Mathematics – Kailasha Foundation https://kailashafoundation.org Fun & Learn Portal Tue, 30 Apr 2019 08:18:16 +0000 en-US hourly 1 https://wordpress.org/?v=5.1.1 NTSE MAT – Directions and Positions https://kailashafoundation.org/2019/03/07/ntse-mat-2/ https://kailashafoundation.org/2019/03/07/ntse-mat-2/#respond Thu, 07 Mar 2019 05:30:22 +0000 https://kailashafoundation.org/?p=35722 NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows: Scholarship of Rs. 1250/- per month for class XI to XII. […]

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NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows:

  • Scholarship of Rs. 1250/- per month for class XI to XII.
  • Scholarship of Rs. 2000/- per month for undergraduates and postgraduates.

Generally, state level exam takes place in the month of November every year and notification come out in the month of September. The next level exam takes place in the month of May every year.

All students of Class X studying in recognized schools are eligible to appear for the Stage-I examination. There will be no domicile restriction.

The examination will comprise these parts namely

  • Mental Ability Test (MAT)
  • Language Test (LT)
  • Scholastic Ability Test (SAT)

For the preparation of such a prestigious exam, Team of Kailasha Foundation will bring a series of quizzes. In NTSE quiz series, this is the 11th quiz of Mental Ability Test of Positions and Direction under the head MAT in NTSE.

Attempt the quiz and find out your score.

Note: In this quiz, for every right answer you will be awarded 4 marks and for every wrong answer minus one mark will be awarded.

Click Here To Start Your Quiz

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Click here for more NTSE Quizzes

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Maths Mock 1 for IIT JEE https://kailashafoundation.org/2018/11/12/maths-mock-1-for-iit-jee/ https://kailashafoundation.org/2018/11/12/maths-mock-1-for-iit-jee/#respond Mon, 12 Nov 2018 11:30:00 +0000 https://kailashafoundation.org/?p=30412 Maths Mock Test for IIT JEE by KFDN Maths Mock Test is brought to you by Kailasha Foundation- Fun & Learn Portal to help you boost yourself for JEE, and other engineering entrance exams with our specially tailored content from the subject. With this test, we have delivered questions from the syllabus of chemistry for IIT JEE […]

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Maths Mock Test for IIT JEE by KFDN

Maths Mock Test is brought to you by Kailasha Foundation- Fun & Learn Portal to help you boost yourself for JEE, and other engineering entrance exams with our specially tailored content from the subject. With this test, we have delivered questions from the syllabus of chemistry for IIT JEE to you in an interactive mock test environment which will help you for the preparation of your Exam.

Instructions:

  1. You have 1 hour to attempt this test.
  2. All questions carry equal marks and each correct answer will give you 4 marks.
  3. You will be awarded minus one mark for each wrong answer.

START YOUR TEST

All content at Kailasha Foundation is free and will always be. Share with friends, challenge them and have fun while learning. That’s why “Fun & Learn”. If you find any error(s) in this Mock test, then do report from the “Contact Us” tab above on our website. Thanks for being a valuable user. Happy Learning!

Other mocks for your preparation

IIT JEE Mock 2

IIT JEE Mock 1

Thermodynamics Mock 1

Thermodynamics Mock 2

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NTSE MAT Letter Group Series Pattern – 15 Questions in 15 Minutes https://kailashafoundation.org/2018/11/02/ntse-mat-letter-group-series-pattern-15-questions-in-15-minutes/ https://kailashafoundation.org/2018/11/02/ntse-mat-letter-group-series-pattern-15-questions-in-15-minutes/#respond Fri, 02 Nov 2018 06:30:02 +0000 https://kailashafoundation.org/?p=29669 NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows: Scholarship of Rs. 1250/- per month for class XI to XII. […]

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NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows:

  • Scholarship of Rs. 1250/- per month for class XI to XII.
  • Scholarship of Rs. 2000/- per month for undergraduates and postgraduates.

Generally, state level exam takes place in the month of November every year and notification come out in the month of September. The next level exam takes place in the month of May every year.

All students of Class X studying in recognized schools are eligible to appear for the stage-I examination. There will be no domicile restriction.

The examination will comprise these parts namely

  • Mental Ability Test (MAT)08
  • Language Test (LT)
  • Scholastic Ability Test (SAT)

For the preparation of such a prestigious exam, Team of Kailasha Foundation will bring a series of quizzes. In NTSE quiz series, this is the seventh quiz of Mental Ability Test under the head MAT in NTSE.

