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Correct answer: 2)

Concept:

• When ethene is burnt in excess of oxygen it gives carbon dioxide and water.
• This reaction is an exothermic reaction and produces heat.

Explanation:

First, we will balance the Carbon atoms.

After balancing the equation becomes: 

C₂H₄+O₂→2CO₂+H₂O

Then the Hydrogen atoms are balanced.

After balancing the equation becomes: C₂H₄+O₂→2CO₂+2H₂O

Finally, Oxygen atoms are balanced.

After balancing the equation becomes:

C₂H₄ + 3O₂→2CO₂+2H₂O

So, one mole of C₂H₄ will form two moles of CO₂.

Conclusion:

Thus, one mole of C2H4 will form two moles of CO2

CONCEPT:

Buoyancy and Archimedes’ Principle

• To float, the weight of the object + person must equal the weight of the water displaced.
• Archimedes’ Principle:

Buoyant force = weight of displaced water = ρ_water × V_displaced × g

• Total weight acting downward = weight of person + weight of wooden block
• We assume the entire block is submerged when the person stands on it to keep both entirely above water.

EXPLANATION:

• Let V be the volume of the wooden block.
• Mass of block = ρ_block × V = 800 × V (in kg)
• Total downward force (weight) =
• Weight of person = 50 × g
• Weight of block = (800 × V) × g
• Total = (800V + 50) × g
• Buoyant force = ρ_water × V × g = 1000 × V × g
• Equating both (for equilibrium):
• Cancel g on both sides:
• Simplifying: 1000V - 800V = 50 ⇒ 200V = 50 ⇒ V = 0.25 m³

Therefore, the correct answer is Option 1) 0.25 m³.

Ohm’s law:

At constant temperature, the current flowing through a resistance is directly proportional to the potential difference across its end.

I ∝ V

\(I=\frac{1}{R}\times V\)

V = I R 

Where V = the potential difference, R = resistance, and I = current flowing.

Ohmic resistance: The resistance that follows ohm’s law is called ohmic resistance.

Additional Information All resistances don’t follow ohm’s law.

Limitations of Ohm’s law

1.    For applying Ohm’s law. the physical conditions such as temperature, dimensions and the connections of the wire or branch or circuit must remain constant. 2.    It is applicable only for liner and bilateral elements or circuits. It is not applicable for non-linear and unilateral elements and circuits such as diodes, Zener diode, rectifiers, voltages regulators etc. 3.    It is unsuitable for non-metallic conductors such as silicon carbide. 4.    The complicated network cannot be solved quickly by this law.

The correct answer is 96 V

Given:

Resistance(R)= 24 Ω= 24 Ω.

Current (I) = 4 A.

Potential difference(V) = ?

Calculation:

Using Ohm's law

\(V=IR\)

Substitute the above values:

V = 4×24

Potential difference(V) = 96 V.

Concept:

A material's electrical resistivity is a measure of how strongly it opposes the flow of current. The ohm meter (m) is the SI unit of electrical resistivity.

Calculation:

Given:

I = 2A

d = 0.2 cm   = 0.002 m

∴ r =  0.001 m

L = 2.0 m

V = 40 v

We know that,

Cross-section Area (A) =  πr²

= 3.141 × 0.001²

= 0.003141 m2                                    

Resistance (R) = \({V \over I}\)

= 20 ohm

Now,

The resistivity of material ( ρ ) = \({RA \over L}\)

= \({20 \times 0.003141 \over 2}\)

=  0.03141 ohm - m

The correct answer is option (3).

Concept:

Calculation:

Given, length l = 90 cm

= 90 × 0.01 m

= 0.9 m

Specific resistance ρ =  1.57×10-8 Ω−m

External diameter D₁ = 1.0 × 10⁻² m

Internal diameter D₂ = 0.8 × 10⁻² m

As the resistance of tube R = \({\rho l \over A}\)

R= \({\rho l \over\frac{\pi}{4} [D^2_1 - D^2_2]}\)

= \({}\)({4 × 1.57×10^{-8} × 0.9 \over\frac{22}{7} (1.0^2 - 0.8^2) × 10^{-4} }\)

= \({}\)({7 × 4 × 1.57×10^{-8} × 0.9 \over 22 (1.0^2 - 0.8^2) × 10^{-4} }\)

= \({}\)(39.564×10^{-8} \over 7.92 × 10^{-4} \)

= 4.99 × 10^{(- 4)} ≈ 500 × 10^(-6)

= 500 μΩ

The correct answer is option (4).

