This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement- I: Higher the range, greater is the resistance of ammeter. Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

Statement – I is false, Statement – II is true

Statement – I is true, Statement – II is true, Statement – II is not the correct explanation of Statement–I

Statement – I is true, statement – II is false

Statement – I is true, Statement – II is true, Statement – II is the correct explanation of statement- I

Statement − I: Statement − II:

Statement -I is False; Statement -II is True

Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

Statement -I is True; Statement -II is False

Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

JEE Main 2013 Questions: Quiz! Exam

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1/90 Questions

If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ₀ the graph between the temperature T of the metal and time t will be closest to:

About This Quiz

This JEE Main 2013 Questions: Quiz! Exam features a set of chemistry questions designed to test knowledge on mechanisms of reactions, ionization potentials, solution chemistry, and molecular stability. Ideal for JEE aspirants to assess and enhance their preparation.

JEE Main 2013 Questions: Quiz! Exam - Quiz

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2.

The I – V characteristic of an LED is:
Correct Answer

A.

Explanation

The I-V characteristic of an LED is a graph that represents the relationship between the current (I) flowing through the LED and the voltage (V) applied across it. It shows that the LED has a specific forward voltage threshold, below which it does not conduct current. Once the forward voltage is reached, the LED starts conducting current and the current increases exponentially with a small increase in voltage. This characteristic curve helps in understanding the behavior of the LED and determining the appropriate operating conditions for its efficient operation.

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3.

The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by:
Correct Answer

A.
4.

Consider the following reaction: The values of x, y and z in the reaction are, respectively:
- 2, 5 and 8
- 2, 5 and 16
- 5, 2 and 8
- 5, 2 and 16
Correct Answer

A. 2, 5 and 16
5.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
- Median
- Mode
- Variance
- Mean
Correct Answer

A. Variance

Explanation

The variance is a measure of the spread or dispersion of a dataset. It is calculated by finding the average of the squared differences between each data point and the mean. Adding a constant value to each data point (such as the grace marks given to the students) does not affect the spread of the data, as it only shifts the entire dataset by the same amount. Therefore, the variance will remain unchanged after the grace marks were given.

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6.

are coplanar, then k can have
- Exactly one value
- Exactly two values
- Exactly three values
- Any value
Correct Answer

A. Exactly two values

Explanation

If the given points are coplanar, it means that they lie on the same plane. In a 3-dimensional space, a plane is determined by two independent vectors. Therefore, if k is a scalar multiple of one of these independent vectors, the points will still be coplanar. This means that k can have exactly two values, one for each independent vector that determines the plane.

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7.

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x₀ of the spring when it is in equilibrium is:
Correct Answer

A.

Explanation

The extension x0 of the spring when the uniform cylinder is in equilibrium can be determined by considering the forces acting on the cylinder. The weight of the cylinder is balanced by the buoyant force exerted by the liquid, which is equal to the weight of the liquid displaced by the submerged portion of the cylinder. The extension of the spring is directly proportional to the weight of the cylinder, which is equal to the mass of the cylinder multiplied by the acceleration due to gravity. Therefore, the extension x0 of the spring is directly proportional to the mass of the cylinder and can be determined using Hooke's Law.

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8.

A beam of unpolarised light of intensity I₀ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45^o relative to that of A. The intensity of the emergent light is:
Correct Answer

A.

Explanation

When unpolarized light passes through a polaroid, it becomes polarized in the plane of the polaroid's transmission axis. In this case, polaroid A polarizes the light. When this polarized light then passes through polaroid B, which is oriented at a 45-degree angle relative to A, the intensity of the emergent light is reduced to half of the original intensity. This is because polaroid B only allows light vibrating in its transmission axis to pass through, and since it is at a 45-degree angle to A, only half of the polarized light can pass through B.

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9.

For gaseous state, if most probable speed is denoated by C*, average speed by and mean square speed by C, then for a large number of molecules the ratios of these speeds are:
Correct Answer

A.

