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Yes, I had a strange dream last night. I went to bed late and was fast asleep. Suddenly, I felt that I was in a fairyland. There was a big garden. The flowers were blooming. The fairies were singing beautiful songs. One fairy came to me and offered me a small chair to sit on and enjoy the song. There I saw a little child playing on the flute. He arrived in the midst of the fairies. Some dwarfs and elves were sitting nearby. The child brought fruits for me. Everyone was dancing and singing happily. It was a pleasant and strange sight for me. Suddenly, I could hear my mother shouting at me to get up and to get ready to go to school. I woke up and was surprised to realize that it was only a pleasant and a strange dream.

Alice and her sister.

Alice : it Alice and White Rabbit. 

Sister : Alice and her sister

Alice : What are you doing? 

Sister : I am reading a book. 

Alice : Let me see the book. 

Sister : Here it is. 

Alice : Are you reading a book without pictures or conversations in it? 

Sister : Yes, I love to read these books. 

Alice : What is the use of reading such a book? It is boring to read. 

Sister : If it is boring for you, Please stay away from me. 

Alice : This hot day makes me feel sleepy. Let me have a nap.

Alice and White Rabbit

Rabbit : Let me check the time. Oh my God. It’s late. I have to hurry. 

Alice : Why are you in such a hurry?

Rabbit : I need to hurry for an important work.

Alice : Stop! Don’t run. I will chase you wherever you go. 

Rabbit : I will go into my hole. You cannot enter it. 

Alice : Why can’t I enter into the hole? 

Rabbit : You are too big to enter into this hole. 

Alice : Then what should I do? 

Rabbit : You have to drink the little bottle on top of the table. 

Alice : Oh Yes. I have shrunk in size after drinking from the bottle. 

Rabbit : (Mistaking Alice for his maid). Go to my cottage and fetch my gloves and fan. 

Alice : (confused) May be I’ll find something at the cottage to help me find my way out. I am hopeful.

The poet wants strength in order to serve God, in every situation.

4 : 5

We have given the marked price = Rs. 625 and selling price = Rs. 500

The required ratio = Selling price/ Marked price

= Rs. 500/Rs. 625

= 4/5

= 4:5

The correct answer is 4 : 5

R = {(2, 3), (4, 2), (6, 1)}

Range = (3,2,1)

y = e^x

Then, dy/dx = e^x

= + ve ∀ x ∈ R

So, for x ∈ R, e^x is an increasing function.

(i) Since, every element in B has pre-image in A, so f₁ is onto function.

(ii) Since, element in B has pre-image of A. So f₂ is onto function. 

(iii) Since 3 ∈ B does not have pre-image A. So f₃ is not onto function.

(iv) Since, 6 ∈ B does not have pre-image of A. So f₄ is not onto function.

Let P(n) : 1 + 3 + 5 + 7+……….. + (2n - 1) = n² 

For n = 1, LHS = 1, RHS = 12  = 1

∴ LHS = RHS 

∴ F(1) is true. 

Let upwards assume P(k) is true for some k ∈ N 

i.e., 1 + 3 + 5 + …. + (2K - 1) = kz 

Adding (k + 1)^th term = 2K + 1, on both sides, we get, 1 + 3 + 5 +……. +(2k -1)(2k + l) = k²  + 2k + 1 = (k +1)² 

which is P(k +1) 

Thus, P(k) ⇒ P(k +1).

Hence, by mathematical induction P(n) is true for all n∈N

Given

5x = 7/2

10x -7 = 0

10x + 0.y -7 = 0

We have

y = 3/2x

3x -2y = 0

3x -2y +0 = 0

Below foot note or below the table, source of the data may be mentioned for verification to the reader, regarding publications, organizations, pages, Journals etc,

It is a brief explanatory note or statement given just below the heading of the table put in a bracket. The statistical units of measurements, such as in ‘000s, Rs., Million tones, crores, Kgs., etc., are usually put in bracket.

Captions: Column headings are called captions. They explain what the column represents. Captions are always written in one or two words on the top of each column. 

Stubs: Row headings are called Stubs. They explain what the row represents. Stubs are usually written in one or two words at the left extreme sid/of each row.

Reference : These lines have been taken from the poem ‘The True Beauty’ composed by Thomas Carew.

Context : In these lines the poet describes the meaning of true beauty. He says that the I charms are not true beauty because they decay with the passing of time. But the spiritual beauty is the true beauty because it never dies. 

Explanation : In this stanza the poet says that red cheeks like rose, red lips like coral and the bright shining eyes like star make a woman beautiful. But these physical charms are temporary. They die with the passage of time. These physical attractions supply fuel to the fires of love. But in the old age these attractions die away and the fire of love also dies. So a man should not be attracted by the physical beauty of a woman. But he should seek love in virtues of a woman.

Paleo-botany.

Meghnad Saha.

The three major branches of Biology are: 

(i) Medical Science- It includes the study of several plants used in medicines. 

(ii) Botany- It includes the study of plants. 

(iii) Zoology- It includes the study of animals.

28th February.

1. Yama: It symbolises self-discipline. There are five Yama, i.e. Non-violence, Satya, Astay, Brahmacharya and Aparigraha. 

2. Niyama: There are five rules. 

(i) The purity of mind and body. 

