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  SAMACHEER KALVI CLASS 10 SEQUENCE AND SERIES ASSIGNMENT 2 1. Find all positive integers which when divided by 3 leaves remainder 2. 2. Prove that the product of two consecutive positive integers is divisible by 2. 3. Use Euclid's Division Algorithm to find the Highest Common Factor of 340 and 412. 4. If d is the HCF of 32 and 60, find x and y satisfying d = 32 x  + 60 y. 5. Find the HCF of 252525 and 363636. 6. If 13824  =  2^a  x  3 ^ b,  then find a and b. 7. Find the greatest numbers consisting of 6 digits which is exactly divisible by 24, 15 and 36? 8. Find the least positive value of x such that (i) 89 = (x+3) mod 4 (ii) 96 = (x/7 ) mod 5. 9. If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which number modulo 17? 10. Solve 3x -2  = 0 ( mod 11 ) 11. Find the remainder when 2⁸¹ is divided by 17? 12. Find the next three terms of the sequence 1/4, 2/9, 3/16,..... 13. Find the first four terms of the sequence whose nth term is give...

PHYSICS  MOTION IN A PLANE CLASS 11 ASSIGNMENT 2 This assignment has been designed in a such a way that it covers all the important topics in the chapter - Motion in a plane. Once students are thorough with the concepts and formulae, they will be in a position to do sums based on these concepts. Sums will be published shortly. 1. Describe the necessity for introducing the concept of vectors. 2. Define scalar and vector quantities.  Give examples. 3. The given quantity has both magnitude and direction.  Is it necessarily a vector? 4. Does a scalar quantity depend on the frame of reference chosen? 5. Distinguish between scalars and vectors. 6. Explain with an example the representation of a vector quantity. 7. Distinguish between position and displacement vectors. 8. Define      a. Equal vectors     b. Negative of a vector     c. Modulus vector     d. Unit vector     e. collinear vectors 9. What is meant by polar vector...

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  ...