2070 Entrance Questions

Let us understand from example

A={1,2,3,4} and B={3,4,5,6}

Compute A−B:

A-B={1,2,3,4} - {3,4,5,6}

A−B={1,2} (elements in $A$ that are not in $B$)

Now compute A−(A−B):

A−(A−B)= A− {1,2}= {1,2,3,4} − {1,2} = {3,4} (elements in A that are not in A−B)

From option A∩B:

A∩B={3,4} (elements common to both A and $B$)

Hence both are satisfied so the correct answer is option b

This is a square root function so it's value can never be negative and can't be more than a so [0,a] is the right answer

Or,

The function y=a^2−x^2 represents the upper half of a circle with radius $a$.

The maximum value of $y$ occurs when x=0, which is y=√(a^2−0^2)=a

The minimum value of y occurs when x=±a, which is y=√(a^2−a^2)=0

So, the range of $y$ is from 0 to $a$ inclusive, which gives us the interval [0,a]

Therefore, the correct answer is: c. [0, a]

Let's simplify the expression inside the logarithm:

(√(a^3)√(a^2) )=√a^3⋅a=√a^4=a^2

Now, compute the logarithm:

log⁡a(a^2)=2

Therefore, the correct answer is: c. 2

Given,

f(x)=x - 1/x^2 where x is Real Number,and x doesn't equal to 0

So for the given function we have put any value of x but not 0

Let us see from options

a.$(-\infty ,0)\cup (0,\infty )$

here (−∞,0) it means except −∞ & 0 you can assume any value of x similarly  (0,∞) it means except ∞ & 0 you can assume any value of x so the correct right answer is options no a

Note:(,) means except these value

b.$(-\infty ,0]\cup [0,\infty )$

here (−∞,0] it means except −∞ you can assume any value of x similarly  [0,∞) it means except ∞ you can assume any value of x but according to the question we don't include the value of x so this option is wrong

Note:[,]means include these value

Hence the correct answer is option a

Given,

Let y= e^x +1---------------(i)

Differentiate equation(i) with respect to x

dy=e^x------------(ii)

Then the questions become

∫dy/y     { from equation (i) and (ii) }

=log(y) + C

=log(e^x +1) +C { substitute the value of equation(i)

Hence the correct answer is option a

Given equation is,

5𝑥^2 – 𝑘𝑥 + 45 = 0 comparing with ax^2 + bx+ c then

a=5, b= -k c=45

Using formula for equal roots

b^2 - 4ac=0

(-k)^2 - 4.5.45 = 0

K^2=900

K= ± 30

Hence the correct answer is option c

Given,

one root is 2+√3 i.e (a+b)  & another root must be 2- √3 i.e (a-b)

Then, Using the formula of quadratic equation is;

x^2 - (sum of the roots)x + product of roots =0-----------(i)

For sum of the roots

=(a+b)+(a-b)

=(2+√3) + (2- √3)

=2+√3 + 2 - √3

=4

For Product of the roots

=(a+b) × (a-b)

=(2+√3) × (2- √3)

=4 - 2√3 + 2√3 -(√3)^2

=4 - 3

=1

Then equation (i) become;

x^2 - (sum of the roots)x + product of roots =0

x^2 - 4x +1=0

Hence the correct answer is option b

put n=1 and the first term is 1 if you put n=2 the add 1st term and 2nd term(2+4=6) of the questions and check from all the options which gives same answer

option

a. n(n+1)=1(1+1)=2 which is true .

b. if you put n=1 in b.(1+1)(1+2)=6 which is not
the first term you can check from each.

c. gives 0 when n=1 .

d gives 1.

So option a is right

Given pairs of lines are

y-x=0  &  y+x=0

for single equation representing

(y-x)* (y+x)=0

y^2 + yx - xy - x^2 = 0

y^2 - x^2 =0

hence the right answer is option a.

This type of discontinuity is known as jump or simple discontinuity.

