I am sick is not a logical statement because this statement is not gives either true or false

Hence, the correct answer is option b. I am sick is

Given,

|𝑥 − 2| = 5

We know, modulus represents -ve and +ve sign

taking -ve sign

-(x-2)=5

-x+2=5

-x=5-2

-x=3

∴x=-2

Again, taking +ve sign

+(x-2)=5

x=5+2

x=7

∴x=-3 , 7

Hence, the correct answer is option d. {-3,7}

Let's see from the example

U={1,2,3,4,5,6,7,8,9,10}

A={2,4,6,8,10}

B={1,3,5,7,9}

Now, A-B={2,4,6,8,10}-{1,3,5,7,9} = {2,4,6,8,10} i.e A

From option

a. B-A={1,3,5,7,9} - {2,4,6,8,10} = {1,3,5,7,9} i.e B≠A

b.  𝐴̅− 𝐵̅  = (U-A)-(U-B)

= [ {1,2,3,4,5,6,7,8,9,10}- {2,4,6,8,10} ] - [ {1,2,3,4,5,6,7,8,9,10}- {1,3,5,7,9} ]

={1,3,5,7,9} - {2,4,6,8,10}

={1,3,5,7,9} i.e B≠A

c. 𝐵̅   - 𝐴̅    = (U-B)-(U-A)

=[ {1,2,3,4,5,6,7,8,9,10}- {1,3,5,7,9} ] - [ {1,2,3,4,5,6,7,8,9,10}- {2,4,6,8,10} ]

= {2,4,6,8,10} - {1,3,5,7,9} = {2,4,6,8,10} i.e A

Hence, the correct answer is option c. 𝐵̅ − 𝐴̅

𝑓(𝑥) = 2𝑥 − 3,  𝑓^−1(𝑥) =?

interchanging x and y

y=2x-3

y+3=2x

x=(y+3)/2

f^-1 (x)=(x+3)/2

Hence, the correct answer is option a. (x+3)/2

We know, the periodic function of sinx,cosx, secx, cosecx is 2π

If Periodic of f(x) is T the peiod of f(ax+b) is T/ |a|

f(x) = sin (2x+5)

then,

=2π/2

=π

Hence, the correct answer is option c. π

If a,b,c be in G.P

then it's G.P is b^2=ac

so according to the questions,

fourth, seventh and tenth terms of a G.P. are l,m,n

then m^2=ln

Hence, the correct answer is option a. m^2=ln

Given,

1.3+3.5+5.7+…..

or, 3+15+35+......

From option put n=1

a. (n+1)(n+2); (1+1)(1+2) = 2.3=6 which is not equal to the questions

b. (n+1)(n+3); (1+1)(1+3) = 2.4=8 which is not equal to the questions

c. 4n^2 - 1: 4x1^2 -1=3 equal to questions

put n=2: 4x2^2  - 1=4x4 -1 = 15

If we put the value of n=1 in option c it gives 3 which is equal to questions. Again, if we put n=2 in option c it gives 15 which is equal to the questions.

Hence, the correct answer is option c. 4n^2 - 1

If the system of equation has zero solutions only then the solution is trivial

Hence, the correct answer is option b. trivial

Given,

5𝑥^2 + 2𝑥 − 𝑘 = 0 comparing with a𝑥^2 + b𝑥 + c = 0

a=5, b=2, c= -k

For reciprocal

𝛼. 𝛽 =1

𝑐/𝑎=1

or,  -k/5 =1

∴ k = -1

Hence, the correct answer is option a. -5

Given,

𝑥^2 – 2𝑥𝑦 + 𝑦^2 + 3𝑥 – 2 = 0 comparing with ax^2+2hxy+by^2+2gx+2fy+c=0

a=1, 2h=-2 =>h=-1,  b=1,  2g=3=>g=3/2,   f=0,  c= -2

From theory,

for parabola

h^2 =ab

(-1)^2= 1x1

1=1(true)

Hence, the correct answer is option b. parabola

Given,

𝑓(𝑥) = 𝑥^3 − 3𝑥

f'(x)= 3x^2 - 3

For critical point;

f'(x)=0

then,

3x^2 -3 =0

or, x^2-1=0

or, x^2 =1

∴ x= ±1

Hence, the correct answer is option c. ±1

"Answer for" means to be held responsible for something. The phrase implies that the government has to take responsibility for road accidents.

