Numerical Based On Square ( Mathematics )

Q. Find the perimeter of a square with the following area:

1. 81 m
2. 36 cm
3. 49 mm
4. 16 dm
5. 4 µm
6. 9 km
7. 25 inches
8. 64 nm

Sol.
1. Area of the Square = 81 m         

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 81 m
               side   =  √ 81 m
                        =  9 m
    ∴   Perimeter of the Square = 4 x ( side ) = 4 x 9 m = 36 m

2. Area of the Square = 36 cm         

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 36 cm
               side   =  √ 36 cm
                        =  6 cm
    ∴   Perimeter of the Square = 4 x (side) = 4 x 6 cm = 24 cm

3. Area of the Square = 49 mm
        

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 49 mm
               side   =  √ 49 mm
                        =  7 mm
    ∴   Perimeter of the Square = 4 x side = 4 x 7 mm = 28 mm

4. Area of the Square = 16 dm
         

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 16 dm
               side   = √ 16 dm
                        = 4 dm
    ∴   Perimeter of the Square = 4 x side = 4 x 4 dm = 16 dm

5. Area of the Square = 4 µm
         

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 4 dm
               side   =  √ 4 dm
                        = 2 dm
    ∴   Perimeter of the Square = 4 x side = 4 x 2 dm =8 dm

6. Area of the Square = 9 km
       

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 9 km
               side   =  √ 9 km
                        =  3 km
    ∴   Perimeter of the Square = 4 x side = 4 x 3 km = 12 km

7. Area of the Square = 25 inches
         

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 25 inches
               side   =  √ 25 inches
                        =  5 inches
    ∴   Perimeter of the Square = 4 x side = 4 x 5 inches = 20 inches

8. Area of the Square = 64 nm
         

    Also, Area of the Square = ( side )²
      ∴   ( side )²  = 64 nm
               side   =  √ 64 nm
                        =  8 nm
    ∴   Perimeter of the Square = 4 x side = 4 x 8 nm = 32 nm


Q. Find the area of a square with the following perimeter:

1. 4 m
2. 8 cm
3. 12 mm
4. 16 dm
5. 36 µm
6. 40 km
7. 44 inches
8. 48 nm

Sol. 
1. Perimeter of the Square = 4 m 
    Also, Perimeter of the Square = 4 x ( side ) 

      ∴  4 x ( side ) = 4 m
                   side  =  ( 4/4 ) m
                            =  1 m
    ∴    Area of the Square = ( side )² = ( 1 x 1 ) m = 1 m

2. Perimeter of the Square = 8 cm 
    Also, Perimeter of the Square = 4 x ( side ) 

      ∴  4 x ( side ) = 8 cm
                   side  =  ( 8/4 ) cm
                            =  2 cm
    ∴    Area of the Square = ( side )² = ( 2 x 2 ) cm = 4 cm

3. Perimeter of the Square = 12 mm
    Also, Perimeter of the Square = 4 x ( side ) 

      ∴  4 x ( side ) = 12 mm
                   side  =  ( 12/4 ) mm
                            =  3 mm
    ∴    Area of the Square = ( side )² = ( 3 x 3 ) mm = 9 mm

4. Perimeter of the Square = 16 dm
    Also, Perimeter of the Square = 4 x ( side ) 

      ∴  4 x ( side ) = 16 dm
                   side  =  ( 16/4 ) dm
                            =  4 dm
    ∴    Area of the Square = ( side )² = ( 4 x 4 ) dm = 16 dm

5. Perimeter of the Square = 36 µm
    Also, Perimeter of the Square = 4 x ( side ) 

      ∴  4 x ( side ) = 36 µm
                   side  =  ( 36/4 ) µm
                            =  9 µm
    ∴    Area of the Square = ( side )² = ( 9 x 9 ) µm = 81 µm

REDOX REACTIONS

REDOX REACTIONS
Reactions which involve change in oxidation number of the interacting species.