An epitaph is a brief inscription written on a tombstone in memory of the deceased. A cemetery is a burial ground, a morgue is a place where dead bodies are kept, and a demagogue is a political leader who seeks support by appealing to popular desires and prejudices rather than by using rational argument.

the correct answer is option a

The correct phrase is "handed it over." The verb "hand over" is followed by the object "it" before "over."

"Calls on" means to visit someone, which fits the context of visiting her sister in her village. "Calls over" means to invite someone to one's place, "calls out" means to shout or summon, and "calls up" means to telephone someone.

The preposition "with" is used to indicate possession or association, making "with five pockets" the correct choice.

The phrase "to hit below the belt" originates from boxing and means to act unfairly or use unethical tactics.

The correct preposition to use with "disapprove" is "of." The phrase "disapprove of" means to regard something as bad, wrong, or inappropriate.

"Switched off" is the correct phrase, meaning to turn off the lights. "Put off" means to postpone, "take off" means to remove or depart, and "left off" means to stop doing something but doesn't fit in this context.

"Many" is an adjective because it describes the noun "people" by indicating the quantity. "Good" is also an adjective, but among the options provided, "Many" is the correct answer because it directly serves as an adjective in its context. "Lawn" is a noun, and "knitting" functions as an adjective in "knitting classes," but it is a gerund used as an adjective. "Many" is straightforwardly an adjective describing "people."

An active voice sentence has the subject performing the action of the verb. In "I know him," the subject "I" is performing the action "know." The other sentences are in the passive voice, where the action is being done to the subject.

"Memoranda" is the plural form of "memorandum," so it takes a plural verb. "Have been" is the correct plural verb phrase for "memoranda."

"Furniture" is a collective noun that is treated as singular in English, so it takes a singular verb. "Police" is a collective noun but is treated as plural, and "families" and "committees" are plural nouns.

The subject "neither...nor" is used to connect two singular nouns or pronouns. In this case, "her" and "they" are both pronouns, and the verb that follows should agree with the plural noun "they". Therefore, the correct form of the verb to use is "are", making the sentence: "Neither her nor they are going to the college."

The term "herd" is used to describe a group of certain animals, typically ungulates (hoofed animals). Specifically:

A group of cattle is indeed called a herd.

A group of sheep is called a flock.

A group of wolves is called a pack.

Therefore, "a herd of cattle" is not incorrect; it is a correct term. The incorrect term among the options given would be "a pack of wolves", as wolves are correctly described as a pack.

The phrase "They daren’t go" is a statement in the negative form, indicating that they do not dare to go. When converting this statement into a question form, we use the auxiliary verb "dare" to form the question tag:

Statement: They daren’t go.

Question: Dare they go?

Therefore, the correct completion of the sentence is "They daren’t go, dare they?"

The phrase "I am hungry" indicates a condition, and to express agreement with this condition, you would use "too" to mean "also" or "as well". Therefore, the complete sentence would be "I am hungry and she is too."

Option b. they are so is incorrect because "so" is not used in this context to indicate agreement.

Option c. so aren’t they is incorrect because it forms a negative question tag, which is not appropriate here.

Option d. they are too is incorrect because it changes the subject and does not agree with "I am hungry".

The correct answer is a. She is too.

The word "religious" is stressed on the first syllable: re-LIG-ious.

Option a. Likelihood: Stress on the first syllable: LIKE-li-hood.

Option c. fantastic: Stress on the second syllable: fan-TAS-tic.

Option d. orthography: Stress on the third syllable: or-THOG-ra-phy.

The correct answer is b. religious.

The word "economical" has four syllables: e-co-nom-i-cal.

Option a. five is incorrect.

Option c. three is incorrect.

Option d. six is incorrect.

The correct answer is b. four.

In many accents, "pull" and "pool" are homophones, meaning they are pronounced the same way despite having different spellings and meanings.

Option a. pot, port: Not typically pronounced the same.

Option b. so, sow: Not pronounced the same.

Option d. did, dead: Not pronounced the same.

The correct answer is c. pull, pool.

The words "they" and "that" both begin with the "th" sound, which is a voiced dental fricative.

Option a. day: Begins with a "d" sound.

Option b. date: Begins with a "d" sound.

