Science > Mathematics > Statistics and Probability > Probability > Sample Space of an Experiment In the last article, we have studied the concept of probability. In this article, we shall study to write a sample space for a given event. The Sample Space for Random Experiments: From a group of 2 boys and 3 […]
Science > Mathematics > Statistics and Probability > Probability > Concept of Probability First attempt to measure probability was done by Italian mathematician Galileo. The classical theory of probability is developed by French mathematicians B. Pascal and P. Fermat while solving a number of problems posed by a French nobleman and gambler Chevalier-de-mere. The famous […]
A sequence is a function whose domain is the set N of natural numbers. The sequence is generally denoted by a and its image is denoted by a(n) or t(n). The terms of the sequence are represented by a1, a2, a3, ….., an or t1, t2, t3, ….., tn A sequence whose range is a subset […]
In last few articles, we have studied arithmetic progression. In this article, we shall study geometric progression (G.P.). A sequence (tn) is said to be a geometric progression (G.P.) if the ratio tn + ! /tn = constant for all n ∈ N The constant ratio is called the common ratio of the G.P. and is denoted by letter ‘r’. […]
In the last article, we have studied the general term of an arithmetic progression. In this article, we shall study to find the sum of arithmetic progression. General Term or nth term of an Arithmetic Progression: If ‘a’ is the first term and ‘d’ is the common difference of an A.P. then the nth term is […]
In this article, we shall study series, progression, and arithmetic progression (A.P.) Series: If a1, a2, a3, ….., an. is a sequence, then the expression a1 + a2 + a3 + …..+ an is called series. Progression: It is not the case every time that the terms of sequence follow certain pattern so that a specific formula for the nth […]
In this article, we shall study different types of nuclear reactions. Nuclear Reactions: A reaction in which there is a change in the composition of the nucleus is called a nuclear reaction. Characteristics of Nuclear Reactions: There is a change in the composition of the nucleus. In nuclear reaction rearrangement of nucleons ( constituents of […]
Isotopes are different atoms of the same elements having the same atomic number but a different mass number. Isotopes of radioactive elements are found to be very useful in different fields like carbon dating, agriculture, medicines, the production of synthetic elements, etc. Important uses of radioisotopes are as follows. Estimation of Age of Rock and […]
The nucleus of an atom is extremely small. The radius of the nucleus is about 10-15 m. In such a small place protons and neutrons are held together. Protons are positively charged so they should get repelled however the majority of the nuclei are stable hence there must be certain factors which affect nuclear stability. Some […]
Researches by J.J. Thomson, Dalton, Rutherford, and Mosley showed that an atom is the smallest but not the ultimate particle of the matter. An atom consists of subatomic particles, protons, neutrons, and electrons called fundamental particles. Besides these, particles like mesons, positrons, neutrinos are also associated with the atomic structure. In this article, we shall […]