in Statistics

S.No. 1 2 3 4 5 6 7 8 9 10

Marks 43 48 65 57 31 60 37 48 78 59

UNIT -7 INDEX NUMBER

1) Construct index number of the price for the year price of 2016 from the

following data by

i) Laspeyre’s Method

ii) Paasche’s Method

iii) Fisher’s Method

Commodity 2008 2008 2019 2019

Price Quantity Price Quantity

A 10 30 12 35

B 9 10 11 15

C 8 15 10 20

D 6 20 7 25


TERM II CLASS: XI 2020-21

SUBJECT: MATHEMATICS REVISION SHEET

SETS

Q1. In a survey it was found that 21 persons liked product 𝑃1, 26 liked product 𝑃2 and 29

liked product 𝑃3. If 14 persons liked products 𝑃1 and 𝑃2; 12 persons liked product 𝑃1 and 𝑃3;

14 persons liked product 𝑃2 and 𝑃3, and 8 liked all the three products. Find how many liked

only one product?

Q2. A survey of 500 television viewers produced the given information; 285 watch football,

195 watch hockey, 115 watch cricket, 45 watch football and cricket, 70 watch football and

hockey, 50 do not watch any of the three games. How many watch exactly one of the three

games?

Q3. There are 20 students in a Chemistry class and 30 students in a Physics class. Find the

number of students who are either in Physics class or Chemistry class in the following cases:

(i) Two classes meet at the same time.

(ii) The two classes meet at different hours and ten students are enrolled in both the

courses.

Q4. Write power set of the set 𝐴 = {𝑎, 𝑏, 𝑐}.

Q5. In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not

Economics. Find the number of students who have taken both Mathematics and Economics

and the number of students who have taken Economics but not Mathematics, if it is given that

each student has taken either Mathematics or Economics or both.

Q6. If U = {𝑥 ∶ 𝑥 ≤ 10, 𝑥 ∈ 𝑁}, 𝐴 = {𝑥 ∶ 𝑥 ∈ 𝑁, 𝑥 𝑖𝑠 𝑝𝑟𝑖𝑚𝑒}, 𝐵 = {𝑥 ∶ 𝑥 ∈ 𝑁, 𝑥 𝑖𝑠 𝑒𝑣𝑒𝑛}, write 𝐴 ∩ 𝐵′ in roster form.

Q7. In a survey of 5,000 people in a town, 2250 were listed as reading English newspaper,

1750 as reading Hindi newspaper and 875 were listed as reading both Hindi as well as

English. Find how many people do not read Hindi or English newspaper. How many people

read only English newspaper?

Q8. In an examination, 80% students passed in Mathematics, 72% passed in Science and

13% failed in both the subjects, if 312 students passed in both the subjects. Find the total

number of students who appeared in the examination.

Q9. Write all subsets of set 𝐴 = {1, 2, 3}.

Q10. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these

medals went to a total of 58 men and only three men got medals in all the three sports. How

many received medals in exactly two of the three sports?

RELATIONS & FUNCTIONS

Q1. Find 𝑥 and y, if (𝑥 + 3, 5) = (6, 2𝑥 + 𝑦).

Q2. Let 𝑓 ∶ 𝑅 → 𝑅 be given by 𝑓(𝑥) = 𝑥2 + 3. Find

(i) {𝑥 ∶ 𝑓(𝑥) = 28}

(ii) The pre-images of 39 and 2 under ‘𝑓’

Q3. Determine the domain and range of the relation R defined by

𝑅 = {(𝑥 + 1, 𝑥 + 5) ∶ 𝑥 ∈ (0, 1, 2, 3, 4, 5)}.