Hence, the correct answer is option b. answer for

"Ran through" means to spend or use up something, often quickly and wastefully. The sentence suggests that he spent all the inherited money within a year.

Hence, the correct answer is option c. ran through

"Stand up for" means to defend someone or something, especially in the face of criticism. The sentence indicates that the mother defended him against his father's blame.

Hence, the correct answer is option d. stand up for

"Take someone for a fool" means to consider or treat someone as if they are foolish or naive. The question is asking whether the person is being perceived as a fool.

Hence, the correct answer is option a. take, for

The phrase "as fit as a fiddle" means to be in very good health or physical condition. After a month of treatment, the sentence suggests that the brother has fully recovered.

Hence, the correct answer is option d. as fit as a fiddle

"Squeamish" refers to someone who is easily upset, especially by things that are considered unpleasant, like blood or dirt.

Hence, the correct answer is option c. easily upset

A "bramble" is a rough, tangled, prickly shrub, often a wild bush with thorns, commonly associated with blackberry bushes.

Hence, the correct answer is option b. wild bush with thorn

"Congruous" means being in agreement or harmony with something. "Consistent" is a synonym, indicating that things fit together well.

Hence, the correct answer is option a. consistent

A "savior" is someone who saves or rescues others, while a "destroyer" does the opposite, causing destruction or harm.

Hence, the correct answer is option b. destroyer

"Scabrous" refers to something that is rough, indecent, or offensive. The opposite of this would be "decent," which means something that is appropriate, moral, or proper.

Hence, the correct answer is option c. decent

"Un-availing" means not producing any useful result or ineffective. The opposite of this would be "successful," which means achieving the desired result or outcome.

Hence, the correct answer is option c. successful

The correct phrase is "died of" when referring to the cause of death due to illness (e.g., cancer), and "died in" when referring to the location or type of incident (e.g., a train accident).

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

"Divide by" is used for mathematical division (e.g., forty by eight), and "divide between" is used when something is being distributed among a specific number of people (e.g., between the two children).

Hence, the correct answer is option d. by, between

The correct preposition to use with "live" when referring to a location is "in" (e.g., a lovely place to live in).

Hence, the correct answer is option a. in

The correct preposition is "angry with" when referring to being upset with someone, and "indifferent to" means having no particular interest or concern about someone.

Hence, the correct answer is option c. with, to

The phrase "relieve me of" is correct when someone is being freed from a burden or discomfort, such as anxiety.

Hence, the correct answer is option b. of

"Lest" means to avoid the risk of something happening. The sentence implies that the food was taken away to prevent the watch from being broken.

Hence, the correct answer is option c. lest

"On the bottle" refers to someone who drinks alcohol frequently or excessively.

Hence, the correct answer is option c. drinking a lot

"On the rocks" is an idiom that means a situation, often a relationship or business, is in serious trouble or at risk of failing.

Hence, the correct answer is option b. in serious trouble

"Call it a night" means to stop doing something, usually because it is late and it's time to rest or go to bed.

Hence, the correct answer is option a. stop some activity

"Bide one's time" means to wait patiently for a suitable opportunity. It does not mean acting like a soldier, which could be seen as a misunderstanding of the idiom. The correct answer would ideally relate to patience and waiting.

Hence, the correct answer is option d. act like a soldier

"Over the hill" often means past one's prime, but in some contexts, it can mean having passed the most difficult part of something.

Hence, the correct answer is option c. most difficult part

The word "pleasurable" has three syllables: "plea-sur-a-ble."

