| 11 | 3 | 49 |
| 5 | 19 | ? |
| 7 | 13 | 100 |
| 1 | 4 | 9 | more...
Introduction
In this chapter students will learn the features of cube and Dice and also learn how to solve problems with the help of Cube and Dice.
CUBES:
A cube is a three dimensional figure, having 8 corners, 6 surfaces and 12 edges. If a cube is painted on all of its surfaces with any colour and further divided into various smaller cubes, we get the following results.
 
(a) Smaller cubes with three surfaces painted will be present on the comers of the big cube.
(b) Smaller cubes with two surface painted will be present on the edges of the big cube.
(c) Smaller cubes with one surface painted will be present on the outer surfaces of the big cube.
(d) Smaller cubes with no surface painted will be present inside the big cube.
If a cube is painted on all of its surfaces with a color and then divided into smaller cubes of equal size, then after separation, number of smaller cubes so obtained will be calculated as under:
Number of smaller cubes with three surfaces painted = 8
Number of smaller cubes with two surfaces painted \[=(n-2)\times 12\]
Number of smaller cubes with one surface painted \[={{(n-2)}^{2}}\times 6\]
Number of smaller cubes with no surfaces painted \[={{(n-2)}^{3}}\]
Where n = No. of divisions on the surfaces of the bigger cube
\[=\frac{length\text{ }of\text{ }edge\text{ }of\text{ }big\text{ }cube}{length\text{ }of\text{ }edge\text{ }of\text{ }one\text{ }smaller\text{ }cube}\]
TYPE-I:
A cube is painted on all of its surfaces with a
single colour and then divided into various smaller
cubes of equal size.
DIRECTIONS: A cube of side 4 cm. is painted black on all of its surface and then divided into various smaller cubes of side 1 cm. each. The smaller cubes so obtained are separated.
Total cubes obtained \[=\frac{4\times 4\times 4}{1\times 1\times 1}=64\]
Here, \[\text{n=}\frac{\text{side of big cube}}{\text{side of small cube}}\text{=}\frac{\text{4}}{\text{1}}\text{=4}\]
 Application
 Format
The Principal Date
ABC School
Delhi
Subject
Respected Sir/ Madam
(Body in two or three paragraph)
(i)
(ii)
(iii)
Yours Obediently
XYZ
2. Write an application to the principal for 5 days' leave that you have already taken due to illness.
The principal October 8, 2011
Ring Bell school
Delhi
Subject: Leave application
Respected Madam,
With most greet and respect I beg to state that I am a student of your school of class Xth B. I had been suffering from fever for 5 days. The doctor had advised me complete bed rest. Thus I was absent from school from 2/ 10/ 2011 to 6/10/ 2011.Therefore, I am requesting you to kindly grant me leave for five days.
I shall be obliged to you.
Yours obediently
Zacob
 The body of a letter to the Editor is given with four blanks I, II, III and IV which should be filled by statements P, Q, R and S:
Through the column of your esteemed newspaper _____________I_____________ of terrorism. Present world has been facing many problems, _______II________. Almost every day there is a blast or attack taking place all over the world. People are afraid of coming out of their houses. Once they come out, they don't know whether they will be return back safely or not. It is a big challenge in front of us. _________III_______. I hope that the governments and the civilized people of the world will work collectively_________IV_________ so that this beautiful world can be made much safer place to live in.
Yours faithfully
Smith
P: we need to address its root cause to eradicate it
Q: to solve this problem
R: I would like to express my views on the issue
S: terrorism is one of them
Choose your answer from the given options:
I II III IV
(A) S R Q P
(B) R S P Q
(C) P S R Q
(D) Q R P S
Answer: (B)
The body of a letter to the Editor is given with four blanks I, II, III and IV which should be filled by statements more...  Types of Letter
Letters can be divided into two types, which are as follows:
(i) Formal letters
(ii) Informal letters
 Formal Letters
Formal letters are of following types:
(i) Official Letter
(ii) Letter to the Editor
(iii) Business Letter
(iv) Application
Informal Letters
These letters are written to:
(i) Friends
(ii) Parents
(iii) Relatives
Format (Informal Letter)
Self Address : Date(dd/mm/yy)
Dear ABC
(i) Introduction
(ii) Main content
(iii) Closing
Yours lovingly/ sincerely
XYZ
C-35
Thomsan Street
London
25th October, 2011
Dear James,
I hope this letter will find you in the best of your health and high spirits. As you know that our annual exam is approaching, so through this letter. I am going to inform you about my preparation for the exam. From the very beginning, I have been paying proper attention towards my studies. So my preparation for the exam is very good. I have almost completed all the subjects. I need to revise properly. This time my expectation is high for the exam. You also tell me about your preparation.
Rest is ok.
Please convey my regards to elders and love to youngers.
Yours Sincerely,
Serena
Format (Formal Letter)
Self Add: Date(dd/mm/yy)
Designation and address of the Receiver
Dear/ Respected Sir
Subject:
Body in 3 paragraphs)
(i) Introduction
(ii) Content
(iii) Closing
Yours Faithfully
XYZ
(i) Write a letter to the manager of electricity board complaining about irregular supply of electricity in your area.
C ? 35 15thOctober, 2011
CedarAvenue
Mumbai
The Manager
Electricity Board
Veer Savarkar
Mumbai
Subject: Complaining against irregular supply of electricity.
