2071 Entrance Questions

Here's the breakdown of the syllables in "education":

e

du

ca

tion

When we pronounce "education," the stress falls on the third syllable: "ca". So, the pronunciation is e-du-CA-tion.

Hence, the correct answer is option c. third

"Arduous" means requiring a lot of effort, being difficult or strenuous. "Difficult" is a synonym that matches this meaning.

Hence, the correct answer is option b. difficult

"Obscure" means not clear or hard to understand. The opposite would be "explicit," which means clear and detailed, leaving no room for confusion or doubt.

Hence, the correct answer is option c. explicit

The initial consonant sound of "chef" is /ʃ/, which is the same as the sound in "chute." The other options have the initial consonant sounds /tʃ/ (chess, child, cheap).

Hence, the correct option is a. chute

The correct prepositions to use are "from" and "at." The phrase should be "I completely differ from you at this point."

Hence, the correct answer is option a. from: at

The correct preposition to use is "for." The phrase should be "We feel sympathy for the poor."

Hence, the correct answer is option d. for

The correct preposition to use is "on." The phrase should be "He insisted on leaving immediately."

Hence, the correct answer is option c. on

The phrase "hole and corner" refers to something that is done secretly or covertly. Therefore, "secret" is the correct synonym.

Hence, the correct answer is option b. secret

"Palatable" means pleasant to taste. While "edible" means fit to be eaten, it doesn't necessarily mean that the food is tasty. "Pungent" refers to a strong, sharp taste or smell, and "sensuous" pertains to the senses but not specifically to taste. Therefore, "palatable" is the best choice.

Hence, the correct answer is option c. Palatable

The prefix "un-" is used to form the antonym of "pleased," resulting in "unpleased." "Mis-" and "dis-" are not appropriate prefixes for "pleased." "None" is incorrect because "unpleased" is a valid word.

Hence, the correct answer is option a. un-

"Omnipresent" means being present everywhere at the same time. "Omniscient" means all-knowing, "theist" means one who believes in the existence of God, and "omnipotent" means all-powerful.

Hence, the correct answer is option a. Omnipresent

"Sitophobia" is the term for the fear of food. "Ergophobia" is the fear of work, "panthophobia" is the fear of suffering, and "hyctophobia" is not a recognized phobia.

Hence, the correct answer is option a. Sitophobia

A "knell" is the sound of a bell, especially when rung solemnly for a death or funeral. The other options do not relate to a funeral bell.

Hence, the correct answer is option b. Knell

The sentence is about an ongoing action that is happening now because of a current situation (prices getting low). "Must be buying" correctly reflects the present continuous tense to indicate that people are currently in the process of buying computers.

Hence, the correct answer is option c. Must be buying

The word "similar" is typically followed by "to" or "like" to compare chipmunks to other ground squirrels. "Like" fits the structure of this sentence best.

Hence, the correct answer is option d. like

The present perfect continuous tense ("has been working") describes an action that started in the past and continues into the present, emphasizing the duration of the activity.

Hence, the correct answer is option a. has been working

The structure "too busy to" indicates that Shyam's level of busyness prevents him from taking care of his health.

Hence, the correct answer is option b. too

The verb "demand" is typically followed by an infinitive form of a verb when expressing what is being demanded. In this case, "to know" is the infinitive form that correctly completes the sentence.

Hence, the correct answer is option c. to know

The sentence is contrasting the regular occurrence of the mail arriving at ten o'clock every day with the exception of Saturday. The word "but also" is used to indicate this contrast or exception.

Hence, the correct answer is option a. but also

The definite article "the" is used before a noun to specify it as something known or already mentioned. "By the month" is a common expression indicating that salary is paid on a monthly basis.

Hence, the correct answer is option a. the

When "every" is used before singular nouns connected by "and," it requires a singular verb. Therefore, "Every boy and every girl is very responsible" is the correct construction.

