Category: CBSE

Get Free NCERT Solutions for Class 10 Maths Chapter 4 Ex 4.4 Quadratic Equations Class 10 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 4.4 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 4 Maths Class 10 Quadratic Equations Exercise 4.4 Provided in NCERT Textbook

Topics and Sub Topics in Class 10 Maths Chapter 4 Quadratic Equations:

Section Name	Topic Name
4	Quadratic Equations
4.1	Introduction
4.2	Quadratic Equations
4.3	Solution of a Quadratic Equation by Factorisation
4.4	Solution of a Quadratic Equation by Completing the Square
4.5	Nature of Roots
4.6	Summary

• Class 10 Maths Quadratic Equations Ex 4.1
• प्रश्नावली 4.1 का हल हिंदी में
• Class 10 Maths Quadratic Equations Ex 4.2
• प्रश्नावली 4.2 का हल हिंदी में
• Class 10 Maths Quadratic Equations Ex 4.3
• प्रश्नावली 4.3 का हल हिंदी में
• Class 10 Maths Quadratic Equations Ex 4.4
• प्रश्नावली 4.4 का हल हिंदी में
• Quadratic Equations Class 10 Extra Questions

You can also download the free PDF of Chapter 4 Ex 4.4 Quadratic Equations NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 4
Chapter Name	Quadratic Equations
Exercise	Ex 4.4
Number of Questions Solved	5
Category	NCERT Solutions

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4.

Ex 4.4 Class 10 Maths Question 1.
Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) 2x² -3x + 5 = 0
(ii) 3x² – 4√3x + 4 = 0
(iii) 2x²-6x + 3 = 0
Solution:

Ex 4.4 Class 10 Maths Question 2.
Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(1) 2x² + kx + 3 = 0
(2) kx (x – 2) + 6 = 0
Solution:

Download NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations PDF

Ex 4.4 Class 10 Maths Question 3.
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.
Solution:

Ex 4.4 Class 10 Maths Question 4.
Is the following situation possible? If so, determine their present ages.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Solution:

Ex 4.4 Class 10 Maths Question 5.
Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find its length and breadth.
Solution:

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Hindi Medium) Ex 4.4

Chapter 4. द्विघात समीकरण

We hope the NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.4, drop a comment below and we will get back to you at the earliest.

Get Free NCERT Solutions for Class 10 Maths Chapter 8 Ex 8.4 Introduction to Trigonometry Class 10 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 8.4 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 8 Maths Class 10 Introduction to Trigonometry Exercise 8.4 Provided in NCERT Textbook.

Topics and Sub Topics in Class 10 Maths Chapter 8 Introduction to Trigonometry:

Section Name	Topic Name
8	Introduction to Trigonometry
8.1	Introduction
8.2	Trigonometric Ratios
8.3	Trigonometric Ratios Of Some Specific Angles
8.4	Trigonometric Ratios Of Complementary Angles
8.5	Trigonometric Identities
8.6	Summary

• Class 10 Maths Introduction to Trigonometry Ex 8.1
• प्रश्नावली 8.1 का हल हिंदी में
• Introduction to Trigonometry Class 10 Ex 8.2
• प्रश्नावली 8.2 का हल हिंदी में
• Introduction to Trigonometry Class 10 Ex 8.3
• प्रश्नावली 8.3 का हल हिंदी में
• Introduction to Trigonometry Class 10 Ex 8.4
• प्रश्नावली 8.4 का हल हिंदी में
• Introduction to Trigonometry Class 10 Extra Questions

You can also download the free PDF of Chapter 8 Ex 8.4 Coordinate Geometry NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 8
Chapter Name	Introduction to Trigonometry
Exercise	Ex 8.4
Number of Questions Solved	5
Category	NCERT Solutions

NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.4

Ex 8.4 Class 10 Maths Question 1.