Respected Sir,
With due respect I would like to draw your kind attention towards irregular supply of electricity in our area. The electricity supply is very irregular more...  Presentation of a Letter
The presentation of the letter can be hand-written for less formal letters that are addressed to friends and family members, especially thank-you letters. In the case that you have illegible handwriting, you may want to consider typing the letter in these cases, although proper etiquette dictates against this type of behavior.
Formal letters which are written on behalf of businesses to or professional contacts should remain typewritten and grammatical and spelling error free. These types of letters should be legible and professional and therefore typing the letter is one of the most effective ways to ensure that the letter demonstrates a professional appearance through the entire course of the letter, thereby creating a positive impression on the recipient of the letter.
As well as outward presentation, it is important to determine the tone which will be written in the letter, including a professional tone or a tone that will be taken with friends or family members in a more informal setting. Read through the letter once it has been completed to ensure that the tone remains the same. The tone can be adjusted based on the language which is used through the letter, as well as the greetings (familiar as opposed to formal).
 Introduction
The art of writing a letter takes practice, knowledge about proper form and the ability to put into words your feelings, thoughts, and/or ideas. If you learn the basic parts of a letter, it will help you to create letters for a variety of occasions.
Parts of a Letter
(i) Your address
At the top of your letter, you will put your address, so the reader will know where to send their reply to.
(ii) Date
Put the date on which the letter was written in the format, Month Day Year i.e. August, 15, 2011.
(iii) The Greeting
The greeting will address the individual that the letter is being sent to. This is usually completed in the form of "Dear Sandeep" or "Hi Reema", for less formal letters.
(iv) The introductory Paragraph
The first paragraph will generally outline the purpose for the letter and the reason that the letter is being sent. This can address any issues that are outstanding and is used to set the tone for the entire rest of the letter. In this first paragraph, the summary of the letter can be found and the intentions which will be displayed through the rest of the letter should be outlined. From the first paragraph of the letter, the individual should be able to note the tone of the letter.
(v) The Body
The body of the letter will expand upon the introductory paragraph and the individual can extend their thoughts and feelings further when it comes to the letter. The body of the letter can be anywhere from multiple pages for personal letters, to one page or two pages for most business letters and other types of proposals.
(vi) The Closing
In the closing of the letter, the individual will close the letter and finish any thoughts that have been mentioned. The closing of the letter comes in various forms; from yours truly, for those individuals that are familiar with one another, to a traditional sincerely which is a versatile closing that can be used in a variety of letters detailing many situations. (vii)
 Introduction
A notice is written in order to inform people or pupils (in a school) about an event or an activity.
It can be about a competition, an exhibition, an inauguration to take place in near future, or any other activities like an excursion, a meeting or a show.
Points to Keep in Mind while writing Notice
(i) To the point
A good notice is always to the point and leaves no scope for further enquiries.
(ii) Language
Language of notice should always be formal.
(iii) Necessary details
A notice should contain all the necessary details such as:
1. Name of the issuing agency (school, etc.)
2. Subject and date of issue/release of the notice
3. Event (what?)
4. Date/time/duration (when?)
5. Place/Venue (where?]
6. Authorized signatory: Name and signature
(iv) Setting
Notice should always be enclosed in a box.
 Format
Below given is the format usually followed in writing notices.
ABC School 15th September, 2011
Notice
Heading
Body
Name
Designation
Example: Your school is going to celebrate its annual day. Write a notice to the school notice board informing the students about it. Give all necessary details.
Modern School 15th September, 2011
Delhi
Notice
Annual Day Celebration
It is hereby informed that school is going to celebrate its annual day as per schedule,
Date - 25thSeptember,2011
Time - 4 PM to 9 PM
Venue more... 
Identify the types of clause in the following sentences:
 James asked his younger brother why he came here. (Subordinate Clause)
Answer: Why he came here
Don't call while I am crossing the road. (Principal Clause)
Answer: Don't call
This is the boy who has got highest marks in the examination. (Sub. Adjective Clause)
Answer: Who has got highest marks in the examination?
He will read and I will play (Coordinate Clause)
Answer: i will play
Identify the types of clause in the following questions:
The teacher asked the student why she came so late. (Subordinate Clause)
(A) Why she came so late (B) So late
(C) The teacher asked (D) The student
(E) None of these
Answer: (a)
Explanation: Subordinate clause is 'whey she came so late'.
I am not aware where he is going. (Principal Clause)
(A) He is going (B) I am not aware where
(C) I am not (D) Where he is
(E) Going
Answer: (b)
Explanation: A Clause which does not depend on any other clause is called a Principle Clause.
 Kinds of Subordinate Clauses
There are three kinds of Subordinate Clauses:
1. Noun Clause
2. Adjective Clause
3. Adverb Clause
 Noun Clause
A clause which acts as a noun or which is used in place of a noun is called a Noun Clause.
To identify the Noun Clause, a question is formed by adding 'what' to the main verb and the clause in which we get its answer is the Noun Clause.
 Subject to a Verb
If any clause comes in place of the subject of a verb then that Noun Clause is a Subject to the verb.
Object to a Verb
If any clause in a sentence takes the place of an object of a Finite Verb, then that
Noun Clause is called an object to the verb.
Object to an Infinite
If in a sentence, a clause begins after the infinite and which acts as an object, then that Noun Clause is an object to the infinite.
Object to a Preposition
If any Clause which comes after the preposition in the form of an object, then that
Noun Clause is an object to the preposition.
Object to a Participle
If any clause comes after any participle and acts as an object, then that Noun
Clause is an object to the participle.
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