Prime numbers from 1 to 100 | Prime Numbers Definition, Properties, Co-Prime (PDF)

In the article, there is a discussion about the definition, properties, Prime numbers from 1 to 100, coprime of prime numbers.

Definition of prime number

Prime numbers are those numbers that are divisible only by 1 and by themselves. A number that is not divisible by any additional number is called a prime number. Prime numbers range from two to infinity.

Properties of Prime Numbers

In the following 8 properties of prime numbers are given.

1. A prime number has only two factors.
2. Zero and 1 are not prime numbers.
3. 2 is an even prime number.
4. All numbers except 2 are prime numbers.
5. A prime number is not divisible by any number other than 1 and itself.
6. The first prime number is 2.
7. All prime numbers are greater than zero and one.
8. All prime numbers greater than one are divisible by one.

Prime numbers from 1 to 10

There are four prime numbers between 1 and 10. 2, 3, 5, 7 are prime numbers between one and 10

Prime numbers table from 1 to 100

Prime numbers from 11 to 20

There are four prime numbers between 11 and 20.

Prime numbers from 21 to 30

There are two prime numbers between 21 and 30.

Prime numbers from 1 to 100

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97 are prime numbers between 1 and 100. There are 25 prime numbers between 1 to 100.

Prime numbers table from 1 to 100

Odd prime numbers from 1 to 100

The number which is not divisible by 2 is called an odd prime number. Prime number except 2 is an odd prime number. There are 24 prime numbers from one to 100.

Odd prime numbers table from 1 to 100

Even prime numbers from 1 to 100

The prime number which is divisible by only two is called an odd prime number. Only 2 odd is a prime number.

Composite numbers from 1 to 100

Composite numbers don’t even exist.

Prime Numbers and Co-prime Numbers

Example

• 5 and 9 are co-primes.
• 6 and 11 are co-primes.
• 18 and 35 are co-primes.

What is Twice Prime Number

Two prime numbers between which there is a difference of 2. Twins are called prime numbers.

Easy Way to Find Prime Numbers

1. Step-1

First, find the nearest square of the given number

2. Step-2

Find the square root of that number

3. Step-3

All the prime numbers that are less than or equal to the number obtained, divide by the given number.

4. Step-4

If the given number is not completely divisible then it is a prime number.

1. First, find the nearest square of the given number
1. Why is 11 not a prime number?

11 is a prime number because it is not divisible by any number other than 1 and itself. 11 can have only two factors.

2. What is the shortcut to find prime numbers from 1 to 100?

3. What is the fastest way to find a prime number?

4. Is there a formula for prime numbers?

6n + 1 or 6n – 1, n = natural number

5. What is the smallest prime number?

2

6. What is the only even prime number?

2

7. Is 3 the smallest prime number?

No! the Smallest prime is 2

8. What is the smallest prime number between 1 to 20?

2 is the smallest prime number between 1 to 20

9. Why 0 and 1 are not prime numbers?

Because zero is a whole number. There is no factor of zero. Similarly, 1 has only one factor. So 0 and 1 are not prime numbers.

10. What is the greatest prime number between 1 to 10?

7 is the greatest prime number between 1 to 10

11. Is 1 a prime number?

No

12. Is 91 a Prime Number?

No

13. Is 2 a Prime Number?

Yes

14. Is 101 a Prime Number?

Yes

15. What is the greatest prime number between 1 to 20?

19

Trigonometry formulas

Whole Numbers Definition, Property, Example Part-2

Whole Numbers Definition

If zero is also included in the natural number( 1, 2, 3, 4, 5, 6, 7 …. ∞ ), then those numbers are Whole numbers.ex – 0, 1, 2, 3, 4, 5, 6, 7, 8 ……. ∞

If W is removed from the word whole, the word becomes a hole word. And we know. That the hole size looks like zero. So from the hole, we will remember zero. Numbers from 0 to infinity are called hole numbers.

Whole Numbers Examples

555, 687, 999, 0, 1800, 1520, 888 etc.

The predecessor of the whole number

The predecessor of the whole number is that number. Which comes 1 digit before the given number. That is, 1 is subtracted from that number to find the predecessor of a whole number.

Ex – What will be the predecessor of 555?

We know To find the predecessor of any number, one is subtracted from that number. Hence the predecessor of 555 is (555-1) = 554.

What will be the predecessor of 2?

Ans – (2-1) = 1

Subtract one of them to find the predecessor of two.

The successor of the whole number

The successor of a whole number is that number. Which comes after 1 digit of the given number. Or to find the successor of a hole number, one is added to that number.

Ex – What will be the successor of 15?

Ans – To find the successor of 15 can be obtained by adding a digit to it. 15 + 1 = 16

What will be the successor of 120?