Option c. thief: Begins with a "th" sound, but not the same as "they" which has a voiced "th".

Therefore, these explanations clarify the correct answers based on stress patterns, syllable counts, and initial consonant sounds in English pronunciation.

The correct answer is d. that.

A jockey is a professional horse rider who rides horses in horse racing or other equestrian events.

Option b. rider: This is a general term for someone who rides horses but does not specifically denote a professional.

Option c. Coach: This typically refers to someone who trains or instructs, not necessarily rides.

Option d. horse courser: This term is less common and typically refers to someone who deals with horses but not necessarily riding them professionally.

The correct answer is a. Jockey.

"Appropriate" means suitable or fitting for a particular purpose or situation. Therefore, "unsuitable" is the opposite, meaning not suitable or not fitting.

Option a. Inevitable: Means unavoidable, not opposite in meaning to "appropriate".

Option b. likely: Means probable, not opposite in meaning to "appropriate".

Option d. suitable: This is a synonym of "appropriate", not the opposite.

The correct answer is c. unsuitable.

"Sporadic" means occurring at irregular intervals or scattered occurrences. Therefore, "occasional" which means happening from time to time fits as a synonym.

Option b. frequently: Means happening often, which is the opposite of "sporadic".

Option c. continuously: Means happening without interruption, also opposite of "sporadic".

Option d. never ending: Means continuous or endless, not a synonym of "sporadic".

The correct answer is a. Occasional.

Therefore, the correct answers for these questions are based on understanding the definitions and meanings of the words provided.

This sentence is incorrectly punctuated because it lacks proper coordination or separation between the clauses. It should be either:

"The man received a gift; the women received a book."

"The man received a gift, and the women received a book."

The comma after "women" suggests a list format, but it does not properly separate the clauses.

Let's briefly review the other options:

Option a. The teacher said, ”Honesty is the best policy”.: This sentence is correctly punctuated with quotation marks around the direct speech.

Option b. He said to me “When did she come to the party”?: This sentence is correctly punctuated with quotation marks around the direct question.

Option d. The man, whom he met, had excellent speech: This sentence is correctly punctuated with commas to indicate the non-restrictive relative clause.

The correct answer is c. The man received a gift, the women, a book.

The word "father" takes the suffix "-y" to form the adjective "fatherly". This suffix changes the noun "father" into an adjective that describes characteristics or qualities related to a father.

Option a. ……is: This suffix is not typically used with the word "father".

Option b. ……some: This suffix is not typically used with the word "father".

Option c. ……ly: This suffix forms adverbs, but "fatherly" is an adjective formed from "father".

The correct answer is d. ……y.

Therefore, the correct answers are based on understanding punctuation rules and suffix usage in English grammar.

The potential difference V is given by:

V=W/Q -------------------(i)

where W is work and Q is charge.

The dimensional formula for work $W$ (which is energy) is:

[W]=[ML^2T^−2]

The dimensional formula for charge $Q$ is derived from the current $I$ and time $T;$

$Q=I\times T$

[Q]=[IT]

Now, substituting these into the equation(i) for potential difference:

[V]=[W] / [Q] = [ML^2T^−2] / [IT] = [ML^2T^−3 I^-1]

So, the correct dimensional formula for potential difference is:

a.[ML^2T^−3 I^-1]

To solve this problem, we will use the principles of kinematics and energy conservation.

Given:

Initial speed when thrown upward: u

Final speed when reaching the ground: 3u

We need to find the height h of the tower.

First, we will use the principle of conservation of energy. The total mechanical energy at the top and at the bottom (ground) should be the same (assuming no air resistance).

Step 1: Maximum height reached above the tower

When the stone is thrown upward with speed u, it will rise to a certain height before coming to rest momentarily. Using the kinematic equation:

v^2=u^2+2as

where:

$v$ is the final velocity (0 at the highest point),

u is the initial velocity,

$a$ is the acceleration (gravity, which is $-g$ when moving upward),

$s$ is the displacement (height above the tower).

