Q1. Represent the rational numbers , , and on a single number line. Q2. Find three distinct rational numbers that lie strictly between and . Solution:Step 1: Make the denominators equal. The LCM of 4 and 2 is 4, Step 2: Make the difference between numerators large enoughMultiplying numerator and denominator by 4 Step 2: […]
Class 9 NCERT Maths – Exercise Set 3.4 Solutions Read More »
Q1. Convert the following rational numbers in the form of a terminating decimal or non-terminating and repeating decimal, whichever the case may be, by the process of long division: Solution:(i) : .Terminating. (ii) : .Non-terminating repeating. Q2. Prove that is an irrational number. Solution:Step 1 (Assumption): Assume is rational. So, , where and are co-prime
Class 9 NCERT Maths – End-of-Chapter 3 Exercise Solution Read More »
The CBSE has changed the Maths Syllabus of class 9 for the Academic Year 2026-27. The NCERT has come out with a new maths book (Ganita Manjiri) as per the new syllabus. The new book does not have an answer key for the exercises as was present in the previous NCERT books. So I have
Q 1. Prove that the determinant is independent of . Solution:Let To evaluate this, we will write the expansion of the determinant along the first row (). Now, calculate the second-order determinants: Next, carefully multiply the terms into the brackets: Notice that the terms and cancel each other out. We can then group the remaining
Class 12 NCERT Maths – Chapter 4 (Determinants) – Miscellaneous Exercise Solutions Read More »
In this post, we apply what we’ve learned about determinants and matrices to examine the consistency of a system of linear equations.Remember the rules from Ex 4.5: Let’s dive into the first two questions of Exercise 4.5! Q 1: Examine the consistency of the system of equations: Solution:First, let’s write the given system of equations
Class 12 NCERT Maths – Chapter 4 (Determinants) – Exercise 4.5 Solutions Read More »
Q 1: Find the adjoint of the matrix Solution:Let the given matrix be . To find , we first need to find the cofactor of each element. The cofactor is calculated as , where is the minor of the element . Writing these cofactors in matrix form, we get the Cofactor Matrix: The adjoint of
Class 12 NCERT Maths – Chapter 4 (Determinants) – Exercise 4.4 Solutions Read More »
Exercise 2.1 is based on the basic concepts of inverse trigonometry. The domain and range of the inverse trigonometric function (principle value branches) is the main concept of the chapter. It is recommended that you revise them before starting the exercise from this page. Also the basic definition of inverse trigonometric function should be known
Q 1: Find the area of the region bounded by the ellipse . SolutionStep 1: Identify the Curve and CoordinatesThe given equation is an ellipse in the standard form . Comparing this with the given equation: We find that: Since , the ellipse is horizontal (elongated along the x-axis). The vertices on the x-axis are
Class 12 NCERT Maths – Exercise 8.1 Solutions, Chapter 8: Application of Integrals Read More »
Introduction Welcome! If you’re looking for the NCERT Solutions for Class 12 Maths Chapter 13, Exercise 13.3, you’re in the right place. Below, you will find detailed, step-by-step solutions for every question in Exercise 13.3, designed to help you clear all your doubts and understand the logic behind each answer. This exercise introduces the core
Welcome! If you’re looking for the NCERT Solutions for Class 12 Maths Chapter 13, Exercise 13.1, you’re in the right place. Below, you will find detailed, step-by-step solutions for every question in Exercise 13.1, designed to help you clear all your doubts and understand the logic behind each answer. This exercise introduces the core concepts
Class 12 NCERT Maths – Chapter 13(Probability), Exercise 13.1 Solutions Read More »
