Rbse Solutions Class 12 Maths Exercise 9.4 | Homogeneous Differential Equations

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 9.4. Learn to identify and solve homogeneous differential equations of the form $\frac{dy}{dx} = f\left(\frac{y}{x}\right)$ using the substitution $y=vx$. Includes finding both general and particular solutions by applying initial conditions. Essential for mastering methods of solving first-order DEs in Chapter 9. A First Order Differential Equation of … Read more

Rbse Solutions Class 12 Maths Exercise 9.3 | Variable Separable Method

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 9.3. Master the Variable Separable Method to find general and particular solutions of first-order differential equations. Includes application problems covering continuous growth (banking, bacteria) and geometric curves. Essential for solving DEs in Chapter 9. This exercise focuses on solving First Order, First Degree Differential Equations using the … Read more

Rbse Solutions Class 12 Maths Exercise 9.2 | Verification of Solutions for Differential Equations

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 9.2. Learn how to verify that a given function (explicit or implicit) is a solution to a corresponding differential equation (DE) by computing and substituting its derivatives ($y’$, $y”$) into the DE. Understand the difference between the number of arbitrary constants in the general solution (equal to … Read more

Rbse Solutions Class 12 Maths Exercise 9.1 | Order and Degree of Differential Equations

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 9.1. Learn to determine the order (highest derivative) and degree (power of the highest derivative) of differential equations. Understand the crucial condition where the degree is not defined (when derivatives appear inside non-polynomial functions like $\sin(y”’)$ or $\cos(y’)$). Essential practice for Chapter 9 fundamentals. The order of … Read more

Rbse Solutions Class 12 Maths Chapter 8 Miscellaneous | Chapter 8: Application of Integrals

17/03/202616/03/2026 by By Subject Experts

Get complete solutions for the NCERT Class 12 Maths Miscellaneous Exercise on Application of Integrals (Chapter 8). Practice calculating the area bounded by curves ($y=x^2$, $y=\sin x$, $y= This exercise reviews finding the area bounded by curves and lines using definite integration. Part 1: Finding Area Under Curves (1-3) 1. Find the area under the … Read more

Rbse Solutions Class 12 Maths Chapter 8 Exercise 8.1 | Area Under Curves

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 8.1. Learn to calculate the area of regions bounded by ellipses ($\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$), circles ($x^2 + y^2 = r^2$), and lines using definite integration ($\int_a^b y dx$ or $\int_c^d x dy$). Includes multiple-choice questions on parabola areas. This exercise focuses on calculating the area … Read more

Rbse Solutions Class 12 Maths Chapter 7 Miscellaneous | Chapter 7: Integrals

17/03/202616/03/2026 by By Subject Experts

Get complete solutions for the NCERT Class 12 Maths Miscellaneous Exercise on Integrals (Chapter 7). This review covers advanced problems using all techniques: Substitution, Integration by Parts, Partial Fractions, Trigonometric Identities, and Properties of Definite Integrals ($\int_a^b f(x) dx$). Essential practice for board exams and competitive tests. This exercise covers various integration techniques including Substitution, … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.10 | Properties of Definite Integrals

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.10. Learn to evaluate complex definite integrals efficiently by applying key properties like P3 ($\int_0^a f(x) dx = \int_0^a f(a – x) dx$) and P6 ($\int_{-a}^a f(x) dx$). Covers integrals of trigonometric, logarithmic, and modulus functions, focusing on parity (odd/even functions) and simplification techniques. This exercise evaluates … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.9 | Definite Integrals by Substitution

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.9, focusing on solving definite integrals using the substitution method. Learn the crucial step of changing the limits of integration and apply the technique to various functions, including trigonometric, inverse trigonometric, and rational functions. Includes application of the Leibniz rule for differentiating an integral. This exercise focuses … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.7 | Integration using Three Special Formulas

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.7. Master the integration of functions involving the square root of a quadratic expression ($\mathbf{\sqrt{x^2 \pm a^2}}$ and $\mathbf{\sqrt{a^2 – x^2}}$). Covers the essential technique of completing the square to transform expressions before applying the three standard formulas. This exercise requires the use of the three special … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.8 | Definite Integrals

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.8. Learn to evaluate definite integrals using the Fundamental Theorem of Calculus, $\int_a^b f(x) dx = F(b) – F(a)$. Covers various types of definite integrals, including trigonometric, inverse trigonometric, exponential, and fractional functions, along with techniques like substitution and algebraic manipulation. This exercise requires evaluating definite integrals … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.6 | Integration by Parts

