September 2024 – The Catalyst Sobha

NCERT, Class 10, Quadratic Equations, Chapter–4, Exercise-4.2 – Step wise solution of each question with complete explanation

Q. 1. Find the roots of the following quadratic equations by factorization: (i) x^2–3x–10=0, (ii) 2x^2+x–6=0, (iii) √2x^2+7x+5√2=0, (iv) 2x^2–x+1/8 =0, (v) 100x^2 –20x+1=0; Q. 2. Solve the problems given…

The Catalyst Sobha September 26, 2024

Class 10th math NCERT Quadratic Equations Chapter - 4 Quadratic Equations Exercise 4.1

NCERT, Class 10, Quadratic Equations, Chapter–4, Exercise-4.1 – Step wise solution of each question with complete explanation

Q. 1. Check whether the following are quadratic equations: (i) (x+1)^2=2(x–3), (ii) x^2–2x=(–2)(3–x), (iii) (x–2) (x+1)=(x–1) (x+3), (iv) (x–3) (2x+1)=x(x+5), (v) (2x–1) (x–3)=(x+5) (x–1), (vi) x^2 +3x+1=(x–2)^2, (vii) (x+2)^3=2x(x^2–1), (viii)…

The Catalyst Sobha September 22, 2024

Class 10th math NCERT Quadratic Equations Chapter - 4 Theory related to Quadratic Equations

Methods for solving a Quadratic Equation – Detailed step wise explanation of every method

(1) Method of finding Common Elements; (2) Discriminant Method; (3) Method of Quadratic Formula; (4) Steps involved in Discriminant Method; (5) Steps involved in the Method of Quadratic Formula; (6)…

The Catalyst Sobha September 21, 2024

Class 10th math NCERT Quadratic Equations Chapter - 4 Theory related to Quadratic Equations

Some facts about the Quadratic Equation we should know:

(1) When an equation will be a Quadratic Equation? (2) What is a constant quantity; (3) What is a constant term; (4) What is a variable quantity; (5) What is…

The Catalyst Sobha September 19, 2024

Class 10th math NCERT Pair of Linear Equations in Two Variables chapter -3 Pair of Linear Equations in Two Variables Exercise 3.3

NCERT, Class 10, Pair of Linear Equations in Two Variables, Chapter–3, Exercise-3.3 – Step wise solution of each question with complete explanation

Q. 1. Solve the following pair of linear equations by the elimination and the substitution method: (i) x+y=5 and 2x–3y=4, (ii) 3x+4y=10 and 2x–2y=2 (iii) 3x–5y–4=0 and 9x=2y+7 (iv) x/2…

The Catalyst Sobha September 18, 2024

Class 9th math NCERT Polynomials Theory regarding polynomials of class 9

Algebraic Identities

(1) (a+b)2=a2+b2+2ab, (2) (a+b+c)2=a2+b2+c2+2ab+2bc+2ca, (3) (a+b)3=a3+b3+3ab(a+b), (4) a3+b3+c3–3abc=(a+b+c)(a2+b2+c2–ab–bc–ca), (5) a2–b2=(a+b)(a–b), (6) a3+b3=(a+b)(a2+b2–ab), (7) a3–b3=(a–b)(a2+b2+ab), (8) Constant quantities; (9) Variable quantities; (10) Constant term; (11) Equation

The Catalyst Sobha September 18, 2024

Class 10th math NCERT Pair of Linear Equations in Two Variables chapter -3 Pair of Linear Equations in Two Variables Exercise 3.2

NCERT, Class 10, Pair of Linear Equations in Two Variables, Chapter–3, Exercise-3.2 – Stepwise solution with proper explanation of each question

Q. 1 Solve the following pair of linear equations by the substitution method. (i) x+y=14 and x–y=4, (ii) s–t =3 and s/3+t/2=6, (iii) 3x–y=3 and 9x–3y=9, (iv) 0.2x+0.3y=1.3 and 0.4x+0.5y=2.3,…

The Catalyst Sobha September 12, 2024

Class 10th math NCERT Pair of Linear Equations in Two Variables chapter -3 Pair of Linear Equations in Two Variables exercise 3.1

NCERT, Class 10, Pair of Linear Equations in Two Variables, Chapter–3, Exercise-3.1 – Stepwise solution with proper graph of each question

Q.1. Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of class X took part in a Mathematics quiz. If the…

The Catalyst Sobha September 9, 2024

Class 9th math NCERT Number Systems Number Systems exercise 1.5

NCERT, Class 9, Number Systems, Chapter–1, Exercise-1.5 – Stepwise solution of each question

Q.1. Find: (i) (64)^(1/2), (ii) (32)^(1/5), (iii) (125)^(1/3); Q.2. Find: (i) (9)^(3/2), (ii) (32)^(2/5), (iii) (16)^(3/4), (iv) (125)^(-1/3); Q.3. Simplify: (i) ((2)^(2/3))×((2)^(1/5)), (ii) [(1/3)^3]^7, (iii) ((11^(1/2))/(11^(1/4)), (iv) ((7)^(1/2))×((8)^(1/2))

The Catalyst Sobha September 7, 2024

Class 10th math NCERT Polynomials chapter - 2 Polynomials exercise 2.1

NCERT, Class-10th, Chapter-2, Polynomials, Exercise-2.1- Proper solution of each question on graph paper

Q.1. The graphs of y= p(x) are given in figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

The Catalyst Sobha September 6, 2024