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MATHEMATICS  CONTINUITY AND DIFFERENTIABILITY CLASS 12 Calculus is one of the most important topics in Math. Especially class 11 and class 12 students need to have a clear understanding about the concepts present in calculus as it has a widespread application in many fields.  The two main topics required for better understanding of Calculus are Algebra and Trigonometry. This is about the continuity of a function. The continuity of all the six trigonometric ratios have been discussed here. Continuity of other functions like modulus, polynomials have also been explained in detail. Some important NCERT sums on continuity have also been included. Class 12 students can go through this to get an idea of how to prove continuity of a function. Suppose f is a real function on a subset of the real numbers and let c be a point in the domain of f.  Then f  is continuous at c   lim  f(x)  =  f(c)   x→c That is, if lim f(x)   =  f(c)...

  MATHEMATICS CLASS 12  RELATIONS AND FUNCTIONS SOLUTIONS TO EXERCISE 1.2 This exercise is about the types of functions. To identify the type of function, either elements like x, y can be used or random values can also be used.  A function f: X -> Y is said to be one-one (or injective), if every element of the domain has one and only one image in the codomain. A function f: X -> Y is said to be onto (surjective) if for every y ∈ Y (codomain) there exists x ∈ X (domain). A function is said to be bijective if it is both one-one and onto. 1. Show that the function f: R∗ -> R∗, defined by f(x) =1/x is one - one and onto where R∗ is the set of all non zero real numbers.  Is the result true, if the domain R∗  is replaced by N with codomain being the same R∗ Let x, y ∈ R∗ such that f(x) = f(y)             f (x)= f(y)            1/x  =  1/y       ⇒  x  =  y There...

  PHYSICS ASSIGNMENT 3 CLASS 12 CURRENT ELECTRICITY 1. What is current electricity? 2. Define electric current.  Give its SI unit. 3. Distinguish between conventional and electronic current. 4. Define emf of a battery.  When is the emf of a battery equal to the potential difference between its terminals? 5. Is electric current a scalar or vector quantity? 6. Distinguish between electromotive force and potential difference. 7. How is the flow of electric current maintained in an electric circuit? 8. State Ohm's law. 9. Define resistance and state its SI unit. 10. Explain how we can measure the resistance of a wire. 11. What are the factors on which the resistance of a conductor depend? 12. Define resistivity and state its SI unit. 13. Define the following and also write their SI units: a. current density b. conductance c. conductivity 14. (i) Which metal has the lowest resistivity?       (ii) What is the order of resistivity of an insulator? 15. (i) What is ...

 PHYSICS ASSIGNMENT 1 CLASS 11 UNITS AND MEASUREMENTS 1. What are physical quantities? 2. Name and define the two types of physical quantities. Give examples. 3. What is measurement of a physical quantity?  4. Write the relationship between the numerical value of a quantity and the size of the unit. 5. What is a physical unit? Write the desirable characteristics of a physical unit. 6. What is a system of units. Mention the various types of system of units. 7. Name all the basic and supplementary units of SI. 8. Define coherent system of units. 9. State the advantages of SI units. 10. State the rules followed in writing SI units in symbolic form. 11. Make a list of various prefixes used for powers of 10. Give some examples.  12. Express the following in metres:       a.  1 nanometre       b.  1 angstrom        c.  1 fermi       d.  1 micron       e.  1 light year  ...

  PHYSICS ASSIGNMENT 2 CLASS 12 ELECTROSTATIC POTENTIAL AND CAPACITANCE 1. Define potential difference and write its SI unit. 2. Define Electric potential and write its SI unit. 3. Derive an expression for the electric potential at a distance r from a point charge q.  What is the nature of this potential? 4. Derive an expression for the potential at a point along the axial line of a short dipole. 5. Derive an expression for the electric potential at any general point at distance r from the centre of a dipole. 6. Show mathematically that the potential at a point on the equatorial line of an electric dipole is zero. 7. Derive an expression for the electric potential at a point due to a group of N point charges. 8. Show that the electric field at any point is equal to the negative of the potential gradient at that point. 9. What is an equipotential surface? Give an example. 10. State and prove the important properties of equipotential surfaces. 11. State and explain the equipoten...

  PHYSICS -  ASSIGNMENT 1               CLASS 12 ELECTRIC CHARGES AND FIELD 1. What is Electric Charge? Name the SI unit. 2. What is Electrostatics? Mention any two applications. 3. State the fundamental Law of Electrostatics. 4. What is meant by Earthing? Mention its importance. 5. What are the basic properties of Electric charge? 6. State the law of Conservation of charge.       Give two examples. 7. State Coulomb's law in Electrostatics.       Express the same  in SI units. 8. Write Coulomb's law in vector form.       Mention its importance. 9. Define Dielectric constant in terms of forces     between two  charges. 10. State the Principle of Superposition of Electrostatic        forces.   Write an expression for the force on a point        charge due to a  distribution of N-1 point charges in     ...