Squaring a number is largely used in mathematical calculations. There are so many rules for special cases. But we will discuss a general rule for squaring which is capable of universal application. The method of squaring is intimately connected with a procedure known as the “Duplex Combination” process. We now go on to a brief study of this procedure.

Example – (207)² = 42849

Explanation-

Duplex of 7 is 72 = 49. Put the unit digit (9) of a duplex in the answer line and carry over the other (4).

(2). 2 X 0 X 7 + 4(carried) = 4; write it down at 2nd position.

(3). 2 X 2 x7 + 02= 28; write down 8 and carry over 2.

(4). 2 X 2 X 0 + 2(carried) = 2; write it down.

Duplex of 7 is 72 = 49. Put the unit digit (9) of a duplex in the answer line and carry over the other (4).

2 X 0 X 7 + 4(carried) = 4; write it down at 2nd position.

2 X 2 x7 + 02= 28; write down 8 and carry over 2.

2 X 2 X 0 + 2(carried) = 2; write it down.

Duplex of 7 is 72 = 49. Put the unit digit (9) of a duplex in the answer line and carry over the other (4).

2 X 0 X 7 + 4(carried) = 4; write it down at 2nd position.

2 X 2 x7 + 02= 28; write down 8 and carry over 2.

2 X 2 X 0 + 2(carried) = 2; write it down.

Duplex of 7 is 72 = 49. Put the unit digit (9) of a duplex in the answer line and carry over the other (4).

2 X 0 X 7 + 4(carried) = 4; write it down at 2nd position.

2 X 2 x7 + 02= 28; write down 8 and carry over 2.

2 X 2 X 0 + 2(carried) = 2; write it down.

22 = 4; write it down.

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Reflection of Light Reflection of light is the phenomenon of bouncing back of light in the same medium on striking the surface of any object. Two laws of reflection (1). The incident ray the reflected ray and the normal at the point of the incident all lies in the same plane. (2). The angle of reflection ( R ) is always equal to the angle of the incident ( I ). ∠r = ∠i

Refraction Of Light Refraction of light is the phenomenon of change in the path of light is going from one medium to another. In going from rarer to denser medium the Ray of light bends towards normal and in going from a denser to rarer medium the Ray of light bends away from normal. No refraction when 1). light is incident normal on a boundary 2). reflection indices of the two media in contact are equal ATECH ACADEMY📚 Achieving Excellence Together With specialization in – +1 |+2 | IITJEE | NEET | MEDICAL | NDA | COMPETITIONS Coaching Notes | Doubt Clearing | Revision | Exam Tips | CBSE | ICSE | NCERT 📕Get a different experience of education with us Contact for Online, Classroom & Home Tutions +91 9041152777 +91 9041062077 https://AtechEdu.com ATECH ACADEMY is a fast, simple, and fun app that I use for learning and growing every day. Get it at https://play.google.com/store/apps/de…

The area of the cylinder is the total region covered by a cylinder in three-dimensional space. The cylinder area is equal to the sum of the area of two circular bases and curved surface area.

The total area of a cylinder is based on :

Curved Surface Area (CSA)

Base Area 1…..The curved surface area of a cylinder (CSA) is defined as the area of the curved surface of any given cylinder having base radius ‘r’, and height ‘h’.. CSA = 2π × r × h Square units 2….The base of the cylinder is in a circular shape. *2 (πr2) * TOTAL SURFACE AREA OF CYLINDER TSA = 2π × r × h + 2πr2= 2πr (h + r) Squar Unit Volume of Cylinder The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Formula = πr2h The volume of the cylinder can be given by the product of the area of base and height. ATECH ACADEMY📚 Achieving Excellence Together With specialization in – +1 |+2 | IITJEE | NEET | MEDICAL | NDA | COMPETITIONS Coaching Notes | Doubt Clearing | Revision | Exam Tips | CBSE | ICSE | NCERT 📕Get a different experience of education with us Contact for Online, Classroom & Home Tutors +91 9041152777 +91 9041062077 https://AtechEdu.com ATECH ACADEMY is a fast, simple, and fun app that I use for learning and growing every day. Get it at https://lnkd.in/gHC8-HW…

Redox reactions are oxidation-reduction chemical reactions in which the reactants undergo a change in their oxidation states. The term ‘redox’ is a short form of reduction-oxidation. All the redox reactions can be broken down into two different processes – a reduction process and an oxidation process.

Types of Redox Reactions

The different types of redox reactions are: Decomposition Reaction Combination Reaction Displacement Reaction Disproportionation Reactions Examples of Redox Reactions

A few examples of redox reactions, along with their oxidation and reduction half-reactions are provided in this subsection.

Example 1: Reaction Between Hydrogen and Fluorine In the reaction between hydrogen and fluorine, the hydrogen is oxidized whereas the fluorine is reduced. The reaction can be written as follows. H2 + F2 → 2HF The oxidation half-reaction is: H2 → 2H+ + 2e– The reduction half-reaction is: F2 + 2e– → 2F– The hydrogen and fluorine ions go on to combine in order to form hydrogen fluoride

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Lt Col Channpreet Singh (Retd) is an Ex Senior GTO from Allahabad SSB.

