Given,

A=[-3,2] i.e {-3,-2,-1,0,1,2}

and B=(-2,3) i.e {-1,0,1,2}

AuB = {-3,-2,-1,0,1,2} u {-1,0,1,2} ={-3,-2,-1,0,1,2} = [-3,2]

Hence, the correct answer is option b. [-3,2]

From the property of set theory

AnA͞ = ɸ

Hence, the correct answer is option c. ɸ

Given,

f(x)=x^2 -6x +6 = 0

Domain means which defined the given function i.e if you put any value in place of x it givens certain value no matter it could be negative or positive

Hence, in the given functions  we can put any value it gives integer

So, domain of the given function is (-∞, ∞)

Hence, the correct answer is option a. (-∞, ∞)

The periodic functions of cotx is ∏ ( using the formula)

Hence, the correct answer is option b. ∏

1

It is the formula of the given questions

Hence, the correct answer is option b. 1

Hence, the correct answer is option d.

Hence, the correct answer is option b

Hence, the correct answer is option a

If A,G,H denotes the arithmetic mean, geometric mean and Harmonic mean

then, the relationship between is A>G>H

Hence, the correct answer is option a. A>G>H

Hence, the correct answer is option c

x^2 + (k+2)x +2k = 0 comparing with ax^2 + bx+c=0

a=1, b=(k+2),  c=2k

then for equal roots

b^2 - 4ac=0

or, (k+2)^2 - 4 x 1 x 2k=0

or, k^2 +4k +4 - 8k=0

or, k^2-4k+4=0

or, (k-2)^2 = 0

k=2

Hence, the correct answer is option d. k=2

Using the formula,

a1/a2  ≠ b1/b2

the lines are consistent and independent. If it has unique solution

Hence, the correct answer is option a. Unique solution

Hence, the correct answer is option b

Hence, the correct answer is option a

Hence, the correct answer is option c.

Hence, the correct answer is option c

We know

When two lines are coincident then Ө =0°  ∴h^2 = ab

Hence, the correct answer is option a. 0°

Given,

x^2 + y^2 -2x -4y +3 = 0 at(2,3) and we need to find the equation of tangent for that put the given point(2,3) in option and check which option satisfy i.e LHS=RHS

from option

a. x+y=5 and point is (2,3)

2+3=5

5=5

Hence, the correct answer is option a. x+y=5

Given

equations are

x^2 + y^2 -10x = 0-------(i) with the cord y=2x-----(ii)

put the point from the option both point will satisfy in equation(Ii)

from option a. (2,4),(0,0)

from equation(ii); at point(2,4)

y=2x

4=2 x 2

4=4

from equation(ii); at point(0,0)

y=2x

0=2 x 0

0=0

Hence, option a. (2,4),(0,0) both point satisfy equation(ii)

Hence, the correct answer is option a. (2,4),(0,0)

Using the formula of Angle between the lines represented by ax^2 + 2hxy + by^2 = 0 is option d

Hence, the correct answer is option d.

Hence, the correct answer is option a

Hence, the correct answer is option d

Given,

f(x)= 2x^3 – 3x^2 – 36x---------(i)

for point if inflection f''(x)= 0 --------(ii)

then, equation(i) becomes

f'(x)= 6x^2 -6x-36=0

f''(x)=12x - 5

then, equation(ii) becomes

12x-6=0

x= 1/2

Hence, the correct answer is option a. 1/2

Hence, the correct answer is option d

Hence, the correct answer is option a.

The dimension of Boltzmann Constant(K) is [M^1 L^2 T^-2 T^-1]

Hence, the correct answer is option c. [M^1 L^2 T^-2 T^-1]

Hence, the correct answer is option b

Given,

Time of flight of a projectile (T)=10seconds

Range(R)=500m

Maximum height(H)=?

we know that,

H=(gT^2)/8       (for applying shortcut trick formula)

=(10 x 10^2)/8

=125m

Hence, the correct answer is option b. 125m

Newton's First Law of Motion, also known as the law of inertia, states that an object at rest will stay at rest and an object in motion will stay in motion unless acted upon by an external force. When the bus starts suddenly, the passengers' bodies tend to remain in their initial state of rest, which makes them feel pushed back.

Hence, the correct answer is option a. Newton's First Law

Centripetal force is the force that keeps an object moving in a circular path, directed towards the center of the circle. Centrifugal force is the apparent force that acts outward on a body moving around a center, arising from the body's inertia. These forces are equal in magnitude and opposite in direction in a rotating reference frame.

