Yeh book class 12 ke students ke liye Riyazi ka doosra hissa hai. Isme aapko integrals, differential equations, aur probability jaise important topics milenge. Yeh book CBSE board ke syllabus ke mutabiq tayyar ki gayi hai.
Is chapter mein aap indefinite aur definite integrals ke baare mein padhenge. Integration ke rules, substitution method, aur partial fractions ka istemal karte hain. Alawa iske, area ke hisaab ke liye integrals ka upyog bhi samjhaya gaya hai.
Yeh section aapko batata hai ki kaise integrals ka istemal karke curves ke beech ka area nikaala jaata hai. Simple aur compound curves ke liye examples diye gaye hain.
Differential equations mein order, degree, aur solving methods jaise separation of variables, homogeneous equations, aur linear differential equations ko cover kiya gaya hai. Har method ke liye step-by-step approach di gayi hai.
Yeh chapter aapko bataata hai ki differential equations ka istemal physics, chemistry, aur economics mein kaise hota hai. Jaise growth models, radioactive decay, aur population models.
Isme vector algebra ke basics, dot product, cross product, aur unke geometric meanings diye gaye hain. Phir 3D geometry mein lines aur planes ke equations aur unke bich ka distance aur angle nikaalna sikhaya gaya hai.
Scalar aur vector quantities, unit vectors, position vectors, aur vectors ka addition/subtraction. Alawa iske, vectors ka magnitude aur direction ka hisaab karna bhi bataya gaya hai.
Line ke equation, plane ke equation, angle between lines, angle between planes, distance from a point to a plane - sab concepts numerical examples ke saath diye gaye hain.
Is chapter mein linear programming problems ka formulation aur graphical method se solution bataya gaya hai. Feasible region, corner points, aur objective function ka optimisation (maxima/minima) important topics hain. Real-world problems jaise production planning aur resource allocation ke examples diye gaye hain.
Probability ke advanced concepts - conditional probability, Bayes' theorem, random variables, probability distributions (Binomial, Poisson, Normal) - sabko cover kiya gaya hai. Har distribution ke formulas, mean, variance, aur practical examples hain.
Binomial distribution ke liye n, p ke values ke saath table di gayi hai. Poisson distribution mein lambda ke differenct values ke saath probabilities di gayi hain. Normal distribution ke liye standard normal table bhi shamil hai.
Yeh book Class 12 ke final exams aur competitive exams ke liye bhi useful hai. Isme diye gaye exercises aur examples se aap concepts ko acchi tarah samajh sakte hain. Har chapter ke end mein miscellaneous exercises aur revision points hain.
