Esters are organic compounds formed by the reaction of an acid (usually a carboxylic acid) with an alcohol. This reaction is known as esterification.

Hence, the correct answer is option a. An acid and an alcohol

Vinegar primarily consists of acetic acid, which gives it its sour taste and pungent smell.

Hence, the correct answer is option a. Acetic acid

Bee stings contain methanoic acid, also known as formic acid, which causes pain and irritation at the site of the sting.

Hence, the correct answer is option d. Methanoic acid

The carboxyl group (-COOH) is present in ethanoic acid, also known as acetic acid. The other options (ethanol, formaldehyde, and ethylene) do not contain a carboxyl group.

Hence, the correct answer is option d. Ethanoic acid

Ascorbic acid (vitamin C) does not contain a carboxyl group (-COOH). The other acids listed—citric acid, lactic acid, and tartaric acid—do contain at least one carboxyl group.

Hence, the correct answer is option d. Ascorbic acid

Formic acid is a strong reducing agent and can reduce Tollen's reagent, mercuric chloride, and potassium permanganate. This reduction ability is due to the presence of both an aldehyde group and an acidic group in formic acid.

Hence, the correct answer is option d. All of above

Spinach contains oxalic acid, which is responsible for the slightly bitter taste and can contribute to the formation of kidney stones in susceptible individuals.

Hence, the correct answer is option a. Oxalic acid

Acetonitrile (CH₃CN) on hydrolysis yields acetic acid and ammonia. The other options do not lead to the formation of acetic acid upon hydrolysis.

Hence, the correct answer is option a. CH3CN

When sodium acetate is heated with soda lime (a mixture of sodium hydroxide and calcium oxide), it undergoes decarboxylation to produce methane gas.

Hence, the correct answer is option c. Methane

Benzyl alcohol is oxidized by potassium permanganate (KMnO₄) to benzoic acid. The oxidation process converts the primary alcohol group (-CH₂OH) into a carboxylic acid group (-COOH).

Hence, the correct answer is option c. Benzoic acid

Oxalic acid (C₂H₄(COOH)₂) is a dicarboxylic acid, meaning it has two carboxyl groups, which significantly increases its acidity compared to monocarboxylic acids like formic acid (HCOOH) or acetic acid (CH₃COOH). The presence of two -COOH groups that can donate protons makes oxalic acid the most acidic among the given options.

Hence, the correct answer is option d. C2H4(COOH)2

The carbylamine reaction, also known as the Hofmann isocyanide synthesis, is a reaction in which a primary amine reacts with chloroform and an alcoholic base to form an isocyanide (carbylamine). This reaction is specific to primary amines.

Hence, the correct answer is option a. 1° amine

Methylamine (CH₃NH₂) is more basic than ammonia (NH₃) and aniline (C₆H₅NH₂) because the electron-donating methyl group increases the electron density on the nitrogen atom, making it more capable of accepting a proton. CH₃NH₃⁺ is a conjugate acid and not basic.

Hence, the correct answer is option b. CH₃NH₂ (Methylamine)

When a Grignard reagent reacts with carbon dioxide, it forms a carboxylic acid after hydrolysis. For example, methyl magnesium bromide (CH₃MgBr) with CO₂ will give ethanoic acid (CH₃COOH).

Hence, the correct answer is option b. Ethanoic acid

The Rosenmund reduction is a chemical reaction that converts acyl chlorides (acid chlorides) into aldehydes using hydrogen gas in the presence of palladium on barium sulfate.

Hence, the correct answer is option c. Rosen Munds reduction

LiAlH₄ (lithium aluminium hydride) is a strong reducing agent that reduces ethanoic anhydride to ethanol.

Hence, the correct answer is option c. Ethanol

This is another example of the Rosenmund reduction, where ethanoyl chloride is reduced to ethanal (acetaldehyde) using H₂ and palladium on barium sulfate.

Hence, the correct answer is option d. Ethanal

The nitro group (-NO₂) is an electron-withdrawing group, and it directs incoming substituents to the meta position during electrophilic aromatic substitution due to the resonance and inductive effects.

Hence, the correct answer is option b. Meta directing

The reduction of benzoic acid with red phosphorus and hydroiodic acid (HI) leads to the formation of toluene (methylbenzene).

Hence, the correct answer is option d. Toluene

Nitrobenzene undergoes electrophilic substitution at the meta position due to the strong electron-withdrawing nature of the nitro group, which deactivates the ortho and para positions.

Hence, the correct answer is option c. Meta posi9on

The functional group of an ester is -COOR, where "R" is an alkyl group. Esters are characterized by this group, which is derived from a carboxylic acid (-COOH) by replacing the hydrogen atom with an alkyl group.