Hence, the correct answer is option b. is

Let's see from the option

a. Some of rice is still left. (Incorrect - should be "Some of the rice is still left.")

b. Time and tide wait for none. (Incorrect - the correct saying is "Time and tide wait for no man.")

c. She absents herself from the college today. (Incorrect - "absents" is not commonly used in this context. "She is absent from college today" would be correct.)

d. None of the squares was properly drawn. (Correct - "None" can be singular when referring to individual items within a group.)

Hence, the correct answer is option d. None of the squares was properly drawn

Let's see from the option

a. However hard she worked, she failed in the exams. (Correct - This is a complex sentence with a dependent clause "However hard she worked" and an independent clause "she failed in the exams.")

b. It rained heavily, however he came to school. (Incorrect - This is a compound sentence with two independent clauses joined by "however.")

c. In spite of heavy rain, he came to school. (Incorrect - This is a simple sentence with a prepositional phrase.)

d. Neither she nor he will come. (Incorrect - This is a compound sentence with a coordinating conjunction "nor.")

Hence, the correct answer is option a. However hard she worked, she failed in the exams

Let's see from the option

Given,

|𝑥 − 3| = 4   then we have to find the value of x

We know,

Modulus represent +ve & -ve so

Taking   +ve                  taking  -ve

+(x-3)=4                            -(x-3)=4

x=4+3                     -x + 3 =4

x=7      -x=4-3

x=-1

Hence, the value of x are 7 & -1

The correct answer is option a. 7 and -1

Given,

𝑥 − 𝑥^2 = 9---------(i) and 2𝑥 = 6---------------(ii)

From equation (ii)

2x=6

x=3

then substitute the value of x in equation(i)

𝑥 − 𝑥^2 = 9

3-3^2≠9

-6≠9

so there is not any common value between equation(i) & (ii) i.e null set

Hence,the correct answer is a.null set

Given,

𝑓(𝑥) =y= 𝑥^2 + 3-------(i) then 𝑓 ¯¹(4)=?

We know that, interchanging the value of x & y

x= y^2 + 3

x-3 =y^2

y=√(x-3)

𝑓 ¯¹(x)=±√(x-3)-----------(ii)

If we put x=4 in equation(ii) we get

𝑓 ¯¹(4)=±√(4-3) = ±1 i.e {1,-1}

Hence,the correct answer is option b.{1,-1}

Given,

cos^2 𝜃 =1/2

cos^2 𝜃 =cos^2 (π/4)

𝜃=nπ±π/4(from Trigonometry general formula)

Hence,the correct answer is option a. 𝜃=nπ±π/4

Given,

𝑐𝑜𝑠 (sin¯¹ 3/5) --------------(i)

Let,

sin¯¹ 3/5=θ

3/5= sin θ

3/5=p/h (using Pythagorean theorem)

for calculating b

we known,

b=√(h^2-p^2)

b=√(5^2-3^2)

b=√25-9

b=√16

b=4

Then, equation (i) become

=Cosθ

=b/h

=4/5

Hence, the correct answer is option b. 4/5

We know,

1/𝑎^2,  1/𝑏^2, 1/c^2 are in A.P

So

1/𝑏^2 = 1/2(1/𝑎^2 + 1/c^2 )

1/𝑏^2 =(c^2 +a^2)/(2a^2 c^2)

2a^2 c^2 = 𝑏^2(a^2 +c^2)

Hence, the correct answer is option a. 2a^2 c^2 = 𝑏^2(a^2 +c^2)

Hence, the correct answer is option d. Nonsingular

Given,

2𝑥 + 𝑦 = 5------------(i)

4𝑥 + 2𝑦 =8

2(2x +y)=8

2x +y=4 --------------------(ii)

Here, equation(i) & (ii) represent two parallel lines so they are inconsistent and independent