0=u^2−2gh1

Solving for h1:

h1=u^2 / 2g

Step 2: Total distance fallen

The stone then falls back down past the initial point and continues to the ground with a speed of 3u. The total height it falls is the sum of the height of the tower h and the height h1.

Using the kinematic equation for the fall from the highest point to the ground:

v^2=u^2+2as

where:

$v$ is the final velocity ($3u$),

$u$ is the initial velocity (0 at the highest point),

$a$ is the acceleration (gravity, $g$),

s is the total distance fallen (from the highest point).

(3u)^2=0+2g(h+h1)

9u^2=2g(h+u^2/2g)

Solving for h:

9u^2=2gh+u^2

9u^2−u^2=2gh

8u^2=2gh

h=8u^2 / 2g

h=4u^2 /  g

So, the correct answer is:

b.     h=4u^2 /  g

In Simple Harmonic Motion (SHM), the acceleration of the particle is directly related to its displacement from the equilibrium position. The equation for acceleration in SHM is:

α=−ω^2x

where:

α is the acceleration,

ω(omega) is the angular frequency,

x is the displacement from the equilibrium position.

Let's see the option

a. Always zero: This is incorrect because the acceleration in SHM is not always zero. It depends on the displacement from the equilibrium position.

b. Always constant: This is incorrect because the acceleration varies with displacement.

c. Maximum at extreme position: This is correct because the displacement $x$ is maximum at the extreme positions (positive or negative amplitude). Since α=−ω^2x, the acceleration is also maximum at these positions (considering the magnitude).

d. Maximum at the equilibrium position: This is incorrect because at the equilibrium position, the displacement $x$ is zero, hence the acceleration $\alpha$ is also zero.

Correct answer is: c. Maximum at extreme position

In Simple Harmonic Motion, the acceleration is proportional to the displacement from the equilibrium position and is directed towards the equilibrium position. It reaches its maximum magnitude at the extreme positions where the displacement is greatest.

When an iron ball is heated, it undergoes thermal expansion. The percentage increase in various dimensions can be analysed using the concepts of linear, area, and volume expansion.

Let's consider the following:

1.Linear Expansion (Diameter): The linear expansion can be described by the formula:

ΔL=αLΔT

where α is the coefficient of linear expansion, $L$ is the original length (diameter in this case), and ΔT is the change in temperature.

2.Area Expansion (Surface Area): The area expansion is given by:

ΔA=2αAΔT

where $A$ is the original surface area.

3.Volume Expansion (Volume): The volume expansion is given by:

ΔV=3αVΔT

where V is the original volume.

Let's consider the percentage increase for each case:

Diameter: The percentage increase in diameter is αΔT×100%

Surface Area: The percentage increase in surface area is 2αΔT×100%

Volume: The percentage increase in volume is 3αΔT×100

Since the coefficient of linear expansion α is the same for the material in all cases, we can compare the factors:

The factor for diameter is $1$.

The factor for surface area is $2$.

The factor for volume is $3$.

Thus, the percentage increase will be largest in the volume, as it has the largest multiplying factor of $3$.

The correct answer is option a. volume

When an iron ball is heated, it expands. The percentage increase in volume will be the largest because volume expansion involves a cubic relationship with temperature change, whereas linear expansion involves a linear relationship and area expansion involves a square relationship. Therefore, the volume increase has the highest percentage change.

To solve this questions, we'll use the concept of Young's modulus and the formula for the elongation of a wire under tensile stress.

The elongation $\Delta L$ of a wire under a force $F$ is given by:

ΔL=FL / AY

where:

$F$ is the applied force,

$L$ is the original length of the wire,

A is the cross-sectional area of the wire,

Y is the Young's modulus of the material.

Since wires A and B are made of the same material, $Y$ is constant. The cross-sectional area $A$ of a wire with diameter $d$ is given by:

A=π(d / 2) ^ 2=πd^2 / 4

Let’s compare the elongation of wire A and wire B.

Given:

Length of wire A: LA

Length of wire B: LB=2LA (length ratio 1:2)

Diameter of wire A: dA

Diameter of wire B: dB=dA/2

Step-by-step Calculation:

So, the increase in length for wire B is 8 times that of wire A.