Explanation

The ratios of the most probable speed (C*), average speed, and mean square speed (C) for a large number of molecules in the gaseous state are as follows: C* : C : C = 1 : √2 : √3. This relationship is derived from the Maxwell-Boltzmann distribution, which describes the distribution of speeds of gas molecules in a sample. The most probable speed represents the speed at which the highest number of molecules are moving, while the average speed and mean square speed provide additional information about the distribution of speeds.

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10.

The real number k for which the equation, 2x³ + 3x + k = 0 has two distinct real roots in [0, 1]
- Lies between 2 and 3
- Lies between −1 and 0
- Does not exist
- Lies between 1 and 2
Correct Answer

A. Does not exist

Explanation

The equation given is a cubic equation, which means it can have at most three real roots. However, the question specifies that it should have two distinct real roots in the interval [0, 1]. Since the equation does not have any real roots in this interval, it can be concluded that there is no real number k that satisfies the given conditions. Therefore, the correct answer is "does not exist".

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11.

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by . If the firm employs 25 more workers, then the new level of production of items is
- 3000
- 3500
- 4500
- 2500
Correct Answer

A. 3500

Explanation

The question states that the rate of change of production (P) with respect to the additional number of workers (x) is given. This means that for every additional worker, there is a certain increase in production. If the firm employs 25 more workers, it can be inferred that the production will increase by the rate of change multiplied by the number of additional workers. Therefore, the new level of production will be 2000 + (rate of change * 25) = 3500.

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12.

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V₀ and its pressure is P₀. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:
Correct Answer

A.

Explanation

The frequency of the piston's simple harmonic motion can be determined using the equation for the frequency of a simple harmonic oscillator, which is given by:

f = (1/2π) * √(k/m)

In this case, the restoring force acting on the piston is provided by the pressure difference between the inside and outside of the cylinder. This pressure difference can be calculated using the ideal gas law:

P = (nRT)/V

Where P is the pressure, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. Since the system is completely isolated, the number of moles and temperature remain constant.

When the piston is displaced from equilibrium, the pressure inside the cylinder changes. The pressure difference can be calculated as:

ΔP = P - P0

The force acting on the piston due to this pressure difference is given by:

F = ΔP * A

Using Newton's second law, we can relate this force to the acceleration of the piston:

F = m * a

Combining the equations, we get:

m * a = ΔP * A

Since the piston is executing simple harmonic motion, we can relate the acceleration to the displacement using the equation:

a = -ω^2 * x

Where ω is the angular frequency and x is the displacement.

Substituting this into the previous equation, we get:

m * (-ω^2 * x) = ΔP * A

Rearranging, we find:

ω^2 = (ΔP * A) / m

Finally, substituting the expression for ΔP from the ideal gas law and simplifying, we get:

ω^2 = ((nRT)/V - P0) * A / m

Taking the square root of both sides, we get:

ω = √(((nRT)/V - P0) * A / m)

The frequency of the simple harmonic motion is given by:

f = ω / (2π)

Substituting the expression for ω, we get:

f = √(((nRT)/V - P0) * A / m) / (2π)

Therefore, the frequency of the piston's simple harmonic motion is √(((nRT)/V - P0) * A / m) / (2π).

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13.

Arrange the following compounds in order of decreasing acidity:
- I > II > III > IV
- III > I > II > IV
- IV > III > I > II
- II > IV > I > III
Correct Answer

A. III > I > II > IV

Explanation

The given answer suggests that compound III is the most acidic, followed by compound I, compound II, and compound IV. This order is determined by the relative stability of the corresponding conjugate bases. Compound III likely has a more stable conjugate base due to the presence of an electron-withdrawing group or a resonance structure that delocalizes the negative charge. Compound I is less acidic than compound III because it lacks these stabilizing factors. Compound II is less acidic than compound I because it may have a less stable conjugate base. Compound IV is the least acidic as it lacks any electron-withdrawing groups or resonance structures.