Hence, the correct answer is option d. -COOR

Functional isomers are compounds with the same molecular formula but different functional groups. Esters and carboxylic acids are functional isomers of each other because they have the same molecular formula but different functional groups (-COOR for esters and -COOH for carboxylic acids).

Hence, the correct answer is option c. Carboxylic acid

Ethanenitrile (also known as acetonitrile, CH₃CN) is reduced to ethane (C₂H₆) when treated with red phosphorus and hydroiodic acid (HI). The reaction involves the complete reduction of the nitrile group (-CN) to a methyl group (-CH₃).

Hence, the correct answer is option b. Ethane

Acid amides (R-CONH₂) undergo hydrolysis to form carboxylic acids (R-COOH) and ammonia (NH₃) or an amine, depending on the conditions.

Hence, the correct answer is option d. Carboxylic acid

In the Hofmann's exhaustive methylation method, tertiary amines (R₃N) do not react with methyl iodide and therefore remain unreactive during the separation process of primary, secondary, and tertiary amines.

Hence, the correct answer is option b. Tertiary amine

The potential difference (V) is defined as the work done (W) per unit charge (Q),

V=W/Q = [ML²T⁻²] / [IT] = [ML²T⁻³I⁻¹].

Hence, the correct answer is option a. [ML²T⁻³I⁻¹].

In Simple Harmonic Motion (SHM), the acceleration is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. At the extreme position, the displacement is maximum, so the acceleration is also maximum

Hence, the correct answer is option b. maximum at extreme position

When an object is placed at the focus of a concave mirror, the reflected rays become parallel and the image forms at infinity.

Hence, the correct answer is option c. infinity

The wavelength of light decreases when it enters a medium with a higher refractive index. Given that the refractive index of glass is higher than air, the wavelength in glass is shorter.

In glass, wavelength will be =λ/μ​
=7200​/1.5 =4800A˚

Hence, the correct answer is option c. 4800A˚

We know,

P=I^2 R

When two resistances are connected in series, current through them is same.

then,

Given,

$L=50mH=0.05H$ and current(I)=4A.

the energy (W) stored in an inductor is given by W=LI^2 1/2 

W=(0.05) x (4)^2 x 1/2 = 0.4J.

Hence, the correct answer is option c. 0.4J

Hard X-rays have higher energy, which corresponds to higher frequency and shorter wavelength compared to soft X-rays.

Hence, the correct answer is option b. Higher frequency

A straight wire has no loops, so the magnetic flux linkage is minimal, resulting in zero self-inductance.

Hence, the correct answer is option a. Zero

When a wave is reflected from a rigid boundary, it undergoes a phase change of π (180 degrees).

Hence, the correct answer is option d. π

Due to the Doppler effect, as the car moves towards you, the frequency of the sound increases, resulting in a higher pitch.

Hence, the correct answer is option a. Higher

The Lyman series of the hydrogen atom consists of transitions where the electron falls to the n=1 energy level from higher energy levels (n≥2). These transitions emit photons in the ultraviolet region of the electromagnetic spectrum

Hence, the correct answer is option a. Ultraviolet

The root mean square (RMS) speed of a gas is inversely proportional to the square root of its molar mass. Hydrogen (H₂) has the smallest molar mass among the options, so it has the highest RMS speed at a given temperature.

Hence, the correct answer is option a. H2

Given,

focal length(f)=-50cm = -0.5m (because it's a concave lens)

P=1/f = 1/-0.5 =  -2D.

Hence, the correct answer is option d. -$2D$.

When lamps are connected in series, the same current flows through both. However, the lamp with higher resistance will dissipate more power, making it burn brighter. The 25W lamp has a higher resistance than the 100W lamp, so it will burn more brightly in this setup.

Hence, the correct answer is option a. 25W, 120V

Given,

T1/2​=1600 years

mean life (τ)=?

We know,

τ=(T1/2) /ln(2)  = 1600 / ln(2) = 2309 years

Hence, the correct answer is option d. 2309 years​

The Rydberg constant depends on the mass of the nucleus and the electron involved in the transitions. For hydrogen, it's a specific value, but for other elements, it varies slightly due to the different nuclear masses. Therefore, it is different for different elements.

Hence, the correct answer is option c. Different for different elements

Given,

Radius of the Earth(R)=6400 km= 6.4 × 10^6 m

permittivity of free space(ε0​)=8.854×10^−12 F/m

The Earth can be modeled as a spherical conductor. The capacitance C of a spherical conductor is given by C=4πε0R

C= 4π x 8.854×10^−12 x 6.4 × 10^6  = 711 μF

Hence, the correct answer is option d. 711 μF

In the number 0.0030×10^11 m, the significant figures are determined by the digits in the decimal part. "0.0030" has two significant figures (the "3" and the "0"). The $1$ does not affect the count of significant figures.