Attempt the quiz and find out your score.

Note: In this quiz, for every right answer you will be awarded 4 marks and for every wrong answer minus one mark will be awarded. You have 15 minutes to attempt the quiz.

Click here to start the quiz

Kailasha Foundation – Bringing Solutions To You

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It could be you to discover the largest till date 50th Mersenne Prime Number https://kailashafoundation.org/2018/01/15/mersenne-prime/ https://kailashafoundation.org/2018/01/15/mersenne-prime/#respond Mon, 15 Jan 2018 06:25:06 +0000 https://kailashafoundation.org/?p=15260 A FedEx employee, Jon Pace discovered the largest so far – 50th Mersenne Prime Number (largest known till date) on 26th December 2017 and you can be the one to find the next. Prime numbers have made maths lovers always curious and it deserves the research time it has been given. The special thing about […]

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A FedEx employee, Jon Pace discovered the largest so far – 50th Mersenne Prime Number (largest known till date) on 26th December 2017 and you can be the one to find the next.

Prime numbers have made maths lovers always curious and it deserves the research time it has been given. The special thing about these Mersenne Prime Numbers is that these are so rare that their discovery rate is less than one per year. Yes, the 50th Mersenne Prime Number is the largest known prime number till date as well.

Hello Maths lovers!

For your love of Maths, I have the perfect thing for you and here it goes. Make a list of questions in your mind (you may already have one) and you’ll find all your answers below, as we at Kailasha Foundation – Fun & Learn Portal, love to clear confusions and make things simple.

  1. Q: What is that number which this article is about?
    A: 277,232,917 − 1. This number is 50th Mersenne Prime and is also the Largest known Prime number till date.
  2. Q: What is a Mersenne Prime?
    A: Mersenne Primes are the special prime numbers of the form Mn = 2n − 1 for some integer where n is also a prime number. Recently discovered all largest prime numbers are Mersenne Primes.
  3. Q: How large is this number?
    A: Big enough to fill an entire shelf of books totalling 9,000 pages! It is a number of 23,249,425 digits.
  4. Q: Will you please describe more? Who works on these prime numbers? How are these found? What’s the use?
    A: Euclid proved that there is no largest prime number, and many mathematicians and hobbyists continue to search for large prime numbers. Many of the largest known primes are Mersenne primes. As of January 2018, the seven largest known primes are Mersenne primes.
    They are named after Marin Mersenne, a French Monk, who studied them in the early 17th century.The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, … (sequence A000043 in the OEIS) and the resulting Mersenne primes are 3731127, 8191, 131071, 524287, 2147483647, … (sequence A000668 in the OEIS).

    The formula for finding the Mersenne Primes isn’t a sure-shot method to find Prime numbers. The formula only takes us to a more likely place to find them.

    Prime numbers are useful in cryptography; however, the largest discovered prime is too large to be used even in cryptography in near future.

  5. Q: Is there any chart or list of the Mersenne Primes?
    A: Yes. It is available on Wikipedia. The 46th, 47th, 48th, 49th and 50th Mersenne Primes are not sure of their respective ranks. There can be more Mersenne Primes in between 45th and 50th
  6. Q: What method is used to find all these 50 prime numbers? What is OEIS?
    A: The first four Mersenne Primes: 3, 7, 31 and 127 were found by Ancient Greek Mathematicians. Thereafter trial division was employed. The 8th Mersenne Prime, 2147483647 was found by Leonhard Euler using Enhanced Trial Division.Thereafter Lucas Sequences were used until 1952 when Raphael M. Robinson found 5 Mersenne Primes in a single year using LLT (Lucas-Lehmer Test) on a SWAC computer.Further developments have two important names: Donald B. Gillies and David Slowinski.

    From 35th through 50th (the latest one), all Mersenne Primes are found using GIMPS.

    All the Mersenne Primes are found using one or more computers, and LLT was the employed method in all of these.

    OEIS is the On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane’s, an online database of integer sequences. It was created and maintained by Neil Sloane while a researcher at AT&T Labs. Foreseeing his retirement from AT&T Labs in 2012 and the need for an independent foundation, Sloane agreed to transfer the intellectual property and hosting of the OEIS to the OEIS Foundation in October 2009. Sloane continues to be involved in the OEIS in his role as President of the OEIS Foundation.