Q4. Let 𝐴 = (1, 2, 3, 4, 6). Let R be the relation on A defined by {(𝑎, 𝑏) ∶ 𝑎, 𝑏 ∈ 𝐴 𝑎 𝑑𝑖𝑣𝑖𝑑𝑒𝑠 𝑏}

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R

Q5. Draw the graph of Signum function 𝑓 ∶ 𝑅 → 𝑅 defined by 𝑓(𝑥) = {

1, 𝑖𝑓 𝑥 > 0 0, 𝑖𝑓 𝑥 = 0−1, 𝑖𝑓 𝑥 < 0

.

Q6. Draw the graph of greatest integer function

Q7.

(i) Determine the domain and the range of the relation R, where {(𝑥, 𝑥3) ∶ 𝑥 is a

prime number less than 10}

(ii) Let 𝑓, 𝑔 ∶ 𝑅 → 𝑅 be defined respectively by 𝑓(𝑥) = 𝑥 + 1 and 𝑔(𝑥) = 2𝑥 − 3.

Find 𝑓 + 𝑔; 𝑓 − 𝑔; 𝑓𝑔.

Q8. The relation R is defined as 𝑅 = [(𝑥, 𝑥 + 5) ∶ 𝑥 ∈ (0, 1, 2, 3, 4, 5)]. Write R in roster

form. Write its domain and range.

Q9. Find domain and range of the real function 𝑓(𝑥), defined by 𝑓(𝑥) = {1 − 𝑥, 𝑥 < 0 1, 𝑥 = 0𝑥 − 1, 𝑥 > 0

}

and draw its graph.

Q10. If 𝑓 ∶ 𝑅 → 𝑅 is defined by 𝑓(𝑥) = [𝑥], the greatest integer function, find its domain,

range and draw its graph.

TRIGONOMETRY

Q1. Find the value of the following:

(i) tan19𝜋

3

(ii) cot (−15𝜋

4)

Q2. If tan 𝑥 =3

4 and 𝑥 lies in the third quadrant, find the values of sin

𝑥

2 , cos

𝑥

2 and 𝑡𝑎𝑛

𝑥

2.

Q3. Prove that: cos 200 cos 400 cos 600 cos 800 =1

16.

Q4. Prove that: tan 500 = tan 400 + 2 tan 100.

Q5. Evaluate: sin 1050 + cos 1050.

Q6. Prove that: sin 𝐴.sin 2𝐴+sin 3𝐴.sin 6𝐴

sin 𝐴.cos 2𝐴+sin 3𝐴.cos 6𝐴= tan 5𝐴.

Q7. Prove that: 𝑐𝑜𝑠2𝑥 + 𝑐𝑜𝑠2 (𝑥 +𝜋

3) + 𝑐𝑜𝑠2 (𝑥 −

𝜋

3) =

3

2.

Q8. Show that: tan 3𝑥 tan 2𝑥 tan 𝑥 = tan 3𝑥 − tan 2𝑥 − tan 𝑥.

Q9. Prove that: cos 2𝑥. cos𝑥

2− cos 3𝑥. cos

9𝑥

2= sin 5𝑥 sin

5𝑥

2.

Q10. What is the value of cos (𝜋

4− 𝑥) cos (

𝜋

4− 𝑦) −𝑠𝑖𝑛 (

𝜋

4− 𝑥) 𝑠𝑖𝑛 (

𝜋

4− 𝑦)?

COMPLEX NUMBERS

Q1. Find the magnitude and conjugate of the number (1

1−4𝑖−

2

1+𝑖) (

3−4𝑖

5+𝑖).

Q2. Find the value of x and y, if (1+𝑖) 𝑥−2𝑖

3+𝑖+

(2−3𝑖) 𝑦+𝑖

3−𝑖= 𝑖.

Q3. If 𝑍1 and 𝑍2 are 1 − 𝑖 and −2 + 4𝑖 respectively, find Im [𝑍1∙𝑍2

𝑍1].

Q4. If +𝑖𝑦 = √𝑎+𝑖𝑏

𝑐+𝑖𝑑 , prove that (𝑥2 + 𝑦2)2 =

𝑎2+𝑏2

𝑐2+𝑑2.

