Difference Between Well-Defined and Not Well-Defined Collections In Mathematics, a collection of objects is called a set only when it is well-defined. This chapter helps Class 11 students clearly understand the difference between well-defined and not well-defined collections using simple examples. Watch Video Explanation Class 11 | Sets – Chapter 1 | Definition, Uses & Well-Defined vs Not Well-Defined Sets…
Class 11 Maths – Sets Chapter 1: What Is a Set? Introduction, Definition & Basics
Introduction to Sets – Class 11 Maths A simple, clear guide to start Chapter 1: Sets Understanding Sets is the first step in Class 11 Maths. This chapter builds the base for topics like Relations, Functions, Probability, and Calculus. If you’re beginning Class 11 or looking for structured learning, this guide explains the basics in the simplest way. 1. What…
If tan A = 1/√3, find all Trigonometric Ratios using Trigonometric Identities?
cot A = 1/tan A = 1/(1/√3) = √3 — (1) Using Trigonometric Identity: 1 + tan²A = sec²A 1 + (1/√3)² = sec²A sec²A = 1 + 1/3 = 4/3 sec A = +√(4/3) = +2/√3 or sec A = -2/√3 (neglecting this value as A is acute angle) Therefore, sec A = 2/√3 Using Trigonometric Identity: 1 +…
The Secret Behind Toppers’ Success
Introduction Imagine this: two students with equal aptitude and school support, but one ends the year scoring 95%+ while the other lingers at 80-85%. What made the difference? Often it’s not just hard work — it’s how you work, and with whom. The top scorers (toppers) routinely supplement their school learning with targeted, smart online coaching. In this post, we…
Best Online Maths Teacher for Class 10
Introduction If there’s one subject that can either make or break a Class 10 student’s confidence, it’s Mathematics. Every year, lakhs of CBSE students across India prepare for this critical board exam, and one of the most common questions parents and students ask is – “How do I find the best maths teacher for Class 10?” Mathematics is not just…
Proof of 3 Important Trigonometric Identities (Class 10 Maths)
Introduction Trigonometric identities often confuse Class 10 students, but they are actually the simplest once you know the logic. These identities are the backbone of trigonometry and are repeatedly used in exams. In this blog, I’ll walk you through the proof of three trigonometric identities with clear steps and examples. You’ll also find a video lesson embedded for easier understanding.…
Example 7: In a ΔPQR, right-angled at Q (see Fig. 8.20), PQ = 3 cm and PR = 6 cm. Determine ∠QPR and ∠PRQ.
Given: PQ = 3 cm, PR = 6 cm, ∠Q = 90° To find: ∠QPR = ? and ∠PRQ = ? Solution: In right ΔPQR, Let ∠PRQ = θ Also, (p / h) = sin θ PQ / PR = sin θ 3 / 6 = sin θ 1/2 = sin θ We know, sin 30° = 1/2 So, θ…
20 MCQs on Polynomials (Class 10)
Class 10 Polynomials – Sample MCQs Enter details, attempt all questions, and click Submit. Full Name Email 1) The degree of 7x⁴ − 3x² + 5 is: 2 3 4 5 2) For p(x)=x²−5x+6, p(2) equals: 0 2 4 6 Submit Test ✅ Thanks for your answers! We have emailed you the detailed results. Your score:
Class 10 Algebra (CBSE) With 20 MCQs
Class 10 Algebra Test (20 Questions) Enter your details and answer all questions. Score will show instantly, and results will be emailed. Full Name Email 1) 2x + 5 = 15 x=5 x=10 x=15 2) 5x = 20 ⇒ x = ? 2 3 4 3) 3x – 7 = 11 x=6 x=5 x=4 4) 2x + 3 = 7…
Example 2: If ∠B and ∠Q are acute angles such that sin B = sin Q, then prove that ∠B = ∠Q
To Prove: ∠B=∠Q\angle B = \angle Q Given: ∠B and ∠Q are acute angles sin B = sin Q Proof: Let us consider two right triangles: ΔABC, right-angled at C ΔPQR, right-angled at R Step 1: Write sine values in each triangle In ΔABC: sinB=ACAB⋯(1)\sin B = \frac{AC}{AB} \quad \cdots (1) In ΔPQR: sinQ=PRPQ⋯(2)\sin Q = \frac{PR}{PQ} \quad \cdots…