     

  7. Q: What is GIMPS?
    A: The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.
  8. Q: How can I be the next person to discover the next prime number?
    A: 
    If you want to join the hunt for the 51st Mersenne prime, you can download the software here, and find instructions here. However, Your competition is with Jon Pace too. 🙂

You can ask more about everything discussed above.

Source of Information: Wikipedia (main source) and a few other web portals

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Wonderful Mathematics – Amazing facts about Maths https://kailashafoundation.org/2017/08/27/magical-mathematics/ https://kailashafoundation.org/2017/08/27/magical-mathematics/#comments Sun, 27 Aug 2017 05:30:16 +0000 http://kailashafoundation.org/?p=6167   Mathematics is the secret to understanding the world. Mathematics, the word itself is a source of stress for many people. A Spanish study suggests that 60 percent students suffer from math anxiety. Is math really so bad or it’s our approach that should be mended? The latter one is correct. Math is the hidden […]

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Mathematics is the secret to understanding the world.

Mathematics, the word itself is a source of stress for many people. A Spanish study suggests that 60 percent students suffer from math anxiety. Is math really so bad or it’s our approach that should be mended?

The latter one is correct.

Math is the hidden tool to understand the world and great academicians find beauty in maths. 

Before going towards mathematics, let us discuss understanding and why is it important to understand?

Understanding has to do with the ability to know the behaviour of stuff around us. Curiosity and zeal to understand are the bed rock to the progress of human race. The process of understanding starts with the search for repetitions, patterns and similarities. This is where mathematics kicks in.

 Disclaimer: As you glide through this article, you will fall in love with mathematics.

Mathematics is the ability to express the world around us in terms of numbers and equations. Without mathematics, this world will stop making sense. Trust me, a human brain is well acquainted with maths and constantly does complex mathematics without you realising it. For instance, when you try to cross a road, your brains takes various numbers like the speed of vehicles on road, your speed, the width of road e.t.c  and tells you the right time to cross the road.

Isn’t it fascinating?

General misconception that maths is all about addition, subtraction, algebra and terrible equations, is the prime cause of maths anxiety.  I will try to emphasise that “maths is the prime tool to understand the world” 

“Mathematics is the science of identifying patterns which perpetuate better understanding.”

Let us begin with simple things:

“All things of beauty have a mathematical form.”

Ever heard of Golden ratio, (1.618:1) it was given by Leonardo da Vinci. He found a repetitive pattern in all physical things that appeal to our eyes. It appears that most of the winners of beauty pageants exhibit golden ratio in their faces. This ratio is also called the universal ratio of balance.

Next time you see something just perfect in all proportions, remember golden ratio.

In the third phase, we shall try to link mathematics to other fields of study.

Everything in this world can be associated with a value, a number that is special to a given physical phenomenon. Even light that we see has wave-length (400- 700 nm) attached to it. A set of variables is attached with all events and those variables have value, for instance, the variables governing economy of a country. Experts use different functions or equations to predict the future market.

Mathematics gives us the power to quantitatively analyse a situation, thereby giving a better understanding. All scholarly subjects will lose their essence once detached from maths.

Let’s analyse the importance of mathematics in the world of computer science:

As stated, maths deals with patterns and the human brain have the ability to decode patterns. Likewise, computers work on algorithms or steps. To design an algorithm the algorithm the programmer has to identify the pattern then convey it to the computer. Essentially all programmers are good at mathematics.

Nature frequently amazes us with its magnificent beauty. Even in the weirdest and confusing events, nature exhibits patterns, which are now being used to predict the weather of a place. While progressing towards the conclusion I would like to remind you that mathematics is the study of patterns.  

 “ The things of beauty are those that we understand and what we understand, essentially has a pattern”

I claim that all that exists, exhibits patterns, hence has a mathematical form, if we somehow manage to decode the pattern of all events simultaneously then we will be able to predict the future. Maths is everywhere, embrace it as one thing is sure you can’t fake maths.

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NTSE MAT – Directions and Positions – 15 Questions in 15 Min https://kailashafoundation.org/2017/08/04/ntse-2/ https://kailashafoundation.org/2017/08/04/ntse-2/#respond Fri, 04 Aug 2017 11:30:26 +0000 http://kailashafoundation.org/?p=4661 NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows: Scholarship of Rs. 1250/- per month for class XI to XII. […]

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NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows:

  • Scholarship of Rs. 1250/- per month for class XI to XII.
  • Scholarship of Rs. 2000/- per month for undergraduates and postgraduates.