Q5. Find argument of 1+𝑖

1−𝑖.

Q6. Express, 5+√2 𝑖

1−√2 𝑖 in the form 𝑎 + 𝑖𝑏.

Q7. Find argument of 1

1−𝑖.

Q8. Find real 𝜃 such that 3+2 𝑖 sin 𝜃

1−2 𝑖 sin 𝜃 is purely real.

Q9. If 𝛼 and 𝛽 are different complex numbers with |𝛽| = 1, then find |𝛽−𝛼

1−�̅�𝛽|.

Q10. What are the real numbers ‘𝑥’ and ‘𝑦’ if (𝑥 − 𝑖𝑦) (3 + 5𝑖) is the conjugate of (−1 − 3𝑖)?

LINEAR INEQUALITIES

Q1. Solve the following system of inequalities graphically:

2𝑥 + 𝑦 ≥ 4, 𝑥 + 𝑦 ≤ 3, 2𝑥 − 3𝑦 ≤ 6.


3𝑥 + 4𝑦 ≤ 12, 4𝑥 + 3𝑦 ≤ 12, 𝑥 ≥ 0, 𝑦 ≥ 0.

Q3. Solve : −5 ≤2−3𝑥

4≤ 9.


2𝑥 + 𝑦 − 3 ≥ 0, 𝑥 − 2𝑦 + 1 ≤ 0, 𝑦 > 3.


𝑥 ≥ 𝑦, 𝑦 ≥ 0, 𝑥 + 2𝑦 ≤ 8, 𝑥 + 𝑦 ≥ 4, 𝑥 − 𝑦 ≤ 0

Name the common region and write down its vertices.

Q6. Solve : 5−2𝑥

3≤

𝑥

6− 5.

Q7. Solve the system of inequalities graphically:

𝑥 + 2𝑦 ≤ 10, 𝑥 + 2𝑦 ≥ 1, 𝑥 − 𝑦 ≤ 0, 𝑥 ≥ 0, 𝑦 ≥ 0.

Q8. Solve the following system graphically and name the vertices of the feasible region

(solution set) along with their coordinates.


𝑥 + 2𝑦 ≤ 10, 𝑥 + 𝑦 ≥ 1, 𝑥 − 𝑦 ≤ 0, 𝑥 ≥ 0, 𝑦 ≥ 0.

Q10. Solve the system of inequalities graphically:

3𝑥 + 2𝑦 ≤ 150, 𝑥 + 4𝑦 ≤ 80, 𝑥 ≤ 15, 𝑥 ≥ 0, 𝑦 ≥ 0.

PERMUTATIONS & COMBINATIONS

Q1. You can go from Delhi to Agra either by car or by bus or by train or by air. In how many

ways can you plan your journey from Delhi to Agra?

Q2. An examination paper consists of 12 questions in two parts, part A has 7 questions and

part B has 5 questions. A candidate is required to answer 8 questions, selecting at least 3 from

each part. In how many ways can he make his selections?

Q3. How many of the natural numbers from 1 to 1000 have none of their digits repeated?

Q4. If 9𝑃5+ 5 9𝑃4

= 10𝑃𝑟 , then find r.

Q5. Find the number of different signals that can be generated by arranging at least two flags

in order (one below the other) on a vertical staff, if five different flags are available.

Q6. How many words each of 3 vowels and 2 consonants can be formed from the letters of

the word “INVOLUTE”?

Q7. If 𝑛𝑃𝑟= 336, 𝑛𝐶𝑟

= 56. Find n and r and hence find 𝑛 − 1𝐶𝑟−1.

Q8. A mathematics paper consists of 10 questions divided into two parts I and II, each part

containing 5 questions. A student is required to attempt 6 question in all, taking at least 2

questions from each part. In how many ways the student select the questions?

Q9. If 𝑛𝐶 5= 𝑛𝐶 7

find n.

Q10. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be

selected if the team has at least one boy and one girl?

