Question:
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n respectively are:
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n respectively are:
Show Hint
Subset counts are always powers of 2.
Updated On: Mar 20, 2026
- \(4,7\)
- \(7,4\)
- \(4,4\)
- 7,7
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Number of subsets: 2ᵐ-2ⁿ=112
Step 2: Try powers of 2: 2⁷-2⁴=128-16=112
Step 3: Hence m=7,n=4.
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Mathematics
- Vector Algebra
- In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
- Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):
- BITSAT - 2025
- Mathematics
- Methods of Integration
- Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
- The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
- BITSAT - 2025
- Mathematics
- Coordinate Geometry
View More Questions
Top BITSAT sets Questions
- Number of subsets of set of letters of word 'MONOTONE' is:
- In a statistical investigation of 1003 families of Calcutta, it was found that 63 families have neither a radio nor a TV, 794 families have a radio, and 187 have a TV. The number of families having both a radio and a TV is:
- If \( a>0, b>0, c>0 \) and \( a, b, c \) are distinct, then \( (a + b)(b + c)(c + a) \) is greater than:
- The modulus of the complex number \( z \) such that \( |z + 3 - i| = 1 \) and \( \arg(z) = \pi \) is equal to:
- Let A,B,C be finite sets. Suppose that n(A)=10, n(B)=15, n(C)=20, n(A∩ B)=8 and n(B∩ C)=6. Then the possible value of n(A∪ B∪ C) is
View More Questions
Top BITSAT Questions
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- Rearrange the following parts to form a meaningful sentence:
P. technological advancement
Q. has led to
R. in many fields
S. a significant leap- BITSAT - 2025
- Sentence Arrangement
- In a mixture of gases, the average number of degrees of freedom per molecule is 6. If the rms speed of the molecule is \(c\), what is the velocity of sound in the gas?
- BITSAT - 2025
- kinetic theory
- A ball is thrown vertically upward with a speed of 49 m/s. How long will it take to return to the thrower’s hand?
- BITSAT - 2025
- Kinematics
- Two identical bodies of mass 1 kg each are moving towards each other with velocities of 5 m/s and 3 m/s, respectively. They collide elastically. What will be the velocity of the body initially moving at 5 m/s after the collision?
- BITSAT - 2025
- Mechanics
View More Questions