The correct answer is c. 1 : 8

The ratio of the increase in length for wires A and B, when subjected to the same force, depends on their lengths and cross-sectional areas. Since wire B is longer and has a smaller cross-sectional area compared to wire A, its elongation is significantly larger, resulting in a ratio of 1:8 for the increase in length.

To solve this questions, we will use the principle of continuity for fluid flow. According to the principle of continuity, the mass flow rate must remain constant for an incompressible fluid flowing through a tube of varying cross-sectional area. Mathematically, this is expressed as:

A1v1=A2v2

where:

A1 is the cross-sectional area at the entrance,

v1 is the velocity at the entrance,

A2 is the cross-sectional area at the exit,

v2 is the velocity at the exit.

Given:

The radius at the entrance, r1, is 3 units.

The radius at the exit, r2, is 2 units.

Step-by-step Calculation:

Cross-sectional Area:

The cross-sectional area A of a tube with radius r is given by:

A=πr^2 

For the entrance:

A1=πr1^2=π(3)^2=9π

For the exit:

A2=πr2^2=π(2)^2=4π

Applying the Continuity Equation:

A1v1=A2v2

Substituting the areas:

9πv1=4πv2

Solving for the Ratio of Velocities:

9v1=4v2

v1 / v2 =4 / 9

So, the ratio of the velocity of liquid entering to leaving the tube is 4:9.

The correct answer is option b. 4 : 9

According to the principle of continuity for incompressible fluids, the product of the cross-sectional area and velocity remains constant. Given the ratio of the radii, the corresponding areas, and thus the velocities, follow the inverse square relationship. This results in the ratio of the velocity of liquid entering to leaving the tube being 4:9.

An isobaric process is one where the pressure remains constant throughout the process. This is the defining characteristic of an isobaric process, distinguishing it from isothermal (constant temperature), adiabatic (no heat exchange), and isochoric (constant volume) processes.

the correct option is d. isobaric

Given:

Mass of ice, mice=50 g=0.05 kg

Initial temperature of ice, T initial=−6ºC

Final temperature of ice, T final=0ºC

Specific heat capacity of ice, C ice=2000 J kg^−1°C^−1

Latent heat of fusion of water, L f=334,000 J kg^−1

Approximately 1.8 grams of water will freeze.

which is nearly equal to option a. 1.785 g

The heat required to raise the temperature of 50 g of ice from -6°C to 0°C is 600 J. This heat is sufficient to cause approximately 1.8 grams of water at 0°C to freeze, as the energy required for freezing is calculated based on the latent heat of fusion of water.

To determine where the image of an object placed at the focus of a concave mirror forms, we use the mirror equation:

1 / f =1 / do + 1 / di

where:

$f$ is the focal length of the concave mirror,

do is the object distance,

di is the image distance.

Given that the object is placed at the focus (do=f), we substitute do=f into the mirror equation:

1 / f =1 / f + 1 / di

1 / di = 0

di=∞

Therefore, when an object is placed at the focus of a concave mirror, the image is formed at infinity.

the correct answer is b. Infinity

According to the mirror equation, when an object is placed at the focus of a concave mirror, the image distance becomes infinite, meaning the image is formed at infinity.

The efficiency of a Carnot engine is determined by the temperatures of the source (T_h) and sink (T_c) between which it operates. The efficiency (η) of a Carnot engine is given by the formula:

η=1−T_c / T_h

where:

T_h is the temperature of the source (hot reservoir),

T_c is the temperature of the sink (cold reservoir).

Given,

Temperature of the source (T_h) = 400 K

Temperature of the sink (T_c) = 300 K

efficiency become

η=1−300/400 = 1−0.75 = 0.25

So, the efficiency of the Carnot engine, when the source temperature is 400 K and the sink temperature is 300 K, is 25%.

Therefore, the correct answer is d. 25%.

When three equal resistors each of resistance r are connected to form a triangle, we need to find the equivalent resistance across any two corners of the triangle.