SEQUENCES AND SERIES

Q1. The ratio of the A.M. and G.M. of two positive numbers a and b is m : n, show that:

𝑎 ∶ 𝑏 = (𝑚 + √𝑚2 − 𝑛2) ∶ (𝑚 − √𝑚2 − 𝑛2).

Q2. If the 𝑝𝑡ℎ, 𝑞𝑡ℎ and 𝑟𝑡ℎ term of a G.P. are 𝑎, 𝑏, 𝑐 respectively, prove that

𝑎𝑞−𝑟 ∙ 𝑏𝑟−𝑝 ∙ 𝑐𝑝−𝑞 = 1.

Q3. Solve the equation for ‘𝑥’ : 2 + 5 + 8 + 11+. … … . + 𝑥 = 345.

Q4. If 𝑎2 , 𝑏2 , 𝑐2 are in A.P., then show that 1

𝑏+𝑐∙

1

𝑐+𝑎∙

1

𝑎+𝑏 are also in A.P.

Q5. Find the values of ‘k’ for which −𝟐

𝟕 , 𝑘, −

7

2 are in G.P. (geometric progression).

Q6. If m times the 𝑚𝑡ℎ term of an A.P. is equal to n times its 𝑛𝑡ℎ term, show that the (𝑚 + 𝑛)𝑡ℎ term of the A.P. is zero.

Q7. The sum of two numbers is ‘6’ times their geometric mean, show that the numbers are in

the ratio (3 + 2√2) ∶ (3 − 2√2).

Q8. Solve for 𝑥, 1 + 6 + 11 + 16+. … … . + 𝑥 = 148.

Q9. In an increasing G.P., the sum of the first and last term is 66, and product of the second

and last but one term is 128. If the sum of the series is 126, find the number of terms in the

series.

Q10. If 𝑎 + 𝑏 + 𝑐 ≠ 0 and 𝑏+𝑐

𝑎∙

𝑐+𝑎

𝑏∙

𝑎+𝑏

𝑐, are in A.P., then prove that

1

𝑎∙

1

𝑏∙

1

𝑐 are also in A.P.

STRAIGHT LINES

Q1. Find the equations of the lines passing through the point (3, −2) and inclined at an angle

of 600 to line √3𝑥 + 𝑦 = 1.

Q2. Find the equation of the lines passing through the point (−3, 5) and perpendicular to the

line through the points (2, 5) and (−3, 6).

Q3. Find the value of k, if the straight line 2𝑥 + 3𝑦 + 4 + 𝑘 (6𝑥 − 𝑦 + 12) = 0 is

perpendicular to the line 7𝑥 + 5𝑦 − 4 = 0.

Q4. Find the vertices of the triangle formed by the lines 𝑦 − 𝑥 = 0, 𝑦 + 𝑥 = 0, which two

lines are perpendicular to each other?

Q5. If 𝑃 (𝑎, 𝑏) is the mid-point of a line segment between axes. Show that equation of the

line is 𝑥

𝑎+

𝑦

𝑏= 2.

Q6. The vertices of the triangle are 𝐴 (2, 3), 𝐵 (4, −1) and 𝐵 (1, 2). Find the length and

equation of the perpendicular drawn from the point A on side BC.

Q7. Find the equation of the line passing through the point (2, 2), such that the sum of the

intercepts on the axes is 9.

Q8. Find image of the point 𝑃 (−8, 12) with respect to the line mirror 4𝑥 + 7𝑦 + 13 = 0.

Q9. Find the equation of the line through the point (3, 2) which makes an angle of 450 with

the line Find the equation of the lines passing through the point 𝑥 − 2𝑦 = 3.

Q10. If p is the length of perpendicular from origin to the line which makes intercepts a, b on

the axes, prove that 1

𝑝2 =1

𝑎2 +1

𝑏2.

CONIC SECTIONS

Q1. Find the focus, directrix and eccentricity of the parabola 3𝑦2 = 8𝑥.