Hence, the correct answer is option c. equal in magnitude opposite direction

For rolling to occur, there must be sufficient friction between the sphere and the surface. On a smooth inclined plane, there is not enough friction to prevent slipping, so the sphere will slide rather than roll.

Hence, the correct answer is option d. smooth inclined plane

To ensure accurate and reliable measurements with a constant volume gas thermometer, the gas should be filled at high temperature and low pressure. High temperature ensures the gas molecules are well-distributed, and low pressure reduces deviations from ideal gas behavior, making the gas behave more ideally.

Hence, the correct answer is option b. high temperature and low pressure

Hence, the correct answer is option d

We know,

K.E= 3KT/2

According to the question; when T=0, K.E=0

Hence, the correct answer is option a. Kinetic Energy

The Carnot cycle consists of four stages: two isothermal (constant temperature) processes and two adiabatic (no heat exchange) processes. Specifically, it includes an isothermal expansion, an adiabatic expansion, an isothermal compression, and an adiabatic compression.

Hence, the correct answer is option c. Two isothermal processes and two adiabatic processes

The wavelength (λ) is the distance between two successive points in the same phase of a wave (e.g., two consecutive crests or troughs). So, the distance between two particles in the same phase is one wavelength.

Hence, the correct answer is option d. λ

The quality often referred to as the "sweetness" of sound is more accurately described by its timbre or tone quality, which is influenced by the periodicity and regularity of the sound wave. Regular and periodic sound waves are perceived as more pleasant or musical, whereas irregular and aperiodic waves can sound harsh or noisy.

Hence, the correct answer is option d. Periodicity and regularity

Given,

Potential difference(V)=10V

capacitor(c)=500uf

charged at a steady rate= 100ų c/s

Time(t)=?

We know,

V=Q/C

or, 10=(100 x t)/(500)

t=50s

Hence, the correct answer is option d. 50s

The intensity of magnetization (also called magnetization) is defined as the magnetic moment per unit volume of a material. It measures how strongly a material is magnetized in response to an applied magnetic field.

Hence, the correct answer is option c. Intensity of magnetization

The relationship between the RMS voltage (VRMS​) and the peak voltage (Vpeak) for a sinusoidal AC signal is:

Vpeak​=VRMS​×√2

For a 220V AC source, the peak voltage can be calculated as follows:​

Vpeak​=220​×√2 ≈311V

Hence, the correct answer is option c. about 310V

Specific Charge(e/m)=1.76*10^11 c/kg

Hence, the correct answer is option b. 1.76*10^11 c/kg

Hence, the correct answer is option d. 4.8*10^-19 j

Harder X-rays have higher energy, which corresponds to higher frequency and shorter wavelength. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. Therefore, higher energy (harder) X-rays have higher frequency.

Hence, the correct answer is option c. the frequency is higher

The Lyman series of spectral lines corresponds to electronic transitions in hydrogen atoms where electrons fall to the n=1 energy level. These transitions release photons in the ultraviolet range of the electromagnetic spectrum.

Hence, the correct answer is option c. ultraviolet

A NAND gate is a digital logic gate that produces an output that is false only if all its inputs are true. It is essentially an AND gate followed by a NOT gate.

Hence, the correct answer is option a. AND gate & NOT gate

When a body is given a negative charge, it means that electrons are added to it. Since electrons have mass (albeit very small), the mass of the body increases slightly when it gains negative charge.

Hence, the correct answer is option a. increases

Hence, the correct answer is option b. Infinity

The critical angle is the angle of incidence above which total internal reflection occurs. It is dependent on the refractive index of the medium. Violet light has the highest refractive index in glass compared to other colors, meaning it bends the most. Because of this higher refractive index, the critical angle for violet light is the smallest.

Hence, the correct answer is option d. violet

The refractive index of a medium is higher for light of shorter wavelengths. Violet light has the shortest wavelength among the given options, so it has the highest refractive index in a given medium.

Hence, the correct answer is option c. violet

For a healthy human eye, the near point (minimum distance for clear vision) is approximately 25 cm, and the far point (maximum distance for clear vision) is at infinity. This range allows the eye to see objects clearly from 25 cm to infinity without strain.

Hence, the correct answer is option d. 25cm and infinite

Avogadro's Law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. This principle allows for the determination of the molecular content of gases based on their volume.

Hence, the correct answer is option b. Avogadro's Law

Ionization energy is the energy required to remove an electron from an atom. Helium (He) has the highest ionization energy because it is a small atom with a strong electrostatic attraction between its nucleus and electrons. Additionally, helium has a stable electron configuration, making it difficult to remove an electron.

