Question:
Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAn + mBm = I} is _______.
Then the number of elements in the set {(n, m) : n, m ∈ { 1, 2….., 10} and nAn + mBm = I} is _______.
Updated On: Jul 24, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 1
Solution and Explanation
The correct answer is : 1
A2 = A and B2 = BR
nA + mB = I,
So, 2n – m = 1, –n + m = 0, 2m – n = 1
So, (m, n) = (1, 1)
Was this answer helpful?
2
1
Top Questions on Operations on Sets
- If \(X = \{\,8^n - 7n - 1 \mid n \in \mathbb{N}\,\}\) and \(Y = \{\,49(n-1) \mid n \in \mathbb{N}\,\}\), then
- LPUNEST - 2023
- Mathematics
- Operations on Sets
- A set \(A\) has 3 elements and another set \(B\) has 6 elements. Then
- LPUNEST - 2023
- Mathematics
- Operations on Sets
- If \(A=\{x \mid x^2-5x+6=0\}\), \(B=\{2,4\}\), \(C=\{4,5\}\), then \(A \times (B \cap C)=\)
- LPUNEST - 2023
- Mathematics
- Operations on Sets
- Let the sets A and B denote the domain and range respectively of the function \(f(x)=\frac{1}{\sqrt[x]-x}\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements
(S1) : A ∩ B = (1, ∞) – N and
(S2) : A ∪ B = (1, ∞)- JEE Main - 2023
- Mathematics
- Operations on Sets
- Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:
- WBJEE - 2023
- Mathematics
- Operations on Sets
View More Questions
Questions Asked in JEE Main exam
- Identify the correct statements: The presence of –NO\(_2\) group in benzene ring A. activates the ring towards electrophilic substitutions. B. deactivates the ring towards electrophilic substitutions. C. activates the ring towards nucleophilic substitutions. D. deactivates the ring towards nucleophilic substitutions. Choose the correct answer from the options given below:
- JEE Main - 2026
- General Chemistry
- Let $\vec{a}=2\hat{i}-\hat{j}-\hat{k}$, $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}+3\hat{k}$. Let $\vec{v}$ be the vector in the plane of $\vec{a}$ and $\vec{b}$, such that the length of its projection on the vector $\vec{c}$ is $\dfrac{1}{\sqrt{14}}$. Then $|\vec{v}|$ is equal to
- JEE Main - 2026
- Vector Algebra
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.- JEE Main - 2026
- Solutions
- The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is \(10^{16}\,\text{s}^{-1}\). The wave number of photon 'C' is \(10^{5}\,\text{cm}^{-1}\). The correct order of energy of these photons is:
- JEE Main - 2026
- General Chemistry
- Given below are two statements: Statement I: The increasing order of boiling point of hydrogen halides is HCl<HBr<HI<HF. Statement II: The increasing order of melting point of hydrogen halides is HCl<HBr<HF<HI. In the light of the above statements, choose the correct answer from the options given below:
- JEE Main - 2026
- General Chemistry
View More Questions
Concepts Used:
Types of Sets
Sets are of various types depending on their features. They are as follows:
- Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
- Singleton Set - It is a set that contains only one element.
- Finite Set - A set that has a finite number of elements in it.
- Infinite Set - A set that has an infinite number of elements in it.
- Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
- Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
- Power Set - It is the collection of all subsets of a set X.
- Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
- Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
- Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.