Q2. Find the length of the axes, coordinates of foci, eccentricity of the conic section

16𝑥2 − 9𝑦2 − 144 = 0.

Q3. Show that 4𝑥2 + 𝑦2 − 8𝑥 + 2𝑦 + 1 = 0 represents an ellipse. Find its eccentricity,

length of latus rectum, coordinates of the foci and the equations of the directrices.

Q4. Find equation of the parabola having vertex at (−1, 1) and focus at (1, 3).

Q5. Find the equation of hyperbola with foci at (0, ± 4) and length of transverse axis is 6.

Q6. Show that the line 3𝑥 + 4𝑦 + 7 = 0 touches the circle 𝑥2 + 𝑦2 − 4𝑥 − 6𝑦 − 12 = 0.

Q7. Find the equation of the circle which passes through the center of the circle

𝑥2 + 𝑦2 + 8𝑥 + 10𝑦 − 7 = 0 and is concentric with the circle

2𝑥2 + 2𝑦2 − 8𝑥 − 12𝑦 − 9 = 0.

Q8. Find the equation of the circle which passes through the origin and cuts off intercepts 3

and 4 on positive part of x-axis and y-axis respectively.

Q9. Find the coordinates of the focus, the equation of directrix, vertex and length of latus

rectum for the parabola 𝑦2 = −12𝑥.

Q10. Show that the equation 𝑦 = 𝑥2 − 2𝑥 + 3 represents a parabola. Find the vertex, focus

and length of latus rectum.

INTRODUCTION TO 3-D

Q1. Three consecutive vertices of a parallelogram ABCD are 𝐴 (3, −1, 2), 𝐵 (1, 2, −4) and

𝐶 (−1, 1, 2). Find the fourth vertex.

Q2. Show that the triangle ABC, with vertices as 𝐴 (0, 7, 10), 𝐵 (−1, 6, 6) and 𝐶 (−4, 9, 6) is

an isosceles right angle triangle.

Q3. A is a point (1, 3, 4) and B is the point (1, −2, −1) A point P moves so that 3𝑃𝐴 = 2𝑃𝐵.

Find the locus of P.

Q4. Show that the points (0, 4, 1), (2, 3, −1), (4, 5, 0) and (2, 6, 2) are the vertices of a

square.

Q5. Find the ratio in which the line segment joining the points (2, 4, 5) and (3, 5, −4) is

divided by the XY-plane.

Q6. Find the ratio, in which the line joining the points 𝑃 (4, 8, 10) and 𝑄 (6, 10, −8) is

divided by XY-plane.

Q7. Find the coordinates of the centroid of the triangle whose vertices are (𝑥1 , 𝑦1 , 𝑧1), (𝑥2 , 𝑦2 , 𝑧2) and (𝑥3 , 𝑦3 , 𝑧3).

Q8. Find the ratio in which YZ-plane divides the line segment joining points (−2, 4, 7) and (3, −5, 8). Also find the coordinates of the point of intersection.

Q9. Using section formula, prove that the three points (−4, 6, 10), (2, 4, 6) and (14, 0, −2)

are collinear.

Q10. A point is on the x-axis. Write its y-coordinates and z-coordinates.

LIMITS AND DERIVATIVES

Q1. Evaluate : lim𝑥 →0

𝑓(𝑥), it is exists, where, 𝑓(𝑥) = {𝑥

|𝑥| 𝑥 ≠ 0

0 𝑥 = 0.

Q2. Find 𝑓′(𝑥) using first principle, where 𝑓(𝑥) = 𝑥 −1

𝑥.

Q3.(i) Find the derivative of cot 𝑥, by using first principle method

(ii) Find the derivative of 𝑓(𝑥) =𝑥

1+tan 𝑥.

Q4.(i) Evaluate : lim𝑥 →1

𝑥15−1

𝑥10−1

(ii) Find derivative of 𝑓(𝑥) = (𝑎𝑥2 + sin 𝑥). (𝑝 + 𝑞 cos 𝑥).

