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## RD Sharma Class 10 PDF Free Download

### RD Sharma Class 10

### RD Sharma Class 10 Solutions Polynomials

- Polynomial – Let x be a variable, n be a positive integer, and a1, a2, a3 ……… a be constants (real numbers), then f (x) = a
_{n}x^{n}+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+ ……… + a_{1}x+ a_{0}is called a polynomial in variable x.

- a
_{n}x^{n}, a_{n-1}x^{n-1}, a_{n-2}x^{n-2}……… a_{1}x, a_{0 }are known as the terms of the polynomial and a_{n}, a_{n-1}…….a_{1}, a_{0 }are their coefficients. - Degree of Polynomial – The exponent of the highest degree term in a polynomial is known as its degree.
- Constant Polynomial – A polynomial of degree zero (0) is called a constant polynomial.
- Linear Polynomial – A polynomial of degree 1 is called the linear polynomial.
- A linear polynomial may be a monomial or a binomial having one term or two terms respectively e.g., ax or ax + b.
- Zero of a Polynomial: For any polynomial p(x), if p(k) = 0, k is called a zero of polynomial p(x).
- A number of zeroes/roots of a polynomial p(x) is always equal to or less than the degree of polynomial p(x).
- If a polynomial p(x) is divided by (x — a), then the remainder will be p(a) = r.
- If a polynomial p(x) is divisible by (x — a), then p(a) = O.

### RD Sharma Class 10 Solutions Chapter 3

- Linear equation: An equation of the form ax + by + c = O, where a, b, c all are real numbers and a ≠ 0, b ≠ 0, is known as a linear equation in two variables x and y. Its graph is always a straight line.
- System of Simultaneous Linear Equations: A pair of linear equations in two variables a
_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 is said to form a system of simultaneous linear equations, where a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2}are real numbers. - A pair of values of x and y which satisfy each of the equations is called a solution or root of the system.
- If the system has at least one solution, it is called consistent and if the system has no solution, it is called inconsistent.
- A pair of linear equations in two variables can be solved by the :

Graphical method— To solve a pair of linear equations in two variables by Graphical method, we first draw the lines represented by them. - If the pair of lines intersect at a point, then we say that the pair is consistent and the coordinates of the point provide us a unique solution.
- If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.
- If the pair of lines are coincident, then it has infinitely many solutions-each point on the line being of solution. In this case, we say that the pair of lines equations is consistent with infinitely many solutions.
- Algebraic method—To solve a pair of linear equations in two variables algebraically, we have (i) Substitution method (ii) Elimination method (iii) Cross-multiplication method.

### RD Sharma Class 10 Solutions Trigonometric Identities

- Trigonometrical Identity: An equation, involving trigonometric ratios of an angle that is true for all values of the angle, is called a trigonometrical identity.
- While solving the trigonometric identities, keep in mind the necessary algebraic identities and learn to use them properly. Practice thoroughly how to use algebraic expressions in solving trigonometric identities.

### RD Sharma Class 10 Solutions Trigonometric Ratios

- Trigonometric Ratios: In the right-angled triangle AMP, Base = AM = x, Perpendicular = PM = y, and Hypotenuse = AP = r.
- It should be noted that sin θ is an abbreviation for “sine of angle θ”, it is not the product of sin and θ. Similar is the case for other trigonometric ratios.
- The trigonometric ratios are defined for an acute angle θ.
- The trigonometric ratios depend only on the value of angle θ.
- Sometimes due to common mistakes, the wrong usage of the trigonometric ratios is done in solving/proving trigonometric identities. Try to memorize all the trigonometric ratios by your own way to overcome this situation.

### RD Sharma Class 10 Solutions Arithmetic Progression

- Sequence: A sequence is an arrangement of terms, which are formed according to some definite patterns. From a definite pattern, we can find the general term (in terms of n).
- Terms: The elements in a sequence are called terms. A sequence is generally written as t
_{n}, where t_{n}is an n^{th}term and t_{1}, t_{2}, … are first, second,… terms of the sequence. - Finite Sequence: A sequence containing a finite number of terms is called a finite sequence.
- Infinite Sequence: A sequence containing an infinite number of terms is called an infinite sequence.
- Arithmetic Progression (AP): Arithmetic progression is a sequence in which each term, except the first term, differs from its preceding term by a fixed number (constant). The constant or fixed number is called the common difference of the arithmetic progression.
- Generally, an arithmetic progression with first term a and common difference d is represented as a, a + d, a + 2d, a + 3d, ….
- To find n
^{th}Term of an AP: The nth term of an AP with first term a and common difference d is given by t_{n }= a + (n – 1) d.

Language | English |

No. of Pages | 2 |

PDF Size | 0.09 MB |

Category | Education |

Source/Credits | – |

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RD Sharma Class 10 PDF Free Download