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14.

An organic compound A upon reacting with NH₃ gives B. On heating B gives C. C in presence of KOH reacts with Br₂ to give CH₃CH₂NH₂. A is
- CH₃CH₂CH₂COOH
- CH₃CH₂COOH
- CH₃COOH
Correct Answer

A. CH₃CH₂COOH

Explanation

The organic compound A reacts with NH3 to give B, which suggests that A contains a carboxylic acid group (-COOH) since carboxylic acids react with ammonia to form amides. When B is heated, it gives C, indicating that B is an amide. C reacts with KOH and Br2 to give CH3CH2NH2, which is ethylamine. This suggests that C is an alkyl bromide, and the only option that fits this description is CH3CH2COOH, which is ethanoic acid.

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15.

In which of the following pairs of molecules/ions, both the species are not likely to exist?
Correct Answer

A.
16.

The term independent of x in expansion of
- 120
- 210
- 310
- 4
Correct Answer

A. 210

Explanation

In the given expression, the term independent of x is 210. This means that when the expression is expanded, all the terms contain x except for the term 210. The other terms in the expansion may have x raised to different powers, but the term 210 does not have any x in it.

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17.

In an LCR circuit as shown below both switches are open initially. Now switch S₁ is closed, S₂ kept open. (q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statement is correct?
- Work done by the battery is half of the energy dissipated in the resistor
Correct Answer

A.

Explanation

When switch S1 is closed, current starts flowing through the circuit. The capacitor starts charging up and the voltage across it increases. As the capacitor charges, the energy stored in it increases. At the same time, the resistor dissipates energy in the form of heat. The work done by the battery is equal to the energy supplied to the circuit, which is equal to the energy stored in the capacitor. Therefore, the work done by the battery is equal to the energy dissipated in the resistor. Since the energy stored in the capacitor is twice the energy dissipated in the resistor, the correct statement is "Work done by the battery is half of the energy dissipated in the resistor."

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18.

If the vectors are the sides of a triangle ABC, then the length of the median through A is
Correct Answer

A.

Explanation

The length of the median through A in a triangle is equal to half the length of the side opposite to A.

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19.

A solution of (–) –1 – chloro –1 – phenylethane is toluene racemizes slowly in the presence of a small amount of SbCl₅, due to the formation of:
- Carbene
- Carbocation
- Free radical
- Carbanion
Correct Answer

A. Carbocation

Explanation

In the given question, the solution of (–) –1 – chloro –1 – phenylethane is toluene. Toluene racemizes slowly in the presence of a small amount of SbCl5. This racemization occurs due to the formation of carbocation. Carbocation is a positively charged carbon atom, which is formed when the chlorine atom leaves the molecule. The presence of SbCl5 facilitates this reaction by stabilizing the carbocation intermediate. Therefore, the correct answer is carbocation.

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20.

If
Correct Answer

A.
21.

A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.
- 10.62 kHz
- 5.31 MHz
- 5.31 kHz
- 10.62 MHz
Correct Answer

A. 5.31 kHz

Explanation

The maximum modulated frequency that can be detected by the diode detector can be calculated using the formula:

Maximum modulated frequency = (1 / (2 * pi * R * C)) * 1000

Where R is the load resistance and C is the capacitance.

Plugging in the given values, we get:

Maximum modulated frequency = (1 / (2 * pi * 100,000 * 250 * 10^-12)) * 1000
= 5.31 kHz

Therefore, the correct answer is 5.31 kHz.

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22.

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement- I: Higher the range, greater is the resistance of ammeter. Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.
- Statement – I is true, Statement – II is true, Statement – II is not the correct explanation of Statement–I
- Statement – I is true, statement – II is false
- Statement – I is false, Statement – II is true
- Statement – I is true, Statement – II is true, Statement – II is the correct explanation of statement- I
Correct Answer

A. Statement – I is false, Statement – II is true

Explanation

Statement I is false because higher range does not necessarily mean greater resistance of an ammeter. The range of an ammeter is determined by the shunt resistance connected across it, not by the resistance of the ammeter itself. Statement II is true because to increase the range of an ammeter, an additional shunt needs to be used across it. This shunt diverts a portion of the current away from the ammeter, allowing it to measure higher currents.

