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)!...

#WRITE A PROGRAM TO OPEN A DATA FILE “STUDENT.DAT” THAT CONTAINS NAME, ADDRESS, TELEPHONE NUMBER AND PATENTS NAME OF SOME STUDENTS. NOE, DISPLAY ALL THE RECORDS WHOSE ADDRESS IS “LALITPUR”. CLS OPEN “STUDENT.DAT” FOR INPUT AS #1 WHILE NOT EOF(1) INPUT #1, N$,A$,T#,P$ IF UCASE$(A$)=”LALITPUR” THEN PRINT N$,A$,T#,P$ END IF WEND CLOSE #1 END   #A SEQUENTIAL DATA FILE “STD.REC” CONTAINS RECORDS OF STUDENTS NAME, ROLL NUMBER, SECTION AND ADDRESS OF 10 STUDENTS. WRITE A PROGRAM TO DISPLAY THE LAST FIVE RECORDS. CLS OPEN “STD.REC” FOR INPUT AS #1 FOR I=1 TO 10 INPUT #1, N$,R,S$,AD$ IF I>S THEN PRINT N$,R,S$,AD$ END IF NEXT I CLOSE #1 END   #A SEQUENTIAL DATA FILE “SALARY.DAT” CONTAINS INFORMATION AS EMPLOYEE CODE, EMPLOYEE NAME, POST AND BASIC SALARY. WRITE A PROGRAM TO DISPLAY THOSE RECORDS WHOSE BASIC SALARY IS BETWEEN 10000 TO 15000 AND POST IS “OFFICER”. CLS OPEN “SALARY.DAT” FOR INPUT AS #1 WHILE NOT EOF(1) INPUT #1,EC,EN$,P$,S IF S>=10000 AND ...

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...

The phenomenon of bending of light and spreading into geometrical shadow after passing through obstacle or slits is called diffraction. The diffraction pattern can be obtained on the screen when width of slit is equivalent to wavelength of light. The bright and the dark fringes obtained on the screen due to diffraction are called secondary maxima and minima. Types of diffraction: On the basis of arrangement of device used, there are two types of diffraction. They are: 1. Fresnel's diffraction: The diffraction which is obtained due to the source slits and screen at a finite distance is called fresnel’s diffraction. In this diffraction, the wave front is spherical. So, diffraction pattern obtained on the screen are quite complex. 2.Fraunhoffer’s diffraction: The diffraction which is obtained due to the source slits and screen at infinite distance is called fraunhoffer’s diffraction. In this diffraction, the wave front is plane. So, diffraction pattern obtained on the sc...

Fear is a universal emotion, deeply ingrained in the human experience. It is an instinctive response to potential threats, but in the modern world, fear often transcends its primal origins. Whether it's the fear of failure, rejection, or the unknown, it can significantly impact various aspects of life, including studies, relationships, business, and more. However, fear doesn't have to be an insurmountable obstacle. By understanding and confronting fear, people can transform it into a powerful force that drives success and personal growth. Students often grapple with the fear of failure, which can manifest as anxiety during exams or hesitation in participating in class. This fear can stem from high expectations, both self-imposed and from others. It can lead to procrastination, avoidance, and a lack of confidence in one's abilities. However, those who learn to manage this fear can turn it into a motivator. By setting realistic goals, seeking help when needed, and embracing...