Generally, state level exam takes place in the month of November every year and notification come out in the month of September. The next level exam takes place in the month of May every year.

All students of Class X studying in recognized schools are eligible to appear for the Stage-I examination. There will be no domicile restriction.

The examination will comprise these parts namely

  • Mental Ability Test (MAT)
  • Language Test (LT)
  • Scholastic Ability Test (SAT)

For the preparation of such a prestigious exam, Team of Kailasha Foundation will bring a series of quizzes. In NTSE quiz series, this is the 11th quiz of Mental Ability Test of Positions and Direction under the head MAT in NTSE.

Attempt the quiz and find out your score.

Note: In this quiz, for every right answer you will be awarded 4 marks and for every wrong answer minus one mark will be awarded.

Click Here To Start Your Quiz

Kailasha Foundation – Bringing Solutions To You

Follow us on FacebookTwitterInstagramLinkedIn for regular updates.

Click here for more NTSE Quizzes

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FORMULA & TRICKS FOR QUANTITATIVE APTITUDE- Part 2 https://kailashafoundation.org/2017/07/31/formula-tricks-quantitative-aptitude-part-2/ https://kailashafoundation.org/2017/07/31/formula-tricks-quantitative-aptitude-part-2/#respond Mon, 31 Jul 2017 05:30:57 +0000 http://kailashafoundation.org/?p=4020 Average Average=(sum / N) where N is total number of objects Weighted Average: The average between two sets of numbers is closer to the set with more numbers. If the value of each item is increased by x, then the average of the group will also increase by x. If the value of each item […]

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Average

Average=(sum / N) where N is total number of objects

Weighted Average: The average between two sets of numbers is closer to the set with more numbers.
If the value of each item is increased by x, then the average of the group will also increase by x.

If the value of each item is decreased by y, then the average of the group of items will also decrease by y.
If the value of each item is multiplied by the same value m, then the average of the group or items will also get multiplied by m.
If the value of each item is multiplied by the same value n, then the average of the group or items will also get divided by n.
If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.

Average of x natural no’s = (x+1)/2

Average of even No’s = (x+1)

Average of odd No’s = x

 Change in the value of a Quantity and its effect on the Average

When one/more than one quantity is not removed but replaced with same no. of quantities of different value,

Change in the no. of quantities and its effect on Average

+ = if quantities are Added, – = if quantities are removed

Time and Work

If a person ‘X’ can complete a piece of work in ‘Y’ days, then

Work Done by X in 1 day = 1/Y

If Utkarsh can complete a piece of work in ‘X’ days and Prashant can complete a piece of work in ‘Y’ days, then

Work done by Utkarsh and Prashant together in 1 day = X+Y/XY

Trick 1: If Adarsh can do a work in D1 days and Bhanu can do the same work in D2 days then Adarsh and Bhanu together can do the same work in (D1 x D2)/ (D1 + D2)

Trick 2: Sometimes the work done is dependent on the number of days worked and efficiency of each worker. Let’s see how the formula changes in this case:

  • If person P1 can do the work in D1 days and M2 persons can do the same work in D2 days then we can say M1.D1 = M2.D2
  • If the persons work T1 and T2 hours per day respectively then the equation gets modified to M1.D1.T1 = M2.D2.T2
  • If the persons has efficiency of E1 and E2 respectively then: M1.D1.T1.E1 = M2.D2.T2.E2

Pipes & Cisterns

Trick: If a pipe A can fill a tank in ‘x’ hours and Pipe B can fill a tank in ‘y’ hours, then

Time Taken by both the pipes to fill the tank together = xy/(x+y)

Time, Speed and Distance

Trick 1: Speed = Distance/ Time and the unit of Speed is Km/hr or m/s

Trick 2: If an object covers a certain distance with a speed of ‘p’ Km/hr and again covers the same distance with a speed of ‘q’ Km/hr, then

Average Speed for the Entire Journey = 2 pq/(p+q)

Boats and Streams

Trick: If the speed of stream is ‘p’ Km/hr and the speed of boat in still water is ‘q’ Km/hr, then

Speed of Boat Downstream = (p + q) Km/hr

Speed of Boat Upstream = (q – p) Km/hr

Mixtures and Alligations

Trick 1: When two different commodities are mixed such that one is cheaper than the other, then:

mixture and alligations

Here Mean Price is CP of mixture per unit quantity.