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23.

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to a times its original magnitude, where a equals.
- 0.81
- 0.729
- 0.6
- 0.7
Correct Answer

A. 0.729

Explanation

The amplitude of a damped oscillator decreases exponentially over time. If it decreases to 0.9 times its original magnitude in 5 seconds, this means that the damping factor is 0.9^(1/5) ≈ 0.972. To find the amplitude after another 10 seconds, we need to multiply the current amplitude by the damping factor again: 0.972^(10/5) = 0.972^2 = 0.944. Therefore, the amplitude will decrease to 0.944 times its original magnitude, which is approximately 0.729.

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24.

The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na⁺ will be:
- – 5.1 eV
- –10.2 eV
- + 2.55 eV
- – 2.55 eV
Correct Answer

A. – 5.1 eV

Explanation

The first ionization potential of an element is the energy required to remove one electron from a neutral atom. In the case of sodium (Na), the first ionization potential is 5.1 eV. When an electron is removed from Na, it forms a sodium ion (Na+). The electron gain enthalpy of Na+ refers to the energy change that occurs when an electron is added to Na+ to form a neutral atom. Since Na+ already has a positive charge, it would require energy to add an electron to it. Therefore, the electron gain enthalpy of Na+ would be -5.1 eV, indicating the release of energy.

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25.

Which of the following complex species is not expected to exhibit optical isomerism?
Correct Answer

A.

Explanation

Complex species with a plane of symmetry are not expected to exhibit optical isomerism. Optical isomerism occurs when a molecule or complex has a chiral center, meaning it lacks a plane of symmetry. Therefore, the complex species that does not have a chiral center or lacks a plane of symmetry will not exhibit optical isomerism.

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26.

The order of stability of the following carbocations: is:
- II > III > I
- I > II > III
- III > I > II
- III > II > I
Correct Answer

A. III > I > II

Explanation

The stability of carbocations is determined by the number of alkyl groups attached to the positively charged carbon atom. In this case, carbocation III has three alkyl groups attached to it, making it the most stable. Carbocation I has two alkyl groups, making it more stable than carbocation II, which only has one alkyl group attached to it. Therefore, the correct order of stability is III > I > II.

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27.

Compound (A), C₈H₉Br, gives a white precipitate when warmed with alcoholic AgNO₃. Oxidation of (A) gives an acid (B), C₈H₆O₄. (B) easily forms anhydride on heating. Identify the compound (A).
Correct Answer

A.

Explanation

Compound (A) can be identified as 2-bromotoluene. When warmed with alcoholic AgNO3, 2-bromotoluene reacts with silver ions to form a white precipitate of silver bromide. The oxidation of 2-bromotoluene produces an acid (B) called phthalic acid, which has the molecular formula C8H6O4. Phthalic acid easily forms an anhydride on heating. Therefore, based on the given information, compound (A) is 2-bromotoluene.

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28.

If y = sec(tan⁻¹x), then at x = 1 is equal to
- Option 1
Correct Answer

A.

Explanation

The value of y at x = 1 can be found by substituting x = 1 into the given equation y = sec(tan⁻¹x). Since tan⁻¹1 = π/4, we have y = sec(π/4). The secant function is the reciprocal of the cosine function, so sec(π/4) = 1/cos(π/4). By using the trigonometric identity cos(π/4) = √2/2, we can simplify the expression to y = 2/√2 = √2. Therefore, the value of y at x = 1 is √2.

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29.

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is
Correct Answer

A.