Hence, the correct answer is option d. 2

Torque (τ) produces a change in angular momentum ($L$). According to the equation τ=dL/dt, the change in angular momentum is parallel to the torque. If torque is aligned with the angular momentum vector $l$, then the change is parallel to l.

Hence, the correct answer is option c. Parallel to l

Diffraction refers to the bending of waves around the edges of an obstacle or aperture. This phenomenon is observed with sound waves when they pass through a narrow opening or around corners, allowing the sound to spread out.

Hence, the correct answer is option d. Diffraction

When a tuning fork vibrates, its two prongs move in opposite directions. This means that when one prong moves outward, the other moves inward, creating a phase difference of π radians (180 degrees) between the two prongs.

Hence, the correct answer is option c. π

In a magnetic field, the force on a charged particle is always perpendicular to its velocity, meaning that the magnetic field does no work on the particle. Therefore, the kinetic energy of the particle remains constant as it moves through the magnetic field.

Hence, the correct answer is option b. Remains constant

The de Broglie wavelength λ is given by $p$

Hence, the correct answer is option d. 1/√2

The sine and cosine functions are 90 degrees (π/2 radians) out of phase with each other. Therefore, the phase difference between the waves represented by y1=a1sin⁡ωt and y2=a2cos⁡ωt is π/2

Hence, the correct answer is option b. π/2

An epitaph is a brief statement written in memory of someone who has died, usually inscribed on a tombstone or plaque.

Hence, the correct answer is option a. epitaph

The correct phrasal verb structure is "handed it over." "Handed over it" is incorrect because the pronoun ("it") must come between the verb and the particle in a separable phrasal verb.

Hence, the correct answer is option c. handed it over

"Calls on" means to visit someone. This phrase correctly indicates that she visits her sister in the village.

Hence, the correct answer is option c. calls on

"With" is the correct preposition to indicate that the coat has five pockets.

Hence, the correct answer is option b. with

"Turned away" means to change direction or turn aside, which is the action the captain might have taken to avoid the icebergs.

Hence, the correct answer is option b. turned away

"As gay as a lark" is an idiom meaning very happy and cheerful. This fits the context of someone recovering and feeling well after treatment.

Hence, the correct answer is option b. as gay as a lark

The correct prepositions are "died of cancer" (indicating the cause of death) and "died in a train accident" (indicating the situation in which the death occurred).

Hence, the correct answer is option d. of, in

"Live in" is the correct preposition to use when referring to residing in a place.

Hence, the correct answer is option a. in

"Went off" is the correct phrasal verb meaning that the gun fired accidentally.

Hence, the correct answer is option a. went off

The correct suffix is "-y" to form "brotherly," which means characteristic of or appropriate to a brother.

Hence, the correct answer is option d. -y

The prefix "un-" is used to form the word "undesirable," meaning not wanted or wished for. While "un-" is commonly used, "dis-" specifically makes "desirable" into "undesirable."

Hence, the correct answer is option a. un-

"Few" means not many, and it is used in a negative sense to indicate that he doesn't have many friends. "A few" would imply that he has some friends, but not many, which is not as strong as "few."

Hence, the correct answer is option a. few

"This evening" is the correct expression in standard English. "Today afternoon" is incorrect; the correct form is "this afternoon." "The backside of a building" is more accurately "the back of a building," and "a worth seeing sight" should be "a sight worth seeing."

Hence, the correct answer is option c. this evening

"Every" is a singular determiner, so the verb must be singular. Therefore, "is" is the correct choice.

Hence, the correct answer is option c. is

In this sentence, "having my hair style criticized" is in the passive voice, where the action of criticizing is done to the speaker's hairstyle. The other sentences are in the active voice, where the subject is performing the action.

Hence, the correct answer is option c. I hate having my hair style criticized.

The Central Processing Unit (CPU) is the component that carries out instructions from programs by performing basic arithmetic, logic, control, and input/output operations.

Hence, the correct answer is option c. CPU

HTML (HyperText Markup Language) is used for structuring content on the web. It is not a programming language but a markup language used to define the structure of web pages.

Hence, the correct answer is option b. HTML

Defragmentation reorganizes fragmented data so that it is stored more efficiently, leading to improved access times and system performance.

Hence, the correct answer is option b. Defragmentation

A pixel is the smallest unit of a digital image that can be displayed and edited on a digital display device.

Hence, the correct answer is option c. Pixel

A monitor is an output device that displays information to the user. The other options (microphone, mouse, scanner) are input devices.

Hence, the correct answer is option b. Monitor

FTP (File Transfer Protocol) is used for transferring files between a client and a server on a computer network.