120+1 = 121

Property of Whole Numbers

Closure Property

If two whole numbers are multiplied and added. So the number received is the whole number. On the other hand, if two whole numbers are divided and subtracted, the number obtained may or may not be a whole number.

The sum of two whole numbers is the whole number.

Whole Number + Whole Number = Whole Number

Ex – 2+2 = 4, 0+1 = 1, 5+8 = 13

Multiplication

Multiplication of two whole numbers is obtained as a whole number.

Whole Number × Whole Number = Whole Number

Ex – 2×2 = 4 , 5×8 = 40, 12×2 = 24

Subtraction

If the smaller whole number is subtracted from the larger whole number then the number obtained will be the whole number. Conversely, if the whole number is subtracted from the smaller whole number, the number received will not be the whole number.

Whole Number “x” – Whole Number “y” = Whole Number ( x>y)

Ex: 4 – 2 = 2, 10 – 5 = 5, 110 – 20 = 90, 999 – 111 = 888

Whole Number “x” – Whole Number ‘y” = Whole Number (x=y)

Ex: 4 – 4 = 0, 15 – 15 = 0, 50 – 50 = 0, 80 – 80 = 0

Whole Number “x” – Whole Number “y” = integer ( x<y)

Ex: 15 – 20 = -5, 40 – 50 = -10, 130 – 140 = -10

Division

The division of two whole numbers will be the whole number only if the dividend is completely divisible by the divisor.

In the above situation, only the whole number can be obtained in case of division. If the quotient is the point or negative. So the whole number will not be received.

Commutative Property

The whole number follows the Commutative Property in addition and multiplication. On the contrary, it does or may not follow.

Two whole numbers can be added in any case, the whole number is obtained. According to the Whole Numbers Definition, these numbers range from zero to infinity

Whole Number “a” + whole Number “b” = Whole Number “b” + Whole Number “a”

a + b = b + a

Ex: 5 + 4 = 4 + 5 In this case, if 5 and 4 are added or 4 and 5 are added, the same answer will come in the two cases.

Multiplication

According to the Whole Numbers Definition, these numbers range from zero to infinity

Whole Number “a” x whole Number “b” = Whole Number “b” x Whole Number “a”

a x b = b x a

Ex: 5 x 4 = 4 x 5| In this case, if 5 and 4 or 4 and 5 are multiplied, the same answer will be given in two cases.

Subtraction

The whole number does not follow the Commutative Property in case of subtraction.

Ex: a – b ≠ b -a

Division

In the case of division, the whole number does not follow the Commutative Property.

Associative Property

If three whole numbers are added or reduced in any case, then, in that case, the whole number is obtained. The whole number in addition and subtraction follows the Associative Property.

In the case of Yoga, the Whole Number follows the Associative Property.

Ex: (a + b) + c = a + (b + c)

Multiplication

In the case of multiplication, the Whole Number follows the Associative Property.

Ex: (a x b) x c = a x (b x c)

Subtraction

In the event of subtraction, the Whole number does not follow the Associative Property.

( a – b ) – c ≠ a – ( b – c )

Division

The whole number does not follow the Associative Property in the position of the part.

Distributive Property

In the case of addition and multiplication, the Whole number follows the Distributive Property.

FAQ

Is 10 a whole number?

True

Is 9 a whole number?

True

What are the first 5 whole numbers?

0, 1, 2, 3, 4

Is seven a whole number?

True

Is 18 a whole number?

True

Is 100 a whole number?

True

Is 13 a whole number?

True

What is a whole number between 1 and 20?

2, 3, 4,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Is 0 a whole number?

Zero is a whole number. It is neither positive nor negative integer. This is the link between Positive and Negative.

Can whole numbers be negative?

No

What are the properties of whole numbers?

The whole number has four properties. 1 – Closure Property, 2 – Commutative Property, 3 – Associative Property, 4 – Distributive Property

Are whole numbers closed under subtraction?

Ans – The whole number is closed under the Subtraction.

Are whole numbers closed under addition?

Ans – The whole number is closed under the Subtraction.

Are whole numbers also natural numbers?

All whole numbers except zero are natural numbers. All-natural numbers are whole numbers. But not all whole numbers are natural numbers.

Are whole numbers rational numbers?

According to the Whole Numbers Definition, these numbers range from zero to infinity. Every whole number can be written in a rational number.

Are whole numbers closed under multiplication?

Yes

Are whole numbers associative under subtraction?

The subtraction of whole numbers is not associative

Which the whole number has no predecessor?

According to the Whole Numbers Definition. The whole zero (0) has no predecessor.

Which of the whole number is not a natural number?

According to the Whole Numbers Definition. Zero (0) is not a natural number.

Which the whole number doesn’t have a successor?

