10th Class

  Paragraph   SEA: LIFE ON WAVE   Human life is full of journeys and adventures. Few of us choose to join defence. Certain men choose navy as their career option. Month on month they are far away their farmilies and their beloved ones, Sea life is very adventurous. Each and every day you find it more exciting. Once, a big fish attacked the ship. Instead of fighting, the fish ate the captain?s leg. One more incident, when we were sailors and first reached near the coast, we came to know about the storm. We quickly moved into the sea to save our life. At the coast the waves are very dangerous. They may destroy anything and even break stones. So life on the sea is great to me.   CITY LIFE   Life is full of joyful moments. Life more...

  Letters         Letters are mainly of three types:   Personal Letter: Those letters which are written to relatives, friends and to known persons Business Letter: Those letters which are written to business mass traders and business firms Official Letter: Those letters which are written to government officers such as postmaster, principal, etc.   A letter consists of six parts:

Heading

The salutation or gretting

The body

The subscription

Signature

Address

 

• Example 1

  You are Mr. Ravi Shankar, an ex-Army Man from the Indian Army. You are staying at WZ-50, Rishi Nagar, Rani Bagh, Delhi-110034 since 1990. Now-a-days your society is facing the problem of lack of parking place for vehicles in your locality. So, you have decided to write a letter to your area’s MCD Officer, Pitampura, Delhi, for providing parking place.   WZ-50, Rishi Nagar, Rani Bagh, more...

Number System   All the numbers we have studied so far are real numbers. The real numbers are divided into two categories which are rational and irrational numbers. All the positive numbers used for counting are called the natural numbers. These start from 1 and end till infinity. The positive numbers which start from zero are called whole numbers. The collections of natural numbers, their negatives along with the number zero are called integers. Rational numbers are the numbers in the form \[\frac{p}{q}\] where \[q\ne 0\] and p, q are integers and irrational q numbers are the numbers which cannot be written in the form p-, where p and q are integers and\[q\ne 0\].   Decimal Expansion of Rational Numbers There are rational numbers which can be expressed as terminating decimals or non- terminating decimals. The non-terminating decimals may be repeating or non- repeating. The rational more...

Polynomials   Polynomials are algebraic expressions having finite terms. The expression \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+{{a}_{n-2}}{{x}^{n-2}}+---+{{a}_{1}}x+{{a}_{0}}\] is called the polynomial of degree n, where \[{{a}_{n}}\ne 0.\] The highest power of the variable in a polynomial is called degree of the polynomial. The polynomials of degree one are called linear polynomial. The polynomials of degree two are called quadratic polynomials. The polynomials of degree three are called cubic polynomials and the polynomials of degree four are called biquadratic polynomials. A real number which satisfies the given polynomial is called zero of the polynomial.   Zeroes of a Polynomial If \[a{{x}^{2}}+\text{ }bx\text{ }+\text{ }c\text{ }=\text{ }0,\text{ }(a\ne o),\]is a quadratic equation whose roots are \[\alpha \] and \[\beta \], then the relation between the roots of the equation and its coefficients is given by: Sum of the roots =\[\alpha +\beta =-\frac{b}{a},\] Product of the roots = \[\alpha \beta =\frac{c}{a}.\]   For a more...

Co-ordinate Geometry   In this chapter we will discuss about the two as well as three dimensional geometry. We will discuss about the position of the points and locate the point in the plane or on the surface. The three mutually perpendicular lines in the plane are called coordinate axes of the plane. The numbers in a plane which represent the position of a point is called coordinates of the point with reference to the coordinate planes. The eight equal regions into which space is divided by three dimensional axes are called octants.   Distance Formula Let us consider the two points \[A\left( {{x}_{1}},\text{ }{{y}_{1}} \right)\] and B(\[{{x}_{2}},\text{ }{{y}_{2}}\]), in a two dimensional plane, then the distance between the two points is given by \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}.}\] If it is a three dimensional plane containing the points \[A\left( {{x}_{1}},\text{ }{{y}_{1}},\text{ }{{z}_{1}} \right)\] and \[B\left( {{x}_{2}},\text{ }{{y}_{2}},\text{ }{{z}_{2}} \right),\]then more...

Pair of Linear Equations in two Variables and Quadratic Equation   Linear Equation in Two Variables A linear equation in two variables is an equation which contains a pair of variables which can be graphically represented in xy-plane by using the coordinate system. For example ax + by = c and dx + e y = f, is a pair of linear equations in two variables' Solutions of the linear equation in two variables are the pair of values of the variables that satisfies the given equation. In other words, we can say that a system of linear equation is nothing but two or more linear equations that are being solved simultaneously. Mostly, the system of equations are used in the business purposes by predicting their future events. They model a real life situation in two system of equations to find the solution and manage their more...

Geometry   In this chapter we will discuss about the similarity of triangles and properties of circles. Two figures having the same shape and not necessarily the same size are called the similar figures. Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Circle is defined as the locus of a point which is at a constant distance from a fixed point. The fixed point is called the canter of the circle and the fixed distance is called the radius of the circle.   Similar Triangles Two triangles are similar, if their corresponding angles are equal and their corresponding sides are in the same ratio. The ratio of any two corresponding sides in two equiangular triangles is always the same.   Basic Proportionality Theorem It states that if a line more...

Trigonometry and Its Application   The word trigonometry is a Greek word consists of two parts 'trigonon' and 'metron' which means measurements of the sides and angles of a triangle. This was basically developed to find the solutions of the problems related to the triangles in the geometry. Initially we use to measure angles in terms of degree, but now we will use another unit of measurement of angles called radians. The relation between the radian and degree measure is given by: 1 radians \[={{\left( \frac{180}{\pi } \right)}^{o}}\]and 1o=\[{{\left( \frac{\pi }{180} \right)}^{o}}\]radians or \[{{\pi }^{c}}\]=\[{{180}^{o}}\]   Trigonametric ratios of allied angles Two angles are called allied angles when their sum or difference is either zero or a multiple of\[90{}^\circ \]. The angles\[-\,\theta ,\text{ }90{}^\circ \pm \text{ }\theta ,\]\[180{}^\circ +\text{ }\theta ,\] etc. are angles allied to the angles \[\theta \] where \[\theta \] is measured in more...