Let's denote the three corners of the triangle as A, B, and C, with resistors $,$ and R3 connected between them.

In a triangle configuration, each resistor is connected between two corners (vertices). When we want to find the equivalent resistance across any two corners (say A and B), we can use the concept of resistors in parallel.

For resistors connected in a triangle configuration, the equivalent resistance RAB across corners A and B is given by:

1/ RAB = 1/ R1 + 1/ R2 + 1/ R3

Since R1=R2=R3=r:

1/ RAB = 1/ r + 1/ r + 1/ r

1/ RAB = 3/r

RAB = r/3

Therefore, the equivalent resistance across any two corners (A and B) of the triangle is r/3

In an LCR (Inductor-Resistor-Capacitor) series circuit driven by an alternating current (AC), the total impedance $Z$ of the circuit is given by the vector sum of the impedance contributions from the inductor (XL), capacitor (Xc), and resistor (R):

Z=√{R^2+(XL−Xc)^2 }

where:

R is the resistance,

XL is the inductive reactance (XL=ωL, where ω is the angular frequency and L is the inductance),

Xc is the capacitive reactance (Xc=1/ωC, where C is the capacitance).

The current I in the circuit is maximum when the impedance Z is minimum.

Let's see from the given options:

a. XL=0: If XL=0, it means there is no inductive reactance. This would reduce the total impedance and potentially increase the current, but this condition alone does not guarantee maximum current.

b. Xc=0: If Xc=0, it means there is no capacitive reactance. Similar to XL=0, this reduces impedance but does not guarantee maximum current without considering the inductive reactance.

c. XL=XC: If XL=Xc, it means that the inductive reactance is equal to the capacitive reactance. In this case, they could potentially cancel each other out, leading to a lower total impedance $Z$ and therefore maximum current.

d.√{(XL^2) + (Xc)^2} =0:This equation suggests a specific condition where the magnitude of the impedance due to inductive and capacitive reactances cancels out exactly, resulting in minimum total impedance and maximum current.

Among these options, option c. XL=Xc is the correct answer for when the alternating current in an LCR circuit is maximum. This condition indicates resonance in the circuit, where the inductive and capacitive reactances are equal and opposite in phase, leading to cancellation of impedance and thus maximum current flow.

Hence the correct answer is option c

When two waves interfere, the resulting interference pattern depends on their phase difference ϕ at the point of observation. The interference will be constructive (maximum) when the phase difference ϕ is an integer multiple of 2π, and it will be destructive (minimum) when the phase difference ϕ is an odd multiple of π.

Given:

Two waves have the same wavelength and amplitude.

They interfere to give a minimum.

For destructive interference (minimum), the condition is ϕ=(2n+1)π, where $n$ is an integer.

From the given option:

a. ϕ=π

b. ϕ=π/2

c. ϕ=3π/2

d. ϕ=0

The correct answer is option a. ϕ=π

This means that the phase difference between the two waves must be π radians (or 180 degrees) to produce a minimum (destructive interference). At this phase difference, the trough of one wave coincides with the peak of the other wave, resulting in cancellation or minimum amplitude at the point of observation.

An α-particle consists of 2 protons and 2 neutrons. Due to the nuclear binding energy, the actual mass of an α-particle is slightly less than the combined mass of these 2 protons and 2 neutrons. This mass defect accounts for the binding energy that holds the nucleus together.

The Correct answer is d. Less than the sum of masses of 2 protons and 2 neutrons

To understand the difference between hard X-rays and soft X-rays, let's consider their properties in terms of frequency, wavelength, and energy:

Properties of X-rays:

a. Frequency and Wavelength: X-rays are a form of electromagnetic radiation. The frequency of X-rays is inversely proportional to their wavelength. Higher frequency corresponds to shorter wavelength and vice versa.

b. Energy: The energy of X-rays is directly proportional to their frequency. Higher frequency X-rays have higher energy.

Hard X-rays vs. Soft X-rays:

Hard X-rays:

-Have higher energy.

-Have higher frequency.

-Have shorter wavelength.

