# Category Archives: School Learning

Question 1. Give an example of a function (i) Which is one-one but not onto. Solution: Let f: R → R given by f(x) =… Read More
Evaluate of each of the following integrals (1-46): Question 1.  Solution: We have, Let —— 1 So,, ———— 2 Hence, by adding 1 and 2… Read More
In the previous article, we have discussed the introduction part and some basic examples of Implicit differentiation. So in this article, we will discuss some… Read More
A sequence is defined as the list of numbers that are arranged in a sequential manner. A series is defined as an arrangement of a… Read More
Chapter 6 Triangles – Exercise 6.5 | Set 1  Question 11. An aeroplane leaves an airport and flies due north at a speed of 1,000… Read More
Question 1. Sides of triangles are given below. Determine which of them are right triangles? In the case of a right triangle, write the length… Read More
Prove the following Question 1. 3sin-1x = sin-1(3x – 4x3), x∈[-1/2, 1/2]  Solution: Let us take x = sinθ, so θ = sin-1x Substitute the value… Read More
Congruence of triangles is the property of two triangles in which all three corresponding sides and corresponding angles are equal. Two triangles are said to… Read More
Implicit differentiation is a method that makes use of the chain rule to differentiate implicitly defined functions. It is generally not easy to find the… Read More
An ordered list of numbers is called sequences. Each number is the sequence is called a term. The sequence usually has patterns that allow us… Read More
An integral which has a limit is known as definite integrals. It has an upper limit and lower limit. It is represented as  f(x) =… Read More
Problem 1: On which axis do the following points lie? (i) P (5, 0) Solution: As its ordinate is 0. So, it lies on x-axis.… Read More
Question 11. If α and β are the zeroes of the quadratic polynomial f(x) = 6x2 + x – 2, find the value of (α/β)… Read More
Question 1. Find the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their coefficients: (i) f(x) =… Read More
Question 1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s… Read More