CBSE - Class 6-12 - Mathematics - Important Formulas

Mathematics - Important  Formulas 

eduvictors.com has added a new section "Mathematics" and has compiled important formulas on different topics.

Here is the list of Mathematics formulas:

1. Algebra Formulas

⓵ Polynomials
⓶ Fractions
⓷ Algebraic Identities
⓸ Exponents
⓹ Roots

CBSE Class 10 - Maths - Quadratic Equations - Summary

Quadratic Equations - Summary

① A polynomial of degree 2 is called quadrilateral polynomial. The general form of a quadrilateral polynomial is ax² + bx+ c, where a, b, c are real numbers such that a ≠ 0 and x is a real variable.


② If p(x) = ax²  + bx + c, a ≠ 0 is a quadratic polynomial and α is a real number, then p(α) = aα² + bα + c is known as the value of the quadratic polynomial p(x).

③ A real number α is said to be a zero of the quadratic polynomial p(x) = ax²  + bx + c, if p(α) = 0.

④ If p(x) = ax²  + bx + c is a quadratic polynomial,then p(x) = 0 i.e. ax²  + bx + c = 0, a ≠ 0 is called a quadratic equation.

⑤ A real number α is said to be root of the quadratic equation ax²  + bx + c = 0, if aα² + bα + c = 0.
In other words, α is a root of ax²  + bx + c = 0 if and only if α is zero pf the polynomial p(x) = ax²  + bx + c.

Class 8 - Our Pasts3 - When People Rebel 1857 and After (Q and A)

When People Rebel 1857 and After

Begum Hazrat Mahal (Awadh)
Women like Rani Laxmi Bai, Hazrat Mahal took an active part in 1857 revolt.

Q & A based on NCERT Chapter

Q1: What was the state of Nawabs and Kings during mid-eighteenth century?

Answer:
ⓐ Nawabs and kings had seen their power erode.
ⓑ They gradually lost their authority and honour.
ⓒ Their freedom have been reduced and their forces were disbanded.
ⓓ Their revenues and territories taken away by stages.


Q2: What was the demand of Rani Lakshmibai of Jhansi that was refused by the British?

Answer: After the death of her husband, Rani Lakshmibai of Jhansi wanted the East India Company to recognise her adopted son as the heir to the kingdom. This demand was refused by the British. Finally, the Company annexed the kingdom as per the Doctrine of Lapse.


Q3: What plea of Nan Saheb was turned down by the East India Company?

Answer: Nana Saheb was the adopted son of Peshwa Baji Rao II. He pleaded that he would be given his father’s pension when the latter died. However, the Company, confident of its superiority and military powers, turned down his plea.


Q4: Who was the Governor General when Awadh was annexed in 1856?

Answer: Dalhousie


Q5: How was Awadh annexed by the East India company?

Answer: In 1801, a subsidiary alliance was imposed on Awadh. In 1856 it was taken over by the company on the pretext of misgovernace and poor administration.

Class 8, 10: Science - Uses of Some Common Metals and Non-Metals

Uses of Some Common Metals and Non-Metals

USES OF SOME COMMON METALS

Metal	Main Uses
Iron	Bridges, Train tracks, Construction Bars, Steel, Engine Parts, Iron sheets etc.
Copper	Electrical Wires, Utensils, Coins etc.
Aluminium	Electric Wires, Utensils, Airplanes, Metallic Paints, Foil for packaging etc.
Silver	Jewellery, Electroplating, photography, Utensils, Coins, silvering of mirrors etc.
Gold	Jewellery and Decorations, Coins
Lead	Batteries, Alloys, Paints, Alloys like solder, Protective screen for X-Rays etc.
Mercury	Thermometers, Barometers, Dental amalgams etc.

CBSE Class 9 - English (Comm.)- SA1- Sample Question Paper (2016)

CBSE Class 9 - English (Comm.)- SA1- Sample Question Paper (2016) 

CBSE Class 9 - Mathematics- SA1- Sample Question Paper (2016)

CBSE Class 9 - Mathematics- SA1- Sample Question Paper (2016) 

CBSE Class 10 - Science- SA1- Sample Question Paper (2016)

CBSE Class 10 - Science- SA1- Sample Question Paper (2016) 

Class 6 - Our Pasts - WHAT BOOKS AND BURIALS TELL US (Q and A)

Class 6 

Our Pasts 

WHAT BOOKS AND BURIALS TELL US 

Q & A based on NCERT Chapter

Megalith with port holes called cists

Q1: How many Vedas are there? Name them.

Answer: There are four Vedas. These are:
1. The Rigveda
2. The Samveda
3. The Yajurveda
4. The Atharveda


Q2: Name the oldest Veda.

Answer: The Rigveda. It was composed 3500 years ago.


Q3: Name the plant mentioned in the Rigveda which was used to prepare a special drink.

Answer: Soma


Q4: In which language The Rigveda was written?

Answer: Vedic Sanskrit


Q5: Give examples of Indo-European languages.

Answer: Sanskrit, Assamese, Gujarati, Hindi, Kashmiri, English, German

CBSE Class 12 Business Studies - Capital Market vs Money Market

Capital Market vs Money Market

Important Differences

Basis	Capital Market	Money Market
1. Participants	Individual Investors, Financial Institutions, Banks, Foreign Investors, Corporate Groups etc.	reserve Bank Of India, Commercial Banks, Financial Institutions, Mutual Fund Houses, Corporate Groups. Individual Investors are not allowed to participate.
2. Instruments Traded	Bonds, Debentures, Equity Shares, Preference Shares etc.	Commercial Papers, Treasury Bills, Certificates of Deposits etc.
3. Investment Outlay	Value of units of security is low, t does not require huge financial outlay.