Hence, the correct answer is option b. inconsistent and independent

Given,

i^7 + 1/i^4

={(i^2)^3} . i + 1/{(i^2)^2}

={(-1)^3} . i + 1/{(-1)^2}

= -i + 1

Hence, the correct answer is option d. -i+1

Given,

=(x + ωy + ω^2 z)/(y + ωz + ω^2 x)

=(x ω^3+ ωy + ω^2 z)/(y + ωz + ω^2 x) (We know ω^3 =1)

=ω( xω^2 + y + ω z)/(ω^2 x + y +ωz)

=ω

Hence, the correct answer is option a. ω

Given,

𝑥^2 + 4𝑥 + 𝑘 = 0 is comparing with ax^2 +bx +c=0

Then a=1, b=4, c=k

For equal roots,

b^2-4ac=0

4^2-4.1.k=0

16=4k

K=4

Hence, the correct answer is option b. 4

Two lines given by the equations a1x+b1y+c1=0 and a2x+b2y+c2=0 are identical if their coefficients are proportional. This means that there exists a constant k such that:

a1=ka2, b1=kb2, and c1=kc2.

This can be expressed as,

a1/a2 = b1/b2 = c1/c2

For two lines to be identical, their equations must be the same up to a constant multiple. This means each corresponding coefficient must be proportional.

If this condition is met, the lines overlap completely, making them identical

Hence, the correct answer is option a. a1/a2 = b1/b2 = c1/c2

Given,

2𝑥^2 – 2𝑥𝑦 + 𝑘𝑦^2 = 0 is comparing with ax^2 +2hxy +by^2=0

a=2, 2h=-2,   b=k

h=-1

For perpendicular

a+b=0

2+k=0

K=-2

Hence, the correct answer is option b. -2

Given,

radius(r)=2 units

We have to find the equation of the circle touching the positive x-axis and y-axis

then, using formula,

(x-2)^2 + (y-2)^2 = r^2

x^2 - 4x + 4 + y^2 - 4y +4 = 4

x^2 - 4x + 4 + y^2 - 4y + 4 - 4 = 0

x^2 + y^2 - 4x - 4y +  4 = 0

Hence, the correct answer is option a. x^2 + y^2 - 4x - 4y +  4

Given,

the point (3,4) lies on the circle 𝑥^2 + 𝑦^2 = 25 so,

3^2 + 4^2 = 25

25=25

𝑥^2 + 𝑦^2 = 25 comparing with 𝑥^2 + 𝑦^2 = r^2

r^2 = 25

r=5 which is radius

The centre of the circle is at (0,0) and it's radius is 5.

The distance d from the centre (0,0) to the line 4x+3y=K is

d= ( | 4 * 0 + 3* 0 - K | ) / √(4^2 + 3^2)

d=| K | / 5

For the line to be tangent to the circle, this distance must equal to the radius of circle

| K | / 5 = 5

| K | =25

k= ± 25

Hence, the correct answer is option c. ± 25

Given,

𝑦 = 𝑏^𝑥----------------(i)

Differentiate equation(i) with respect to x

dy/dx = b^x log(b)

Here,in option there is ln so

dy/dx = b^x ln|b|

Hence, the correct answer is option d. b^x ln|b|

Given,

y=𝑥^2 +2𝑥 + 2-----------------(i)

Differentiate equation (i) with respect to x

dy/dx = 2x + 2

According to the questions,

dy/dx = 0

2x + 2 =0

2x = -2

x = -1

Hence, the correct answer is option d. -1

Given,

y= 𝑥^3 +3𝑥^2– 9𝑥 + 2------------------(i)

Differentiate equation (i) with respect to x

dy/dx = y' = 3x^2 + 6x - 9 -------------------(ii)

Again, differentiate equation(ii) with respect to x

y"= 6x +6

For point of inflection

y"=0

6x+6=0

6x= -6

x =-1

Hence, the correct answer is option a. -1

We know,

h (Planck's constant) has dimensions of [M L^2 T^−1].

e (elementary charge) has dimensions of $[IT]$.

