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)!...

                                                                  New Syllabus Course Title: Scientific Communication                                                                   Full Marks:50 Course No: SC 101                                                   ...

anti: anticlimax, anti-nationalist, antibody be: becalm, befog, beset, bewitch bi/tri: bicycle, tricycle co: co-author, co-driver, co-worker ex: ex-Prime Minister, exit, expand, ex-husband inter: international, interact, intermission, interchange macro: macrostructure, macroeconomics micro: microscope, microbus mini: minibus, miniskirt mis: misuse, misbehave mono: monopoly, monolingual multi: multicultural, multilingual out: outbuilding, outnumber, outboard, outperform over: over-smart, overreact, overjoyed, overcoat post: postpone, postgraduate, post-war pre: pre-defined, precondition, pre-match re: repair, reawake, reunion, rewrite semi: semi-permeable, semicircle sub: subconscious, sub-tropical, submarine super: supermarket, supertanker trans: transplant, transnational, translate under: underweight, underpaid, underdeveloped de: deforest, degenerate dis: dislike, dishonest, disadvantage in: indirect, injustice non: non-stop, non-alcoholic, non-sense un: une...

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 Calculus.  Course Objectives: The objective of this course is to acquaint students with the concepts of Calculus and differential equations and their applications. It aims at enabling students to build knowledgebase in Calculus.  Course Contents Unit 0. Review of Elementary Calculus: Functions, Graphs, Evaluations of limits, Continuity, Discontinuity, Test of continuity and properties of continuous functions. [10 Lectures]  Unit 1. Tangents and Normals:  Tangents and Normals, Subtangents, Subnormal and their lengths, Derivatives of arc length, Polar equations of subtangents and subnormal, Angle between radius vector and tangent, Length of perpendicular from pole on tangent, Pedal equations and Angle between two curves. [10 Lectures]  Unit 2. Higher Order Derivatives and Mean Value Theorems:  Higher order derivati...

Gravity and Gravitation Central Force A central force between two particles is one which is directed along the line joining the two particles and whose magnitude is a function of the distance between them. If one particle is fixed in its position, the central force acting on the other is $\vec{F}$, then the torque acting on it is: $$ \vec{\tau} = \vec{r} \times \vec{F} = 0 $$ Since, $$ \vec{\tau} = \frac{d\vec{J}}{dt} $$ $$ 0 = \frac{d\vec{J}}{dt} $$ $$ \Rightarrow \vec{J} = \text{constant} $$ Again, we know, $$ \vec{J} = \vec{r} \times \vec{p} $$ $$ \vec{r} \cdot \vec{J} = \vec{r} \cdot (\vec{r} \times \vec{p}) = (\vec{r} \cdot \vec{r})\, \vec{p} = 0 $$ This shows that $\vec{r}$ and $\vec{J}$ are perpendicular to each other, and the motion of the particle is confined to a plane. Central force can be represented as: $$ \vec{F} = \frac{C}{r^2}\,\hat{r} $$ For gravitational force, $$ C = Gm_1 m_2, \qquad \text{then} \qquad \vec{F} = \frac{Gm_1 m_2}{r^2}\,\hat{r} $$ For...