All whole numbers have successors.

Which the whole number is not a rational number?

According to the Whole Numbers Definition. The rational numbers whose values are completely positive. The same number is the whole number.

Quiz

Definition of Natural Number and property, for example, Sum part-1

Definition of Natural Number and property, example, Sum part-1

Definition of Natural Number

The definition of natural number is hidden in its name itself. how?

The number that is used in counting natural things. These are called natural numbers.

It is also called counting numbers. Because this number is used to count anything.

Natural numbers are positive integers. The values of integer numbers range from – ∞ to + ∞. One part of which is a positive integer and the other negative integer. A positive integer is a natural number.

Natural number value

The value of a natural number varies from 1 to ∞.

Ex – 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ……… ∞

Natural Numbers Examples

Find the number of pens shown in the above picture.
To find the number of pens present in this picture, we will start counting the pens from one end.

Let’s start counting the pen from right to left.

Thus the first red pen, Second blue pen, Third green pen, Fourth yellow pen, Fifth orang pen, Sixth black pen

An object is started to be counted by one. No to zero. This proves it. Of zero is not a natural number.

We started counting pens from one to six. So the number of pens is six.

Property of Natural Number

1. Closure Property
2. Associative Property
3. Commutative Property
4. Distributive Property

Closure Property

Adding and multiplying any two or more natural numbers gives a natural number.

The sum of two natural numbers is a natural number.

ex – 2+2 = 4. 5+3 = 8, 9+2 = 11

Multiplication

The result of two natural numbers is a natural number.

Ex – 2×4 = 12, 5×8 = 40, 7×3 = 21

Subtraction

The subtraction of two natural numbers may or may not be a natural number. If the smaller natural numbers are subtracted from the larger natural numbers, then the obtained numbers will be natural numbers.

Conversely, if the larger natural number is subtracted from the smaller natural number, then the number obtained will not be a natural number.

Ex 5 – 3 = 2, 7 -10 = -3

Division

The quotient of two natural numbers may or may not be a natural number.

Ex – 10/8 = 1.25, 10/5 = 2

Associative Property

Associative property of natural number is correct in case of addition and multiplication.

a + ( b + c ) = ( a + b ) + c

Multiplication

a × ( b × c ) = ( a × b ) × c

Associative property of natural number is not correct in the case of Subtraction and Division.

Subtraction

a – ( b – c ) ≠ ( a – b ) – c

Division

a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c

Commutative Property

Commutative Property of natural number is correct in case of addition and multiplication

Ex – x + y = y + x and a × b = b × a.

Commutative Property of natural number is not correct in case of addition and multiplication.

x – y ≠ y – x and x ÷ y ≠ y ÷ x.

Distributive Property

Distributive Property of natural number is correct in case of addition and multiplication

a × (b + c) = ab + ac

Distributive Property of natural number is not correct in case of addition and multiplication.

a × (b – c) = ab – ac.

Natural Numbers from 1 to 100

Which natural number has no successor?

No!
There is no natural number that has no successor. All-natural numbers have successors.

Which natural number has no predecessor?

No!
There is no natural number that has no predecessor. All-natural numbers have a predecessor.

Who invented natural numbers?

Natural numbers always existed. But we started studying it seriously since the time of Greek philosophers, Pythagoras and Archimedes.

What is the smallest natural number?

1 is the smallest natural number.

What is the natural number with an example?

1, 2, 3, 4, 5, 6, 7, 8, 9 …….

What is the natural number definition?

The numbers that are used to count natural objects. It is called a natural number.

What is the natural number symbol?

The natural number is represented by “N“.

which natural number is nearest to 8485?

8484 and 8486

Which natural number is equal to its cube?

27 is a cube of 3. 8 is a cube of 2. 64 is a cube of 4 etc.

Are natural numbers negative?

No!
Natural numbers are only positive.

Are natural numbers rational?

No!
Because an object cannot be counted in p / q. Can we tell a pen that the number of pens is 2/5. No no When counting an item, it is considered to be the same.

Are natural numbers whole numbers?

All whole numbers are natural numbers except zero.

Are natural numbers countable?

Yes

Are natural numbers real numbers?

Yes

Can a natural number be decimal?

No

Can Natural Numbers be Rational?

No

Can a natural number be decimal?

No

A natural number is also known as

counting numbers

Natural number to 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

What is the sum of natural numbers from 1 to 100?

5050

Three natural numbers after 1500

Ans – 1501, 1502, 1503

All Trigonometry Formulas For Class 10, 11, 12 (PDF)

All Trigonometry Formulas For Class 10, 11, 12 (PDF)

Trigonometry Formulas For Class 10

Trigonometry is an important part of math. Trigonometry is important in terms of board examination. Therefore, to solve the problems of trigonometry, it is necessary to remember the formulas. For this reason, in this article of All Trigonometry Formulas For Class 10, 11, 12, we have shown how to remember through logic.

