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Tuesday, 28 April 2020

NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.2


NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.2

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NCERT Solutions for class 10 Maths Chapter 3 Exercise 3.2 pair of linear equations in two variables in Hindi Medium and English Medium updated for new academic session 2020-2021 based on latest NCERT Books.
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NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.2
Class:10Subject:Maths – गणितChapter 3:Exercise 3.2
10 Maths Chapter 3 Exercise 3.2 Solutions
NCERT Solutions for class 10 Maths Chapter 3 Exercise 3.2 in English medium and Hindi Medium are given below updated for CBSE Academic session 2020-2021. To download solutions visit at NCERT Solutions for class 10 Maths Chapter 3 main page. Join the Discussion Forum to share your knowledge with the other users.
Class 10 Maths Exercise 3.2 Solutions

10th Maths Exercise 3.2 Solutions in English
10th Maths प्रश्नावली 3.2 का हल हिंदी में
Class 10 Maths Chapter 3 Main Page
Important Questions For Practice
1. Find the value of k for which pair of linear equations 3x + 2y = –5 and x – ky = 2 has a unique solution. [Answer: k≠-2/3]
2. Express y in terms of x in the expression 3x – 7y = 10. [Answer: y = (3x-10)/7]
3. Find three consecutive numbers such that seven times the smallest number may be equal to three times the sum of the other two. [Answer: 9, 10, 11]
4. If 2x + 5y = 4, write another linear equation, so that lines represented by the pair are coincident. [Answer: 4x+10y=8]
5. Jamila sold a table and a chair for ₹1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair, she would have got ₹1065. Find the cost price of each. [Answer: Cost of table = ₹500, cost of chair = ₹400]
6. Check whether the graph of the pair of linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 is intersecting lines or parallel lines. [Answer: parallel lines]
QUESTIONS FROM CBSE BOARD PAPERS
1. A number consists of three digits whose sum is 17. The middle are exceeds the sum of the other two by 1. If the digits be reversed, the number is diminished by 369. Find the number. [Answer: 692]
2. If the lines 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then find value of k. [Answer: k=15/4]
3. After covering a distance of 30 km at a uniform speed, there is some defect in a train engine and therefore, its speed is reduced to 4/5 to its original sp

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eed. Consequently, the train reaches its destination late by 45 minutes. Had it happened after covering 18 km more, the train would have reached 9 minutes earlier than it did. Find the speed of the train and the length of the journey. [Answer: Speed = 30 km/h, length of journey = 120 km]
4. If we draw lines of x = 2 and y = 3 what kind of lines do we get? [Answer: intersecting lines]
5. A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Find the quantity of each of the solutions to get the resultant mixture. [Answer: 6 litres 90% solutions and 15 litres 97% solutions].
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NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1


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NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1

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NCERT Solutions for class 10 Maths Chapter 3 Exercise 3.1 pair of linear equations in two variables download in PDF form or use it online. NCERT Solutions for class 10 Maths are now updated for new academic session 2020-21.
NCERT Solutions Offline Apps 2020-2021 of Solutions are modified as per latest CBSE Curriculum 2020-21 in both the medium (Hindi Medium and English Medium) or View in Video Format applicable for UP Board, Gujrat board as well as CBSE board NCERT Books. Download (Exercise 3.1) in PDF format.

NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1
Class:10Subject:Maths – गणितChapter 3:Exercise 3.1
10 Maths Chapter 3 Exercise 3.1 Solutions
NCERT Solutions for class 10 Maths Chapter 3 Exercise 3.1 in English medium and Hindi Medium are given below updated for new academic session 2020-21. Download options are given on the page or on main page of NCERT Solutions Class 10 Maths Chapter 3. Visit to Discussion Forum to ask your doubts and answers to the questions asked by others.
Class 10 Maths Exercise 3.1 Solutions


