COMEDK · Maths · 20. Sets and Relations
The total number of subsets of a finite set \(A\) has 56 more elements than the total number of subsets of another finite set \(B\). What is the number of elements in the set A?
- A 5
- B 6
- C 7
- D 8
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
Let sets \(A\) and \(B\) have \(m\) and \(n\) elements, respectively. Then, \(2^{m}-2^{n}=56 \Rightarrow 2^{n}\left(2^{m-n}-1\right)=56\)…
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 digit in the unit's place of \(5^{834}\) isCOMEDK 2019 Easy
- Let \(\alpha, \beta\) be the roots of the equation \(a x^{2}+b x+c=0\). A root of the equation \(a^{3} x^{2}+a b c x+c^{3}=0\) isCOMEDK 2017 Medium
- Middle term in the expansion of \(\left(x^{2}+\dfrac{1}{x^{2}}+2\right)^{n}\) isCOMEDK 2021 Hard
- If the foci of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{b^{2}}=1\) and the hyperbola \(\frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25}\) coincide, then the value of \(b^{2}\) isCOMEDK 2018 Easy
- In the interval \((0,1)\) the function \(f(x)=x^2-x+1\) isCOMEDK 2025 Easy
- \(\int \dfrac{(x-1)}{(x+1)^3} e^x d x=P(x)+c\) then \(P(x)=\)COMEDK 2025 Medium
More PYQs from COMEDK
- The direction ratios of the line which is perpendicular to the lines \(\frac{x-7}{2}=\frac{y+17}{-3}=\frac{z-6}{1}\) and \(\frac{x+5}{1}=\frac{y+3}{2}=\frac{z-4}{-2}\) areCOMEDK 2015 Medium
- The Standard Reduction potential at 25°C for \((\text{MnO}_4)^{-1}/\text{H}^+\) is +1.49 V. The \(E^0\) values for four redox couples:
(a). \(\text{Co}^{3+}/\text{Co}^{2+}\), (b). \(\text{Cr}^{3+}/\text{Cr}\), (c). \(\text{Au}^{3+}/\text{Au}\) and (d). \(\text{Ag}^+/\text{Ag}\) are +1.81 V, –0.74 V, +1.50 V and +0.8 V respectively.
Identify the two reduced species which cannot be oxidised by \((\text{MnO}_4)^{-1}/\text{H}^+\)COMEDK 2025 Medium - A body weight \(50 \mathrm{~g}\) in air and \(40 \mathrm{~g}\) in water. How much would it weight in a liquid of specific gravity \(1.5\) ?COMEDK 2018 Easy
- Given, two vectors \(\hat{\hat{i}}-\hat{\mathfrak{j}}\) and \(\hat{\hat{i}}-2 \hat{\mathfrak{j}}\). The unit vector, coplanar with the two given vectors and perpendicular to \((\hat{\hat{\mathbf{i}}}-\hat{\hat{\mathfrak{j}}})\) isCOMEDK 2015 Easy
- In which of the following changes, entropy decreases?COMEDK 2022 Easy
- The maximum of the function \(3 \cos x-4 \sin x\) isCOMEDK 2013 Easy