Trigonometric Ratio

In a right-angled triangle, the opposite side of a given angle is perpendicular, the opposite side of the right angle is the hypotenuse and the third side is the base.

In ΔABC,
∠=90°,∠C=θ

∴ The side AC is the hypotenuse,
AB is perpendicular
and BC is the base.

From the Pythagoras theorem,

Relationship between arms and angles

Finding the formulas of cosec, sec, and a cot can be obtained by reversing the formulas of sin, cos, and tan.

This means that the formula of cosec will be the inverse of sin, the formula of sec will be the inverse of sec, the formula of cot will be inverse of tan. The numerator is replaced by the numerator and denominator.

Ratios Of Particular Angle Trigonometry Formulas For Class 10

The ratio formula of trigonometry is very important from this point of view. Which is important for all classes of students. In The Ratio Trigonometry Formulas For Class 10, you can remember sin, cos, and tan value. and the other three are opposite like this sin is to Reverse cosec. cos is Reverse to sec and tan Reverse to cot

The trigonometrical function of the sum

There are definite relations between trigonometric functions of two angles of a triangle.

In this article, “Trigonometry Formulas For Class 10” of math is given. It is based on these relations, especially their sum and difference.

5 आधुनिक समद्विबाहु समकोण त्रिभुज का क्षेत्रफल का सूत्र 2020 (right-angled isosceles triangle)

इस नोट्स में 5 समद्विबाहु समकोण त्रिभुज का क्षेत्रफल का सूत्र एवं इन सूत्रों का निगमन व इससे सम्बंधित प्रशन दिए गए है

आसान समद्विबाहु समकोण त्रिभुज की परिभाषा

समद्विबाहु समकोण त्रिभुज में एक कोण का मान 90० अन्य दोनों कोणों का मान 45० और दो भुजाये बराबर होती है।

समद्विबाहु समकोण त्रिभुज का क्षेत्रफल का सूत्र का निगमन

प्रथम साधारण क्षेत्रफल सूत्र का निगमन

इस सूत्र का प्रयोग सभी त्रिभुजो में किया जाता है।

द्वितीय क्षेत्रफल सूत्र का निगमन

जहाँ A = क्षेत्रफल, b = आधार भुजा और h त्रिभुज की उचाई।

माना भुजा AB = a, भुजा BC = b (AB = BC)

इस त्रिभुज की दो भुजाये बराबर और एक कोण समकोण होता है। तो तीसरी भुजा पाइथागोरस प्रमेय कर लेते है। जो निम्न है।

जहाँ AC कर्ण भुजा, AB और BC दो समान भुजाये।

अतः तीसरी भुजा AC = a √ 2

🔺ABC में ∠B = 90० और भुजा AB = भुजा B

त्रिभुज ABC का क्षेत्रफल =

तृतीय क्षेत्रफल सूत्र का निगमन

उपरोक्त सूत्र में 2/2 से गुणा करने पर

समीकरण 2 AC = a √ 2 = कर्ण का मान उपरोक्त समीकरण में रखने पर

चतुर्थ क्षेत्रफल सूत्र का निगमन

इस विधि में सर्वप्रथम निम्न सूत्र का प्रयोग करते है।

जहाँ A = क्षेत्रफल

a = द्वितीय भुजा

b = तृतीय भुजा

c = तृतीय भुजा

s = परिमाप / 2 = p/2

उपरोक्त सूत्र में s का मान p/2 रखने पर क्योकि s का मान परिमाप (p) का आधा होता है।

जहाँ भुजा a = c (समद्विबाहु त्रिभुज की दो भुजाये बराबर होती है।

चतुर्थ क्षेत्रफल सूत्र (A4)

यदि समद्विबाहु समकोण त्रिभुज का परिमाप (p) और भुजाये ज्ञात हो तो क्षेत्रफल ज्ञात करने के लिए उपरोक्त सूत्र का प्रयोग करेगे।

चतुर्थ क्षेत्रफल सूत्र का निगमन

दोस्तों इस सूत्र को आप सिद्ध करके कमेंट बॉक्स में लिखे!

3 समद्विबाहु त्रिभुज का क्षेत्रफल ज्ञात करने का सूत्र

समद्विबाहु त्रिभुज का क्षेत्रफल ज्ञात करने का सूत्र निम्न है

समद्विबाहु त्रिभुज के प्रशन (Sambahu Tribhuj Question)

1. एक समद्विबाहु की दो भुजाओ की लम्बाई क्रमशः 15 cm और 22 cm तो त्रिभुज का क्षेत्रफल ज्ञात कीजिये?