Trick 2: When x amount of commodity 1 is replaced with commodity 2 of y quantity n times, then:

mixture and alligations

Quadratic Equations

ax2 + bx + c = 0.

py2 + qy + c = 0

Trick 1:

Sum of roots = -b/a

Product of roots = c/a

Trick 2: A quadratic equation ax2 + bx + c = 0 will have reciprocal roots when a = c

Approximation

Trick 1: Use the BODMAS rule to solve the simplification questions. This is the basis of simplification questions.

Trick 2: Round of decimal numbers to the nearest whole numbers to get the approximate value of the equation.

Ratio Proportion

Ratio is a fraction of two values. It can be represented in any of the following ways:

=> x/y,   x : y , x÷y

  • In ratio of the form x : y,  x is called as the antecedent/first term and y is the consequent/second term.
  • Generally, ratio is a handy way to compare two terms.
  • For example : 4 / π > 1 , it is clear that 4 > π
  • One thing that has to be remembered while comparing two numbers in a ratio is that they should be represented in same units. For example, if x is in meters and y in litres they cannot be compared by using ratio as they are expressed in different units – meters vs litres.

 

A proportion is the equality of two ratios/ fractions.

  • If x : y = a : b, it can be written as  x : y :: a : b and it is said that x, y, a, b are in proportion.
  • Here x and b are called extremes, while y and a are called mean terms.
  • Product of means=Product of extremes
    Thus,
    x :y :: a : b  => (y∗a)=(x∗b)
  • If x : y=a : b

b is called the fourth proportional to x, y and a.
a is called the third proportional to x and y.

  • Sub-duplicate: Sub-duplicate ratio of (a:b) is (a^1/2: b^1/2)
  • Duplicate ratio of (a:b) is (a^2:b^2)
  • Triplicate Ratio:Triplicate ratio of (a:b) is (a^3:b^3)
  • Sub-triplicate Ratio: Sub-triplicate ratio of (a:b) is (a^1/3:b^1/3)
  • If a/b=c/d then, a+b/a−b=c+d/c−d This is known as Componendo and Dividendo.
  • We say that x is directly proportional to y, if x=ky for some constant k and we write, x∝y
  • We say that x is inversely proportional to y, if xy=k for some constant k and we write, x∝1y

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FORMULA & TRICKS FOR QUANTITATIVE APTITUDE- Part 1 https://kailashafoundation.org/2017/07/30/formula-tricks-quantitative-aptitude-part-1/ https://kailashafoundation.org/2017/07/30/formula-tricks-quantitative-aptitude-part-1/#comments Sun, 30 Jul 2017 04:30:26 +0000 http://kailashafoundation.org/?p=4015 Percentage To express x% as a fraction, divide it by 100 ⇒ x% = x/100 To express a fraction as %, multiply it by 100 ⇒ x/y = [(x/y) × 100] % x% of y is given by (y × x/100 ) If X’s age is a% more than Y’s age, the Y’s age is less than […]

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Percentage

To express x% as a fraction, divide it by 100 ⇒ x% = x/100

To express a fraction as %, multiply it by 100 ⇒ x/y = [(x/y) × 100] %

x% of y is given by (y × x/100 )

If X’s age is a% more than Y’s age, the Y’s age is less than X’s age by [ a / (100+a)] * 100%

If ‘M’ is x% of ‘N’ and ‘P’ is y% of ‘N’ then ‘M’ is (x/y) * 100% of ‘P’.

If the sides of the triangle, rectangle, square, circle, rhombus etc is

  • Increased by a%. Its area is increased by2a+(a2/100)
  • If decreased b%. Its areas is decreased by,-2b+(b2/100)

The students in a school are ‘P’. It increased by x% during the 1st year, increased by y% during 2nd year and again increased by z% during 3rd year. The students in school after 3 years will be,

P *[(100+x)/100] * [(100+y)/100] * [(100+z)/100]

 Problem on Ages

  1. If the current age is x, then n times the age is nx.
  2. If the current age is x, then age years later/hence = x + n.
  3. If the current age is x, then age years ago = x – n.
  4. The ages in a ratio a:ill be ax and bx.
  5. If current age is x, then 1/n of the age is x/n.

