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Lesson Posted on 26/07/2021 Learn Class IX-X Tuition

Arun

I am a tutor with 7 years of experience in teaching Sanskrit and Hindi . I have taken classes in person...

( + ) ' ' ( ) , - + = ; + = ; + = ... read more

**सन्धि** (सम् + धि) शब्द का अर्थ है 'मेल' या जोड़। दो निकटवर्ती वर्णों के परस्पर मेल से जो विकार (परिवर्तन) होता है वह संधि कहलाता है। संस्कृत, में परस्पर स्वरो या वर्णों के मेल से उत्पन्न विकार को सन्धि कहते हैं। जैसे - सम् + तोष = संतोष ; देव + इंद्र = देवेंद्र ; भानु + उदय = भानूदय।

- सन्धि के भेद

सन्धि तीन प्रकार की होती हैं -

- स्वर सन्धि (या अच् सन्धि)
- व्यञ्जन सन्धि { हल संधि }
- विसर्ग सन्धि

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Comments Answered on 13/06/2021 Learn Class IX-X Tuition

Bhavna

POWER=120W TIME=20 min=1200sec Energy=Power*Time E=120W*1200sec E=144000J E=144000J=144Kilojoule

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Answers 9 Comments Answered on 11/04/2021 Learn Class IX-X Tuition

Satyam

60 * 2 = 6 * a a= 10

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Answers 9 Comments 1 Answered on 24/08/2021 Learn Class IX-X Tuition

Gourav

Tungsten is a metal whose melting point is very high. It is used in bulbs because tungsten will not catch fire in the bulb. But it is not used in fuse wires because fuse wires need a low melting point.

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Answers 7 Comments 2 Lesson Posted on 18/06/2017 Learn Class IX-X Tuition

Numerical problems on force and pressure

Soumi Roy

I am an experienced, qualified tutor with over 8 years of experience in teaching maths and Science across...

Example 1: A force of 1200 N acts on the surface of area 10 cm2 normally. What would be the thrust and pressure on the surface?Given: Force F = 1200 N, Area A = 10 cm2 = 10 ×10-4 m2 = 10-3 m2Thrust = Normal pressure = F = 1200 NPressure P = F/A 1200N10−3m21200N10−3m2 ... read more

**Example 1:**

A force of 1200 N acts on the surface of area 10 cm^{2} normally. What would be the thrust and pressure on the surface?

Given:

Force F = 1200 N, Area A = 10 cm^{2} = 10 ×10^{-4} m^{2} = 10^{-3} m^{2}

Thrust = Normal pressure = F = 1200 N

Pressure P = F/A 1200N10−3m21200N10−3m2

= 1.2 ×× 10^{6} N/m^{2}

**Example 2****:**

The elephant weighs 20,000 N stands on one foot of area 1000 cm^{2}. How much pressure would it exert on the ground?

Given:

Force applied by elephant F = 20,000 N, area A = 1000 cm^{2} = 1000/100×100m^{2 }= 0.1 m^{2}

The pressure is given by

Pressure P = F/A

= 20,000N/0.1m2

= 2,00,000 N/m^{2}.

**Example 3:**

Calculate the pressure produced by a force of 800 N acting on an area of 2.0 m^{2}.

**Solution:**

Pressure is defined as force per unit area or P = F / A

P = (800 N) / (2.0 m2

)

P = 400 N / m2

= 400 Pa

**Example 4:**

The pressure of a gas contained in a cylinder with a movable piston is 300 Pa. The area of the piston is 0.5 m^{2}. Calculate the force that is exerted on the piston.

**Solution**

Pressure is defined as force per unit area or P = F / A

We multiply both sides of the equation by the area to solve for the force as

F = P A

F = (300 Pa) (0.5 m2

)

F = 150 (Pa) m2

= 150 (N / m2

) m2

F = 150 N

**Example 5:**

A swimming pool of width 9.0 m and length 24.0 m is filled with water to a depth of 3.0 m. Calculate pressure on the bottom of the pool due to the water.

**Solution:**

The pressure due to a column of fluid is calculated as the product of the height of the fluid times

the density of the fluid times the acceleration due to gravity. For water the density is d = 1000 kg /

m3

.

? P = d h g

? P = (1000 kg / m3

) (3.0 m) (9.8 m / s2

)

? P = 29400 kg m2 / m3

s2

To simplify the units we cancel one m term in the m2

term in the numerator and one m term in

the m3

term in the denominator to get

? P = 29400 kg m / s2

m2

We know that 1N = 1 kg m / s2

so we can write

? P = 29400 N / m2

= 29400 Pa

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Comments 65 Lesson Posted on 21/03/2017 Learn Class IX-X Tuition

Fastest way How to check if a number is a Perfect Square or not

Debraj Paul

I had completed b.Tech,m.Tech (d). I am an experienced, qualified icse board school teacher with over...

Squares of all integers are known as perfect squares. In this lesson, we will discuss a very interesting Mathematical shortcut: How to check whether a number is a perfect square or not. There are some properties of perfect squares which can be used to test if a number is a perfect square or not. They... read more

Squares of all integers are known as perfect squares. In this lesson, we will discuss a very interesting Mathematical shortcut: How to check whether a number is a perfect square or not. There are some properties of perfect squares which can be used to test if a number is a perfect square or not. They can definitely say if it is not the square. (i.e. Converse is not necessarily true).

All perfect squares end in 1, 4, 5, 6, 9 or 00 (i.e. Even number of zeros). Therefore, a number that ends in 2, 3, 7 or 8 is not a perfect square.