So, the dimensions of h/e are [M L^2 T^−1] / [IT] =[M L^2 T^−2 I^−1].

From given option,

Magnetic field: [M T^−2 I^−1]

Electric field: [M L T^−3 I^−1]

Magnetic flux: [M L^2 T^−2 I^−1]

Electric flux: [M L^2 T^−1 I^−1]

Hence, the correct answer is option c. Magnetic flux

In 0.00300, there are 2 significant figures (3 and the trailing zero after the decimal).

The ×10^11 part is a scaling factor and does not affect the significant figures.

Hence, the correct answer is option d. 2

μs (coefficient of static friction) is typically greater than μk (coefficient of kinetic friction) because it takes more force to start moving an object than to keep it moving.

Hence, the correct answer is option a. μs≥μk

Torque (τ) is the time derivative of angular momentum ($L$), meaning τ=dL/dt.

This implies that the torque and the change in angular momentum are parallel to each other.

Hence, the correct answer is option b. parallel to L

The Poisson's ratio (ν) of a material is defined as the negative ratio of transverse strain to axial strain. It typically ranges between 0 and 0.5 for most materials.

Let's see from the given option

0.10: Possible for certain materials, indicating relatively low lateral contraction.

0.20: Possible for many common materials, indicating moderate lateral contraction.

0.40: Also possible, especially for rubbery materials, indicating significant lateral contraction.

0.65: Unusual for typical materials, as it exceeds the theoretical maximum value of 0.5 for isotropic elastic materials. A Poisson's ratio greater than 0.5 would imply that the material would expand laterally more than it contracts longitudinally, which is not possible under normal conditions.

Hence, the correct answer is option d. 0.65

Given,

The depth of water at which an air bubble of radius (r)=0.4mm=0.4×10^−3 m

surface tension of water(γ)=72×10^−3 N/m

we need to consider the balance between the force due to surface tension and the hydrostatic pressure difference.

The pressure inside a bubble due to surface tension is given by:

Pinside−Poutside=2γ/r

The hydrostatic pressure at depth $h$ in water is given by:

Poutside=Patm+ρgh

For the bubble to be in equilibrium, the pressure inside the bubble (due to surface tension) must equal the sum of atmospheric pressure and the hydrostatic pressure at depth $h$:

2γ/r = ρgh---------(i)

Where:

$\rho$ is the density of water ≈1000 kg/m^3

$g$ is the acceleration due to gravity =9.8 m/s^2

then equation(i) becomes

h=2γ/rρg

h=(2 x 72×10^−3 N/m) / (1000 kg/m^3 x 9.8 m/s^2 x 0.4×10^−3 m )

h=(144 x 10^-3) / (3.92 x 1)

h=0.03674m

h=3.673cm

Hence, the correct answer is option c. 3.674 cm

When a cylinder is heated, its dimensions expand due to thermal expansion. Given that the length of the cylinder increases by 2%, we can use the concept of linear expansion and area expansion to determine the increase in the area of the base.

Linear Expansion

For a material with a coefficient of linear expansion α, the change in length ΔL is given by: ΔL=L⋅α⋅ΔT where ΔT is the change in temperature.

Given that the length increases by 2%, we can express this as:

ΔL/L= 0.02

Area Expansion

The area expansion is related to the linear expansion by the formula:

ΔA=2α⋅A⋅ΔT

or ΔA/A=2ΔL/L

Since ΔL/L=0.02

we have:

ΔA/A=2×0.02=0.04

Therefore, the area of the base will increase by:

Hence, the correct answer is option d. 4%

In a pressure cooker, food is cooked at a pressure higher than atmospheric pressure. This is done to increase the boiling point of water, which allows food to cook faster.