10th Maths Exercise 3.1 Solutions in English
10th Maths प्रश्नावली 3.1 का हल हिंदी में
Download 10th Maths Exercise 3.1 in PDF
Class 10 Maths Chapter 3 Main Page
Important Terms For Pair Of Linear Equations
The graph of a pair of linear equations in two variables is represented by two lines.
1. If the lines intersect at a point, the pair of equations is consistent. The point of intersection gives the unique solution of the equations.
2. If the lines are parallel, then there is no solution the pair of linear equations is inconsistent.
3. If the lines coincide, then there are infinitely many solutions. The pair of linear equations is consistent. Each point on the line is a solution of both the equations.
Important Questions For Practice
1. If x = 3m –1 and y = 4 is a solution of the equation x + y = 6, then find the value of m. [Answer: m=1]
2. What is the point of intersection of the line represented by 3x – 2y = 6 and the y-axis. [Answer: (0, -3)]
3. In a deer park, the number of heads and number of legs of deer and human visitors were counted and it was found that there were 39 heads and 132 legs. Find the number of deer and human visitors in the park. [Answer: Dear: 27, Visitors: 12]
4. For what value of p, system of equations 2x + py = 8 and x + y = 6 have no solution. [Answer: p=2]
5. From Delhi station if we buy 2 tickets to station A and 3 tickets to station B, the total cost is ₹77, but if we buy 3 tickets to station A and 5 tickets to station B, the total cost is ₹124. What are fares from Delhi to station A and to station B? [Answer: ₹13, ₹17]
6. A motor cyclist is moving along the line x – y = 2 and another motor cyclist is moving along the line x – y = 4 find out their moving direction. [Answer: move parallel]
7. A farmer sold a calf and a cow for ₹760, thereby, making a profit of 25% on the calf and 10% on the cow. By selling them for ₹767.50, he would have realised a profit of 10% on the calf and 25% on the cow. Find the cost of each. [Answer: Cost of cow = ₹350, cost of calf = ₹300]
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Saturday, 25 April 2020

NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4

NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.4

Important Questions On Polynomials

1. Sum and product of two zeroes of x^4 – 4x³ – 8x² + 36x – 9 are 0 and – 9 respectively. Find the sum and product of its other two zeroes. [Answer: 4, 1]
2. Obtain zeroes of 4√3x²+5x – 2√3 and verify relation between its zeroes and coefficients. [Answer: -2/√3, √3/4]
3. What must be subtracted from 8x^4 + 14x³ – 2x² + 7x – 8 so that the resulting polynomial is exactly divisible by 4x² + 3x – 2? [Answer: 14x – 10]
4. Find all zeroes of the polynomial 2x³ + x² – 6x – 3 if two of its zeroes are 3 and – 3. [Answer: √3, -√3, – 1/2]
5. If √2 is a zero of (6x³ + √2x² –10x – 4√2), find its other zeroes. [Answer: -√2/2, -2√2/3]

Questions For Practice

1. On dividing the polynomial x³ – 5x² + 6x – 4 by a polynomial g(x), quotient and remainder are (x –3) and (– 3x + 5) respectively. Find g(x). [Answer: x² – 2x + 3]
2. What must be added to 4x^4 + 2x³ – 2x² + x – 1 so that the resulting polynomial is divisible by x² – 2x – 3? [Answer: 61x – 65]
3. If sum and product of two zeroes of the polynomial x³ + x² – 3x – 3 are 0 and 3 respectively, find all zeroes of the polynomial. [Answer: √3, -√3, -1]
4. If -1/2 is a zero of the polynomial 2x³ + x² – 6x – 3, find the sum and product of its other two zeroes. [Answer: 0, 3]
5. If α and β are zeroes of y² + 5y + m, find the value of m such that (α + β)² –αβ = 24. [Answer: 1]