For all the numbers ending in 1, 4, 5, 6, & 9 and for numbers ending in even zeros, then remove the zeros at the end of the number and apply following tests:

**Digital roots are 1, 4, 7 or 9. No number can be a perfect square unless its digital root is 1, 4, 7, or 9. You might already be familiar with computing digital roots. (To find digital root of a number, add all its digits. If this sum is more than 9, add the digits of this sum. The single digit obtained at the end is the digital root of the number.)****If unit digit ends in 5, ten’s digit is always 2.****If it ends in 6, ten’s digit is always odd (1, 3, 5, 7, and 9) otherwise it is always even. That is if it ends in 1, 4, and 9 the ten’s digit is always even (2, 4, 6, 8, 0).****If a number is divisible by 4, its square leaves a remainder 0 when divided by 8.****Square of even number not divisible by 4 leaves remainder 4 while square of an odd number always leaves remainder 1 when divided by 8.****Total numbers of prime factors of a perfect square are always odd.**

**4539 **ends in 9, digit sum is 3. Therefore, **4539 **is **not **a perfect square.

**5776 **ends in 6, digit sum is 7. Therefore, **5776 may **be a perfect square.

**Step 1: A perfect square never ends in 2, 3, 7 or 8.**

This is the first observation you will make to check if the number is a perfect square or not. For example, consider the example 15623.

**15623**

By just noticing the number itself, we can conclude that 15623 cannot be a perfect square. We do not have to go to Step 2.

**Step 2: Obtain the digital root of the number****:**

How does the digital root of a number would help in determining if a number is a perfect square or not. It turns out; a perfect square will always have a digital root of 0, 1, 4 or 7.

Take the number 15626 for example. This number ends in digits 6. So it satisfies Step 1. But still we cannot conclude, this number as a perfect square.

Let’s take the digital root of this number.

**1**** 5 6 2 6 = 5 + 6 = 11 = 1 + 1 = 2**

So, the digital root of this number is 2. A perfect square will never have a digital root 2. Hence, we can conclude 15626 is not a perfect square.

Now, there is a rider for this shortcut though, even if both Steps are satisfied, that does not guarantee that the number is a perfect square.

Let us take up an example here. Consider the number **623461**, which is not a perfect square.

Notice that the unit digit is 1. This number could be a perfect square. Let us take the digital root.

**6**** 2 3 4 6 1**

The digital root of 623461 is 4. So it satisfies both Step 1 and 2. Still we cannot conclude that 623461 is a perfect square though.

However, this shortcut comes in really handy to eliminate obvious choices which are not a perfect square to solve competitive examination where you need to find the perfect squares.

**Is 14798678562 a perfect square? Is 15763530163289 a perfect square?**

Examine both the units digits and the digital roots of perfect squares to help determine whether or not a given number is a perfect square.

As we know a perfect square can only end in a 0, 1, 4, 5, 6, or 9; this should allow us to determine whether the first of our numbers is a perfect square. However, it isn't sufficient to draw a conclusion about the second number.

Again as we know that if a perfect square ends in 9; it’s tens digit is always even. Alas, even if we do this, it won't rule out numbers ending in 89, because '...89' is a possible square.

However, as we know no number can be a perfect square unless its digital root is 1, 4, 7, or 9; so, find the digital root of our second number. It’s 5. As 5 isn't in this list, then the number is definitely not a perfect square.

So, we can conclude, a number cannot be an exact or perfect square if:

- it ends in 2, 3,7 or 8

- it terminates in an odd number of zeros

- its last digit is 6 but its penultimate (tens) digit is even

- its last digit is not 6 but its penultimate (tens) digit is odd

- its last digit is 5 but its penultimate (tens) digit is other than 2

- its last 2 digits are not divisible by 4 if it is even numbe

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Comments 11 Answered on 05/05/2021 Learn Class IX-X Tuition

Arockia Michael Divya J

Mode=3Median-2Mean

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Answers 15 Comments 1 Answered on 23/03/2020 Learn Class IX-X Tuition

Apoorva P.

Double coincidence of wants occurs when two individuals swap their goods, in exchange for one another. This is also referred to as the 'perfect barter exchange'. In such cases, both the individuals are happy to exchange their good or commodities. For example, if two individuals want to exchange and... read more

Double coincidence of wants occurs when two individuals swap their goods, in exchange for one another. This is also referred to as the 'perfect barter exchange'. In such cases, both the individuals are happy to exchange their good or commodities.

For example, if two individuals want to exchange and place on a loaf of bread and a bag of apples, then this is known as double coincidence of wants. This results in an efficient transaction between the two individuals.

These types of transactions were practised during the barter economy system (cashless system), where two people had to swap each other's goods or commodities in exchange for one another. This type of system had its own limitations and drawbacks. One of the main limitations was that two people should have goods that they're willing to exchange.

For example, a loaf of bread cannot be exchanged for a bicycle because it would be no good. Then, there is no double coincidence of wants. However, if you can swap a loaf of bread for a bag of apples, then it satisfies the double coincidence of wants.

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Answers 19 Comments Answered on 19/04/2016 Learn Class IX-X Tuition

Birender Kumar

Tutor

PCPA means - Percent Compounded Per Annum. It also indicates that the Rate is for compound interest not for simple interest. Its true that it used for previous years CI.

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Answers 19 Comments Answered on 05/05/2015 Learn Class IX-X Tuition

Lakshmi Kumari

Tutor

Lencho was an honest and hard working farmer. He is the main character in the story---'a letter to god'.

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