Hence, the correct answer is option a. three

The fear of blood is called hemophobia

Hence, the correct answer is option d. hemophobia

Given,

[𝑃] =[𝑎]/[𝑉^2]

𝑜𝑟 [𝑎] =[P][V^2] = [𝑀 𝐿^−1 𝑇^−2] [𝐿^6] = [𝑀 𝐿^−5 𝑇^−2]

Hence, the correct answer is option b. [𝑀 𝐿^−5 𝑇^−2]

The number "1400" has two significant figures if the zeros are not counted as significant. Unless specified otherwise (like by writing it in scientific notation or including a decimal), trailing zeros in a whole number are not considered significant.

Hence, the correct answer is option c. 2

The displacement is the straight-line distance from the initial point to the final point.

Using the Pythagorean theorem,

Displacement= √(8^2 + 6^2) m

Hence, the correct answer is option d. √(8^2 + 6^2) m

The range R of a projectile is given by R={v^2 sin⁡(2θ)} / g

If the initial velocity $v$ is doubled, the range becomes R′={(2v)^2sin⁡(2θ)} /g=4R

Therefore, the range will increase by 4 times.

Hence, the correct answer is option b. 4 times

Weight is the force exerted by gravity on a mass. However, due to the centrifugal force caused by Earth's rotation, the effective weight is reduced. If the rotation speed increases, the centrifugal force increases, reducing the effective weight further.

Hence, the correct answer is option a. smaller

According to Archimedes' principle, a body submerged in a fluid experiences a buoyant force equal to the weight of the fluid displaced. Here, the balloon filled with water will be neutrally buoyant, meaning the weight of the water is exactly counteracted by the buoyant force, so its apparent weight in water is zero.

Hence, the correct answer is option d. zero

The Kelvin scale and Celsius scale are offset by 273.15, but their increments are the same. An increase of 270°C corresponds directly to an increase of 270 K.

Hence, the correct answer is option c. 270K

The root mean square (rms) speed of gas molecules is inversely proportional to the square root of the molar mass of the gas. Hydrogen (H₂) has the smallest molar mass among the options, so it has the highest rms speed.

Hence, the correct answer is option a. H₂

A black body is an idealized physical object that absorbs all incident electromagnetic radiation and re-emits it in a continuous spectrum that depends only on the temperature of the body.

Hence, the correct answer is option c. continuous spectrum

A convex mirror diverges light rays, creating a wider field of view compared to plane and concave mirrors. This is why convex mirrors are often used in vehicles for rear-view mirrors.

Hence, the correct answer is option c. convex mirror

The blue color of the sky is due to Rayleigh scattering, where shorter (blue) wavelengths of sunlight are scattered more than longer (red) wavelengths by the molecules in the atmosphere.

Hence, the correct answer is option a. scattering of light

This condition is called myopia (nearsightedness), where the person can see objects close up but not at a distance. The corrective lens required has a negative power,

calculated as $f$

f=−0.5m

$p=\; 1/-0.5$ m = −2D

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

positive charge means loss of electrons so its mass decreases.

Hence, the correct answer is option b. decreases

When capacitors are connected in series, the reciprocal of the total capacitance is the sum of the reciprocals of the individual capacitance:

1/Ctotal = 1/C1 + 1/C2 + 1/C3 = 1/3 + 1/3 + 1/3 = 1µF

Hence, the correct answer is option a. 1µF

Kirchhoff's voltage law states that the sum of the electromotive forces and the potential differences (voltage) around any closed loop or circuit is equal to zero. This law is based on the principle of conservation of energy, which implies that the total energy supplied in a circuit loop is equal to the total energy consumed.

Hence, the correct answer is option b. energy

When a charged particle moves in a magnetic field, it experiences a force perpendicular to its velocity, which changes its direction but not its speed. Since the magnetic force does no work, the kinetic energy of the particle remains constant.

Hence, the correct answer is option c. remains constant

Self-inductance is the property of a coil or circuit that causes it to oppose changes in the current flowing through it by inducing a voltage. A straight wire has no loops or coils, so its self-inductance is effectively zero.