Hence, the correct answer is option b. He

Given,

Weight(W)= 0.4gram

Volume(V)=10 ml

Normality(N)=1N

Equivalent(E)=40

we know that,

W=VEN/1000

0.4=(10 x 40 x 1)/1000

∴ 0.4 = 0.4

Hence, the correct answer is option c. neutral

Solid NaCl: As a solid, sodium chloride does not conduct electricity because the ions are fixed in place within the crystal lattice. However, when dissolved in water or melted, NaCl becomes conductive due to free-moving ions.

Diamond: Diamond does not conduct electricity because it has no free electrons or ions; all carbon atoms are bonded in a rigid structure.

Pure H₂SO₄: In its pure, concentrated form, sulfuric acid does not conduct electricity well. However, when it is diluted, it ionizes and becomes conductive.

Hence, the correct answer is option d. All

The pH scale measures the acidity or basicity of a solution. An acidic solution has a pH less than 7. Solutions with pH greater than 7 are basic (alkaline), and a pH of exactly 7 is neutral.

Hence, the correct answer is option a. <7

Let's see from the given option

Mg(OH)₂ (Magnesium hydroxide): A strong base in aqueous solution, though it's only slightly soluble in water.

Cu(OH)₂ (Copper(II) hydroxide): Generally considered a weak base, as copper(II) hydroxide is only sparingly soluble in water and does not dissociate fully.

Zn(OH)₂ (Zinc hydroxide): Also a weak base, with limited solubility in water and weak basic properties.

HgO (Mercury(I) oxide): This compound can behave as a base but is less strong compared to others in aqueous solutions.

Hence, the correct answer is option a.Mg(OH)₂ (Magnesium hydroxide)

Let's see from the given option

a. Initial Concentration of Reactants: The rate of a reaction typically depends on the concentration of the reactants. Increasing the concentration usually increases the rate because more reactant molecules or ions are present to collide and react.

b. Temperature: The rate of a reaction generally increases with temperature. Higher temperatures increase the kinetic energy of molecules, leading to more frequent and energetic collisions, thus speeding up the reaction.

c. Pressure: For reactions involving gases, the rate can be affected by pressure. Increasing the pressure increases the concentration of gaseous reactants, which can lead to an increased reaction rate.

d. Volume: While volume can influence the concentration of reactants (and thereby indirectly affect the rate of reaction), it does not directly affect the rate in a simple or straightforward manner. The direct effect on the rate comes from changes in concentration, not volume itself.

Hence, the correct answer is option d. Volume

Let's see from the given option

a. F₂: Fluorine is a strong oxidizing agent, not a reducing agent.

b. MgO: Magnesium oxide is not a reducing agent; it is an oxide.

c. Al: Aluminum can act as a reducing agent because it can donate electrons in reactions.

d. CrO₃: Chromium trioxide is an oxidizing agent, not a reducing agent.

Hence, the correct answer is option c. Al

Let's see from the given option

a. Good oxidizing agents: Alkali metals are not good oxidizing agents; they are more likely to be reduced.

b. Good reducing agents: Alkali metals are excellent reducing agents because they easily lose their single valence electron to form cations.

c. Both(a) & (b): This is incorrect because alkali metals are not good oxidizing agents.

d. None: This is incorrect as alkali metals are indeed good reducing agents.

Hence, the correct answer is option b. Good reducing agent

Let's see from the given option

a. Smell: Pure water has no distinctive smell.

b. Taste: Tasting is not a standard method for testing water.

c. Hydrated CuSO₄: This test detects the presence of water by turning from white to blue.

d. Anhydrous CuSO₄: This is the dry form of copper(II) sulfate, which turns blue in the presence of water.

Hence, the correct answer is option d. Anhydrous CuSO4

Let's see from the given option 

a. F₂: Fluorine has the highest affinity for hydrogen among the halogens due to its high electronegativity.

b. Cl₂: Chlorine has a lower affinity for hydrogen compared to fluorine.

c. Br₂: Bromine has an even lower affinity for hydrogen than chlorine.

d. I₂: Iodine has the lowest affinity for hydrogen among these options.

Hence, the correct answer is option a. F2

Let's see from the given option

a. Planar: H₂O₂ is not planar; it has a non-planar structure due to the presence of lone pairs on the oxygen atoms.

b. Non-planar: The structure of H₂O₂ is non-planar with a dihedral angle of about 90° between the O-O bonds.

c. Spherical: The structure of H₂O₂ is not spherical.

d. Linear: H₂O₂ is not linear; it has a bent or non-planar structure.