(a) 22√26 या 15√(1711/2 )

(b) 22√16 या 15√(1711/2 )

(c) 11√26 या 16√(1711/2 )

(d) 22√26 या 16√(1711/2 )

हल

प्रशन में यह नहीं बताया गया है। की कौन सी भुजा समान है। प्रथम भुजा को समान फिर दूसरी भुजा को समान माना जायेगा। इसलिए क्षेत्रफल के दो मान आयेगे।

माना – 15 cm वाली भुजाये समान है।

अतः परिमाप = 2a + b

= 2 ✖️ 15 + 22

= 30 + 22

परिमाप = 52 cm

हम जानते है s = परिमाप (p) / 2

s = 52 / 2

s = 26

निम्न सूत्र में s का मान रखने पर

माना 22 cm वाली दो भुजाये समान है।

परिमाप = 2a + b

= 2 ✖️ 22 + 15

= 44 + 15

परिमाप = 59 cm

हम जानते है s = परिमाप /2 = 59 / 2

उत्तर 22√26 या 15√(1711/2 ) है

2. एक समद्विबाहु त्रिभुज की समान और असमान भुजाओ का अनुपात 3:5 है। यदि इसका परिमाप 110 cm है। तो इसका क्षेत्रफल क्या होगा?

(a) 125

(b) 250

(c) 250 √ 11

(d) 125 √ 11

हल – दिया समान और असमान भुजाओ का अनुपात = 3:5 , परिमाप (p) = 110 cm

माना समान भुजाये (a) = 3x

असमान या तीसरी भुजा (b) = 5x जो निम्न चित्र में दिखया गया है।

परिमाप (p) =2a + b

110 = 2 ✖️ 3x + 5x

110 = 6x + 5x

110 = 11x

11x = 110

x = 10

अतः समान भुजाये (a) = 3x = 3 ✖️ 10 = 30 cm

असमान भुजा (b) = 5x = 5 ✖️ 10 = 50 cm

नोट – जब समद्विबाहु त्रिभुज का परिमाप और भुजाये ज्ञात हो तो निम्न सूत्र का प्रयो करते है।

उत्तर (c) 250 √ 11 सही है

ट्रिक से 3 समद्विबाहु त्रिभुज का क्षेत्रफल का सूत्र याद करे?

किसी भी मैथ के प्रश्नों को हल करने के लिए सूत्र की आवश्यकता होती है। लेकिन इन सूत्रों को लंबे समय तक याद रखना मुश्किल हो जाता है। इस नोट्स में समद्विबाहु त्रिभुज का क्षेत्रफल का सूत्र ट्रिक के माध्यम से कैसे याद लम्बे समय तक याद रखे बताया गया है। samdibahu tribhuj ka kshetrafal ka formula samdibahu tribhuj ka kshetrafal ka sutra

यदि इन सूत्रों को ट्रिक के माध्यम से याद किया जाये तो यह लम्बे समय तक याद रहते है। समद्विबाहु त्रिभुज (Isosceles triangle) 3 महत्वपूर्ण सूत्र जो निम्न है।

प्रथमः समद्विबाहु त्रिभुज का क्षेत्रफल का सूत्र

जहाँ A = समद्विबाहु त्रिभुज का क्षेत्रफल,

s = समद्विबाहु त्रिभुज के परिमाप का आधा = p/2

b = आधार भुजा

a और c दो समान भुजाये

ट्रिक – sabc (साबस)

जहाँ s = समद्विबाहु त्रिभुज का आधा

b = आधार

a और c समद्विबाहु त्रिभुज की दो समान भुजाये है

आप ने यह ट्रिक तो याद कर ली लेकिन इस ट्रिक से सूत्र को कैसे लिखे?

1. सबसे पहले इस ट्रिक को करणी में लिखे

2. इस ट्रिक में चार अल्फाबेट है तो s को चार बार लिख ले

3. अब इक s में a को, दुसरे s में से b को, तीसरे s में c को घटा दे और चौथे s को वैसे ही रहने दे

हम जानते है कि समद्विबाहु त्रिभुज में दो भुजाये बराबर होती है। भुजा a = भुजा c, जहाँ भुजा b आधार , s परिमाप का आधा।

