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                                                   ...

The cow is considered a sacred animal in Nepal and holds great cultural and religious significance. It is also an important source of livelihood for many Nepalese farmers, providing milk, meat, and dung for fuel and fertilizer. In Hinduism, cows are considered sacred and are associated with the goddesses Lakshmi and Gauri, who are considered to be the embodiment of wealth, fertility, and motherhood. The cow is also a symbol of non-violence and is believed to possess healing powers. The cow is also a symbol of wealth and status in Nepal. Many families, especially in rural areas, own cows as a sign of prosperity and a source of income. Cows are considered a valuable asset, and their ownership is often used as a measure of social status. In addition, cows are often given as gifts at weddings and other important events. The cow is also considered a symbol of motherhood and is often depicted in art and religious iconography as a nurturing figure. In Hinduism, the cow is seen as a repres...

Course Objectives At the end of this course the student should be able to acquire sufficient basic knowledge in physic and apply this knowledge for higher studies and research in physics MECHANICS [50] Course Contents:  1. Review of Laws of Motion:  1.1 Dynamics of a particle, General equations of motion, Types of forces, Conservation laws, Work-Energy theorem, Conservative forces, 1.2 Motion of a body near the surface of the earth, Linear restoring force, Potential energy curve, Non-conservative forces. [3 hours]  2. Linear and Angular Momentum:  2.1 Conservation of linear momentum, Centre of mass, Collision of two particles, 2.2 Deflection of a moving particle by a particle at rest, Rocket, Angular momentum and torque, 2.3 Motion under central force, Areal velocity, 2.4 Examples of conservation of angular momentum. [5 hours]  3. Gravitational Potentials and Fields:  3.1 Central Forces, Inverse square-law of force, 3.2 Gravitational field and poten...

Conservation of Linear Momentum The total quantity of motion contained in a body is called linear momentum . It is denoted by $\vec{P}$ and defined as the product of mass and velocity of the body. For a body of mass $m$ and velocity $v$, its linear momentum $\vec{P}$ in vector form is given by: $$\vec{P} = m\vec{v}$$ In terms of magnitude only, $$P = mv$$ SI unit of linear momentum is $\text{kg m s}^{-1}$ or Ns, and dimensional formula is $[MLT^{-1}]$. Law of Conservation of Linear Momentum It states that, "the total linear momentum of a system of particles remains constant, provided that no external force acts on the system" . Proof: From Newton's second law of motion , $$F = \frac{dP}{dt}$$ In absence of force, $$\frac{dP}{dt} = 0 \;\Rightarrow\; P = \text{constant}$$ Proof (for a system of particles): Let us consider a system of $n$ particles of total mass $M$. Then, $$M = m_1 + m_2 + \cdots + m_n$$ So, $$P = P_1 + P_2 + \cdots + P_n$$ Differe...