Hence, the correct answer is option b.  Non Planar

Let's see from the given option

a. Nitrous oxide (N₂O): Nitrous oxide is commonly known as laughing gas.

b. Nitrogen trioxide (N₂O₃): This is not laughing gas.

c. Nitric oxide (NO): This is not laughing gas.

d. Nitrogen pentoxide (N₂O₅): This is not laughing gas

Hence, the correct answer is option a. Nitrous oxide

Let's see from the given option

a. Haber's process: This process is used to synthesize ammonia, not nitric acid.

b. Ostwald's process: This is the correct process for industrial preparation of nitric acid from ammonia.

c. Contact process: This process is used to produce sulfuric acid, not nitric acid.

d. Lead-chamber process: This process is used to produce sulfuric acid, not nitric acid.

Hence, the correct answer is option b. Ostwald's process

Let's see from the given option

a. Chlorine (Cl₂): Chlorine is diatomic.

b. Oxygen (O₂): Oxygen is diatomic.

c. Hydrogen (H₂): Hydrogen is diatomic.

d. Neon (Ne): Neon is a noble gas and exists as single atoms, not diatomic.

Hence, the correct answer is option d. Neon

Let's see from the given option

a. Dehydrating agent: Sulfuric acid (H₂SO₄) is a strong dehydrating agent.

b. Oxidizing agent: Concentrated sulfuric acid can act as an oxidizing agent.

c. Dibasic acid: Sulfuric acid is actually a dibasic acid (it has two replaceable hydrogen ions).

d. Reducing agent: H₂SO₄ is not a reducing agent; it is more commonly known for its oxidizing and dehydrating properties

Hence, the correct answer is option d. Reducing agent

Let's see from the given option

White vitriol refers to zinc sulfate (ZnSO₄), not zinc oxide.

Calamine is an old name for a mixture of zinc oxide and iron oxide, and while it was historically used to describe zinc oxide alone, it's more specifically associated with the mixed form.

Philosopher's wool is another term for zinc oxide, historically used in alchemical contexts.

Malachite is a copper carbonate mineral, not related to zinc oxide.

Hence, the correct answer is option b. Calamine

Methane (CH₄) has a tetrahedral geometry with bond angles of approximately 109.5°.

Hence, the correct answer is option d. Tetrahedral

Alkanes are saturated hydrocarbons with single bonds.

Hence, the correct answer is option b. CnH2n+2

L.P.G (Liquefied Petroleum Gas) primarily consists of butane and isobutane.

Hence, the correct answer is option b. Butane and isobutane

Let's see from the given option

Wurtz reaction involves the coupling of two alkyl halides using sodium, which typically produces alkanes with a greater number of carbon atoms than the starting materials. It does not directly produce methane, as it generally results in longer-chain alkanes when using more complex alkyl halides.

Grignard reagent can be used in specific reactions to eventually produce methane, though not directly. For example, it can react with carbon dioxide and then be reduced to form methane.

Sodalime decarboxylation is a method used to prepare methane from carboxylic acids by removing carbon dioxide.

Reduction methods, such as hydrogenation of carbon dioxide or other suitable precursors, can yield methane.

Hence, the correct answer is option b.Wurtx reaction

The iodoform test is positive for alcohols with the structure R-CH(OH)-CH3, where R is usually a methyl or ethyl group, which includes ethanol.

Hence, the correct answer is option b. Ethanol

Fructose is a ketose sugar, meaning it contains a ketone group. It is also a hexose because it has six carbon atoms.

Hence, the correct answer is option b. ketose

Rosenmund's reduction is a method to reduce acid chlorides to aldehydes using hydrogen gas (H2) in the presence of a palladium catalyst (Pd) supported on barium sulfate (BaSO4). The barium sulfate acts as a poison to the palladium, preventing further reduction to alcohols.

Hence, the correct answer is option d.H2 /Pd +BaSO4

When a Grignard reagent reacts with formaldehyde (the simplest aldehyde), it produces a primary alcohol after hydrolysis. The general reaction is:

R-MgX+HCHO→R-CH2OH

where R is the alkyl group from the Grignard reagent. This reaction results in a primary alcohol with the general formula R-CH2OH.

Hence, the correct answer is option b. Primary alcohol

The definite article "the" is used here because "the guitar" refers to a specific musical instrument that is known in the context.