Soft X-rays:

-Have lower energy.

-Have lower frequency.

-Have longer wavelength.

Let's see from the option

a. Higher intensity: Intensity is not the defining characteristic that differentiates hard X-rays from soft X-rays. Both types can vary in intensity.

b. Lower frequency: This is incorrect because hard X-rays have higher frequency compared to soft X-rays.

c. Higher frequency: This is correct. Hard X-rays have higher frequency than soft X-rays.

d. Higher speed: All X-rays, regardless of being hard or soft, travel at the speed of light in a vacuum, so this is not a differentiating factor.

The Correct answer is option c. Higher frequency

Hard X-rays are characterized by their higher frequency compared to soft X-rays. This higher frequency corresponds to higher energy and shorter wavelength, distinguishing hard X-rays from soft X-rays.

Given:

Current gain, (β)=50

Load resistance, (RL)=4 kΩ=4000 Ω

Input resistance, (Rin)=500 ΩR

To find the voltage gain (Av) of a common emitter transistor amplifier, we can use the following formula:

Av=β×RL/Rin

where:

β is the current gain,

RL is the load resistance,

Rin is the input resistance.

Av=50×4000Ω / 500Ω

Av=50×8

Av=400

The Correct answer is option a. 400

To determine the frequency at which an air column in a tube closed at one end resonates, we need to understand the resonant frequencies of such a tube. A tube closed at one end supports standing waves with a node at the closed end and an antinode at the open end.

The fundamental frequency (f1) and higher harmonics (odd harmonics) are given by:

fn=(2n−1)⋅v / 4L

where:

fn is the nth harmonic frequency,

$v$ is the speed of sound in air (given as 320 m/s),

L is the length of the tube (given as 1 meter),

n is the harmonic number (1 for the fundamental, 3 for the first overtone, etc.).

Fundamental Frequency (n=1):

f1=(2 x 1−1) x 320 / 4 x 1

f1=320 / 4

f1= 80Hz

First Overtone (n=2):

f2=(2 x 2−1) x 320 / 4 x 1

f2=960 / 4

f2= 240Hz

Second Overtone (n=3):

f3=(2 x 3−1) x 320 / 4 x 1

f3=1600 / 4

f3= 400Hz

Given these calculations, the correct answer from the provided options is:

The Correct answer is option d. 80 Hz

Given wave equation is:

y=0.25sin(500t−0.0025x) is comparing with y=Asin(ωt−kx)

where:

$A$ is the amplitude of the wave,$\omega$ is the angular frequency, $k$ is the wave number, $t$ is time, $x$ is the position.

then,

The angular frequency($\omega$

The wave number(k)=0.0025.,

The wave number k is related to the wavelength $\lambda$ by the equation:

k=2π / λ

λ= 2π / k

λ= 2π / 0.0025 = 800π

Thus, the wavelength of the wave is 800π meters.

The Correct answer is option d 800π meters.

Lucas reagent is a solution of zinc chloride (ZnCl2) in concentrated hydrochloric acid ($\text{HCl}$). It is used to classify alcohols of low molecular weight. The reagent is used to test for the presence of primary, secondary, and tertiary alcohols based on their reactivity with Lucas reagent.

Valeric acid, also known as n-valeric acid, is a straight-chain alkyl carboxylic acid with the chemical formula C5 H10 O2. According to IUPAC nomenclature, it is named pentanoic acid because it has a five-carbon chain with a carboxylic acid functional group.

The correct answer is option a. Pentanoic acid

The blood-red coloration is due to the formation of ferric thiocyanate (Fe(SCN)3), which occurs when ferric chloride (FeCl3) is added to a sodium extract containing thiocyanate ions (SCN^−). Thiocyanate ions are formed when nitrogen and sulphur are present in the organic compound and are converted to thiocyanate during the sodium fusion test (Lassaigne's test). Thus, the presence of nitrogen (and sometimes sulphur) is confirmed.

