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RD Sharma Class 12 Solutions Chapter 16 - Tangents and Normals (Ex 16.1) Exercise 16.1

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Last updated date: 16th May 2024
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RD Sharma Class 12 Solutions Chapter 16 - Tangents and Normals (Ex 16.1) Exercise 16.1 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 16 - Tangents and Normals Exercise 16.1 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 16 - Tangents and Normals Ex 16.1 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.


Tangents are lines that only meet a given curve and at the point of contact, their normal is a line perpendicular to it. One explanation of why tangents are so important is that they give slopes of straight lines. Normal lines are also important when dealing with orientation questions, especially in higher dimensions. The RD Sharma Class 12 Chapter 16 Solutions will give a basic understanding of Tangents and Normals along with the important questions asked in board exams.


Vedantu provides an excellent and free PDF of RD Sharma Class 12 Tangents and Normals Solutions according to the NCERT curriculum so that students can score good marks in their board exams.

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Competitive Exams after 12th Science

About Class 12 RD Sharma Textbook Solutions Chapter 16 - Tangents and Normals

These RD Sharma Solutions For Class 12 Maths Chapter 16 are prepared by experts who have vast experience in the subject. The experts have done a lot of research to provide unique and step by step solutions to all-important questions of Tangents and Normals so that students can understand the concepts easily and ace their exams with good marks. 


Let us Look into a Few of the Important Topics from RD Sharma Class 12 Tangents and Normals Solutions.

  • The slope of a line

  • Slopes of Tangent and Normal

  • Finding the slopes of the tangent and the normal at a given point

  • Finding the point on a given curve at which tangent is parallel or perpendicular to a given line

  • Equations of tangents and normal

  • Finding the equations of tangent and normal to a curve at a given point

  • Finding tangent and normal parallel or perpendicular to a given line

  • Finding tangent or normal passing through a given point

  • Miscellaneous applications of Tangents and Normals

  • Finding the equations of tangent and normal

  • Finding the equation of the curve

  • The angle of intersection of two curves

  • Orthogonal curves


Tips to prepare for the exam using RD Sharma Solutions for Class 12 Maths Chapter 16

These tips will help students to secure good marks in their board exams from the Tangents and Normals chapter.

  • Understand the basic concepts of lines, types of lines, and their properties before attempting Tangent and Normal questions.

  • Understand the concepts of Tangents and Normal lines clearly and also remember the basic formulas which are used to define Tangents and Normals.

  • Students are advised to download the free PDF of RD Sharma Solutions For Class 12 Maths Chapter 16 available on the Vedantu platform which provides solutions easily and understandably. Exercises in RD Sharma Solutions For Class 12 Maths Chapter 16


Conclusion

The RD Sharma Class 12 Tangents and Normals Solutions are prepared according to the CBSE syllabus to the NCERT curriculum. So these solutions are very useful for Class 12 students to prepare for their board exams which also have a lot of practice problems for students to improve their subject knowledge. 

FAQs on RD Sharma Class 12 Solutions Chapter 16 - Tangents and Normals (Ex 16.1) Exercise 16.1

1. What is a tangent?

A tangent at a point on a curve is a straight line that touches the curve at that point and has the same slope as the curve's gradient/derivative. You may derive how to obtain the equation of the tangent to the curve at any point from the definition. The equation of the tangent to this curve at x = x0, given a function y = f(x), may be calculated as follows: 


Find the curve's gradient/derivative at the point x = x0: To do so, one must first calculate dydxx=x0. In the same way that the slope of a straight line is called m, we'll call this value m.


Find the equation of the straight line with slope m that passes through the point (x0, y(x0) y–y1x–x1=m is a simple formula that can be obtained.

2. What is normal?

A straight line that meets the curve at a point on the curve and is perpendicular to the tangent at that point is called a normal. If n is its slope, and m is the slope of the tangent at that point or the value of the gradient/derivative at that point, we obtain mn = -1. Finding the normal to a given curve y = f(x) at a point x = x0 involves the following steps:


Find the curve's gradient/derivative at the point x = x0: This first step is identical to the approach for determining the equation of the tangent to the curve, i.e. m = dydxx=x


Determine the normal slope 'n': We have n=1m since the normal is perpendicular to the tangent.

3. How can the tangent be found and what is a gradient?

The tangent can be found by following these steps:

  • Draw the tangent line as well as the function.

  • To calculate the equation for the tangent line's slope, use the first derivative.

  • Enter the x value for the point you're looking into.

  • Write the tangent line's equation in point-slope form.

  • Finally, check the equation on the graph for accuracy.

The steepness of a graph at any point is referred to as the gradient. The gradient of the graph at any point is referred to as slope. As a result, both can be considered identical.

4. What are the applications of Tangent and Normal?

The Applications Of Tangent Are: 

If we are driving around a corner and hit something slick on the road (oil, ice, water, or loose gravel) and our automobile starts to skid, it will continue in a tangent to the curve direction.


Similarly, if we hold a ball in our hands and swing it circularly before releasing it, the ball will fly out in a tangent to the circle of motion.


The Applications Of Normal Are: 

When you are speeding around a circular track in an automobile, the force pushing you outwards is proportional to the curve of the road. Surprisingly, the force that propels you around the corner is directed normal to the circle, towards the circle's centre.


At each point where the spoke meets with the centre, the spokes of a wheel are aligned normal to the circular shape of the wheel.

5. How to prepare for the chapter Tangents and Normals?

Students have a strong foundation to prepare for the chapter - tangents and normal. Students need to have a great base to build further knowledge on the chapter. Students should grasp concepts like tangents, normal, applications of a tangent, applications of normal, gradient, curve, derivative, slope etc. Students should also prepare for the chapter - tangents and normal by solving sample papers related to the chapter, as practice will help them more. To get free study materials, people can visit the Vedantu app and website.