द्वितीय समद्विबाहु त्रिभुज का क्षेत्रफल का सूत्र

यह सूत्र साधारण तौर पर सभी त्रिभुजो में प्रयोग किया जाता है।

जहाँ A = समद्विबाहु त्रिभुज का क्षेत्रफल का सूत्र, b = आधार, h = उचाई

ट्रिक – आउच

जहाँ

“आ”का अर्थ = त्रिभुज का आधार

“उच” का अर्थ = उचाई

“आधा” का अर्थ = 1/2

तृतीय समद्विबाहु त्रिभुज का क्षेत्रफल का सूत्र

ट्रिक – आधार का चाचा घर में चार भुज वर्ग के पीछे वर्ग

नोट – यहाँ पर का, की, के, में आदि शब्द निर्थक है।

जहाँ

“आधार ” का अर्थ = त्रिभुज की आधार भुजा b

“चा” का अर्थ = चार

“घर” का अर्थ = करणी

“चार” का अर्थ = 4

“भुज” का अर्थ = भुजा

“वर्ग” का अर्थ = a2

“पीछे” का अर्थ = ऋण

“आधार” का अर्थ = आधार भुजा

“वर्ग” का अर्थ = वर्ग भुजा

3 तरीको से समद्विबाहु त्रिभुज का क्षेत्रफल कैसे ज्ञात करे? (Isosceles triangle)

इस नोट्स में समद्विबाहु त्रिभुज का क्षेत्रफल (samdibahu tribhuj ka kshetrafal) ज्ञात करने की तीन विधि का वर्णन किया गया है

प्रथम विधि

तीनो भुजाये और परिमाप (s) पता होने पर समद्विबाहु त्रिभुज का क्षेत्रफल कैसे ज्ञात करे?

इस विधि में समद्विबाहु त्रिभुज का क्षेत्रफल तभी ज्ञात किया जा सकता है। जब तक इसकी भुजाये और परिमाप ज्ञात हो।

उदहारण

निम्न चित्र में एक समद्विबाहु त्रिभुज दिखया गया है। जिसकी दो समान भुजाये a, आधार b और परिमाप p है। तो इसका क्षेत्रफल क्या होगा?

Step-1 इस विधि में सर्वप्रथम निम्न सूत्र का प्रयोग करते है।

जहाँ A = क्षेत्रफल

a = द्वितीय भुजा

b = तृतीय भुजा

c = तृतीय भुजा

s = परिमाप / 2 = p/2

Step-2 उपरोक्त सूत्र में s का मान p/2 रखने पर क्योकि s का मान परिमाप (p) का आधा होता है।

जहाँ भुजा a = c (समद्विबाहु त्रिभुज की दो भुजाये बराबर होती है।

यदि समद्विबाहु त्रिभुज का परिमाप (p) और भुजाये ज्ञात हो तो क्षेत्रफल ज्ञात करने के लिए उपरोक्त सूत्र का प्रयोग करेगे।

उदहारण प्रशन

1. एक समद्विबाहु त्रिभुज जिसकी दो भुजाये 30 cm, आधार 50 cm और परिमाप 110 cm तो इसका क्षेत्रफल क्या होगा?

हल-

दिया है भुजा c = a = 30

आधार = 50

s =परिमाप (p)/2 = 110 = 110 / 2 = 55

निम्न सूत्र में

या

फिर p का मान और भुजाओ का मान निम्न सूत्र में रखने पर

द्वितीय विधि

आधार (b) और उचाई (h) पता होने पर समद्विबाहु त्रिभुज का क्षेत्रफल कैसे ज्ञात करे?

यदि समद्विबाहु त्रिभुज का आधार और उचाई ज्ञात हो तो इस विध का प्रयोग करते है।

दिखाए गए त्रिभुज का आधार b और उचाई h है तो इसका क्षेत्रफल उनके आधार और उचाई के गुणनफल का आधा होगा । अतः निम्न सूत्र में आधार और उचाई का मान रखकर इसका क्षेत्रफल ज्ञात कर लेते है ।

जहाँ b = आधार और h = उचाई है।

उदहारण प्रशन

2. एक समद्विबाहु त्रिभुज जिसका आधार 50 cm और उचाई 25 cm है। तो इसका क्षेत्रफल क्या होगा?

हल

दिया है । आधार (b) = 50 cm

उचाई (h) = 25 cm

आधार और उचाई का मान निम्न सूत्र में रखने पर ।

\mathbf{A= \frac{1}{2}\times b \times h }
{A= \frac{1}{2}\times 50 \times 25 }
{A= 25 \times 25 }
Ans \: A= 625 \, cm^{2}

तृतीय विधि

केवल भुजाये पता होने पर समद्विबाहु त्रिभुज का क्षेत्रफल कैसे ज्ञात करे?

इस विधि का प्रयोग तब करते है जब समद्विबाहु त्रिभुज की भुजाये दी हो तो निम्न सूत्र का प्रयोग करके क्षेत्रफल ज्ञात कर सकते है।

\mathbf{A=\frac{b}{4}\sqrt{4a^{2}-b^{2}}}

जहाँ a समद्विबाहु त्रिभुज के दो समान भुजाये है।

b = आधार

A = क्षेत्रफल

3. एक त्रिभुज जिसकी दो समान भुजाये 30 cm आधार 50 cm तो इसका क्षेत्रफल क्या होगा?

