January 21, 2022

## Set Theory(NCERT Exemplar )

Here we have given the solutions of  some important questions of chapter 1 (Set Theory) of NCERT Exemplar book . Short answer type questions 1. Write the following sets in the roaster  form (i) (ii) (iii) Sol. (i) On solving the equation      , we get  Thus     . (ii)       gives    which implies Thus  (iii) Since every prime no. has  only two factors 1 and number itself. This implies         2.  Write the following sets in the roaster  form: (i)  (ii) (iii) Sol. (i) On solving   , we get     ,  which implies  either …

## Polynomials : Definition, Types of polynomials and Examples, Degree of a polynomial

Polynomial:  An algebraic expression is an expression which is made up of variables and constants along with some algebraic operations.  The several parts of an algebraic expression seperated by + or – operations are called the terms of the  expression. e.g. (i)   is  an algebraic expression with three terms  and three variables . (ii)   is  an algebraic expression with three terms  and two variables . (iii)    is  an algebraic expression with two terms  and one variable . (iv)      is  an algebraic expression with one terms  and one variable. In an algebraic expression , if the …

## Solved examples on rational numbers

Here we are giving some practice  questions based  on  rational numbers. 1. Are the following statements are true or false? Give reason  for your answers. (i)  every whole number is a natural numbers. (ii) every integer is a rational number . (iii)There are infinitely many rational numbers between any two given rational numbers. (iv) 0 is a rational  number. (V)Every rational number is a whole number. ANS. (i) False , beacuse ‘0’ is a whole  number not a natural number. (ii)True,  because every integer can be expressed in the form , so it is a rational number. (iii) True (iv) …

## Various types of numbers: natural numbers, whole numbers, integers and rational numbers

Various types of numbers: natural numbers, whole numbers, integers and rational numbers Various types of numbers : According to the properties and how they are represented in the number line, the numbers are classified into different types.  Natural numbers The natural numbers are those numbers that are used for counting and ordering.  The set of natural numbers is often denoted by the symbol ,        The least natural number is 1 and there are infinitely  many natural numbers.  They are located  at the right side of the number line (after 0) Properties of natural numbers:  (i) closure property: …

## zeros of quadratic polynomials

Geometrical interpretation  of zeros of quadratic  polynomials: A polynomial of degree 2 is called a quadratic polynomial.  For any quadratic polynomial , , the graph of the corresponding equation     has one of the two shapes either open upwards like U or open   downwards like ,   ∩   depending on whether a > 0 or a < 0. (These curves are called parabolas.)  The zeroes of a quadratic polynomial ,  are precisely the  x-coordinates of the points where the parabola representing intersects the x-axis. Now the following three cases can happen. Case-(i)   The graph cuts x-axis at two distinct points. …

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