(ii) Contentment 

(iii) Self-evaluation 

(iv) Devotion or complete surrender to God 

(v) Rigorous penance. 

3. Asana (Yogic postures) 

4. Pranayama (Regulated breath) 

5. Pratyahara (Sense detachment)

6. Dharma (Inner abstraction) 

7. Dhyana (Meditation) 8. Samadhi (State of bliss) All these elements of eightfold path are the universal commandants for all human beings. In fact, Yoga is not only the physical concept but more than that, it controls the mind, body and the entire human actions and reactions.

World Yoga Day celebrated on 21st June.

1. Bhaskaracharya I gave the Pell’s equation 8x + 1 = y² . In this equation x = 1 and y = 3 which can be written (x, y) = (1, 3), we can solve many equations like (x, y) = (6, 17). 

2. For many centuries, the approximate value of % was considered 14. But Bhaskara-I did not accept this value and believed that n has an irrational value which later proved to be true. Some of the contributions of Bhaskara I to mathematics are: Numbers and symbolism, the categorization of mathematics, the names and solution of the first degree equations, quadratic equations, cubic equations and equations which have more than one unknown value, symbolic algebra, the algorithm method to solve linear indeterminate equations which was later suggested by Euclid, and formulated certain tables for solving equations that occurred in astronomy.

Dr. Birbal Sahni was an Indian paleo-botanist. He studied the fossils of the Indian sub-continent. He was also a geologist and took an interest in archaeology. 

His greatest contribution lies in the study of the botany of the plants. His researches are useful in continent division theory, in finding the age of south plateau, the growth of Himalayas after the formation of glosipatris vegetation and in studies of fossils in Botany.

24th September 2014.

24th September 2014

The answer is (D) Meghnad Saha

Homi Jehangir Bhabha.

The answer is (A) ISRO

The answer is (B) C. Bose

Bappu – Boak – Newquark.

India’s self-sustaining missile developing programme is Brahmos.

The answer is (C) Latin

Nalanda, Varanasi, and Taxila.

Sushruta performed first plastic surgery of nose.

The expression for trigonometrical function sin x in Mahabhashkariya was given as.

\(\frac{Sin\,x\,=\,16x(\pi\, -\, x)}{5\pi^2\,-\,4\pi(\pi-x)}\)

0 ≤ x ≤ \(\frac{\pi}{2}\).

Wilson theorem- It is propounded by Bhaskarachaiya-I. 

According to Wilson’s theorem, any integer, p > 1 is a prime number, if and only if (p -1)! = – 1. He also derived the formula 8X² + 1 = if which is called as Pell’s equation.

Word science is derived from the Latin word Scientia, which means to know. A systematic knowledge of nature verified by experiments is called Science. 

Objectives of Science: 

The main objectives of science are: 

1. To understand the functional role of nature and explain it in a complete form. 

2. To provide knowledge of the laws of nature after verifying them by experiments.

3. To control nature by the applications of results of experiments performed through keen observation. 

4. To improve and make human life easier by the use of available natural resources and solving the problems.

5. To eradicate superstitions (false notions) prevailing in the society.

The answer is (C) Three

Saha ionisation equation is an expression that relates the ionisation state of an element to the temperature and pressure. The equation is a result of combined ideas of quantum mechanics and statistical mechanics and is used to explain the spectral classification of stars. The expression was developed by the Indian astrophysicist Meghnad Saha.

The branch of Science in which we study Mathematics and Statistics is known as Abstract Science.

Meghnad Saha

Bhaskaracharya – I

The answer is (B) Sushrat

The answer is (B) Brahmagupta

The answer is (D) Pell’s equation

The modern age is an era of science. The achievements of Science are possible due to the continuous efforts and research of scientists. Aryabhatta was the first scientist who told that the earth is spherical and it rotates on its axis, by which day and night formed. Brahmagupta was the first mathematician who gave the law of working of zero. Raman effect was given by Chandra Shekar Venkataraman. He passed the monochromatic light rays of mercury through some transparent substances and obtained spectrum on an ordinary spectrograph. He saw new lines in the spectrum and named them Raman lines. He declared Raman effect in a meeting of scientists on 16th March 1926. He was awarded Noble prize of Physics in 1930. Raman effect helped in understanding the molecular structure of a substance. Much research work was done on Raman effect after Laser rays.

The answer is (D) All the above

The various steps taken in scientific methods are:

1. To identify the problem- The problem should be identified and defined. The selected problem must have a narrow range and specific aim, otherwise, the solution of the problem cannot be worked out. 

2. To formulate a hypothesis- Hypothesis is a logical explanation which accounts for the observation. It is an important step in the scientific approach. 

3. Testing or experimenting hypothesis- When a hypothesis has been put forward, it is tested by experiments. 

4. Data collection- Observation and identification of the problem is followed by a collection of data, to answer the question relevant to the problem.

5. Finding, the result- Result may be direct or indirect. It should be repeated. 

6. Again retesting- Repeated results are accurately established and they do not need further verification. 

7. To generalise the principle or law- A thoroughly tested fact regarding scientific finding or phenomenon is known as the principle or law. It is found to be reliable for its prediction.

Professor Satyendra Nath Bose

Aryabhattiya Bhasya