 If the present age of Sharma Jee is ‘x’ years, then

‘n’ years hence, Age of Sharma Jee would be = (x + n) years

‘n’ years ago, Age of Sharma Jee would be = (x – n) years

Super Tip: You don’t need to always start forming equations from where the question starts.

Number Series

The only difficult part about solving questions on number and alphabet series is determining the pattern. Once you practice 40-50 questions on this topic, you will be aware of 90% of the possible pattern. A shortcut is to read the tricks on solving series questions. Some of them are highlighted here:

Trick 1: Calculate the difference between the immediate or alternate numbers and observe the pattern in the differences.

Trick 2: Observe the sequence for Prime Number series

Trick 3: Observe the sequence for Geometric series, Perfect Squares/Cubes.

Profit & Loss

Cost Price-The price at which an article is purchased is known as cost price (C.P.)

Selling Price-The price at which the article is sold is known as selling price (S.P.)
Profit = SP-CP (SP>CP)
Loss = CP-SP (CP>SP)

Profit % = (Profit x 100)/CP
Loss% = [(CP – SP)/CP] x 100
CP= {100 /(100+profit%)} x SP
CP={100/(100-loss%)} x SP

S.P. = C.P. x [(100 + profit%) / 100]

S.P. = C.P. x [(100 – loss%) / 100]

 

If there is a Profit of x% and loss of y % in a transaction, then the resultant profit or loss% is given by [x – y – (x × y/100)]

Note- For profit use sign + in previous formula and for loss use – sign. If resultant is positive then overall its profit. However, if it is negative then overall we have a loss.

If a cost price of m articles is equal to the selling Price of n articles,

(C.P of m article = S.P. of n article) then Profit percentage

(m – n)/n×100%

 

If m parts are sold at x% profit, n parts are sold at y % profit and p parts are sold at z% profit Rs. ‘R’ is earned as overall profit than the value of total consignment
 R ×100 / (mx +ny +pz)

Ankit purchases a certain no. of the article at m  rupee and the same no. at n a rupee. He mixes them together and sells them at p a rupee then his gain or loss

[{2mn/(m+n)p} -1]× 100

 

Marked price = Cost price + Markup

Always Remember: Markup is an extra price on Cost Price. So, Markup is always calculated on CP

%Markup = [Markup/CP]*100

Discount (if SP < MP) = MP – SP i.e. SP = MP – Discount

Always Remember: Discount is deducted from Marked Price. So, Discount is always calculated on MP and

%Discount = [Discount/MP]*100

Trick 1: If most of the information given in the form of percentages in the question, start by assuming CP = 100.

Trick 2:  Discount is usually given on marked price. Hence, in this case, marked price will be higher than the final selling price.

 

Simple and Compound Interest

Principal: – The money borrowed or lent out for certain period is called the principal or the Sum.

Interest: – Extra money paid for using other money is called interest

The cost of borrowing money is defined as Simple Interest. It is of two types – simple interest or compound interest. Simple interest (SI) is calculated only on the principal (P) whereas Compound interest (CI) is calculated on the principal and also on the accumulated interest of previous periods i.e. “interest on interest.” This compounding effect makes a big difference in the amount of interest payable on the principal.

Simple interest is:

Simple Interest = Principal x Interest Rate x Term of the loan (Time of Loan)

SI = P x i x n/100 when the interest rate is taken in percent.

Compound Interest

CI = P [(1 + i)n – 1]

where P = Principal, i = annual interest rate in percentage terms, and n = number of compounding periods.

Compounding periods: When calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest. So for every INR 100 principal over a certain period of time, the amount of interest accrued at 10% annually will be lower than interest accrued at 5% semi-annually, which will, in turn, be lower than interest accrued at 2.5% quarterly.

In the formula for calculating compound interest, the variables “i” and “n” have to be adjusted if the number of compounding periods is more than once a year. That is, “i” has to be divided by the number of compounding periods per year, and “n” has to be multiplied by the number of compounding periods. Therefore, for a 10-year loan at 10%, where interest is compounded semi-annually (number of compounding periods = 2), i = 5% (i.e. 10% / 2) and n = 20 (i.e. 10 x 2).

The following table demonstrates the difference that the number of compounding periods can make over time for an INR 10,000 loan taken for a 10-year period.