Q5.(i) Find the derivative of 𝑓(𝑥) = √cos 𝑥 , using first principle.

(ii) Evaluate : lim𝑥 →3

𝑥4−81

2𝑥2−5𝑥−3

Q6. Find the derivative of 1

𝑎𝑥2+𝑏 , with respect to x.

Q7. For the function 𝑓(𝑥) = {𝑎 + 𝑏𝑥, 𝑥 < 14 , 𝑥 = 1𝑏 − 𝑎𝑥, 𝑥 > 1

Lt𝑥 →1

𝑓(𝑥) = 𝑓(1). Find the possible value of a

and b.

Q8. Find Lt𝑥 →1

[𝑥2+1

𝑥+100].

Q9. Find the derivative of 𝑓(𝑥) = 10𝑥, using first principle.

Q10. Evaluate : Lt𝑥 →0

cos 2𝑥−1

cos 𝑥−1.

STATISTICS

Q1. Find the mean and variance for the following frequency distribution:

Classes 0-10 10-20 20-30 30-40 40-50

Frequency 5 8 15 16 6

Q2. Find standard deviation (S.D.) for the data:

Wages up to (in Rs) 15 30 45 60 75 90 105

No. of workers 12 13 65 107 157 202 222

Q3. Calculate the standard deviation for the following:

Age in years 20-30 30-40 40-50 50-60 60-70 70-80 80-90

No. persons 12 13 65 107 157 202 222

Q4. Find the mean and variance for the following data:

Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210

Frequencies 2 3 5 10 3 5 2

Q5. Calculate mean, variance and standard deviation for following data:

Classes 30-40 40-50 50-60 60-70 70-80 80-90 90-100

Frequencies 3 7 12 15 8 3 2

Q6. The mean and standard deviation of 20 observations are found to be 10 and 2

respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the

correct mean and standard deviation if wrong observation 8 is replaced by 12.

Q7. The mean and standard deviation of 100 observations were calculated as 40 and 5.1

respectively by a student who took by mistake 50 instead of 40 for one observation. What are

the correct mean and standard deviation?

Q8. Find mean, variance and standard deviation using short cut method.

Height in

(cm)

70-75 75-80 80-85 85-90 90-95 95-100 100-105 105-110 110-115

No. of

children

3 4 7 7 15 9 6 6 3

Q9. Calculate the mean deviation about median for the following data:

Classes 0-10 10-20 20-30 30-40 40-50 50-60

Frequencies 6 8 14 16 4 2

Q10. The diameters of circles (in mm) drawn in a design are given below:

Diameters 33-36 37-40 41-44 45-48 49-52

No. of circles 15 17 21 22 25

Calculate the standard deviation and mean diameter of the circles

PROBABILITY

Q1. A card is drawn from a pack of 52 cards.

(i) How many points are there in the sample space?

(ii) Calculate the probability that card is an ace of spade.

(iii) Calculate the probability that the card is

(a) an ace

(b) a black card

Q2. A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face

with number ‘3’. If die is rolled once, determine.

(i) P (2)

(ii) P (1 or 3)

(iii) P (not 3)

Q3. Two cards are drawn from a well shuffled pack of 52 cards. Find the probability:

(i) one is black, other is red

(ii) both are king

(iii) both are face cards. (Given : Twelve face cards)

Q4. What is the probability that:

(i) a non-leap year has 53 Tuesday?

(ii) a leap year has 53 Wednesday?

(iii) a leap year has 53 Friday and 53 Saturdays?

Q5. A coin is tossed twice, then find the probability of getting at at-least one head.

Q6. A card is drawn from a well shuffled deck of 52 cards, then find the probability of red

king card.

Q7. A bag contains 9 balls of which 4 are red, 3 are blue and 2 are yellow. The balls are

similar in shape and size. A ball is drawn at random from the bag. Calculate the probability

that it will be:

(i) red

(ii) not blue

(iii) either red or blue

Q8. A die is rolled. Let ‘E’ be the event “die shows prime number” and ‘F’ be the event “die

shows even number”. Are E and F mutually exclusive?