The correct answer is option b. nitrogen

Formaldehyde (HCHO) undergoes the Cannizzaro reaction because it is a non-enolizable aldehyde, meaning it lacks alpha hydrogen atoms. In the presence of a strong base, formaldehyde undergoes disproportionation to yield methanol (CH₃OH) and formate ion (HCOO⁻), which can further be protonated to form formic acid (HCOOH).

The Friedel-Crafts alkylation reaction is the appropriate method to convert benzene to toluene. In this reaction, benzene reacts with a methyl halide (like methyl chloride) in the presence of a Lewis acid catalyst (such as AlCl₃), resulting in the formation of toluene. The other reactions listed are not suitable for this conversion.

The Correct answer is option a. Friedel-Crafts reaction

Hematite (Fe₂O₃) is an important iron ore mineral. It is the most abundant and widely distributed iron oxide mineral found in nature.

Iron Ore: Hematite is primarily composed of iron oxide. It is mined as an iron ore due to its high iron content and widespread availability.

Chemical Composition: The chemical formula for hematite is Fe₂O₃, indicating that it is predominantly made up of iron and oxygen.

Uses: Hematite is a major source of iron for the steel industry. It is also used in pigments, jewellery, and as a mineral specimen.

Fluorine (F) has the highest electronegativity among bromine (Br), iodine (I), chlorine (Cl), and itself. Fluorine's position in the periodic table and its high nuclear charge contribute to its strong attraction for electrons, making it the most electronegative element.

The correct answer is option d. Fluorine (F)

Zinc sulphate heptahydrate (ZnSO₄ · 7H₂O) is commonly known as white vitriol. It is a colourless crystalline solid that appears white in its hydrated form.

The correct answer is option a. white vitriol

Brass is an alloy composed primarily of copper (Cu) and zinc (Zn). The proportion of copper and zinc can vary to create brass alloys with different properties suitable for various applications, such as musical instruments, decorative items, and plumbing fittings.

The correct answer is option a. Copper and Zinc

Dolomite is a mineral composed of calcium magnesium carbonate, often with the chemical formula CaCO₃ · MgCO₃. It is a common rock-forming mineral found in sedimentary rocks and is a significant source of magnesium.

The correct answer is option b. CaCO₃ · MgCO₃

Zinc (Zn) has an atomic number of 30, which means it has 30 electrons. To determine its electronic configuration:

Step 1: Noble gas core ([Ar]): Zinc is located after argon (Ar) in the periodic table, which has 18 electrons. Therefore, zinc starts with the noble gas core configuration [Ar].

Step 2: Filling orbitals:

4s²: The 4s orbital can hold up to 2 electrons, so zinc fills its 4s orbital with 2 electrons.

3d¹⁰: The 3d orbitals can hold up to 10 electrons, so zinc fills its 3d orbitals with 10 electrons.

Given,

Molar mass of KMnO4=39.1 (K)+54.9 (Mn)+4×16.0 (O)=158.0 g/mol.

equivalent weight of KMnO4 in neutral medium =Molar mass of KMnO4 / 3 = 158 / 3 = 52.6

The correct answer is option a. 52.6

Bohr's model was later modified by Somerfeld to explain some the spectral lines which Bohr's was not able to explain.

The correct answer is option b. Somerfeld

The molar mass of oxygen ($\text{O}$) is approximately 16.00 g/mol.

Use the molar mass to convert grams of oxygen to moles.

Moles of O=Mass / Molar Mass = 8.0 g / 16.00 g/mol = 0.5 mol

Avogadro's number (NA) tells us how many atoms are in one mole of a substance. It is 6.022×10^23 atoms/mol.

Number of atoms=Moles of O×NA=0.5×6.022×10^23=3.011×10^23 atoms

The Correct answer is option a. 3.011×10^23 atoms

The CGS unit of specific conductance (also known as conductivity), let's first understand the concept and units involved.

Specific conductance (κ) is a measure of a material's ability to conduct electric current. In the SI system, its unit is Siemens per meter (S/m). However, in the CGS (centimetre-gram-second) system, the units differ.

In the CGS system:

Conductivity is typically measured in units of reciprocal ohms (ohm^−1) per centimetre (cm^−1).