Hence, the correct answer is option c. the

The preposition "for" is used with the present perfect continuous tense to indicate the duration of time an action has been ongoing.

Hence, the correct answer is option a. for

The past perfect tense "had done" is used to indicate an action completed before another past event (his father coming).

Hence, the correct answer is option c. Had done

The third conditional form, which is used to express hypothetical situations in the past, uses "would have been given" to indicate what would have happened if the condition had been met.

Hence, the correct answer is option b.would have been given

The correct tag question for the positive statement "I'm always right" is "aren't I". The form "aren't I" is the accepted convention, though it might seem counterintuitive.

Hence, the correct answer is option c. aren't I

The subject "everything" is singular, so the verb should also be singular. Hence, "is" is the correct choice.

Hence, the correct answer is option c. is

Let's see from the given option

a. They strictly have prohibited Smoking in the hospital. This is awkward and less commonly used.

b. They strictly prohibit Smoking in the hospital.This sentence correctly expresses the ongoing rule or regulation against smoking in the hospital. It captures the general, continuous nature of the prohibition.

c. They are strictly prohibiting Smoking in the hospital. This suggests an ongoing action, which does not fit the usual expression of established rules.

d. They have strictly prohibited Smoking in the hospital. This implies a past action rather than a current, ongoing rule.

Hence, the correct answer is option b.They strictly prohibit Smoking in the hospital.

In the passive voice, the object of the active sentence becomes the subject. For the present simple tense question "Do we eat sand?" the passive form is "Is sand eaten?" where "is" is used to match the present simple tense of the original question.

Hence the correct answer is option a.ls sand eaten?

Adding the prefix "un-" to "likely" forms "unlikely," which means not likely.

Hence, the correct answer is option b. Un

"Grumpy" means irritable or in a bad mood, which is similar to being "angry." The other options do not match the meaning of "grumpy."

Hence, the correct answer is option a. Angry

"Ominous" means something that suggests a bad outcome or is threatening. Its antonym would be something positive or hopeful, such as "encouraging."

Hence, the correct answer is option c. Encouraging

A kennel is a shelter or place for dogs, just as a sty is a shelter or place for pigs.

Hence, the correct answer is option a. Pig

"Mercy" is a noun, referring to compassion or forgiveness. The other options are verbs or adjectives.

Hence, the correct answer is option d. mercy

In the word "education," the stress is on the second syllable: ed-u-ca-tion.

Hence, the correct answer is option b. second

"Bellicose" describes someone who is inclined to fight or quarrel. The other options describe different characteristics or beliefs unrelated to fighting.

Hence, the correct answer is option a. Bellicose

Among megabytes (MB), gigabytes (GB), and terabytes (TB), a megabyte is the smallest unit of storage. A gigabyte is 1,024 megabytes, and a terabyte is 1,024 gigabytes.

Hence, the correct answer is option a. Megabyte

ROM (Read-Only Memory) is static (unchanging) and non-volatile (retains data without power). RAM (Random Access Memory) is volatile and does not retain data when power is lost. BIOS (Basic Input/Output System) is stored in ROM, and cache is typically volatile.

Hence, the correct answer is option b. ROM

Digital computers represent data as discrete signals (binary code), whereas analog computers use continuous signals.

Hence, the correct answer is option b. Digital Computer

Windows, Unix, and OS/2 are all operating systems. They manage hardware and software resources on a computer.

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

Biometrics refers to the measurement and analysis of unique physical or behavioral characteristics, such as fingerprints and retinal scans, used for identifying and verifying individuals for security purposes.

Hence, the correct answer is option a. Biometrics

A virus is a type of malicious software that can replicate itself and spread to other programs or disks, causing damage or disruption.

Hence, the correct answer is option b. Virus

A modem (modulator-demodulator) connects to a telephone line to facilitate communication between computers over phone networks.

Hence, the correct answer is option a. a telephone line

Binary numbers consist only of the digits 0 and 1. The number 202 contains digits other than 0 and 1, making it non-binary.

Hence, the correct answer is option c.202

UNIVAC stands for Universal Automatic Computer, which was one of the earliest computers designed for general-purpose computing.

Hence, the correct answer is option a.Universal Automatic Computer

A modem is necessary to connect to the internet via telephone lines or cable. A NIC (Network Interface Card) is also important for network connections but works in conjunction with a modem or router. The joystick, CD drive, and other listed devices are not essential for internet connectivity.

Hence, the correct answer is option b. Modem