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RELATIONS AND FUNCTIONS-Notes
Cartesian Products of Sets Let \(A\) and \(B\) be two non-empty sets. The Cartesian product of \(A\) and \(B\), denoted by \(A\times B\), is defined...
SETS--Objective Questions for Entrance Exams
The concept of Sets forms the logical foundation of modern mathematics and plays a decisive role in competitive examinations such as JEE (Main & Advanced), NEET, BITSAT, KVPY, Olympiads, and state eng...
Miscellaneous Exercise on Chapter 1.php
Q1. Decide, among the following sets, which sets are subsets of one and another: \(\mathrm{A = \{ x : x \in \mathbb{R}\text{ and x satisfy }x^2 – 8x + 12 =...
SETS-Exercise 1.5
Q1. Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. Find (i) A...
SETS-Exercise 1.4
Q1. Find the union of each of the following pairs of sets : (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = {a, e, i, o, u} B = {a, b, c} ...
SETS-Exercise 1.3
Q1. Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : (i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 } (ii) { a, b, c } ...
SETS-Exercise 1.2
Q1. Which of the following are examples of the null set (i) Set of odd natural numbers divisible by 2 (ii) Set of even prime numbers ...
SETS-Exercise 1.1
Q1. Which of the following are sets ? Justify your answer. (i) The collection of all the months of a year beginning with the letter J. (ii) The ...
SETS-True/False
The chapter “Sets” forms the conceptual foundation of modern mathematics and plays a decisive role in shaping logical thinking at the senior secondary level. True and False questions, though seemi...
SETS-Notes
SETS A set is a well-defined collection of distinct objects, called elements or members of the set. The phrase well-defined means that it mu...
WAVES-Objective Questions for Entrance Exams
The chapter Waves forms a vital bridge between basic mechanics and advanced physical phenomena encountered in sound, optics, and modern physics. In competitive examinations such as JEE (Main & Advance...