Question 1. Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = -3, and at x = 5. Solution: To prove that

Solve the following questions. The questions are designed to test your conceptual understanding of algebra at a Class 9 level. This sheet includes evaluation, factorization, simplification, and solving equations. 📘

Solve the following questions. Show all necessary steps. Focus on evaluating, simplifying, and solving algebraic expressions and equations. 📘 Section A: Evaluate the Expression Q1. Evaluate: when Q2. Evaluate: when

Question 1: Evaluate Minors and Cofactors of the elements of the following determinant: (i) Solution: Element a₁₁ = 2 Element a₁₂ = -4 Element a₂₁ = 0 Element a₂₂ =

Question 1: Find the area of the triangle with vertices at the points given: (i) Solution:Using the formula for the area of triangle: Substituting the points: Expanding: (ii) Solution:Substituting the

Evaluate the determinants in Exercises 1 and 2 Question 1: Solution: Question 2 (i) Solution: (ii) Solution: Question 3: If , Then show that Solution: Now, , Hence Proved Question

Question 1: If and are symmetric matrices, prove that is a skew‑symmetric matrix. Solution: Because and are symmetric, their transposes equal themselves: and . Consider the transpose of : By definition,

Question 1: Matrices A and B will be inverse of each other only if (A) (B) (C) , (D) Solution: Two square matrices of the same order, say and ,

Question 1: Find the transpose of each of the following matrices: (i) (ii) (iii) Solution 1: (i) Let . Then (ii) Let . Then (iii) Let . Then Question 2

Question 1:  Let Find: (i)  (ii)  (iii)  (iv)  (v)  Solution(i)   (ii)  (iii)  (iv)   Row 1 × Col 1 :  Row 1 × Col 2 :  Row 2 × Col 1 :  Row 2 × Col 2 :  (v)  Row 1 × Col 1 :  Row 1 × Col 2 :  Row 2 × Col 1 :  Row 2 × Col 2 :  Question 2: Compute the following (i)  (ii)  (iii)  (iv) 

Question 1. In the matrix Solution: (i) The order of the matrix is  (ii) The number of elements is  (iii) Elements:  Question 2. If a matrix has 24 elements, what

Chapter 2: Inverse Trigonometric Functions Board: CBSE Question 1: Prove that Solution:Let , where . Then, Now, we know Therefore, Substituting the value of , Question 2: Prove that ,

Derivative of Trigonometric Functions Derivative of Inverse Trigonometric Functions

Formulas in NCERT 1. 2. 3. Other Important formulas to calculate limits 4. 5. 6. 7. 8. 9. 10.

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to