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NCERT Solutions for Class 10 Maths PDF Updated for Session
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Find duplicate ratio of:. Find the triplicate ratio of:. Find sub-duplicate ratio of:. Find the sub-triplicate ratio of:. Find the reciprocal ratio of:. Find the ratio compounded of the reciprocal ratio of 28, the sub-duplicate ratio of 49 and the triplicate ratio of 5: 4.

Required compounded ratio. Find the fourth proportional to:. Find the third proportional to:. Find the mean proportional between:. If x 2 , 4 and 9 are in continued proportion, find x. What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional? Let the number added be x.

Thus, the required number which should be added is 3. What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion? Let the number subtracted be x. Thus, the required number which should be subtracted is 2. Since y is the mean proportion between x and z. Hence, proved. If q is the mean proportional between p and r, show that:.

Given, q is the mean proportional between p and r. If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second. Let x, y and z be the three quantities which are in continued proportion. Now, we have to prove that. That is we need to prove that.

If y is the mean proportional between x and z, prove that:. Given, y is the mean proportional between x and z. Given four quantities a, b, c and d are in proportion. Show that:. Hence proved. Find two numbers such that the mean mean proportional between them is 12 and the third proportional to them is Let a and b be the two numbers, whose mean proportional is Now, third proportional is Therefore, the numbers are 6 and Find the third proportional to.

Let the required third proportional be Concise Mathematics Class 10 Icse Solutions Chapter 24 Raw p. Given, , prove that:. If ; then prove that:. Applying componendo and dividendo,. If ; prove that:. If a, b and c are in continued proportion, prove that:. Given, a, b and c are in continued proportion. Using properties of proportion, solve for x:. Applying componendo and dividendo, we get,. Squaring both sides,. Again applying componendo and dividendo,. If , express n in terms of x and m.

If , show that:. Find the:. Find the value of x, if:. Duplicate ratio of. What quantity must be added to each term of the ratio x: y so that it may become equal to c: d? Let the required quantity which is to be added be p.

Then, we have:. A woman reduces her weight in the ratio 7 : 5. What does her weight become if originally it was 84 kg? Find two numbers such that the mean proportional between them is 14 and third proportional to them is Let the required numbers be a and b.

Given, 14 is the mean proportional between a and b. Also, given, third proportional to a and b is Using 1 , we have:. Thus, the two numbers are 7 and Hence, z is mean proportional between x and y. If , find the value of. There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3: 1. How any more girls should be added to the council so that the ratio of the number of boys to the number of girls may be 9: 5? Let the number of boys be 3x and number of girls be x.

Le n number of girls be added to the council. From given information, we have:. Thus, 6 girls are added to the council.

Hence, use componendo and dividend to find the values of:. If , use properties of proportion to find:.

If x, y, z are in continued proportion, prove that. By alternendo. Hence Proved. By componendo and dividendo,. If , find:. Through our Selina solutions, understand topics such as market value, face value, dividend, premium, rate of dividend etc.

In addition, learn how to calculate income and return from share investments using the formulae given in this ICSE Mathematics Class 10 chapter. This chapter explains the graphical method of representing solutions on a number line and the algebraic method of solving linear inequations.

The textbook questions in ICSE Mathematics Class 10 Chapter 5 require you to write solutions involving proofs based on quadratic equations. For instance, you may come across questions asking you to prove whether the given equation is a quadratic equation.

The given information in the textbook problems for this chapter includes integers, reciprocals etc. Find out how to calculate the sub-duplicate ratio, sub-triplicate ratio or reciprocal ratio as per the data given in the exercise questions. Selina ICSE Class 10 Maths solutions Chapter 8 assist you to use the remainder theorem and the factor theorem for solving problems related to polynomials.

Learn the steps to factorise the expression given in the exercise questions with our solutions for concise Mathematics Class 10 Selina textbook Chapter 8. Also, study the concept of matrices in detail by learning more about addition, subtraction and multiplication of a 2x2 matrix.

Use our expert answers to learn how to find the first term and common difference in an arithmetic progression. In addition, learn the concept of the general term of an arithmetic progression and its application. Practise Selina textbook questions and answers to thoroughly grasp the concepts in Chapter For additional help to grasp the concepts, view our ICSE Class 10 Maths video lessons with simplified explanations on the concept of geometric progression by a Maths expert.

As per the ICSE Class 10 Maths syllabus , Chapter 12 covers topics such as reflection of a point in a line, reflection of a point in the origin and invariant points. ICSE Mathematics Class 10 Chapter 13 discusses the concept of section formula and mid-point formula in co-ordinate geometry. Also, study the application of the mid-point formula and the section formula by practising with our solutions for this chapter.

Through the Chapter 14 Selina Maths Class 10 solutions, learn to find the point of intersection between two lines. Find out how to prove that Concise Mathematics Class 10 Icse Solutions Chapter 5 Dvd two lines are concurrent as per the information given in the exercise questions. Understand the applications of the basic proportionality theorem and angle bisector theorem for solving Maths problems.

In this chapter, you will get to know about the constructions and theorems related to loci. Revise concepts such as the side-angle-side criterion of congruence and the angle-side-angle criterion of congruence. Practise the different types of questions and answers from this chapter to learn to calculate the value of angles as per a given construction or as per the given data.

Our experts have lucidly explained the concepts for effective learning. Learn the right way to prove that two tangents are equal. Revise the steps needed to find the radius of a circle or to calculate the length of a chord of an outer circle which touches the inner circle.

Read the steps of construction given by our experts in Selina ICSE Class 10 Maths solutions Chapter 19 to understand how to draw circles correctly with the given data. Also, revise constructions such as a circumscribed circle, an incircle in a triangle, perpendicular bisectors etc. Follow the steps shared by subject experts for drawing accurate diagrams to answer the questions from Chapter Find out how to calculate the volume and surface area of a circular cylinder.

Also, revise the steps to accurately measure cylindrical, conical and spherical objects, and accordingly, calculate their cost. Understand the mathematical methods using trigonometric identities to solve algebraic trigonometric expressions with the support of our Selina ICSE Class 10 Maths solutions Chapter Our Selina solutions cover answers for all the Chapter 21 questions in the Maths textbook by Selina Publications.

Selina ICSE Class 10 Maths solutions Chapter 22 can be used to revise the methods to calculate distances and heights in real-life scenarios.

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