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 7.6 on Integrals. Master the Integration by Parts (ILATE) rule for product functions. Covers various types, including inverse/logarithmic functions ($\int x \tan^{-1} x dx$), powers ($\int x^2 e^x dx$), and integrals of the form $\int e^x [f(x) + f'(x)] dx$. This exercise focuses on the integration technique … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.5 | Integration using Partial Fractions Solutions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.5. Master the technique of Partial Fraction Decomposition to integrate rational functions with linear, repeated, and irreducible quadratic factors. Includes advanced substitution problems like $\int \frac{1}{x(x^n + 1)} dx$ and $\int \frac{1}{e^x – 1} dx$. This exercise involves integrating rational functions by decomposing them into simpler fractions … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.4 | Integration using Special Formulas

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.4 on Integrals. Learn to apply the six standard formulas for integration involving $\mathbf{x^2 \pm a^2}$ and $\mathbf{\sqrt{x^2 \pm a^2}}$. Covers the crucial technique of completing the square and integrating types like $\int \frac{px+q}{\text{quadratic}} dx$. This exercise focuses on using the six standard integration formulas involving $\mathbf{x^2 … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.3 | Integration using Trigonometric Identities Solutions

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 7.3 on Integrals. Learn to transform complex trigonometric integrals using Product-to-Sum, Power Reduction ($\sin^2 x$, $\cos^4 x$), and other key identities. Covers types like $\int \sin A \cos B dx$ and $\int \frac{\cos x – \sin x}{1 + \sin 2x} dx$. This exercise requires transforming the integrand … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.1 | Integrals Solutions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.1 on Integrals. Learn to find the anti-derivative of functions like $\sin 2x$, $\cos 3x$, and $(ax+b)^2$ using the method of inspection and applying fundamental integration formulas for polynomials and exponential functions. This exercise introduces the basic concept of integration (finding the anti-derivative) using fundamental formulas and … Read more

Rbse Solutions Class 12 Maths Chapter 7 Exercise 7.2 | Integration by Substitution Solutions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 7.2 on Integrals. Master the method of substitution (u-Substitution) to solve complex integrals involving algebraic, trigonometric, and exponential functions, including types like $\int f(g(x))g'(x) dx$ and special trigonometric forms like $\int \frac{1}{1 \pm \tan x} dx$. This exercise focuses entirely on integration by the method of substitution … Read more

Rbse Solutions Class 12 Maths Chapter 6 Miscellaneous

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for the Class 12 Maths (NCERT) Miscellaneous Exercise on Chapter 6. Covers complex optimization problems (geometric shapes, cost minimization), advanced rates of change, maxima/minima of transcendental functions, and proofs of monotonicity using the Mean Value Theorem. This exercise covers a mix of topics including Maxima/Minima, Rates of Change, and Proving Monotonicity. 1. Maxima … Read more

Rbse Solutions Class 12 Maths Chapter 6 Exercise 6.3 | Maxima and Minima

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 6.3. Solve problems on Local Maxima and Minima (First and Second Derivative Tests), Absolute Extrema on closed intervals, and complex Optimization problems for geometry (e.g., box volume, cylinder surface area, cone volume). 1. Global Maxima and Minima (Basic Functions) (i) $f(x) = (2x – 1)^2 + 3$ … Read more

Rbse Solutions Class 12 Maths Chapter 6 Exercise 6.2 | Increasing and Decreasing functions

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 6.2. Learn how to determine the intervals of increasing and decreasing functions using the first derivative test ($f'(x) > 0$ or $f'(x) < 0$). Includes proofs for trigonometric, logarithmic, and polynomial functions. This exercise applies the derivative, $f'(x)$, to determine the intervals of increasing and decreasing behavior … Read more

Rbse Solutions Class 12 Maths Chapter 6 Exercise 6.1 Rates of Change

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 6.1. Master the application of derivatives to solve Rates of Change problems, including calculating rates for area, volume, surface area, marginal cost, and marginal revenue. Includes ladder, cone, and spherical balloon examples. This exercise focuses on Rates of Change, which involves using the derivative to find how … Read more

Rbse Solutions Class 12 Maths Chapter 5 Miscellaneous

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths Miscellaneous Exercise on Chapter 5 (NCERT). Tackle advanced problems in Logarithmic, Implicit, and Parametric Differentiation, including derivatives of $f(x)^{g(x)}$ forms, inverse trigonometric functions, and complex proofs involving the second derivative. This exercise covers a wide range of differentiation techniques, including the Chain Rule, Product Rule, Quotient Rule, Logarithmic Differentiation, … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.7: Second Order Derivatives

17/03/202616/03/2026 by By Subject Experts

Full solutions for Class 12 Maths (NCERT) Exercise 5.7. Learn to find the second order derivative ($\frac{d^2 y}{dx^2}$) for various functions using the Chain, Product, and Quotient rules, and prove identities involving derivatives like $\frac{d^2 y}{dx^2} + y = 0$. The second order derivative of a function $y = f(x)$ is the derivative of the … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.6: Parametric Differentiation