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.Solution:

Ex 8.4 Class 10 Maths Question 2.
Write all the other trigonometric ratios of ∠A in terms of sec A.
Solution:

Download NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry PDF

Ex 8.4 Class 10 Maths Question 3.
Evaluate:

Solution:

Ex 8.4 Class 10 Maths Question 4.
Choose the correct option. Justify your choice.
(i) 9 sec² A – 9 tan² A = ……
(A) 1
(B) 9
(C) 8
(D) 0

(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ………..
(A) 0
(B) 1
(C) 2
(D) -1

(iii) (sec A + tan A) (1 – sin A) = ………….
(A) sec A
(B) sin A
(C) cosec A
(D) cos A

(iv) \(\frac { 1+{ tan }^{ 2 }A }{ 1+cot^{ 2 }A }\) = ………..
(A) sec² A
(B) -1
(C) cot² A
(D) tan² A
Solution:

Ex 8.4 Class 10 Maths Question 5.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

Solution:

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry (Hindi Medium) Ex 8.4

We hope the NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.4, drop a comment below and we will get back to you at the earliest.

Get Free NCERT Solutions for Class 10 Maths Chapter 4 Ex 4.3 Quadratic Equations Class 10 Maths NCERT Solutions are extremely helpful while doing homework. Exercise 4.3 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 4 Maths Class 10 Quadratic Equations Exercise 4.3 Provided in NCERT Textbook

Topics and Sub Topics in Class 10 Maths Chapter 4 Quadratic Equations:

Section Name	Topic Name
4	Quadratic Equations
4.1	Introduction
4.2	Quadratic Equations
4.3	Solution of a Quadratic Equation by Factorisation
4.4	Solution of a Quadratic Equation by Completing the Square
4.5	Nature of Roots
4.6	Summary

• Class 10 Maths Quadratic Equations Ex 4.1
• प्रश्नावली 4.1 का हल हिंदी में
• Class 10 Maths Quadratic Equations Ex 4.2
• प्रश्नावली 4.2 का हल हिंदी में
• Class 10 Maths Quadratic Equations Ex 4.3
• प्रश्नावली 4.3 का हल हिंदी में
• Class 10 Maths Quadratic Equations Ex 4.4
• प्रश्नावली 4.4 का हल हिंदी में
• Quadratic Equations Class 10 Extra Questions

You can also download the free PDF of Chapter 4 Ex 4.3 Quadratic Equations NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 4
Chapter Name	Quadratic Equations
Exercise	Ex 4.3
Number of Questions Solved	11
Category	NCERT Solutions

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3.

Ex 4.3 Class 10 Maths Question 1.
Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(i) 2x² – 7x + 3 = 0
(ii) 2x² + x – 4 = 0
(iii) 4x² + 4√3x + 3 = 0
(iv) 2x² + x + 4 = 0
Solution:

Ex 4.3 Class 10 Maths Question 2.
Find the roots of the quadratic equations by applying the quadratic formula.
(i) 2x² – 7x + 3 = 0
(ii) 2x² – x + 4 = 0
(iii) 4x² – 4√3x + 3 = 0
(iv) 2x² – x + 4 = 0
Solution:

Download NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations PDF

Ex 4.3 Class 10 Maths Question 3.
Find the roots of the following equations:

Solution:

Ex 4.3 Class 10 Maths Question 4.
The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is \(\frac { 1 }{ 3 }\) Find his present age.
Solution:

Ex 4.3 Class 10 Maths Question 5.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Solution:

Ex 4.3 Class 10 Maths Question 6.
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Solution:

Ex 4.3 Class 10 Maths Question 7.
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Solution:

Ex 4.3 Class 10 Maths Question 8.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solution:

Ex 4.3 Class 10 Maths Question 9.
Two water taps together can fill a tank in 9\(\frac { 3 }{ 8 }\) hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Solution:

Ex 4.3 Class 10 Maths Question 10.
An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bengaluru (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.
Solution:

Ex 4.3 Class 10 Maths Question 11.
Sum of the areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares.
Solution:

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations (Hindi Medium) Ex 4.3

Chapter 4. द्विघात समीकरण

We hope the NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Ex 4.3, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations Exercise 4.3, drop a comment below and we will get back to you at the earliest.

Get Free NCERT Solutions for Class 10 Maths Chapter 5 Ex 5.4 PDF. Arithmetic Progressions Class 10 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 5.4 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 5 Maths Class 10 Arithmetic Progressions Exercise 5.4 provided in NCERT TextBook.