Hence, the correct answer is option a. zero

The photoelectric effect involves the emission of electrons from a material when it is exposed to light. This phenomenon is explained by the conservation of energy: the energy of the incoming photons is transferred to the electrons, providing them with enough energy to escape from the material.

Hence, the correct answer is option a. energy

The emission of a β-particle (which is an electron or positron) does not change the mass number because it involves the conversion of a neutron to a proton or vice versa. The mass number, which is the sum of protons and neutrons, remains unchanged.

Hence, the correct answer is option c. remains the same

In a p-n junction diode, if the reverse bias voltage exceeds a certain threshold (known as the breakdown voltage), a sudden and large increase in current occurs. This phenomenon is called breakdown, and it can be either Zener or avalanche breakdown depending on the mechanism.

Hence, the correct answer is option d. suddenly increases

The general form of a wave equation is $)$, where k=2π/λ the wave number. 

Here, k=62.4

so λ=2π/62.4≈0.1 units

Hence, the correct answer is option b. 0.1 units

When a wave is reflected from a rigid support, the phase of the wave changes by π (180°). This phase change occurs because the wave undergoes an inversion upon reflection.

Hence, the correct answer is option d. π

Due to the Doppler effect, when the source of sound (in this case, the car) moves towards the observer, the frequency of the sound increases, resulting in a higher pitch being heard.

Hence, the correct answer is option a. higher

The Lyman series of hydrogen corresponds to electronic transitions that end at the ground state (n=1). These transitions emit photons in the ultraviolet region of the electromagnetic spectrum.

Hence, the correct answer is option a. ultraviolet

In the complex K3[Fe(CN)6​], potassium (K) has an oxidation state of +1. Cyanide (CN) has an oxidation state of -1. Since the complex is neutral overall, the oxidation state of iron (Fe) can be calculated as follows:

3(+1)+(oxidation state of Fe)+6(−1)=0

+3+(oxidation state of Fe)−6=0

Oxidation state of Fe=+3

Hence, the correct answer is option b. +3

The molar mass of oxygen O2​ is approximately 32 g/mol. The number of moles in 8.0 g of oxygen is:

Moles of O2​=(8.0 g)/(32 g/mol) = 0.25mol

The number of molecules in 0.25 mol is:

Number of O2​ molecules=0.25×6.023×10^23≈1.50575×10^23

Since each O2 molecule contains 2 oxygen atoms:

Number of oxygen atoms=2×1.50575×10^23=3.0115×10^23

Hence, the correct answer is option b. 3.0115×10^23

The Aufbau principle states that electrons occupy atomic orbitals in the order of increasing energy, starting with the lowest energy level and moving to higher ones as needed.

Hence, the correct answer is option c. Aufbau principle

The Lyman series corresponds to electron transitions from higher energy levels to the n=1 level. These transitions emit photons in the ultraviolet region of the electromagnetic spectrum.

Hence, the correct answer is option c. ultra-violet region

Sodium chloride (NaCl) crystallizes in a face-centered cubic (FCC) structure. In this structure, each sodium ion is surrounded by six chloride ions, and each chloride ion is surrounded by six sodium ions, forming a cubic lattice.

Hence, the correct answer is option d. face-centered cubic

Electron affinity is the energy released when an atom in the gas phase accepts an electron. While fluorine is the most electronegative element, chlorine has a higher electron affinity due to lesser electron-electron repulsion in its larger 3p orbital compared to fluorine's smaller 2p orbital.

Hence, the correct answer is option d. chlorine

The Haber process is used to synthesize ammonia (NH₃) by combining nitrogen (N₂) and hydrogen (H₂) gases under high pressure and temperature in the presence of an iron catalyst.

Hence, the correct answer is option a. Haber’s process

SO2​ (sulfur dioxide) is an acidic oxide because it reacts with water to form sulfurous acid (H2SO3​), an acidic solution. The other options, N2O, CO, and ZnO, are not acidic oxides.