He took Premature retirement in 2018 after serving the Indian Army for almost 22 years. He is an Alumnus of the National Defence Academy (89 Course) and the Indian Military Academy ( 99 Course). The officer was commissioned into the Corps of Signals and has done his MTech in IT and Telecommunications from DAVV, Indore. He has served over varied terrains and appointments in Counter Insurgency operations in J&K, North East, and Central India. He was an instructor at the Military College of Telecommunication Engineering, Mhow, and represented Indian Army as a staff officer in the UN mission in Eritrea-Ethiopia. Post-retirement, he had a short stint with Globacom, a telecom company in Nigeria. He has also worked with Maharaja Ranjit Singh AFPI and Mai Bhago AFPI at Mohali, which are the leading feeder institutes of the region for the Officer Training Academies like NDA, OTA, IMA, AFA, and Naval Academy. Currently, he is pursuing his passion for training young minds for the Armed Forces as a freelancer through his firm “C3 Services” and is based out of Chandigarh. He is also an established and certified Life Coach and a mentor. He is a certified TVET trainer under the Ministry of Skill Development and has been nominated as an Incubation Enabler for linking up educational institutions with the national framework by IIEST (Industrial Incubation for Entrepreneurship and Skill Development Federation).

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Here’s a simple trick to square any number that ends in 1. Subtract 1 from the number. Square the difference. Squaring of such number is easy as it ends in ‘0’ Add the difference twice to its square. Add 1.

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Aptitude tricks and tips to find squares of numbers easily. Shortcuts to help you find squares in seconds! Today we are going to learn effective shortcut methods to find the squares of numbers close to 100. Number close to 100:- Find the square of no. 98?

Answer: Step-1:- Take a base value of 100. Step-2:- Find the deviation with 100. (Remember to consider the sign). 98 is 2 less than 100. So, we need to subtract 2 from 100 which means the deviation is -2. Step-3:- For unit digit find the square of deviation = (-2)2 = 04. Step-4:- Add deviation to the given no. for which we need to find the square. Here, 98 + (-2 ) = 96. This is the value of tens place. So the answer is 9604. This answer is incorrect. If we do the square of any two-digit no. greater than 31, the square will always have 4 digits in it. Here we need to find the square of 98 which means the square will have 4 digits. Hence, we need to add “0” before the deviation square. So, the answer is 9604. Number close to 1000:-

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Ganesh Chaturthi is here! The religious-cultural festival is a 10-day-long celebration of Lord Ganesha’s birth. In Hinduism, Lord Ganesha is the epitome of wisdom, remover of obstacles (Vighnaharta), a symbol of happiness, master of knowledge (Vidya). In India, religious ceremonies always begin with offerings to Lord Ganesha. He holds the unique distinction of being the “Prathama Pujaya” (first lord to be worshipped). The most worshipped deities in the Hindu pantheon, Ganesha is also known as the lord of prosperity and wealth. Ganesh Chaturthi is the perfect opportunity to learn some of the eternal lessons that Lord Ganesha offers.

As per a legend, Kubera, the God of wealth, was very proud of his boundless fortune. One day, he organized a gorgeous feast; among other famous guests, the divine couple, Shiva and Pârvatî, with their son Ganesha, were also invited.

Ganesh Ji, still a child, started to eat and he appeared to be insatiable. Soon, the other guests found plates and dishes empty. Alas! Not satisfied with all the available food, Ganesh started to devour plates and dishes, the furniture, and all the content of Alakapuri, the main city of Kubera. When his hunger was still not satisfied, the child Ganesha threatened to swallow Kubera himself. Frightened, the God of wealth rushed forward to Shiva’s feet to implore his help, since Ganesh’s voracious appetite seemed to be unlimited.

The remedy was simple but spectacular: Shiva gave his loving son a handful of toasted cereal grains. Ganesh ate it and, wonderfully, his hunger stopped immediately.

This legend teaches us that a handful of common food, given with love, and eaten with devotion, is more important and more sustaining than the banquet offered by Kubera to impress the Gods.

From a different angle, this story shows that assets and properties cannot bring peace and satisfaction to anybody. The only path to self-realization and self-satisfaction requires us to burn our ‘Vasana.’ The destruction of the vasana is symbolized by the consumption of the grilled rice; indeed, when the rice has been cooked, it loses its germinative capacity.

Similarly, the seeds of our hidden desires lose strength and the possibility to come back further. Lord Ganesha’s Big Head inspires us to think big and profitably.

His big ears prompt us to listen patiently, Narrow eyes point to deep Concentration, long nose to poke inquisitively, and smallmouth to speak less and listen more. And the Prasada to share and care. Jai Ganesha! Jai Ganesh Devaa! Mata Jiskee Parvati, Pita Mahadeva! Jai Ganesh,Jai Ganesh Devaa!

Let’s Celebrate Ganesh Chaturthi in the right spirit, let’s share and care and Stay Blessed forever!