Shortcut Trick: Rule of 72 

The Rule of 72 calculates the approximate time over which an investment will double at a given rate of return or interest “i”, and is given by (72 / i). It can only be used for annual compounding.

For example, an investment that has a 6% annual rate of return will double in 12 years. An investment with an 9% rate of return will double in 8 years.

 

Trick 1: Formula for calculating simple interest is simple.

S.I. = PTR/100

What if the rate is R1, R2 and R3 in the 1st, 2nd and 3rd year. In this case, the amount after 3 years would be:

A = P (1 +R1/100) (1 + R2/100) (1 + R3/100)

 

Trick 2: Formula for calculating compound interest is a little more complex.

A = P [1+ r/100]t

This formula applies when interest is compounded annually.

When interest is compounded half yearly, rate = 2r

compounded quarterly, rate = 4r

compounded monthly, rate = 12r

 

Trick 3: When the rate of interest is not equal every year:

A = P [1+ r1/100]t1 [1+ r2/100]t2 …. and so on

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NTSE SAT Mathematics – 15 Questions in 15 Minutes https://kailashafoundation.org/2017/07/14/ntse-sat-mathematics-15-questions-in-15-minutes/ https://kailashafoundation.org/2017/07/14/ntse-sat-mathematics-15-questions-in-15-minutes/#respond Fri, 14 Jul 2017 14:30:21 +0000 http://kailashafoundation.org/?p=3763 NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows: Scholarship of Rs. 1250/- per month for class XI to XII. […]

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NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows:

  • Scholarship of Rs. 1250/- per month for class XI to XII.
  • Scholarship of Rs. 2000/- per month for undergraduates and postgraduates.

Generally, state level exam takes place in the month of November every year and notification come out in the month of September. The next level exam takes place in the month of May every year.

All students of Class X studying in recognized schools are eligible to appear for the stage-I examination. There will be no domicile restriction.

The examination will comprise these parts namely

  • Mental Ability Test (MAT)
  • Language Test (LT)
  • Scholastic Ability Test (SAT)

For the preparation of such a prestigious exam, Team of Kailasha Foundation will bring a series of quizzes. In NTSE quiz series, this is the eighth quiz of Scholastic Ability Test under the head SAT in NTSE.

Attempt the quiz and find out your score.

Note: In this quiz, for every right answer your will be awarded 4 marks and for every wrong answer minus one mark will be awarded. You have 15 minutes to attempt the quiz.

KFDN LOGO - Copy - Copy

Hello ! Welcome to your NTSE SAT - Mathematics

Instructions:

Time: 20:00 min                                                                                                          Full Marks: 60

  1. There is negative marking of -1.00 for all incorrect answers chosen.
  2. There is no deduction for NOT attempted question.
  3. All questions carry equal marks and all 15 questions are of 4 marks each.
  4. All Questions are compulsory.

(Powered By: Kailasha Foundation - Fun & Learn Portal)

Name
Email
1. If sin x = cos y, x + y is equal to
2. A rhombus of side 5cm has two angles of 120. Its diagonals are
3. A wire of length 25 cm is bent so as to lie along the arc of a circle of diameter 100cm. The angle subtended at the centre by the arc is
4. The angle of a regular polygon of n sides, in the circular system, is k radians. k is equal to
5. The statement (sin x + sin y)2 > (sin x – sin y)2 is
6. If tan35tan55 = sin A, angle A is equal to
7. NTSE mathematics
8. The square root of (x2 + 4x + 4)(x2 + 6x + 9) is

NTSE Mathematics
9. The value of 12 +22 + 32+ ... + n2 is

NTSE Mathematics
10. The solution set of the inequality 8x - x2 -12 >= 0 : x belongs to N is
11. If f(x) = x+ 1, g(x) = 2x + 3 and h(x) = g(f(x)) evaluate h(1)
12. If x = (2t)/(1+t2) and y = (1-t2)/(1+t2) then x2 + y2 is equal to

NTSE Mathematics
13. NTSE mathematics
14. If f(x) = (sin x – cos x)2, the maximum value of f(x) is
15. 2(sin6x + cos6x) – 3(sin4x + cos4x) + 1 is equal to

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The post NTSE SAT Mathematics – 15 Questions in 15 Minutes appeared first on Kailasha Foundation.