Hence, the correct answer is option a. SO2​

According to VSEPR theory, BeF2​ has a linear shape. Beryllium (Be) forms two bonds with fluorine (F) and has no lone pairs, leading to a linear geometry with a bond angle of 180°.

Hence, the correct answer is option b. linear

Potassium permanganate (KMnO4​) is not a primary standard because it is not stable enough (it can decompose) and is typically used in titrations after being standardized. Primary standards like oxalic acid, potassium dichromate, and potassium bromate are stable, pure, and have known composition.

Hence, the correct answer is option d. potassium permanganate

A Lewis base is a substance that can donate a pair of electrons. Ammonia (NH3​) has a lone pair of electrons on the nitrogen atom, making it a Lewis base.

Hence, the correct answer is option d. NH3

The unit of equivalent conductivity is  S cm^-1

Hence, the correct answer is option c. S cm^-1

1 calorie is the amount of heat energy required to raise the temperature of 1 gram of water by 1 degree Celsius, and it is equivalent to 4.184 Joules.

Hence, the correct answer is option a. 4.184 Joules

The Gibbs-Helmholtz equation relates the change in free energy (ΔG) of a system to the enthalpy (ΔH) and entropy (ΔS) changes at a constant temperature T.

ΔG=ΔH−TΔS

Hence, the correct answer is option b. ΔG=ΔH−TΔS

For a third-order reaction, the rate constant k has units of mol^−2 L^2 s^−1. The unit is derived by setting up the rate equation and ensuring that the overall rate has units of mol L^−1 s^−1.

Hence, the correct answer is option b. 𝑚𝑜𝑙^−2 𝐿^2 𝑠^−1

The Friedel-Crafts alkylation reaction involves the reaction of benzene with an alkyl halide in the presence of a Lewis acid catalyst like anhydrous AlCl₃. This reaction introduces an alkyl group into the benzene ring.

Hence, the correct answer is option a. Friedel-Crafts reaction

The Victor Meyer test is a qualitative test used to distinguish between primary, secondary, and tertiary alcohols. The test involves converting the alcohol to a nitroalkane, which reacts differently depending on whether the alcohol is primary, secondary, or tertiary.

Hence, the correct answer is option a. Victor Meyer's test

Williamson's synthesis is a method used to prepare ethers. It involves the reaction of an alkoxide ion with a primary alkyl halide, leading to the formation of an ether.

Hence, the correct answer is option d. ether

Rosenmund's reduction involves the hydrogenation of acyl chlorides to aldehydes using a palladium catalyst supported on barium sulfate (Pd-BaSO₄). The BaSO₄ reduces the activity of the Pd catalyst, preventing over-reduction to the alcohol.

Hence, the correct answer is option d. Pd-BaSO₄

When phenol reacts with concentrated nitric acid in the presence of concentrated sulfuric acid, it undergoes nitration to form picric acid (2,4,6-trinitrophenol).

Hence, the correct answer is option a. picric acid

This reaction is the Hofmann bromamide degradation reaction, where benzamide reacts with bromine and sodium hydroxide to form aniline, which is an aromatic amine.

Hence, the correct answer is option a. aniline

Amino acids are organic compounds that contain both an amino group (–NH₂) and a carboxyl group (–COOH). These groups are characteristic of amino acids and define their properties.

Hence, the correct answer is option c. –NH₂ and –COOH groups

Martius yellow is an acid dye. Acid dyes are typically used to dye protein fibers like wool, silk, and nylon by forming ionic bonds with the positively charged groups in the fibers.

Hence, the correct answer is option b. acid dyes

Green vitriol, also known as iron(II) sulfate heptahydrate, has the chemical formula FeSO₄·7H₂O. It is a common hydrate form of iron(II) sulfate.

Hence, the correct answer is option b. FeSO₄·7H₂O

Zinc blende, also known as sphalerite, is the most important ore of zinc. It consists primarily of zinc sulfide (ZnS) and is the chief source of zinc in the world.

Hence, the correct answer is option b. Zinc blende