Mathematics

What is Euclid Division AlgorithmEuclid’s Division Lemma: For any two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, where 0 ≤ r < b. For Example (i) Consider number 23 and 5, then: 23 = 5 × 4 + 3…

Graphical Method Of Solving Linear Equations In Two VariablesLet the system of pair of linear equations be a1x + b1y = c1                       ….(1) a2x + b2y = c2                      ….(2) We know that given two lines in a plane, only…

Solving A Quadratic Equation By Factoring Since, 3x2 – 5x + 2 is a quadratic polynomial; 3x2 – 5x + 2 = 0 is a quadratic equation. Also, 3x2 – 5x + 2 = 3x2 – 3x – 2x + 2 = 3x (x – 1) – 2(x – 1) = (x – 1) (3x – 2) In the same way : 3x2 – 5x…

Heights And Distances Angle Of Elevation The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e. the case when we raise our head…

Heights And Distances Angle Of Elevation The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e. the case when we raise our head…

How do you find the Surface Area of a Sphere and a HemisphereLet radius of sphere = r. ThenSurface area of a sphere = 4πr2Curved surface area of a hemisphere = 2πr2Total surface area of a hemisphere = 3πr2Volume of the sphere = …

Sum Of The First n Terms Of An Arithmetic Progression The sum of first n terms of an A.P. is given by Sn = n/2          or       Sn = n/2 Note: (i) If sum of n terms Sn is given then general term Tn = Sn – Sn-1 where Sn-1 is sum of (n – 1)…

Pair Of Linear Equations In Two VariablesA statement of equality of two algebraic expressions, which involve one or more unknown quantities is known as an equation. If there are two unknown quantities then equation is called linear equation…

Areas Of Parallelograms And TrianglesParallelograms on the same base and between the same parallels are equal in area.Area of a parallelogram is the product of its any side and the corresponding altitude.Parallelogram on the same base and…

How To Find The Area Of A Sector Of A Circle If the arc subtends an angle of θ at the centre, then its arc length is ( frac{text{ }!!theta!!text{ }}{text{180}}text{ }!!times!!text{ }!!pi!!text{ r} ) Hence, the arc length ‘l’ of a sector of…