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NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2

February 1, 2022February 1, 2022 by Dattu

NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.2. https://mcqquestions.guru/ncert-solutions-for-class-10-maths-chapter-1-ex-1-2/

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 1
Chapter Name	Real Numbers
Exercise	Ex 1.2
Number of Questions Solved	7
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2

Ex 1.2 Class 10 Question 1.
Express each number as a product of its prime factors:
(i) 140
(ii) 156
(iii) 3825
(iv) 5005
(v) 7429.
Solutions:
(i) 140

(ii) 156
Exercise 1.2 Class 10 Maths

(iii) 3825
1.2 Class 10 Maths Chapter 1

(iv) 5005

Exercise 1.2 Class 10
(v) 7429.
So, 7429 = 17 x 19 x 23
Ex 1.2 Class 10

Exercise 1.2 Class 10 Maths Question 2.
Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of two numbers,
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
Solutions:
(i) 26 and 91
Class 10 Maths Chapter 1 Exercise 1.2

(ii) 510 and 92
Ex 1.2 Class 10 Maths

(iii) 336 and 54
Ex 1.2 Class 10 Maths Exercise 1.2 Class 10 Maths

1.2 Class 10 Maths Chapter 1 Question 3.
Find the LCM and HCF of the following integers by applying the prime factorisation method.
(i) 12,15 and 21
(ii) 17,23 and 29
(iii) 8, 9 and 25
Solutions:
(i) 12,15 and 21
Exercise 1.2 Class 10 Maths

(ii) 17,23 and 29
Class 10 Ex 1.2

(iii) 8, 9 and 25
Class 10 Maths Ex 1.2

Exercise 1.2 Class 10 Question 4.
Given that HCF (306,657) = 9, find LCM (306, 657).
Solutions:
Given that HCF (306, 657) = 9
We know that LCM x HCF = Product of two numbers
Class 10 Maths Chapter 1 Exercise 1.2 Solutions

Class 10 Maths Chapter 1 Exercise 1.2 Question 5.
Check whether 6ⁿ can end with the digit 0 for any natural number n.
Solutions:
Since prime factorisation of 6ⁿ is given by 6ⁿ= (2 x 3)ⁿ = 2ⁿ x 3ⁿ
Prime factorisation of 6ⁿ contains only prime numbers 2 and 3.
6ⁿmay end with the digit 0 for some ‘n’ if 5 must be in its prime factorisation which is not present.
So, there is no natural number VT for which 6ⁿ ends with the digit zero.

Ex 1.2 Class 10 Maths Question 6.
Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
Solutions:

Both N₁ and N₂ are expressed as a product of primes. Therefore, both are composite numbers.

Exercise 1.2 Class 10 Maths Question 7.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Solutions:
By taking LCM of time taken (in minutes) by Sonia and Ravi, we can get the actual number of minutes after which they meet again at the starting point after both start at same point and of the same time, and go in the same direction.
Class 10 Maths Chapter 1 Exercise 1.2 Solutions

Therefore, both Sonia and Ravi will meet again at the starting point after 36 minutes.

We hope the NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.2 help you. If you have any query regarding NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers Ex 1.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2

January 18, 2022January 18, 2022 by Dattu

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2. https://mcqquestions.guru/ncert-solutions-for-class-10-maths-chapter-8-ex-8-2/

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 8
Chapter Name	Introduction to Trigonometry
Exercise	Ex 8.2
Number of Questions Solved	4
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2

Class 10 Ex 8.2 Question 1.
Evaluate the following:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 1
Solution:

Ex 8.2 Class 10 Question 2.
Choose the correct option and justify your choice:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 4
Solution:

Exercise 8.2 Class 10 Question 3.
If tan (A + B) = √3 and tan (A – B) = \(\frac { 1 }{ \surd 3 }\); 0° < A + B ≤ 90°; A > B, find A and B.
Solution:
tan (A + B) = √3
⇒ tan (A + B) = tan 60°
⇒ A + B = 60° ……(i)
tan (A – B) = \(\frac { 1 }{ \surd 3 }\)
⇒ tan (A – B) = tan 30°
⇒ A – B = 30° ……..(ii)
Adding equation (i) and (ii), we get
2A = 90° ⇒ A = 45°
From (i), 45° + B = 60° ⇒ B = 60° – 45° = 15°
Hence, ∠A = 45°, ∠B = 15°

Exercise 8.2 Class 10 NCERT Solution Question 4.
State whether the following statements are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Solution:
NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 7

We hope the NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4

January 18, 2022January 18, 2022 by Dattu

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4. https://mcqquestions.guru/ncert-solutions-for-class-10-maths-chapter-7-ex-7-4/

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 7
Chapter Name	Coordinate Geometry
Exercise	Ex 7.4
Number of Questions Solved	8
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4