Questions from Board Papers

1. Obtain all zeroes of the polynomial 2x^4 – 2x³ – 7x² + 3x + 6 if two factors of this polynomial are (x ± √3/2). [Answer: 2, -1, ±√3/2]
2. One zero of x³ – 12x² + 47x – 60 is 3 and the remaining two zeroes are the number of trees planted by two students. Find the total number of trees planted by both students. [Answer: 9]
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Chapter 2 exercise 2.3


NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.3
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NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.3 Polynomials PDF in Hindi Medium and English Medium download in PDF or View in Video Format free all solutions or study online for academic session 2020-2021.
Class 10 Maths Solutions and Offline Apps are updated on the basis of new Curriculum 2020-21 for CBSE students as well as UP Board students using NCERT Books 2020-21. Download (Exercise 2.3) in PDF format to use it offline or use online given below.
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NCERT Solutions For Class 10 Maths Chapter 2 Exercise 2.3
Class: 10
Subject: Maths – गणित
Chapter 2: Exercise 2.3
10 Maths Chapter 2 Exercise 2.3 Solutions
NCERT Solutions for class 10 Maths Chapter 2 Exercise 2.3 Polynomials English medium as well as Hindi Medium given below to download or use it online free for academic year 2020-21. Visit to discussion forum to share your knowledge or ask your doubts.
Class 10 Maths Exercise 2.3 Solutions
10th Maths Exercise 2.3 Solutions in English
10th Maths प्रश्नावली 2.3 का हल हिंदी में
Download 10th Maths Exercise 2.3 in PDF
Class 10 Maths Chapter 2 Main Page
Questions From Board Papers
1. What real number should be subtracted from the polynomial 3x³ + 10x² – 14x + 9, so that the polynomial 3x – 2 divides it exactly? [Answer: 5]
2. If α and β are the zeroes of the polynomial x² – 5x + m such that α – β = 1, find m. [Answer: 6]
3. If the sum of squares of zeroes of the polynomial x² – 8x + k is 40, find the value of k. [Answer: 12]
4. Write a quadratic polynomial, the sum of whose zeroes is – 3 and their product is also – 3.
5. If α and β are zeroes of the polynomial t2 – t – 4, form a quadratic polynomial whose zeroes are 1/α and 1/β. [Answer: 4t² + t – 1]
Important Questions On Polynomials For Board Papers
1. Find the value of k such that 3x² + 2kx + x – k – 5 has the sum of zeroes as half of their product. [Answer: 1]
2. If α and β are zeroes of x² – x – 2, find a polynomial whose zeroes are (2α + 1) and (2β + 1). [Answer: x² – 4x – 5]
3. Find values of a and b so that x^4 + x³ + 8x² + ax + b is divisible by x² + 1. [Answer: a = 1, b = 7]
Questions for Practice
1. A person distributes k books to some needy students. If k is a zero of the polynomial x² – 100x – 20000, then find the number of books distributed. [Answer: 200]
2. If (k + y) is a factor of each of the polynomials y² + 2y – 15 and y³ + a, find values of k and a. [Answer: k = 3, – 5 and a = 27, – 125]
3. If x^4 + 2x³ + 8x² + 12x + 18 is divided by (x² + 5), remainder comes out to be (px + q), find values of q and q. [Answer: p = 2, q = 3]
4. –5 is one of the zeroes of 2x² + px – 15, zeroes of p(x² + x) + k are equal to each other. Find the value of k. [Answer: 7/4]
5. If two zeroes of x^4 – 6x³ – 26x² + 138 x – 35 are (2 ± √3), find other zeroes. [Answer: -5, 7]
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Thursday, 23 April 2020

Chapter 2 exercise 2.2

NCERT SOLUTION CLASS 10 MATHS CHAPTER 2 EXERCISE 2.2

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Friday, 17 April 2020

Chapter 2 exercise 2.1

Wednesday, 15 April 2020

NCERT Solutions For Class 10 Maths Chapter 2



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NCERT Solutions For Class 10 Maths Chapter 2

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NCERT Solutions for class 10 Maths chapter 2 Polynomials all exercises in Hindi and English medium (UP Board & CBSE Board) PDF form to free download updated for new academic session 2020-21.
Download Class 10 NCERT Solutions Apps 2020-2021 for offline use. पाठ 2 बहुपद की प्रश्नावली 2.1, 2.2, 2.3, 2.4 के सभी प्रश्नो के हल विस्तार पूर्वक दिए गए हैं. Visit to Discussion Forum to ask your doubts and share your knowledge with the other users.

