Sujit Prasad Kushwaha

This is the mathematics formulae book for class 12 students. Here, we have covered all the formulae needed to solve the questions of Mathematics. Permutation The total arrangement of total objects taken some or all at a time is called permutation. The permutation of 'n' objects taken 'r' at a time is denoted by $^np_{r}$ and is defined by; 1. $^np_{r}=\frac{n!}{(n-r)!}$ 2. Permutation of an object, all different;$$=\frac{n!}{p!\,q!\,r!}$$ where,  n=total objects p=repetition of first kind  q=repetition of second kind r=repetition of third kind 3. Circular permutation= $(n-1)!$ 4. If clockwise and anticlockwise arrangement are not distinguishable [necklace of beads and beads into bracelet]; Total number of permutation=$\frac{(n-1)!}{2}$ Combination The selection of total objects taken some or all at a time is called combination. The combination of 'n objects taken 'r' at a time is denoted by $^nc_{r} \, or \, c(n,r)$ and defined by; $$^nc_{r}=\frac{n!}{(n-r)!...

  The national flag of Nepal is a unique and distinct symbol that represents the country and its people. It is one of the only national flags in the world that is non-quadrilateral in shape, consisting of two single pennons or pennants. The flag's design is simple yet powerful, with a crimson red background that is the color of the country's national flower, the rhododendron. This color also holds significant meaning as it represents victory in war, symbolizing the brave spirits of the Nepalese people. The blue border of the flag represents peace and harmony, which have been prevalent in the country since the age of Gautama Buddha, who was born in Nepal. The blue color symbolizes the serene and tranquil nature of the Nepalese people and the country's historical and cultural significance. The two triangles on the flag represent the Himalaya Mountains, which are an integral part of the country's identity and are considered sacred by many Nepalese. The two triangles on...

Have you ever thought what are the most commonly used Mathematics Formulae? Yes, many of you have. Let me convert your imagination into reality. Here are some of the most commonly used mathematics formulas: 1. Quadratic Formula:  $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ where a, b, and c are coefficients of quadratic equation. 2. Pythagoras Theorem: $$a^2+b^2=c^2$$ where a, b, and c are the length of the sides of a right-angle triangle. 3. Distance Formula: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinate of two points in a plane. 4. Area of a Circle: $$A=\pi{r^2}$$ where r is the radius of the circle. 5. Volume of a Sphere: $$V=\frac{4}{3}\pi{r^3}$$ where r is the radius of the sphere. 6. Volume of a Cylinder: $$V=\pi{r^2}h$$ where r is the radius and h is the height of the cylinder. 7. Area of a Triangle: $$A=\frac{1}{2}bh$$ where b is the base of the triangle and h is the height. 8. Slope-intercept formula: $$y=mx+c$$ where m is the slope o...

Syllabus: Introduction and characteristics of aromatic compounds Huckel's rule of aromaticity  Kekule structure of Benzene Resonance and Isomerism Preparation of benzene from decarboxylation of sodium benzoate, phenol, and ethyne only Physical properties of benzene Chemical properties of benzene: Addition reaction; hydrogen, halogen, Electrophilic substitution reactions; orientation of benzene derivative (o,m and p), nitration, sulphonation, halogenations, Friedel-Crafts reaction (alkylation and acylation), combustion of benzene (free combustion only) and uses Phenols  

Course Description: This course is designed for first year of Four years B.Sc. program. The main aim of this course is to provide knowledge of Analytical Geometry and Vector Analysis.   Course Objectives: The objective of this course is to acquaint students with the basic concepts of Analytical Geometry and Vector Analysis. It aims at enabling students to build good knowledgebase in the subject of Analytical Geometry and Vector Analysis  Unit 1. Transformation of Coordinates:  Introduction to polar, cylindrical and spherical coordinates, Transformation, Rotation, Process involving combination of translation and rotation of axes, Invariants in orthogonal transformation. [10 Lectures]  Unit 2. Conic Sections and their properties:  Introduction, Conic section as a locus of a point and as a section of a cone, Central conic sections, Ellipse and hyperbola, Derivation of their equations in standard forms, Auxiliary circles and eccentric angle, Equations of...