Question 1.
Determine the ratio, in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7).
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 1

Question 2.
Find a relation between x and y, if the points (x, y), (1, 2) and (7, 0) are collinear.
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 3

Question 3.
Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 4

Question 4.
The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 6

Question 5.
The class X students school in krishnagar have been alloted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m fron eaach other. There is trianguler grassy lawn in the plot as shoen in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
(i) Taking A as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of ∆PQR, if C is the origin?
Also, calculate the areas of the triangles in these cases. What do you observe?
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 8
Solution:

Question 6.
The vertices of a VABC are A(4, 6), B(1, 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively. such that \(\frac { AD }{ AB } =\frac { AE }{ AC } =\frac { 1 }{ 4 } \). calculate the area of the ∆ADe and compare it with the area of ∆ABC.
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 11

Question 7.
Let A(4, 2), B(6,5) and C(1, 4) be the vertices of ∆ABC.
(i) The median from A meters BC at D. Find the coordinates ofthe point D.
(ii) Find the coordinates of the point P on AD, such that AP : PD = 2 : 1.
(iii) Find the coordinates of points Q and R on medians BE and CF respectively, such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do you observe?
[Note: The points which is common to all the three medians is called centroid and this point divides each median in the ratio 2 : 1]
(v) If A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are the vertices of ∆ABC, find the coordinates of the centroid of the triangles.
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 14

Question 8.
ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1), P, Q, R and S are the mid-points of Ab, BC, CD and DA respectively. Is the quadrilateral PQRS a square? a rectangle? or a rhombus? Justify your answer.
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 18

We hope the NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3

January 18, 2022January 18, 2022 by Dattu

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3. https://mcqquestions.guru/ncert-solutions-for-class-10-maths-chapter-7-ex-7-3/

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 7
Chapter Name	Coordinate Geometry
Exercise	Ex 7.3
Number of Questions Solved	5
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3

Question 1.
Find the area of the triangle whose vertices are:
(i) (2, 3), (-1, 0), (2, -4)
(ii) (-5, -1), (3, -5), (5, 2)
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 1

Question 2.
In each of the following find the value of ‘k’ for which the points are collinear.
(i) (7, -2), (5, 1), (3, k)
(ii) (8, 1), (k, -4), (2, -5)
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 2

Question 3.
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 3

Question 4.
Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 4

Question 5.
You have studied in Class IX, that a median of a triangle divides it into two triangles of equal areas. Verify this result for ∆ABC whose vertices are A (4, -6), B (3, -2) and C (5, 2).
Solution:
NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 5

We hope the NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3, help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6

January 18, 2022January 18, 2022 by Dattu

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6. https://mcqquestions.guru/ncert-solutions-for-class-10-maths-chapter-6-ex-6-6/

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 6
Chapter Name	Triangles
Exercise	Ex 6.6
Number of Questions Solved	10
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6

Question 1.
In the given figure, PS is the bisector of ∠QPR of ∆PQR. Prove that \(\frac { QS }{ SR } =\frac { PQ }{ PR } \)
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6 1
Solution:

Question 2.
In the given figure, D is a point on hypotenuse AC of ∆ABC, DM ⊥ BC and DN ⊥ AB. Prove that:
(i) DM² = DN X MC
(ii) DN² = DM X AN

Solution:

Question 3.
In the given figure, ABc is triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC² = AB² + BC² + 2BC X BD

Solution:

Question 4.
In the given figure, ABC is atriangle in which ∠ABC 90° and AD ⊥ CB. Prove that AC² = AB² + BC² – 2BC X BD

Solution:

Question 5.
In the given figure, Ad is a median of a triangle ABC and AM ⊥ BC. Prove that
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6 11
Solution:

Question 6.
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
Solution:

Question 7.
In the given figure, two chords AB and CD intersect each other at the point P. Prove that:
(i) ∆APC ~∆DPB
(ii) AP X PB = CP X DP
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6 16
Solution:

Question 8.
In the given figure, two chords Ab and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that:
(i) ∆PAC ~ ∆PDB
(ii) PA X PB = PC X PD

Solution:

Question 9.
In the given figure, D is a point on side BC of ∆ABC, such that \(\frac { BD }{ CD } =\frac { AB }{ A{ C }^{ \bullet } } \) Prove that AD is the bisector of ∆BAC.

Solution:

Question 10.
Nazima is fly fishing in a stream. The trip of her fishing rod is 1.8m above the surface of the water and the fly at the end of the string rests on the water 3.6m away and 2.4 m from a point directly under the trip of the rod. Assuming that her string (from the trip of the rod to the fly) is that, how much string does she have out (see the figure)? If she pills in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Solution:

We hope the NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.6, drop a comment below and we will get back to you at the earliest.