Q9. In a single throw of tow dice, what is the probability of getting a total of 8 on the faces of

the dice?

Q10. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both. If

one student is selected at random, find the probability that

(i) the student opted for NCC or NSS

(ii) the student has opted neither NCC nor NSS.

Case Study Problems


TERM-II CLASS-XI 2020-21

SUBJECT: INFORMATICS PRACTICES REVISION SHEET

UNIT-1: INTRODUCTION TO COMPUTER SYSTEM

1. Expand the term EPROM.

2. Name any tow utility softwares.

3. Define gigabyte and terabyte.

4. What is the meaning of term non-volatile primary memory?

5. Write memory type and storage of second generation computers.

6. What is the use of parallel processing and superconductors in fourth generation of computers.

UNIT-2: INTRODUCTION TO PYTHON

1. Why is considered as cross platform?

2. Write the areas where Python can be used.

3. Why Python is considered not strong on type-binding?

4. Name the modes for writing Python code.

5. How is a keyword different from an identifier?

6. Name any two numeric data types.

7. What do you mean by a lexical unit?

8. Write any two naming rules for creating a variable.

9. What will be the output of the following code?

a, b = 9,9

a, b = b+2, a+3

10. Write a program to calculate profit from the sales you have made.

11. What is the error in following code? Write corrected code and mentions the corrections by

underlining them:

Number = Input(“Enter a number”

DoubletheNumber = Number/2

Print (Double)

12. What are comments used for?

13. Give example of complex numbers in Python.

14. What do you mean by index in Python?

15. How is a list different from the dictionary? Give example to show the difference.

16. What do you mean by value and type of an object?

17. What is the difference between ‘/’ and ‘//’ in Python?

18. What is the purpose of if statement? Name the different forms of if statement?

19. Write a Python program to display lowest of three numbers, create its flowchart also.

20. Write a Python program to arrange three numbers entered by a user in ascending order.

21. Give an example to show the use of range( ) function.

22. Write the output of following code:

x=10

y=0

while x>y:

print(x,y)

x=x-1

y=y+1

23. What is a list and how a list can be traversed?

24. Write Python statement to replicate following list 3 times:

[1,5,9]

25. Write example code of append and extend methods for list manipulation.

26. Write a program to find the mean of a given list of numbers.

27. Write a program to search for an element in a given list of numbers.

28. Write a program to find the second largest number of a list of numbers.

29. How is a list different from the dictionary?

30. Write any two ways of creating dictionaries.

31. Write a Python program to create a dictionary containing names of runners as keys and number

of their gold medals as values.

32. What do you mean by pretty printing a dictionary?

33. Write an example to show the use of update( ) method of a dictionary.

UNIT-3: DATABASE CONCEPTS AND THE STRUCTURED QUERY LANGUAGE

1. What do you mean by a Database Management System and what are its advantages?

2. Write about Foreign key and Candidate key?

3. What is the importance of Referential Integrity in a DBMS?

4. Which are the different categories in which SQL commands can be classified?

5. Write about different types of Constraints.

6. Answer the question based on the table VOTER given below.

(i) Write the command to delete all the rows of particular voter from the table

voter where voter ID between 10 and 20.

(ii) Delete the table physically.

(iii) Write the ‘create table’ command for creating the table specification given below.

7. Write the queries below:

1). Show Name, Department, Salary of the employees whose father name starts with

letter ‘S’.

2). Show Name, Date of Joining of employees who don’t get any commission.

3). Display the Name, Father name, Commission of employees who are not from

management or accounts department.

4). Display Empno, Name, Department of employees who are getting salary more than

11999 sorted by salary.

5). Display Name, Salary, Commission of employees who are from sales department and

getting salary between 10000 and 20000.

poem: childhood

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