Typically, a pressure cooker operates at about 15 psi (pounds per square inch) above atmospheric pressure. Since 1 atmosphere is approximately 14.7 psi, this means the total pressure inside the cooker is:

1 atm+ (15 psi) / (14.7 psi/atm) ≈2 atm

The increased pressure in a pressure cooker raises the boiling point of water, allowing food to cook at a higher temperature and thus more quickly. This pressure is generally around 2 atmospheres.

Hence, the correct answer is option d. Two atmosphere

The mean free path (λ) of a gas is given by the equation:

λ=(kBT)/(√2 π d^2 p)

Where:

kB is the Boltzmann constant

$T$ is the absolute temperature

$d$ is the diameter of the gas molecules

$P$ is the pressure

At constant pressure, the mean free path varies directly with temperature. Therefore, the mean free path of a gas varies as:

λ∝T

Hence, the correct answer is option d. T

The efficiency η of a Carnot engine is given by:

η=1−TC / TH -------------(i)

Where:

TC is the absolute temperature of the cold reservoir (ice point)

TH is the absolute temperature of the hot reservoir (steam point)

Converting the temperatures to Kelvin:

Ice point TC=0°C=273.15 K

Steam point TH=100°C=373.15 K

then equation(i) becomes

η=1−273.15/373.15

$\eta =1-0.732$

η=0.268

Converting to percentage:

η=0.268×100%=26.8%

Hence, the correct answer is option b.26.81%

The phenomenon where waves bend around the corners of an obstacle or spread after passing through small openings is called diffraction.

Hence, the correct answer is option d. diffraction

When a tuning fork vibrates, its prongs move in opposite directions. This means that when one prong moves outward, the other prong moves inward, and vice versa. This motion is characterized by a phase difference of π(180 degrees).

Hence, the correct answer is option c. π

For a convex mirror, the mirror equation is:

1/f=1/u + 1/v

Where,

$f$ is the focal length of the mirror.

v is the image distance from the mirror.

u is the object distance from the mirror.

Given that the object is placed at the focus of the convex mirror (u=−f), we can use the mirror equation:

1/f=1/(-f) + 1/v

1/f + 1/f =1/v

2/f= 1/v

v=f/2

Hence, the correct answer is option d. f/2

The appearance of the sky depends on the presence of an atmosphere and how it scatters sunlight.

On Earth, the sky appears blue because the atmosphere scatters shorter wavelengths of light (blue and violet) more than longer wavelengths (red and yellow). This scattering is called Rayleigh scattering.

However, the moon lacks a significant atmosphere. Without an atmosphere to scatter sunlight, there is no medium to diffuse the light and create the blue sky effect.

From the moon's surface, the sky would appear black because there is no atmosphere to scatter the sunlight.

Hence, the correct answer is option : a. Black

Lens Shape and Refractive Index: A double convex shape means that both surfaces of the air bubble curve outward. However, the key factor here is the refractive index difference between the glass and the air.

Refractive Indices: Glass has a higher refractive index (around 1.5) compared to air (which has a refractive index of approximately 1).

Refraction and Divergence: When light passes from a medium of higher refractive index (glass) to a medium of lower refractive index (air), it diverges. This is the opposite of what happens when light passes from a lower to a higher refractive index medium, where it converges.

Hence, the correct answer is option c. Divergent lens

When two prisms are combined, the resulting optical effects depend on their orientation and the properties of the prisms. Generally, prisms are known for their ability to disperse light into its constituent colors (dispersion) and to change the direction of the light beam (deviation).

Hence, the correct answer is option c. Dispersion and deviation both

An electron microscope uses the wave nature of electrons. The principle behind the electron microscope is based on the wave-particle duality of electrons. According to quantum mechanics, electrons exhibit both particle-like and wave-like properties. The wavelength of an electron is much smaller than that of visible light, which allows electron microscopes to achieve much higher resolution and magnification than optical microscopes. This wave nature enables the electron microscope to visualize structures at the atomic level.