OXIDATION
Addition of oxygen/electronegative element to a substance or removal of hydrogen /electropositive element from a substance.
                                                                       OR
Loss of electron(s) by any species
                                                                       OR
An increase in the oxidation no. of the element in the given substance.


OXIDISING AGENT
Acceptor of electron(s)
                                                                       OR
A reagent which can increase the oxidation number of an element in a given substance are called as oxidants.

REDUCTION
Removal of oxygen/electronegative element from a substance or addition of hydrogen/electropositive element to a substance.
                                                                       OR      
Gain of electron(s) by any species
                                                                       OR
An decrease in the oxidation no. of the element in the given substance.

REDUCING AGENT

Donor of electron(s)

                                                                       OR

Oxidation number denotes the oxidation state of an element in a compound ascertained according to a set of rules formulated on the basis that electron pair in a covalent bond belongs entirely to more electronegative elements.

8 Rules for calculation of the oxidation number

1.  In elements, in the free or the uncombined state, each atom bears an oxidation number of zero

• Ex:.  O₂  ,  CL₂  , O_{3  ,}  P₄  ,  S_{8  ,} Na , Mg , Al

2.  For ions composed of only one atom, the oxidation number is equal to the charge on the ion

• Ex:.  oxidation number of Na+ is +1
• Ex:.  oxidation number of Mg2+  is +2

3.  All alkaline earth metals have an oxidation number of +2

4.  Aluminium is regarded to have an oxidation number of +3 in all of its compounds.

5.  The oxidation number of oxygen in most of the compounds is -2. 

     In peroxides ( e.g., H₂O_2, Na₂O₂ ) each oxygen atom is assigned an oxidation number of -1

     In super-oxides ( e.g., KO₂, RbO₂) each oxygen atom is assigned an oxidation number of - (1/2)

     When oxygen atom is bonded to fluorine ( e.g., OF_2, O₂F₂ ) the oxygen is assigned to have a oxidation number of +2 and +1 respectively.
6.  The oxidation number of hydrogen is +1, except when it is bonded to metals in binary compounds. For example, in LiH, NaH, CaH₂ its oxydation number is -1
7.  In all its compounds, fluorine has an oxidation number of -1
     Other halogens ( Cl, Br and I) also have an oxidation number of -1 as halide ions in their compounds
8.  The algebraic sum of the oxidation number of all the atoms in a compound must be zero.
     In poly-atomic ion, the algebraic sum of all the oxidation numbers of atoms of the ion must equal the charge on the ion.
     Thus, the sum of oxidation number of three oxygen atoms and one carbon atom in the carbonate ion, ( CO₃ )2-  must equal -2.

CH 1 Reproduction In Organisms

1. Life Span
The period from birth to the natural death of an organism is called its life span.
Examples : 1. Butter Fly ( 1-2 weeks )  2. Tortoise ( 100-150 years )

2. Clone

The individual which are morphologically and genetically similar to each other and are exact copies of their parents are called clones. 

Examples : 1. Amoeba ( Produced by binary fission ), 2. Yeast ( Produced by budding )

3. Reproduction

The biological process in which in which an organism gives rise to young ones ( offspring ) similar to itself, is called reproduction.

→ it enables the continuity of the species, generation after generation.

→ factors affecting reproduction

     1. Organism Habitat

     2. Internal Physiology 

 

All toppers of cbse class 12th 2013

All India Toppers 2013

Paras Sharma   99%
School  - Lancer Convent Senior Secondary School ( Outer Delhi )
Stream - Commerce stream
mathematics - 100, accountancy- 100, economics - 100 and business studies - 100 and  English 95.
He scored 495 out of 500.

Sopan Khosla  99%
School  - DPS ( Jabalpur,   Madhya Pradesh ) 
Stream - Science stream

All Delhi Govt. School Toppers 2013

Ankit Saini   97.4%
School  - Rajkiya Pratibha Vikas Vidyalaya 

Stream - Commerce stream

Lalit Lakra   96.2%
School  -  SV school ( Paschim Vihar, Delhi) 
Stream - Science stream

Momina Sheikh  95.2%

School - Shakti Nagar

Stream - Arts stream

Diksha  95.2%

School - Nangloi

Stream - Arts stream

Taruna  92.8%

Stream - vocational stream

CBSE Class 12th Result 2013

CBSE board class 12th results 2013 has been declared by the Central Board of Secondary Education (CBSE) on 27th May, Monday as announced earlier.