NCERT Solutions For Class 10 Maths Chapter 2
Class:10Subject:Maths – गणितChapter 2:Polynomials
10th Maths Chapter 2 Solutions
Class 10 Exercises solutions are solved in both English as well as Hindi medium in order to help all type of students following latest CBSE Syllabus 2020-21. In prashnavali 2.1, 2.2, 2.3 & 2.4 गणित solutions, if there is any inconvenient to understand, please inform us, we will short out at our level best.
NCERT Solutions For Class 10 Maths Chapter 2

NCERT Solutions 10th Maths

NCERT Solutions 10th Maths

NCERT Solutions 10th Maths

NCERT Solutions 10th Maths

10th Maths Chapter 2 Exercise 2.1




10th Maths Chapter 2 Exercise 2.2




10th Maths Chapter 2 Exercise 2.3




10th Maths Chapter 2 Exercise 2.4




What Do You Understand By A Polynomial?
What Is A Monomial?
What Is Binomial?
Which Algebraic Expression Is Called Trinomial?
Zeros Of Polynomials
The value(s) of the variable for which the value of a polynomial in one variable is zero is (are) called zero(s) of the polynomial. To verify the relationship between the zeroes and coefficients of a given quadratic polynomial, we can find the zeroes of p(x) by factorisation. By taking sum and product of these zeros, we can verify the following results.
Historical Facts About Polynomials
1. An elegant way of dividing a polynomial by a liner polynomial was introduced by Paolo Ruffin in 1809. His method is known as Synthetic division, which facilitates the division of a polynomial by a linear polynomial or binomial of the form x – a with the help of the coefficients involved.
2. Determining the zeros of polynomials, or finding roots of algebraic equations is among the oldest problems in mathematics. The modern way, we use today only developed beginning in the 15th century. Before that, linear equations were written out in words.
History of the mathematical notations
1. The use of the equal to (=) sign is in Robert Recorde’s book (The Whetstone of Witte in 1557). Plus sign (+) the sign of addition, minus sign (−) the sign of subtraction and the use of an alphabet for an unknown variable in Michael Stifel’s book (Arithemetica integra in 1544).
2. René Descartes, in 1637, introduced the concept of plotting the graph of a polynomial equation. Just because of him, the popularity of use of letters of the alphabet to denote constants and letters from the end of the alphabet (x, y, z, etc.) to denote variables (like 2x, 3y, 7z, etc.) in the general formula for a polynomial in one variable.


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Tuesday, 14 April 2020

Chapter 1 exercise 1.4

NCERT Solutions for class 10 Maths Chapter 1 Exercise 1.4 Real numbers in PDF Hindi Medium and English Medium or View in Video Format free to download for academic session 2020-2021 based on latest NCERT Books.

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Chapter 1 exercise 1.3


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NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.3
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NCERT Solutions for class 10 Maths Chapter 1 Exercise 1.3 Real numbers in Hindi Medium and English Medium or View in Video Format free to download or use it online without downloading for academic session 2020-2021.
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Chapter 1 exercise 1.2

NCERT Solutions for class 10 Maths Chapter 1 Exercise 1.2 वास्तविक संख्याएँ / Real Numbers in Hindi Medium and English Medium PDF form to free download updated for new academic session 2020-21 based on new NCERT Books.

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NCERT Solutions For Class 10 Maths Chapter 1 Exercise 1.2
Class: 10
Subject: Maths – गणित
Chapter 1: Exercise 1.2
10 Maths Chapter 1 Exercise 1.2
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