Concept:

• Resistance - is the opposition offer in the flow of current. It's Unit is ohm(Ω )

• Resistances in series:

• When two or more resistances are connected one after another, the same current flows through them are called resistances in series.

• The net resistance/equivalent resistance (R) of resistances in series is given by:

• Equivalent resistance,

• ​

⇒ R = R1 + R2

• Resistances in parallel:

• When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.

• The net resistance/equivalent resistance(R) of resistances in parallel is given by\(⇒ R = \frac{R_1R_2}{R_1+R_2}\)

Calculation:

R1 = 6 Ω  , R2 = 9 Ω  are in series

⇒ R1 + R2 = 15 Ω 

R1 and R2 collectively are in parallel with R3 = 15 Ω.

⇒ \(\frac{1}{R1+R2} + \frac{1}{15}\) = \(\frac{2}{15}\) 

⇒ 7.5 Ω 

∴ **The correct option is 2)**R=1R1+1R2+.....Unknown node type: spanUnknown node type: span

Concept :

Resistance - is the opposition offered in the flow of current. It's Unit is ohm (Ω )

Ohm's Law - states that current through two points in a conductor is directly proportional to the voltage across two points.

 \(V = \frac{I}{R}\)

There are mainly two ways of the combination of resistances:

1. Resistances in series:

• When two or more resistances are connected one after another, the same current flows through them are called resistances in series.
• The net resistance/equivalent resistance (R) of resistances in series is given by:
• Equivalent resistance,

​

⇒ R = R1 + R2

2. Resistances in parallel:

• When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.
• The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(⇒ R = \frac{R_1R_2}{R_1+R_2}\)

Calculation:

We know that 

V = I _eq

⇒ R_eq = V/I

⇒ R_eq = \(\frac{45}{0.45}\) = 100 Ω 

⇒\(\frac{1}{100}\)  =  \(\frac{1}{300}+\frac{1}{R2}\) 

⇒ R₂ = 150 Ω 

∴ The correct answer is option 1).

Concept:

• Magnetic field intensity -  is a measure of how strong or weak any magnetic field is.
• The SI unit of B is Ns/(Cm) = Tesla (T)
• Lorentz Force -  The force a magnetic field exerted on a charge q moving with velocity v is called magnetic Lorentz force and it is represented by

​F_B = qvBSinθ.

Given: 

Magnetic field intensity(B)= 0.80T

Particle = He2+ 

Angle of interaction(θ) = 90º 

Charge on particle(q) = 1.6× 10-19

Velocity of particle(v)= 105 m/s

∵ F_B = qvBSinθ 

⇒ FB = qvBSin90º

⇒ FB = 2× 1.6× 10-19 × 105 × 0.80× 1

⇒ F_B = 2.56 × 10-14 N

∵ Option 3) is the right option.

Correct answer: 2)

Concept:

• The number of moles in a given mass of a substance can be found by dividing the mass by the formula mass expressed in g/mol.
• The value of the mole is equal to the number of atoms in exactly 12 grams of pure carbon-12 (12 g C = 1 mol C atoms = 6.022 × 10²³ C atoms).

Explanation:

Given,

Mass of SbF₃ = 179 g/mol

Mass of CCl₂F₂ = 121 g/ mol

Moles of 1 gram of freon = \(\frac{Mass}{Molar ; mass}\)

= \(\frac{1}{121}\)

= 0.0083

According to the balanced equation, 

2CCl4 + 2SbF3  → 3CCl2F2 + 2SbCl3

3 moles of CCl2F2  are produced from 2 moles of SbF3

So, 0.008 mole of CCl2F2 will produced from moles \(\frac{2}{3}\times 0.0083\) moles of SbF3

=0.0055

Mass of SbF3 = 0.0055 x 179

= 0.986 g

Conclusion:

Thus, SbF3 are needed to produce one gram of Freon-12, CCl2F2 = 0.986 g