Hence, the correct answer is option b. Wave nature

For a system of charges to be in equilibrium, the net force on each charge must be zero. This means that the vector sum of the electrostatic forces acting on each charge must cancel out.

Straight Line: Placing three charges on a straight line rarely leads to a stable equilibrium because the forces usually do not cancel out symmetrically.

Equilateral Triangle: In an equilateral triangle, the symmetry ensures that the forces can balance out perfectly. Each charge experiences forces from the other two charges, and due to the symmetry, these forces can cancel out.

Rectangle: A rectangle does not offer the same symmetry as an equilateral triangle, making it unlikely for the forces to balance perfectly.

Cube: Placing charges on the corners of a cube involves three-dimensional interactions, which do not generally lead to a simple equilibrium for just three charges.

Hence, the correct answer is option b. On corners of an equilateral triangle

Given,

Radius of Earth(R)=6400 km=6400×10^3 m

To find the capacitance of the Earth, we can model the Earth as a spherical conductor. The formula for the capacitance  C of an isolated spherical conductor is given by:

C=4πϵ0R -------------------(i) 

Where,

ϵ0 is the permittivity of free space (ϵ0≈8.85×10^−12 F/m)

R is the radius of the sphere

then, equation (i) become

C=4π×8.85×10^−12 F/m×6400×10^3 m

C≈1.11265×6400×10^−7 F

C≈711×10^−6 F

C≈711 μF

Hence, the correct answer is option d. 711 μF

Resistivity (ρ) is a material property and is constant for a given material at a specific temperature.

The formula for resistance $R$ of a wire is:

R=ρL/A

where:

ρ is the resistivity (specific resistance) of the material,

L is the length of the wire,

A is the cross-sectional area of the wire.

Here we have,

Wire 1: Length L, Cross-sectional area 4A

Wire 2: Length 2L, Cross-sectional area A

While the resistance $R$ of each wire will differ due to their lengths and cross-sectional areas, the resistivity ρ remains constant for both wires since they are made of the same material.

Thus, the ratio of their specific resistances is:

ρ1/ρ2 = ρ/ρ = 1:1

Hence, the correct answer is option a.1:1

The magnetic field B inside a long solenoid is given by B=μ0nI, where μ0 is the permeability of free space, $n$ is the number of turns per unit length, and $I$ is the current.

Hence, the correct answer is option c. µ0ni

Electrons are held in atoms due to the electrostatic force of attraction between the negatively charged electrons and the positively charged nucleus. This force is known as the Coulomb force.

Hence, the correct answer is option b. Coulomb forces

The Balmer series of the hydrogen atom lies in the visible region of the electromagnetic spectrum. The Lyman series lies in the ultraviolet region, while the Brackett and Paschen series lie in the infrared region.

Hence, the correct answer is option c. Balmer

The mean life $\tau$ is related to the half-life t1/2 by the relation τ=(t1/2)/(ln2)

For a half-life of 1600 years:

τ=(1600)/(ln2) ≈ 1600/0.693 ≈ 2309 years

Hence, the correct answer is option d. 2309 years

The Rydberg constant is a fundamental physical constant that is the same for all elements. It is used in the calculation of the wavelengths of spectral lines of hydrogen and other elements in the Rydberg formula.

Hence, the correct answer is option c. A universal constant

For a given principal quantum number n, the number of orbitals is given by n^2. For n=3, the number of orbitals is 3^2=9.

OR,

There are 3 subshells for n=3 s,p and d so s contains 1 orbital p contains 3 and d contains 5 orbitals so total number of orbitals =9

Hence, the correct answer is option d. 9

The molar mass of water (H₂O) is 18 g/mol.

The number of moles in 18 grams of water is (18 g) / (18 g/mol)=1 mole

Hence, the correct answer is option b. 1

After one half-life (30 minutes), the amount of radioisotope left is half of the original amount. After two half-lives (60 minutes), the amount left is 1/4th of the original amount.