In the CBSE Class 12th Result 2013 declared on Monday, Chennai once again put up the best performance with a pass percentage of 91.83.

The results this year in particular assumes significance for students who aspire to make it to the IITs as weightage is given for the Class XII performance.

Accordingly, the cut off score for the top 20 percentile will be 391 for general category students this year, a statement issued by the CBSE said. For OBC, it will be 389, SC 350 and ST 338.

Rank holders in the JEE advance under the new format must be among the top 20 performers for admission to the IITs.

Over 82 per cent students cleared the 2013 Class XII CBSE examinations, with girls once again outshining the boys and the Chennai region beating others in the overall pass percentage.

The results were declared across the country today, with the total pass percentage standing at 82.10 per cent, an increase of about two per cent over the last year, said a statement. 

In all, 9,44,721 students registered for the Class XII examination this year, which was also an increase of 15.81 per cent over 2012.

Girls continued to fare better than boys with 87.98 per cent clearing the exam as compared to 77.78 per cent boys.

The results of CBSE 12th 2013 are now available on the official website of CBSE board athttp://cbseresults.nic.in/.

In addition to that, the candidates can also check their CBSE board class 12th results 2013through SMS as CBSE has provided different numbers for all service holders, those are:

• For MTS users: Type: cbse12 rollno, Send SMS to 543216
• For BSNL Users: cbse12 rollno, Send SMS to 57766
• For Tata Teleservice (Indicom, Docomo): Type cbse12 rollno, Send SMS to 54321, 51234,5333300
• For Aircel users: Type cbse12 rollno, Send SMS to 5800001
• For Airtel users: Type cbse12 rollno, Send SMS to 5207011
• For NIC users: Type cbse12 rollno, Send SMS to 9212357123
• For Vodafone users: Type cbse12 rollno, Send SMS to 50000
• For Jagran users: Type cbse12 rollno, Send SMS to 57272

The Central Board of Secondary Education had conducted the CBSE class 12th examination from March1, 2013 to April 17, 2013 in which lakhs of students appeared and were waiting for their CBSE 12th results 2013 anxiously for their results since then.

The CBSE board class 12th results 2013 are considered even more important as it opens the gates for the students to take admission for further education as many states including Bihar, Meghalaya, Assam, Kerala, Karnataka, Tamil Nadu and Rajasthan have already declared their results of class 12th board.

Moreover, the results of AIEE JEE (Main) exam has already been declared by CBSE and the declaration of CBSE class 12th results would enable the students admission to IIT, NIT and other engineering institutes which would begin after the declaration of class 12th results by CBSE.

Many schools including Kendriya Vidyalayas, Jawahar Navodaya Vidyalayas, private schools, Government Schools, Independent Schools and Central Tibetean Schools are affiliated from CBSE at present and is considered to be one of the biggest exam of the country.

To Check CBSE Class 12th results 2013: Click here

Delhi: CBSE Chairman Vineet Joshi has said that students now get a chance to verify their marks. The candidate can either apply online or download the offline form. However, the request can be made only after 31 days of declaration of the result on the internet.

 

Candidates applying online should send the printout of page generated on submission of form along with a demand draft of requisite fee to the regional office concerned. Candidates of Delhi region can also deposit fee at designated Schools of Delhi Region.

 

Compartment examinations from 6th July 

 

The compartment examinations of High School will be held on July 16. Students can obtain forms from the DIOS office. The first chance compartmental examination will be held on 16th July 2013. Regular candidates are required to route their requests through their respective schools. The institutions must ensure that the list of compartmental candidate reaches the respective regional offices with fee upto 21.06.2013 or with late fee of Rs 10/- per day upto 29.06.2013.