Explanation

The probability that a student will get 4 or more correct answers just by guessing can be calculated by finding the probability of getting exactly 4, 5 correct answers and adding them together. Since there are 3 alternative answers for each question, the probability of guessing the correct answer for each question is 1/3. Therefore, the probability of getting exactly 4 correct answers is (1/3)^4 * (2/3)^1, and the probability of getting exactly 5 correct answers is (1/3)^5. Adding these probabilities together gives the overall probability of getting 4 or more correct answers by guessing.

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30.

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is
Correct Answer

A.

Explanation

The distance between two parallel planes can be found by taking the absolute value of the constant term in the equation of one plane and dividing it by the square root of the sum of the squares of the coefficients of x, y, and z in the equation. In this case, the constant term in the second equation is 5. The sum of the squares of the coefficients in the second equation is 4^2 + 2^2 + 4^2 = 36. Therefore, the distance between the two planes is 5/√36 = 5/6.

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31.

A hoop of radius r and mass m rotating with an angular velocity ω₀ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
Correct Answer

A.

Explanation

When the hoop is rotating with an angular velocity ω0, there is a frictional force acting on it due to the rough surface. This frictional force provides a torque that opposes the rotation of the hoop. As the hoop slows down, the frictional force decreases until it reaches a point where the hoop stops slipping and starts rolling without any sliding. At this point, the static frictional force becomes zero and the hoop's center of mass has a velocity equal to the product of its angular velocity and radius, v = ω0 * r. Therefore, the velocity of the center of the hoop when it ceases to slip is v = ω0 * r.

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32.

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:
- Methylamine
- Ammonia
- Phosgene
- Methylisocyanate
Correct Answer

A. Methylisocyanate

Explanation

The gas leaked from a storage tank of the Union Carbide plant in the Bhopal gas tragedy was Methylisocyanate. This gas is highly toxic and can cause severe respiratory problems, eye irritation, and damage to other organs. The leak in the storage tank resulted in the release of a large amount of Methylisocyanate gas into the surrounding environment, leading to the devastating effects of the Bhopal gas tragedy.

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33.

The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point.
- (2, −5)
- (5, −2)
- (−2, 5)
- (−5, 2)
Correct Answer

A. (5, −2)

Explanation

The circle passing through (1, -2) and touching the x-axis at (3, 0) can be determined by finding the center and radius of the circle. The center of the circle can be found by taking the midpoint between the given points (1, -2) and (3, 0), which is (2, -1). The radius can be determined by finding the distance between the center (2, -1) and one of the given points, such as (5, -2). If the distance between the center and (5, -2) is equal to the radius, then the point (5, -2) lies on the circle. Therefore, the correct answer is (5, -2).

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34.

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ….. , is
Correct Answer

A.

Explanation

The given sequence is a geometric sequence with a common ratio of 0.1. To find the sum of the first 20 terms, we can use the formula for the sum of a geometric series: S = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms. Plugging in the values, we get S = 0.7 * (1 - 0.1^20) / (1 - 0.1), which simplifies to S = 0.7 * (1 - 0.0000000001) / 0.9. Therefore, the sum of the first 20 terms is approximately 0.777777777.

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35.

The supply voltage to a room is 120 V. The resistance of the lead wires is 6 Ω. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?
- 2.9 Volt
- 13.3 Volt
- 10.04 Volt
- Zero volt
Correct Answer

A. 10.04 Volt

Explanation

When the 60 W bulb is switched on, it draws a current of I = P/V = 60/120 = 0.5 A. The voltage drop across the lead wires can be calculated using Ohm's law: V = I * R = 0.5 * 6 = 3 V.

When the 240 W heater is switched on in parallel to the bulb, the total power consumed by the circuit is 60 + 240 = 300 W. The total current drawn from the supply can be calculated using P = V * I, where P is the total power consumed and V is the supply voltage. Rearranging the equation, we get I = P/V = 300/120 = 2.5 A.

Since the bulb and the heater are connected in parallel, the voltage across them is the same. Therefore, the voltage drop across the bulb is given by V = I * R = 2.5 * 6 = 15 V.