हल

दिया समान भुजाये (a) = 30, आधार (b) = 50 cm , A = ?

\mathbf{A=\frac{b}{4}\sqrt{4a^{2}-b^{2}}}
\rightarrow {A=\frac{50}{4}\sqrt{4\times 30^{2}-50^{2}}}
\rightarrow {A=\frac{50}{4}\sqrt{4\times 900-22500}}
\rightarrow {A=\frac{50}{4}\sqrt{4\times 900-2500}}
\rightarrow {A=\frac{50}{4}\sqrt{3600-2500}}
\rightarrow {A=\frac{50}{4}\sqrt{1100}}
\rightarrow {A=\frac{50}{4}\sqrt{11\times 100}}
\rightarrow {A=\frac{50\times 10}{4}\sqrt{11}}
Ans\: {A=125\sqrt{11}}

101 Memorable Gk For Class 2 Question Answer With Quiz

6 Important Topics Gk For Class 2 Question Answer

In this article, we have covered 6 important topics gk for class 2 question answer which are as follows.1- About animal, birds, body parts, plant, public figure, state and capital gk for class 2 question answer and other gk questions for class 2

gk for class 2 question answer,

Q1 – How many legs does a cow have?

Ans – Four Legs

Q2 – What type of animal is a cow vegetarian or non-vegetarian?

Ans – vegetarian

Q3 – What is a cow’s child called?

Ans – Cow-calf

Q4 – Which is the tallest animal on earth?

Ans – Giraffe

Q5 – What is the fastest running animal?

Ans – Tiger

Q6 -Which is the largest living animal on the ground?

Ans – elephant

Q7 – Are lions pets?

Ans – No

Q8 – Which animal is called the king of the jungle?

Ans – Lion

Q9 – What kind of animal is a lion vegetarian or non-vegetarian?

Ans – non-vegetarian

Q10 – Which animal has the highest smelling ability?

Ans – Dogs

Q11 – What do we get from a cow?

Ans – Milk

Q12 – How many legs does a monkey have?

Ans – Two Legs

Q13 – How many bones does an adult human body have?

Ans – 306

Several types of birds are shown in the following paragraph. We provide gk questions for class 2.

Q14 -Which is the national bird of India?

Ans – Peacock

Q15 – What is the smallest bird on earth?

Ans – Hummingbird

Q16 – What is the world’s largest bird?

Ans – Ostrich

Q17 – What is a bird that can speak in human voices?

Ans – Parrot

In this following paragraph, we provided best gk questions for class 2 students from the human body parts

Q18 – How many bones does an adult human body have?

Ans – 306

Q19 – Which part of our body is always functioning?

Ans – Heart

Q20 – Which is the smallest bone in the human body?

Ans – Stepic

Q21 – Which is the largest bone in the human body?

Ans – firmer

Q22 – How many fingers do we have in our hands?

Ans – 10 fingers

Q23 – How many fingers are there in our bodies?

Ans – 20 fingers

Q24 – How many fingers do we have on our feet?

Ans – 10 fingers

Q25 – How many eyes does a human body have?

Ans – Two eyes

Q26 – What is the main function of eyes in the human body?

Ans – To see

Q27 – How many legs do our bodies have?

Ans – Two legs

Q28 – How many hands do we have?

Ans – Two Hands

Q29 – What is the main function of the nose in the human body?

Ans – to smell

Q30 – What is the main function of the tongue in our body?

Ans – Taste detection

The following paragraphs are easy gk for class 2 question answer from plants.

Q31 – What is the main function of plant roots?

Ans – Absorbing mineral salts and water from the ground.

Q32 -Where does plant food become?

Ans – In leaves

Public Figure

In the following questions, the names of great persons of India are given. Regarding whom you will be asked questions, there will be four options. One of which you have to choose the right option.

Q33 – Who is the Father of the Nation of India?

Ans – Mahatma Gandhi.

Q34 – Who is Sachin Tendulkar?

Ans – Cricketer.

Q35 – Who is the first Prime Minister of India?

Ans – Pandit Jawaharlal Nehru.

Q36 – The current Prime Minister of India.

Ans – Narendra Modi.

Q37 – Who is called Iron Man?

Ans – Sardar Vallabh Bhai Patel.

Q38 – First Woman President of India.

Ans – Pratibha Devi Singh Patil

Q39 – Who is known as Missile Man?

Ans – A P J Abdul Kalam.

Q40 – Who is B.R Ambedkar?

Ans – Indian Constitution Maker.

Q41 – Who is Indira Gandhi?

Ans – Father of the Nation

Q42 – First woman Prime Minister of India.

