COMEDK · Maths · 20. Sets and Relations
Two finite sets have '\(m\)' and '\(n\)' number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of \(\mathrm{m}\) and \(\mathrm{n}\) are respectively.
- A 7, 7
- B 4, 4
- C 4, 7
- D 7, 4
Answer & Solution
Correct Answer
(D) 7, 4
Step-by-step Solution
Detailed explanation
The number of subsets of a set with \(m\) elements is \(2^{m}\). The number of subsets of a set with \(n\) elements is \(2^{n}\). Given the condition \(2^{m} - 2^{n} = 112\). Factoring out \(2^{n}\), we get \(2^{n}(2^{m-n} - 1) = 112\). Expressing \(112\) as a product of a power…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The general solution of \(\left(\dfrac{d y}{d x}\right)^2=1-x^2-y^2+x^2 y^2\) isCOMEDK 2023 Medium
- A subset of the additive group of real numbers which is not a sub group, isCOMEDK 2016 Easy
- The sum of the series
\(\frac{1^{2}}{1 \cdot 2}+\frac{1^{2}+2^{2}}{2 \cdot 3}+\frac{1^{2}+2^{2}+3^{2}}{3 \cdot 4}+\ldots\) upto 20 terms isCOMEDK 2014 Medium - If \(z=\sqrt{3}+i\), then the argument of \(z^2 e^{z-i}\) is equal toCOMEDK 2023 Medium
- From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be \(30^{\circ}\) and \(60^{\circ}\) respectively. The height at which the aeroplane is flying in \(\mathrm{km}\), isCOMEDK 2016 Medium
- The sum of non-prime positive divisors of 450 isCOMEDK 2018 Medium
More PYQs from COMEDK
- Convert Benzene \(\rightarrow\) 3-Bromophenol by choosing appropriate reagents \([(i)\) to (v)] in the correct sequence.
\((i)\mathrm{NaNO}_2 / \mathrm{HCl}\left(0^{\circ} \mathrm{C}\right) \quad (ii) Conc. \mathrm{HNO}_3 / \mathrm{H}_2 \mathrm{SO}_4 \quad (iii) \mathrm{H}_2 \mathrm{O} / 283 \mathrm{~K} \quad (iv) \mathrm{Fe} / \mathrm{HCl} \quad (v) \mathrm{Br} 2 / \mathrm{Fe}\)COMEDK 2025 Hard - A force of \(-F\hat{i}\) acts at the origin of the coordinate system. The torque about the point \((0,1,-1)\) is:COMEDK 2025 Medium
- A plot of kinetic energy of emitted photoelectrons from a metal versus the frequency of incident radiation gives a straight line, the intercept of which
A. Depends on the nature of the metal used
B. Depends on the intensity of radiation
C. Depends both on the intensity and the nature of metal used
D. Is a constant and is same for all metals which is independent of the intensity of Incident radiationCOMEDK 2025 Easy - The total number of numbers greater than 1000 but less than 4000 that can be formed using 0,2,3,4 (using repetition allowed) areCOMEDK 2023 Easy
- \(\int_{1}^{e} \log x d x=\)COMEDK 2015 Medium
- A stone is dropped from a height \(h\). It hits the ground with a certain momentum ' \(p\) '. If the same stone is dropped from a different height h' such that percentage change in momentum is \(41.4 \%\), then the height from which the stone is dropped is \(\mathrm{h}^\prime=x \mathrm{~h}\), where \(x\) is:COMEDK 2025 Medium