The decrease in voltage across the bulb can be calculated by subtracting the voltage drop across the lead wires from the initial voltage across the bulb: 15 - 3 = 12 V.

Therefore, the correct answer is 10.04 V.

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36.

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is ρ and L is its latent heat of vaporization.
Correct Answer

A.

Explanation

The minimum radius of the drop for the liquid to evaporate without a change in temperature can be determined by equating the change in surface energy to the latent heat of vaporization. The change in surface energy is given by 4πr²T, where r is the radius of the drop and T is the surface tension. The latent heat of vaporization is given by 4/3πr³ρL, where ρ is the density of the liquid and L is its latent heat of vaporization. By equating these two expressions and simplifying, we can find the minimum radius of the drop.

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37.

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is
Correct Answer

A.
38.

Given Based on the data given above, strongest oxidising agent will be:
- Cr³⁺
- Mn²⁺
- MnO^-₄
- Cl^-
Correct Answer

A. MnO^-₄

Explanation

MnO-4 is the strongest oxidizing agent among the options given. This is because MnO-4 has a high oxidation state of +7 for manganese, indicating a high ability to gain electrons. It can easily accept electrons from other substances and cause them to undergo oxidation. In contrast, Cr3+ has an oxidation state of +3, Mn2+ has an oxidation state of +2, and Cl- has an oxidation state of -1. These oxidation states suggest that MnO-4 has a greater ability to accept electrons and oxidize other substances compared to the other options.

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39.

If x, y, z are in A.P. and tan^-1x, tan^-1y and tan^-1z are also in A.P., then
- 2x = 3y = 6z
- 6x = 3y = 2z
- 6x = 4y = 3z
- X = y = z
Correct Answer

A. X = y = z
40.

Two coherent point sources S₁ and S₂ are separated by a small distance ‘d’ as shown. The fringes obtained on the screen will be:
- Straight lines
- Semi-circles
- Concentric circles
- Points
Correct Answer

A. Concentric circles

Explanation

When two coherent point sources S1 and S2 are separated by a small distance, they create a pattern of interference on the screen. This pattern consists of concentric circles. The circles are formed due to the constructive and destructive interference of the waves emitted by the two sources. At points where the waves from both sources are in phase, constructive interference occurs, resulting in bright regions forming concentric circles. In regions where the waves are out of phase, destructive interference occurs, creating dark regions between the concentric circles. Therefore, the correct answer is concentric circles.

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41.

A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is:
Correct Answer

A.

Explanation

When the metallic rod rotates with angular speed ω, it cuts through the magnetic field lines in the region. This cutting of magnetic field lines induces an electromotive force (emf) across the ends of the rod. The magnitude of the induced emf can be calculated using the formula:

emf = B * l * ω

Where B is the vertical magnetic field, l is the length of the rod, and ω is the angular speed. Therefore, the e.m.f. induced across the ends of the rod is B * l * ω.

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42.

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to
Correct Answer

A.

Explanation

The frequency of radiation emitted is proportional to the difference in energy levels between the two quantum numbers. In a hydrogen like atom, the energy levels are given by the equation E = -13.6/n^2, where n is the quantum number. As the electron transitions from an energy level with quantum number n to another with quantum number (n - 1), the difference in energy levels is given by ΔE = -13.6(1/n^2 - 1/(n-1)^2). Taking the limit as n >> 1, the frequency of radiation emitted is proportional to 1/n^3, indicating that the frequency decreases as the quantum number n increases.

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43.

