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)!...

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...

 1. Read the following passage and answer the questions given below briefly: [10] There is a considerable scientific disagreement about the medical hazards of the new pollutants; about the effects of DDT now found in human bodies, about the diseases due to smog, or about the long range effects of fallout. But the crucial point is that the disagreements exists, for they reveal that we have risked these hazards before we know what harm they might do. Unwittingly we have loaded the air with substances that interfere with the functioning of the blood. Because we wanted to build nuclear bombs and kill mosquitoes; we have burdened our bodies with strontium-90 and DDT, with consequences that no one can now predict. We are, in effect, conducting a high experiment ourselves. A generation hence-too late to help-public health statistics may reveal what hazards are associated with these pollutants. ('Science and Survival,' Barry commoner) a) What are the three pollutants with which man has...

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 Attempt all the questions. 1. Read the following passage and answer the questions given below. [10] Pollution-the simple visible kind of pollution is now worldwide. When Apollo 8 took photographs of the earth's surface, where did they reveal the most serious smog and polluted air? Not Los Angeles, which as somehow got the reputation of having biggest and nastiest smog, but over Osaka and Tokyo in Japan. Along this strips, 34 tons of dirt a month fall on every square kilometer, compared to a mere 17 tons in New York. Coastal vessels collide regularly or run aground because they cannot see each other's navigation lights in day-light, or because light buoys are invisible. Traffic policeman go back to the police-station after four hours of duty and breathe pure oxygen from the oxygen cylinders to re-oxygenate their carbon monoxide loaded blood. In cafes and shopping centers coin-in-the slot machines give oxygen to shoppers who feel themselves about to collapse. In school, children...