OR

𝑚/𝑚0= (1)/(2^(1/t half)) = (1) / (2^(1/30)) o𝑟 𝑡 = 2.30 = 60 𝑚𝑖𝑛𝑢𝑡𝑒

Hence, the correct answer is option c. 60 minutes

In HOCl, the oxidation state of oxygen is -2, and the oxidation state of hydrogen is +1. Let the oxidation state of chlorine be $x$. The sum of the oxidation states in the molecule is zero:

+1+x+(−2)=0⟹x=+1

Hence, the correct answer is option a. +1

Mass of iron in one molecule of haemoglobin= (0.33×67200)/(100) = 221.76 g

The number of moles of iron in one molecule of haemoglobin:

(221.76 g) / (55.85 g/mol)  ≈3.97≈4

Hence, the correct answer is option b. 4

Metallic character increases as you move down a group in the periodic table and decreases as you move across a period from left to right. Element C has the electronic configuration 2,8,1, which means it has one electron in its outermost shell, similar to elements in Group 1 (alkali metals). Alkali metals are the most metallic. Therefore, element C is the most metallic.

Hence, the correct answer is option c. C=2,8,1

VSEPR (Valence Shell Electron Pair Repulsion) theory is used to predict the geometry of molecules based on the repulsion between electron pairs in the valence shell of the central atom. However, VSEPR theory applies to covalent compounds, where atoms share electron pairs.

a. NaCl: Sodium chloride (NaCl) is an ionic compound, not a covalent molecule. It consists of a lattice of sodium ions (Na⁺) and chloride ions (Cl⁻) rather than discrete molecules with a specific geometry. Therefore, VSEPR theory cannot be used to predict its molecular geometry.

b. H₂O: Water is a covalent molecule with a bent geometry, which can be predicted using VSEPR theory.

c. CH₄: Methane is a covalent molecule with a tetrahedral geometry, which can be predicted using VSEPR theory.

d. NH₃: Ammonia is a covalent molecule with a trigonal pyramidal geometry, which can be predicted using VSEPR theory.

Hence, the correct answer is option a. NaCl

To determine the effect of increasing the concentrations of the reactants on the rate of reaction, we need to consider the rate law for the reaction. The rate law expresses the rate of reaction as a function of the concentrations of the reactants, raised to powers called the reaction orders.

The general form of the rate law for the reaction 2A+B→C+D can be written as:

Rate=k[A]^m [B]^n

where k is the rate constant, and $m$ and n are the reaction orders with respect to reactants $A$ and $B$, respectively.

Since the reaction orders ($m$ and $n$) are not provided, we'll assume the reaction is first-order with respect to each reactant (a common assumption unless otherwise specified). Thus, the rate law becomes:

Rate=k[A]^1 [B]^1=k[A][B]

If the concentrations of both $A$ and B are increased by three times, the new concentrations will be [A]′=3[A] and $[B]$.

Substituting these new concentrations into the rate law: New Rate=k[A]′[B]′=k(3[A])(3[B])=k3^1 [A]3^1[B]=9k[A][B]

The new rate is 9 times the original rate.

Hence,  the correct answer is option c. 9 times

An aqueous solution of NaCl (sodium chloride) is neutral because NaCl is a salt formed from the reaction of a strong acid (HCl) and a strong base (NaOH). When NaCl dissolves in water, it dissociates completely into sodium ions (Na⁺) and chloride ions (Cl⁻):

NaCl→Na^+ + Cl^−

Neither of these ions hydrolyze in water to form H⁺ (protons) or OH⁻ (hydroxide ions). Therefore, the solution remains neutral, with a pH of around 7.

a. Acidic: This would be the case if the salt were formed from a strong acid and a weak base.

b. Basic: This would be the case if the salt were formed from a weak acid and a strong base.

d. Could be acidic or basic depending upon temperature: The pH of the solution might slightly vary with temperature, but for NaCl, it will not be significant enough to make the solution acidic or basic. The solution will remain neutral.