Topics and Sub Topics in Class 10 Maths Chapter 5 Arithmetic Progressions:

Section Name	Topic Name
5	Arithmetic Progressions
5.1	Introduction
5.2	Arithmetic Progressions
5.3	Nth Term Of An AP
5.4	Sum Of First N Terms Of An AP
5.5	Summary

• Class 10 Maths Arithmetic Progressions Ex 5.1
• प्रश्नावली 5.1 का हल हिंदी में
• Class 10 Maths Arithmetic Progressions Ex 5.2
• प्रश्नावली 5.2 का हल हिंदी में
• Class 10 Maths Arithmetic Progressions Ex 5.3
• प्रश्नावली 5.3 का हल हिंदी में
• Class 10 Maths Arithmetic Progressions Ex 5.4
• प्रश्नावली 5.4 का हल हिंदी में
• Arithmetic Progressions Class 10 Extra Questions

You can also download the free PDF of  Ex 5.4 Class 10 Arithmetic Progressions NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	5
Chapter Name	Arithmetic Progressions
Exercise	Ex 5.4
Number of Questions Solved	5
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Exercise 5.4

Ex 5.4 Class 10 Maths Question 1.
Which term of the AP: 121, 117. 113, ….., is its first negative term?
Solution:

Ex 5.4 Class 10 Maths Question 2.
The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP?
Solution:

Download NCERT Solutions For Class 10 Maths Chapter 5 Arithmetic Progressions PDF

Ex 5.4 Class 10 Maths Question 3.
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 at the top. If the top and the bottom rungs are \({ 2 }\frac { 1 }{ 2 } m\) apart, what is the length of the wood required for the rungs?

Solution:

Ex 5.4 Class 10 Maths Question 4.
The houses of a row are numbered consecutively from 1 to 49. Show that there is value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Solution:

Ex 5.4 Class 10 Maths Question 5.
A small terrace at a football ground comprises of 15 steps each of which is 50  m long and built of solid concrete. Each step has a rise of \(\frac { 1 }{ 2 } m\) and a tread of \(\frac { 1 }{ 2 } m\). Calculate the total volume of concrete required to build the terrace.

Solution:

CLASS 10 MATHS CHAPTER 5 EXERCISE 5.4 AP SOLUTIONS IN HINDI

We hope the NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions Exercise 5.4, drop a comment below and we will get back to you at the earliest.

Get Free NCERT Solutions for Class 10 Maths Chapter 11 Ex 11.1 PDF. Constructions Class 10 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 11.1 Class 10 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 11 Maths Class 10 Constructions Exercise 11.1 provided in NCERT TextBook.

Topics and Sub Topics in Class 10 Maths Chapter 11 Constructions:

Section Name	Topic Name
11	Constructions
11.1	Introduction
11.2	Division Of A Line Segment
11.3	Construction Of Tangents To A Circle
11.4	Summary

• Constructions Class 10 Ex 11.1
• प्रश्नावली 11.1 का हल हिंदी में
• Constructions Class 10 Ex 11.2
• प्रश्नावली 11.2 का हल हिंदी में
• Extra Questions for Class 10 Maths Constructions

NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.1

NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.1 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.1

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 11
Chapter Name	Constructions
Exercise	Ex 11.1
Number of Questions Solved	5
Category	NCERT Solutions

Ex 11.1 Class 10 Maths Question 1.
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Solution:

Ex 11.1 Class 10 Maths Question 2.
Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are \(\frac { 2 }{ 3 }\) of the corresponding sides of the first triangle.
Solution:

You can also download the free PDF of  Ex 11.1 Class 10 Constructions NCERT Solutions or save the solution images and take the print out to keep it handy for your exam preparation.