CBSE Class 10 - Real Numbers Problems on Euclid's Division Algorithm(2016)

Real Numbers Problems on
Euclid's Division Algorithm(2016)

Q1(CBSE 2012): Using Euclid’s division algorithm, find the HCF of 240 and 228.

Answer: By Euclid’s division algorithm,
⇒ 240 = 228 × 1 + 12
⇒ 228 = 12 × 19 + 0
∴ HCF (240, 228) = 12


Q2(CBSE 2014): The length, breadth and height of a room are 8m 25 cm, 6m 75 cm and 4 m 50 cm respectively. Find the length of the longest rod that can measure the three dimensions of the room exactly.

Answer:
∵ 1m = 100 cm
∴ 8 m 25 cm = 825 cm
6 m 75 cm = 675 cm
4 m 50 cm = 450 cm
The length of the longest rod = HCF(825, 675, 450)
⇒ 825 = 675 × 1 + 150
675 = 150 × 4 + 75
150 = 75 × 2 + 0
∴ HCF(825, 675) = 75
450 = 75 × 6 + 0
∴ HCF(450, 75) = 75
∴ HCF (825, 675, 450) = 75×
Thus, the length of the longest rod is 75 cm.

Q3(NCERT Exemplar): Write whether every positive integer can be of the form 4q + 2, where q is an integer.Justify your answer.

Answer: No, every positive integer cannot be expressed as only of the form 4q + 2.

CBSE Class 10 - Social Science- SA1- Sample Question Paper (2016-17)

CBSE Class 10 - Social Science- SA1- Sample Question Paper (2016) 

CBSE Class 10 - Maths (SA1) - Trigonometric Identities

CBSE Class 10 - Maths (SA1) - Trigonometric Identities

CBSE Class 9 - Science- SA1- Sample Question Paper (2016)

CBSE Class 9 - Science- SA1- Sample Question Paper (2016) 

CBSE Class 10 - Maths - Polynomials (SA1) - Few Questions from NCERT Exemplar

POLYNOMIALS 

(Questions and Answers from NCERT Exemplar)

 

Here follows few questions that have asked in previous examination papers.

CBSE Class 9 - Science - SA1 - IMPROVEMENT IN FOOD RESOURCES - BEE KEEPING (Q and A)

IMPROVEMENT IN FOOD RESOURCES
BEE KEEPING

Q & A

image courtesy: openclipart

Q1: Name the insect which produces food eaten by man?

Answer: Honey bee is the only insect that produces food eaten by man. It generates honey which has medicinal, nutritional and cosmetic value.


Q2(CBSE 2012): What are the common names of Apis dorsata, Apis Florae and Apis cerena Indica?

Answer: A. dorsata : Rock bee
A. Flora   : Little bee
A. cerena Indica: Indian bee


Q 3(CBSE 2012): Name the talian bee variety imported to India for honey? State the reasons for this?

Answer: Apis mellifera: Italian bee variety has also been brought in to increase yield of honey for the following reasons:
1. These bees have high honey collecting capacity
2. They sting less
3. Stay in beehive for longer periods.
4. Breeds very well.


Q4: Define 'Apiculture'  or 'Bee Keeping'.

Answer: The scientific method of rearing honeybees for honey and wax is called ‘Apiculture’ or ‘Bee keeping’.


Q5: Are bees social insects?

Answer: Yes. They live in colonies (bee hive), exhibit team work and have division of labour.

CBSE Class 9 - SA1 - Maths - Lines and Angles (Questions and Answers)

Lines and Angles 

(Questions and Answers)

 

Here follows few questions that have asked in previous examination papers.

CBSE Class 9 - English (C) - The Road Not Taken - Summary (#eduvictors)

The Road Not Taken

Summary

The poem is a metaphor about the dilemma of making decisions that we have to make in our lives.

Poet: Robert Frost (March 26, 1874 – January 29, 1963)

Summary

It was autumn and the leaves had turned yellow. The poet or the traveller was passing through a wood. He stood at a place where the road forked into two different directions. The roads were covered with yellow leaves. It appeared nobody had passed through these roads since morning. The port was in a fix which road to take. He could choose only one path. He glanced at both the roads. One of the roads bent in the bushes while the other one was grassy. Fewer people had travelled by that road. He chose to walk on that road. He kept the other road for some other day though he did not hope to come back to that place again.

CBSE Class 9 - Maths - SA1 - Polynomials (Problems Usually Asked)

Polynomials 

Problems Asked in SA1 Papers

You may download this post as pdf.
Q1: Solve the following question using factor theorem.



Q2:

CBSE Class 10 - Maths - SA1 - Problems on Trigonometric Identities

 Problems on Trigonometric Identities

Solve the following using trigonometric identities

Q1:

Q2:

CBSE Class 9 English - Unit 6 - The Brook (Questions and Answers)

The Brook 

(Questions and Answers asked in exam papers in previous years.)

Q1: Where does the the brook come from? Where is it destined to be?


Answer: The brook starts its journey from dwelling place of birds (such as coot and hern) in the hills. Finally it flows into the overflowing river.


Q2: What is the message of the poem about life?

Answer: The poem tells that life is eternal.


Q3: How does the brook behave at the origin?

Answer: At the origin, the brook is happy, bubbly and full of noise like a small child.


Q4: Who is the poet of poem 'The Brook'? What parallelism does he draw in his poem?

Answer: Alfred Lord Tennyson is the poet. He draws a parallelism between the journey of the brook with the life of a man.