Ans – Pratibha Devi Singh Patil

Q43 – First President of India.

State Capitals

In the following paragraphs, GK question related to the state and their capitals is related to class 2, which is a very important Gk For Class 2 Question Answer.

Q44 – Where is the capital of Andhra Pradesh located?

Q45 – Where is the capital of Arunachal Pradesh located?

Ans – Itanagar

Q46 – Where is the capital of Assam located?

Ans – Dispur

Q47 – Where is the capital of Bihar located?

Ans – Patna

Q48 – Where is the capital of Chhattisgarh located?

Ans – Raipur

Q49 – Where is the capital of Goa located?

Ans – Panaji

Q50 – Where is the capital of Gujarat located?

Ans – Gandhinagar

4 साधारण ब्याज का सूत्र, परिभाषा, सवाल

साधारण ब्याज

इस आर्टिकल में “साधारण ब्याज का सूत्र”, परिभाषा और इस कैप्टर से आये सभी महत्वपूर्ण सवालो का हल| जो प्रतियोगी परीक्षा की दृष्टी से महत्वपूर्ण है|

परिभाषा

यदि किसी धनराशि को निश्चित दर से किसी निश्चित समय के लिए उधार लिया जाये तो समय समाप्ति के बाद मूलधन के अतिरिक्त धन देना होता है| इस अतिरिक्त धन को व्याज कहते है|

“एकांक ब्याज की दर से किसी मूलधन पर एकांक समय में लगे ब्याज को साधारण ब्याज कहते हैं”

उदहारण

Q – 500 रुपया का 20% की दर से 3 वर्ष का साधारण व्याज ज्ञात कीजिये?

हल

\mathbf{साधारण\, ब्याज = \frac{मूलधन\times दर\times समय}{100}}

जहाँ p = 5000, r = 20%, t = 3 वर्ष, SI = ?

\mathbf{SI = \frac{500\times 20\times 3}{100}}

= 3000 Rs

साधारण व्याज का सूत्र

\mathbf{1\cdot साधारण\, ब्याज = \frac{मूलधन\times दर\times समय}{100}} \mathbf{2\cdot मूलधन = \frac{साधारण\, ब्याज\times 100}{दर\timesसमय}} \mathbf{3\cdot दर = \frac{साधारण\, ब्याज\times 100}{मूलधन\timesसमय}} \mathbf{4\cdot समय = \frac{साधारण\, ब्याज\times 100}{मूलधन\timesदर}}

Note

साधारण ब्याज का सूत्र जिसमे में 100 को सामिल किया गया है| क्योकि दर प्रतिशत में होता है| प्रतिशत को संख्या में बदलने के लिए 100 से भाग देना होता है|

सवालो में यदि समय दिन में दिए जाये तो उसमे 365 दिन से भाग देते है| या फिर समय महीनो में दिए हो तो 12 से भाग देते है|

महत्वपूर्ण सवाल

Q1 – 1000 रु का 20% की दर से 73 दिन का साधारण व्याज ज्ञात कीजिये?

हल

दिया है साधारण ब्याज (p) = 1000 रु,दर (r) = 20%, समय (t) = 73 दिन = 73/365

\mathbf{SI = \frac{p\times r\times t}{100}} \mathbf{SI = \frac{100\times 20\times 73}{100\times365}}

= 400 Ans

Q2 – 9000 रु का 12% की दर से 3 महीने का साधारण ब्याज क्या होगा?

हल

दिया है p = 9000 रु, r = 12%, t = 3

\mathbf{SI = \frac{p\times r\times t}{100}} \mathbf{SI = \frac{9000\times 12\times 3}{100\times12}}

= 270 रु

Q3 – 5000 रु का कितने प्रतिशत की दर से 3 वर्ष का साधारण ब्याज 300 रु होता है?

हल

दिया है p = 500, r = ?, t = 3 वर्ष

\mathbf{r= \frac{SI\times 100}{p\times t}} \mathbf{r= \frac{3000\times 100}{5000\times 3}}

= 20%

Q4 – वह कौन सी धन राशी है| जिसका 5% की दर से 6 वर्ष का साधारण ब्याज 1800 रु होगा?

हल

दिया है p = ?, r = 5%, SI = 1800, t =6 वर्ष

\mathbf{p = \frac{SI\times 100}{r\times t}} \mathbf{p = \frac{1800\times 100 }{5\times6}}

= 600

Q5 – 8000 रुका 10% की दर से कितने समय में 9600 रु हो जायेगा?

हल

दिया है t = ?, SI = 9600, p =800, r =10%

\mathbf{t= \frac{SI\times 100}{p\times r}} \mathbf{t= \frac{1600\times 100}{800\times 10}}

= 2 वर्ष