Download NCERT Solutions For Class 10 Maths Chapter 11 Constructions PDF

Ex 11.1 Class 10 Maths Question 3.
Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are \(\frac { 7 }{ 5 }\) of the corresponding sides of the first triangle.
Solution:

Ex 11.1 Class 10 Maths Question 4.
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1\(\frac { 1 }{ 2 }\) times the corresponding sides of the isosceles triangle.
Solution:

Ex 11.1 Class 10 Maths Question 5.
Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are \(\frac { 3 }{ 4 }\) of the corresponding sides of the triangle ABC.
Solution:

Ex 11.1 Class 10 Maths Question 6.
Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are \(\frac { 4 }{ 3 }\) times the corresponding sides of ∆ABC.
Solution:

Ex 11.1 Class 10 Maths Question 7.
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are \(\frac { 5 }{ 3F }\) times the corresponding sides of the given triangle.
Solution:
Steps of Construction:
1. Construct a ∆ABC, such that BC = 4 cm, CA = 3 cm and ∠BCA = 90°
2. Draw a ray BX making an acute angle with BC.
3. Mark five points B₁, B₂, B₃, B₄ and B₅ on BX, such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B_5.
4. Join B₃C.
5. Through B₅, draw B₅C’ parallel to B₃C intersecting BC produced at C’.
6. Through C’, draw C’A’ parallel to CA intersecting AB produced at A’.
Thus, ∆A’BC’ is the required right triangle.

Justification:

Class 10 Maths Constructions Mind Maps

Construction

Construction implies drawing geometrical figures accurately such that triangles, quadrilateral and circles with the help of ruler and compass.

Division of a Line Segment

A line segment can be divided in a given ratio (both internally and externally)
Example:
Divide a line segment of length 12 cm internally in the ratio 3:2.
Solution :
Steps of construction :
(i) Draw a line segment AB = 12 cm. by using a ruler.
(ii) Draw a ray making a suitable acute angle ∠BAX with AB.

(iii) Along AX, draw 5 ( = 3 + 2) arcs intersecting the ray AX at A₁? A₂, A₃, A₄ and A₅ such that
AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅
(iv) Join BA₅.
(v) Through A₃ draw a line A₃P parallel to A₅B making ∠AA₃P = ∠AA₅B, intersecting AB at point P.
The point P so obtained is the required point, which divides AB internally in the ratio 3 : 2.

Similar Triangles

(i) This Construction involves two different situation.
(a) Construction of a similar triangle smaller than the given triangle.
(b) Construction of a similar triangle greater than the given triangle.
(ii) The ratio of sides of the triangle to be constructed with the corresponding sides of the given triangle is called scale factor.
Example:
Draw a triangle ABC with side BC = 7 cm. ∠B = 45°, ∠A = 105°. Construct a triangle whose sides are (4/3) times the corresponding side of ∆ABC.

Solution :
Steps of construction :
(i) Draw BC = 7 cm.
(ii) Draw a ray BX and CY such that ∠CBX= 45° and
∠BCY = 180° – (45° + 105°) = 30°
Suppose BX and CY intersect each other at A.
∆ABC so obtained is the given triangle.
(iii) Draw a ray BZ making a suitable acute angle with BC on opposite side of vertex A with respect to BC.
(iv) Draw four (greater of 4 and 3 in 4/3) arcs intersecting the ray BZ at B₁, B₂, B₃, B₄ such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄.
(v) Join B₃ to C and draw a line through B₄ parallel to B₃C, intersecting the extended line segment BC at C’.
(vi) Draw a line through C’ parallel to CA intersecting the extended line segment BA at A’. Triangle A’BC’ so obtained is the required triangle.

Tangents to a Circle

Two tangents can be drawn to a given circle from a point outside it.
Example:
Draw a circle of radius 4 cm. Take a point P outside the circle. Without using the centre of the circle, draw two tangents to the circle from point P.
Solution :

Steps of construction :
(i) Draw a circle of radius 4 cm.
(ii) Take a point P outside the circle and draw a secant PAB, intersecting the circle at A and B.
(iii) Produce AP to C such that AP = CP.
(iv) Draw a semi-circle with CB as diameter.
(v) Draw PD ⊥ CB, intersecting the semi-circle at D.
(vi) With P as centre and PD as radius draw arcs to intersect the given circle at T and T’
(vii) Join PT and PT’. Then, PT and PT’ are the required tangents.
Note:
If centre of a circle is not given, then it can be located by finding point of intersection of perpendicular bisector, of any two nonparallel chords of a circle.

NCERT Solutions for Class 10 Maths Chapter 11 Constructions (Hindi Medium) Ex 11.1

We hope the NCERT Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.1, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 11 Constructions Exercise 11.1, drop a comment below and we will get back to you at the earliest.