The number of subsets of \( \{1, 2, 3, \ldots, 9\} \) containing at least one odd number is
Show Hint
- 324
- 396
- 496
- 512
The Correct Option is C
Solution and Explanation
Total subsets of a set with 9 elements = $2^{9} = 512$.
Step 2: Subsets with NO Odd Numbers
Odd numbers: $\{1, 3, 5, 7, 9\}$ (5 numbers). Even numbers: $\{2, 4, 6, 8\}$ (4 numbers).
Subsets containing only even numbers = $2^{4} = 16$.
Step 3: Calculation
Required subsets = Total subsets - Subsets with only even numbers.
$512 - 16 = 496$.
Final Answer: (c)
Top MET Physics Questions
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- MET - 2020
- Physics
- Photoelectric Effect
- A parallel plate capacitor has an electric field of \(10^5\) V/m between the plates. If the charge on the capacitor plate is 1 \(\mu\)C, the force on each capacitor plate is
- MET - 2019
- Physics
- Electrostatics
- 1 g of water at atmospheric pressure has volume of 1 cc and when boiled it becomes 1681 cc of steam. The heat of vaporisation of water is 540 cal/g. Then the change in its internal energy in this process is
- MET - 2019
- Physics
- Thermodynamics terms
- The temperature coefficient of resistance of a wire is 0.00125 °C\(^{-1}\). At 300 K, its resistance is 1 \(\Omega\). At what temperature the resistance of the wire will be 2 \(\Omega\)?
- MET - 2019
- Physics
- Current electricity
- A physicist works in a laboratory where the magnetic field is 2 T. She wears a necklace enclosing area 0.01 m\(^2\) in such a way that the plane of the necklace is normal to the field and is having a resistance \(R = 0.01\ \Omega\). Because of power failure, the field decays to 1 T in time \(10^{-3}\) s. Then what is the total heat produced in her necklace?
- MET - 2019
- Physics
- Electromagnetic induction
Top MET radiation Questions
Top MET Questions
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- MET - 2020
- Photoelectric Effect
- If \(f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & 1<x \end{cases}\), then
- MET - 2019
- Continuity
Helicopters are very different from airplanes. They can do three things that airplanes cannot do. First, when airplanes move upward, they must also move forward, but helicopters can move straight up without moving ahead. Second, helicopters can fly backward, which airplanes cannot do. Third, helicopters can use their rotors to hover in the air, which is impossible for airplanes. Helicopters can perform actions that airplanes cannot, they are used for different tasks. Since, helicopters can take off without moving forward, they do not need a runway for take off. They are used in congested areas where there is no room for airplanes or in isolated areas, which do not have airports. Because they can hover, they are used on firefighting missions to drop water on fires. They are used in logging operations to lift trees out of forests. Helicopters are used as air ambulances to airlift patients out of situations, which are difficult to reach by conventional ambulances. The police used helicopters to follow suspects on the ground or to search for cars on the ground. Of course, helicopters have military uses because of their design and capabilities.
- MET - 2019
- Reading Comprehension
- Find the missing character.
- MET - 2019
- Number Patterns
- 6, 9, 12, 15, 18, ?
- MET - 2019
- Number Patterns