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 5.6. Learn how to find the derivative $\frac{dy}{dx}$ for functions defined parametrically, mastering the formula $\frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta}$ and techniques for simplifying complex trigonometric results. For functions defined parametrically by $x = f(t)$ and $y = g(t)$, the derivative $\frac{dy}{dx}$ is found using the formula: $$\frac{dy}{dx} = … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.5

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 5.5. Master Logarithmic Differentiation to solve complex products, quotients, and functions of the form $f(x)^{g(x)}$. Includes solutions for Implicit Differentiation problems like $x^y + y^x = 1$. 1. $y = \cos x \cdot \cos 2x \cdot \cos 3x$ We use logarithmic differentiation since it’s a product of … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.3: Implicit Differentiation and Inverse Trigonometric Functions

17/03/202616/03/2026 by By Subject Experts

Complete solutions for Class 12 Maths (NCERT) Exercise 5.3 on Differentiation. Learn to find $\frac{dy}{dx}$ using Implicit Differentiation and simplify complex Inverse Trigonometric Functions with substitutions before differentiating. This exercise requires finding $\frac{dy}{dx}$ using Implicit Differentiation (Questions 1-8) and applying trigonometric substitutions to simplify and differentiate Inverse Trigonometric Functions (Questions 9-15). Implicit Differentiation (Questions 1 … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.4: Differentiation

17/03/202616/03/2026 by By Subject Experts

Full solutions for Class 12 Maths (NCERT) Exercise 5.4. Practice differentiating functions involving the natural exponential ($e^x$) and logarithmic ($\log x$) functions, mastering the Chain Rule and Quotient Rule in combination with trigonometric and inverse functions. This exercise focuses on differentiating functions involving exponential functions ($e^x$) and logarithmic functions ($\log x$ or $\ln x$), primarily … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.2: Differentiation

17/03/202616/03/2026 by By Subject Experts

Full solutions for Class 12 Maths (NCERT) Exercise 5.2 on Differentiation. Master the Chain Rule, Product Rule, and Quotient Rule for complex functions, and learn how to prove non-differentiability at specific points. We will use the Chain Rule, Product Rule, and Quotient Rule to find the derivatives $\frac{dy}{dx}$. Differentiate the functions (Exercises 1 to 8) … Read more

Rbse Solutions Class 12 Maths Chapter 5 Exercise 5.1: Continuity

17/03/202616/03/2026 by By Subject Experts

Comprehensive solutions for Class 12 Maths (NCERT) Exercise 5.1 on Continuity and Differentiability. Learn to prove continuity, find points of discontinuity, and determine unknown constants ($k, a, b$) for continuous piecewise functions. 1. Function $f(x) = 5x – 3$ This is a polynomial function, and all polynomial functions are continuous everywhere. 2. Function $f(x) = … Read more

Rbse Solutions for Class 11 maths Chapter 3 Miscellaneous | Trigonometric Functions

17/03/202616/03/2026 by By Subject Experts

Get detailed, step-by-step solutions for NCERT Class 11 Maths Chapter 3 Miscellaneous Exercise . Master advanced trigonometric proofs involving extensive use of the Sum-to-Product formulas (e.g., $\sin C \pm \sin D$, $\cos C \pm \cos D$) and Half-Angle Identities. Learn how to determine the exact values of $\mathbf{\sin(x/2)}$, $\mathbf{\cos(x/2)}$, and $\mathbf{\tan(x/2)}$ when given $\tan x$, … Read more

Class 12 Maths Chapter 1: Relations and Functions – Short Notes (English & Hindi)

17/03/202631/01/2026 by Aman Singh

Mastering Class 12 Maths Chapter 1 on Relations and Functions is essential for both board exams and competitive exams like JEE. This chapter builds on the concepts learned in Class 11 and introduces more advanced topics. These short notes, in both English and Hindi, provide a quick and effective way to revise key concepts, definitions, … Read more

RBSE Class 12 Maths old papers : Your Secret Weapon to Scoring High – Decoding Old Question Papers!

17/03/202631/01/2026 by Aman Singh

Namaste, dear students of Rajasthan Board (RBSE) Class 12, and worried parents! The board exams are a significant milestone in every Indian student’s academic journey, and Mathematics often feels like the make-or-break subject. If you’re aiming to not just pass but to truly excel and score those coveted high marks in your RBSE Class 12 … Read more

Cracking the Code: Your Comprehensive Guide to the RBSE Class 12 Maths Syllabus 2025-26

17/03/202631/01/2026 by Aman Singh

For students in Rajasthan aspiring to pursue careers in engineering, data science, research, or any field demanding strong analytical skills, excelling in the RBSE Class 12 Mathematics examination is non-negotiable. The RBSE Class 12 Maths Syllabus 2025-26 is not just a collection of chapters; it’s the definitive framework that will guide your preparation, from foundational … Read more