]]> https://kailashafoundation.org/2017/07/14/ntse-sat-mathematics-15-questions-in-15-minutes/feed/ 0 NTSE MAT Letter Group Series Pattern – 15 Questions in 15 Minutes https://kailashafoundation.org/2017/07/08/ntse-sat-letter-group-pattern-15-questions-15-minutes/ https://kailashafoundation.org/2017/07/08/ntse-sat-letter-group-pattern-15-questions-15-minutes/#respond Sat, 08 Jul 2017 14:30:32 +0000 http://kailashafoundation.org/?p=3505 NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows: Scholarship of Rs. 1250/- per month for class XI to XII. […]

The post NTSE MAT Letter Group Series Pattern – 15 Questions in 15 Minutes appeared first on Kailasha Foundation.

]]>
NTSE (National Talent Search Exam) for students is meant to identify and nurture talent. The NTSE exam is conducted every year at two levels: – Stage-I (State Level) and stage-II(National Level). About one thousand scholarships are awarded for different stages of education as follows:

  • Scholarship of Rs. 1250/- per month for class XI to XII.
  • Scholarship of Rs. 2000/- per month for undergraduates and postgraduates.

Generally, state level exam takes place in the month of November every year and notification come out in the month of September. The next level exam takes place in the month of May every year.

All students of Class X studying in recognized schools are eligible to appear for the stage-I examination. There will be no domicile restriction.

The examination will comprise these parts namely

  • Mental Ability Test (MAT)08
  • Language Test (LT)
  • Scholastic Ability Test (SAT)

For the preparation of such a prestigious exam, Team of Kailasha Foundation will bring a series of quizzes. In NTSE quiz series, this is the seventh quiz of Mental Ability Test under the head MAT in NTSE.

Attempt the quiz and find out your score.

Note: In this quiz, for every right answer you will be awarded 4 marks and for every wrong answer minus one mark will be awarded. You have 15 minutes to attempt the quiz.

KFDN LOGO - Copy - Copy

Hello ! Welcome to your NTSE MAT - Letter Group Series Pattern

Instructions:

Time: 20:00 min                                                                                                          Full Marks: 60

  1. There is negative marking of -1.00 for all incorrect answers chosen.
  2. There is no deduction for NOT attempted question.
  3. All questions carry equal marks and all 15 questions are of 4 marks each.
  4. All Questions are compulsory.

(Powered By: Kailasha Foundation - Fun & Learn Portal)

Name
Email
1. AZBY, ?, EVFU, GTHS.
2. STOP, TOPS, OPST, ?
3. EXTRAVAGANZA, TRAVAGANZA, TRAVAGANZ, AVAGANZ, ?
4. ACEGI, JLNPR, SUWYA, ?, KMOQS.
5. WRZRO, ABVUM, VQASP, ?, UPBTQ, CDTSK. Find the missing group.
6. ACMYA, FHNDF, ?, PRNNP, UWMSU, ZBNXZ.
7. ?, UMFRJ, FHUCU, TVGQI, GITDV, SUHPH
8. DIRECTIONS: All groups of letters are alike in some way. This is followed by five alternatives one of which is similar to the four groups of letters. Find the correct answer in each case.

QRP, GHI, RTS, KJI
9. DIRECTIONS: All groups of letters are alike in some way. This is followed by five alternatives one of which is similar to the four groups of letters. Find the correct answer in each case.

PRQ, NMO, WXV, LMK
10. DIRECTIONS: All groups of letters are alike in some way. This is followed by five alternatives one of which is similar to the four groups of letters. Find the correct answer in each case.

MKI, FDB, VTR, GEC
11. In the following series, find the missing term.

?, MLKLJN, MONLKM, ONPLNM, OQPONM, QPRNPO
12. DIRECTIONS: There are five groups of letters in the following questions. Of these, four are alike in some manner and one of them is different. Identify the one that is different.

 
13. DIRECTIONS: There are five groups of letters in the following questions. Of these, four are alike in some manner and one of them is different. Identify the one that is different.

 
14. DIRECTIONS: There are five groups of letters in the following questions. Of these, four are alike in some manner and one of them is different. Identify the one that is different.
15. DIRECTIONS: There are five groups of letters in the following questions. Of these, four are alike in some manner and one of them is different. Identify the one that is different.

You can always contact system administrator here for any kind of technical glitches.



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The post NTSE MAT Letter Group Series Pattern – 15 Questions in 15 Minutes appeared first on Kailasha Foundation.

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