12th Mathematics Chapter Study Material English Medium 2021 By S Rajan M Sc M Phil M Ed [top] Jun 2026

Every element is related to itself. For all

Find $X = A^-1B$. $$X = \frac17 \beginpmatrix 3 & 1 \ -1 & 2 \endpmatrix \beginpmatrix 7 \ -11 \endpmatrix$$ $$X = \frac17 \beginpmatrix 21 - 11 \ -7 - 22 \endpmatrix = \frac17 \beginpmatrix 10 \ -29 \endpmatrix = \beginpmatrix 10/7 \ -29/7 \endpmatrix$$ Result: $x = \frac107, y = -\frac297$.

Do not jump straight to the exercises. Read the brief introduction written by Rajan sir to understand the real-world application of the chapter. Every element is related to itself

Use the area properties under the standard normal curve table carefully. Practice word problems regarding coin tosses and dice. Chapter 12: Discrete Mathematics

Evaluate: $\tan^-1(1) + \tan^-1(2) + \tan^-1(3)$. Solution: Let $A = \tan^-1(1) + \tan^-1(2)$. Here $x=1, y=2$. Since $xy = 2 > 1$, use the extended formula. $$A = \pi + \tan^-1\left(\frac1+21-(1)(2)\right) = \pi + \tan^-1\left(\frac Do not jump straight to the exercises

Area=∫abf(x)dxArea equals integral from a to b of f of x space d x

This public link is valid for 7 days and shares a thread, including any personal information you added. This link or copies made by others cannot be deleted. If you share with third parties, their policies apply. Can’t copy the link right now. Try again later. Practice word problems regarding coin tosses and dice

A relation that simultaneously satisfies reflexive, symmetric, and transitive properties. Types of Functions

In-depth coverage of matrix inversion, Cramers' rule, and consistency of linear equations.

Provides clear visual algorithms for Cramer’s Rule, Matrix Inversion Method, and Gauss-Jordan elimination. It includes extensive practice sets for testing consistency. 2. Complex Numbers

Partially – the syllabus has been restored to pre-COVID levels. However, 90% of the content (matrices, calculus, vectors) remains valid. Just add the missing topics (e.g., certain parts of probability) from NCERT.