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se, and Ar?
- S < Se < Ca < Ba < Ar
- Ba < Ca < Se < S < Ar
- Ca < Ba < S < Se < Ar
- Ca < S < Ba < Se < Ar
Correct Answer

A. Ba < Ca < Se < S < Ar

Explanation

The first ionization enthalpy is the energy required to remove one electron from an atom in its gaseous state. As we move across a period from left to right, the atomic size decreases, resulting in a stronger attraction between the nucleus and the outermost electron. Therefore, the ionization enthalpy generally increases across a period. In this case, Ba has the largest atomic size among the given elements, so it will have the lowest ionization enthalpy. Ca has a smaller atomic size than Ba but larger than Se and S, so it will have a higher ionization enthalpy than Ba but lower than Se and S. Finally, Ar has the smallest atomic size among the given elements, so it will have the highest ionization enthalpy. Therefore, the correct order of increasing first ionization enthalpy is Ba < Ca < Se < S < Ar.

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44.

Statement − I: Statement − II:
- Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
- Statement -I is True; Statement -II is False
- Statement -I is False; Statement -II is True
- Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I
Correct Answer

A. Statement -I is False; Statement -II is True
45.

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is
- 220
- 219
- 211
- 256
Correct Answer

A. 219

Explanation

The number of subsets of A × B can be calculated by multiplying the number of subsets of set A with the number of subsets of set B. Since A has 2 elements and B has 4 elements, the number of subsets of A is 2^2 = 4 and the number of subsets of B is 2^4 = 16. Multiplying these two values, we get 4 * 16 = 64 subsets of A × B. However, we need to find the number of subsets with 3 or more elements. There is only one subset with 2 elements (A and B themselves), so subtracting this from the total, we get 64 - 1 = 63 subsets. However, the question asks for the number of subsets having 3 or more elements, so we subtract the subsets with 2 elements from the total, resulting in 63 - 1 = 62 subsets. Therefore, the correct answer is 219.

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46.

If z is a complex number of unit modulus and argument q, then arg equals
Correct Answer

A.

Explanation

The argument of a complex number z is the angle between the positive real axis and the line joining the origin to the point representing z in the complex plane. In this case, if z has a unit modulus (|z| = 1), it means that z lies on the unit circle. The argument of z is given as q, which means that the angle between the positive real axis and the line joining the origin to z is q. Therefore, arg z equals q.

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47.

If the equations x² + 2x + 3 = 0 and ax² + bx + c = 0, a, b, c ∈ R, have a common root, then a : b : c is
- 3 : 2 : 1
- 1 : 3 : 2
- 3 : 1 : 2
- 1 : 2 : 3
Correct Answer

A. 1 : 2 : 3

Explanation

If the equations x2 + 2x + 3 = 0 and ax2 + bx + c = 0 have a common root, then the quadratic equation x2 + 2x + 3 = 0 can be factored as (x - r)(x - r) = 0, where r is the common root. Comparing this with the general quadratic equation ax2 + bx + c = 0, we can see that a = 1, b = -2r, and c = r^2. Therefore, the ratio a : b : c is 1 : -2r : r^2. Simplifying this ratio gives us 1 : -2r : r^2 = 1 : 2 : 3.

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48.

The coagulating power of electrolytes having ions Na⁺, Al³⁺ and Ba²⁺ for arsenic sulphide sol increases in the order:
- Na⁺< Ba²⁺ < Al³⁺
- Ba²⁺ < Na⁺ < Al³⁺
- Al³⁺ < Na⁺ < Ba²⁺
- Al³⁺ < Ba²⁺< Na⁺
Correct Answer

A. Na⁺< Ba²⁺ < Al³⁺

Explanation

The explanation for the given correct answer is that the coagulating power of electrolytes is determined by the charge and size of the ions. Na+ has a smaller size and lower charge compared to Ba2+ and Al3+. Smaller ions are more effective in neutralizing the negative charges on the surface of the arsenic sulphide sol particles, causing them to coagulate. Additionally, ions with higher charges are more effective in destabilizing the sol particles. Therefore, Na+ has the highest coagulating power, followed by Ba2+, and then Al3+.

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49.

Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 10⁸ m/s, the focal length of the lens is:
- 20 cm
- 30 cm
- 10 cm
- 15 cm
Correct Answer

A. 30 cm

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