Hence, the correct answer is option a. File Transfer Protocol

RAM (Random Access Memory) is volatile memory, meaning it loses its data when the power is turned off. SSDs, DVDs, and USB flash drives are non-volatile storage devices.

Hence, the correct answer is option b. RAM

Safari is a web browser developed by Apple. Bing is a search engine, Linux is an operating system, and Microsoft Office is a suite of productivity software.

Hence, the correct answer is option a. Safari

The operating system (OS) manages hardware resources and provides services for software applications. It acts as an intermediary between the user and the hardware.

Hence, the correct answer is option b. Operating System

React Native is a popular framework for building mobile applications that can run on both Android and iOS platforms using a single codebase.

Hence, the correct answer is option a. React Native

Given,

2(x−3)+4=10

or, 2x−6+4=10

or, 2x−2=10

or, 2x=10+2

or, 2x = 12

∴ x= 6

Hence, the correct answer  is option d. 6

The inequality 3≤x<8 includes 3 but not 8, so the correct interval notation is [3,8)

Hence, the correct answer is option a. [3,8)

Given,

(x,y)=(2,2)

r=√(x^2+y^2) = √(2^2+2^2) = √8 =2√2 

θ=tan^−1(x/y) = tan^−1(2/2) = tan^−1(1)

​θ=45°

Hence, the correct answer is option a. r=2√2 , θ=45°

Given,

∣2x−3∣=5

we know modulus represent -ve & +ve sign

so,

taking -ve;  -(2x−3)=5

-2x+3=5

-2x=5-3

-2x=2

x= -1

again taking +ve sign;  +(2x−3)=5

2x=5+3

2x=8

x=4

∴ x= 4 and -1

Hence, the correct answer is  a. 4 and -1

Given,

f(x)=x^3−3x^2+2

To find the stationary points, we first take the derivative and set it equal to zero:

f′(x)=3x^2−6x

then,

f′(x)=0

3x^2−6x =0

3x(x−2)=0

either, 3x=0 ⟹ x=0

or, (x-2)=0 ⟹ x=2

Hence, the correct answer is option a.(0,2)

The sum of three cube roots of unity is 0 i.e 1+ω+ω^2=0

Hence, the correct answer is option a. 0

Given,

y=sin⁡^3(x)----------(i) then dy/dx=?

Differentiating equation(i)

Using the chain rule:

dy/dx = 3sin^2 (x) cos(x)

Hence, the correct answer is option a. 3sin^2 (x) cos(x)

Given,

∫x^2 dx

= (x^3)/3 + C

Hence, the correct answer is option a. (x^3)/3 + C

Given,

f(x)=2x+3 and g(x)=x^2,

then $)=?$

(f∘g)(x)is defined as $)$.

f(g(x))=f(x^2)=2(x^2)+3=2x^2+3

Hence, the correct answer  is option a. 2x^2+3

Given,

3x+4y=7------(i)

and 6x+8y=14.

2(3x+4y)=14

3x+4y=7-------(ii)

Here equation(i) and (ii) are so it has Infinitely many solutions

Hence, the correct answer is option a. Infinitely many solutions

For a quadratic equation to have real and equal roots, the discriminant must be zero:

b^2−4ac=0

Hence, the correct answer is option b. b^2−4ac=0

For the lines to be perpendicular, the condition is:

h^2=ab

Hence, the correct answer is option c. h^2=ab

Given,

f(x)=x^3−6x^2+9x+1

f'(x)=3x^2 -12x + 9

then according to the questions

f'(x)=0

or, 3x^2 -12x + 9 = 0

or, x^2−4x+3=0

on solving (x−3)(x−1)=0⟹x=1 or x=3

Hence, the correct answer is option c. x=3

Given,

g(x)=x^4 - 4x^3 + 6x^2

for point of inflection, g''(x)=0

then,

g'(x)=4x^3−12x^2+12x

g′′(x)=12x^2−24x+12

then, for the point of inflection

g''(x)=0

12x^2−24x+12

or x^2 - 2x +1 =0 ⟹x=1

Hence, the correct answer is option b. x= 1

Given,

(x1​,y1​)= (3,4) and the line 3x−4y+12=0.

using distance formula,

d= | Ax1​+By1​+C | / √(A^2 + B^2) 

then,

d= ∣ 3(3)−4(4)+12 | / √(3^2 + (-4)^2)  =  ∣ 9−16+12 ∣ / √(9+16) = 5/5 = 1

Hence, the correct answer is option c. 1

Two lines are coincident if the discriminant of the quadratic form is zero.

For ax^2 + 2hxy + by^2 = 0, the discriminant condition is:

h^2−ab=0

Thus, for coincidence:

h^2=ab

Hence, the correct answer is option a. h^2=ab