[PDF] RD Sharma Class 10 PDF

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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 xⁿ + a_n-1 x^n-1 + a_n-2 x^n-2 + ……… + a₁x+ a₀ is called a polynomial in variable x.

a_n xⁿ, a_n-1 x^n-1, a_n-2 x^n-2 ……… a₁x, a₀are known as the terms of the polynomial and a_n, a_n-1 …….a₁, a₀are 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 a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂= 0 is said to form a system of simultaneous linear equations, where a₁, a₂, b₁, b₂, c₁, c₂ 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 t₁, t₂, … 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.