Hence, the correct answer is option c. Neutral

An aqueous solution of NaCl (sodium chloride) is neutral because NaCl is a salt formed from the reaction of a strong acid (HCl) and a strong base (NaOH). When NaCl dissolves in water, it dissociates completely into sodium ions (Na⁺) and chloride ions (Cl⁻):

NaCl→Na^+ + Cl^−

Neither of these ions hydrolyze in water to form H⁺ (protons) or OH⁻ (hydroxide ions). Therefore, the solution remains neutral, with a pH of around 7.

a. Acidic: This would be the case if the salt were formed from a strong acid and a weak base.

b. Basic: This would be the case if the salt were formed from a weak acid and a strong base.

d. Could be acidic or basic depending upon temperature: The pH of the solution might slightly vary with temperature, but for NaCl, it will not be significant enough to make the solution acidic or basic. The solution will remain neutral.

Hence, the correct answer is option c. Neutral

The pH of pure water decreases as the temperature increases because the ionization of water is an endothermic process. At higher temperatures, more H^+ and OH^- ions are produced. Even though the product of the concentrations of H^+ and OH^- ions (Kw) increases, the water remains neutral (equal concentrations of H^+ and OH^-), but the pH drops below 7

Hence, the correct answer is option c. <7.0

When treated with dilute nitric acid (HNO₃), manganese (Mn) is the metal that generates hydrogen gas (H₂). This is because manganese and magnesium are highly reactive metals, capable of displacing hydrogen from nitric acid. Other metals like zinc (Zn) react with dilute HNO₃ to produce nitrous acid (HNO₂) instead.

Hence, the correct answer is option  b. Mn.

To determine the normality (N) of a sulfuric acid (H₂SO₄) solution, we need to consider the molarity (M) and the number of hydrogen ions that can be donated by one molecule of the acid. Sulfuric acid is a diprotic acid, meaning it can donate two hydrogen ions.

The formula to convert molarity to normality for a diprotic acid is:

$$N=2\times M$$

Given that the molarity of the H₂SO₄ solution is 1 M, the normality would be:

$$N=2\times 1M=2N$$

Hence, the correct is option b. 2N H₂SO₄

The hydrogen molecule with parallel spin of two nuclei is called ortho hydrogen. In molecular hydrogen, there are two isomeric forms based on the nuclear spins of the protons. When the spins are aligned parallel, it is referred to as orthohydrogen, and when the spins are aligned antiparallel, it is known as parahydrogen.

Hence, the correct answer is option  a. Ortho hydrogen

Ammonia is industrially manufactured using the Haber process, which involves the direct combination of nitrogen and hydrogen gases under high pressure and temperature in the presence of a catalyst. The Solvay process is for producing sodium carbonate, the Ostwald process is for producing nitric acid, and the Down's process is for producing sodium metal.

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

Haematite (Fe2O3) is an iron ore and a major source of iron. It is mined for the extraction of iron and used in the production of steel and other iron products.

Hence, the correct answer is option a. Fe

A nucleophile is a species that donates an electron pair to an electrophile. BF3 (boron trifluoride) is not a nucleophile; it is an electron-deficient compound and acts as an electrophile. NH3 (ammonia), H2O (water), and OH^- (hydroxide ion) all have lone pairs of electrons and can act as nucleophiles.

Hence, the correct answer is option a. BF3

The anti-Markovnikov addition of HBr is observed when HBr is added to an alkene in the presence of peroxides. This reaction follows a radical mechanism, leading to the addition of the hydrogen atom to the more substituted carbon atom. Propene, an alkene, will undergo anti-Markovnikov addition of HBr in the presence of peroxides.

Hence, the correct answer is option a. Propene

When oxalic acid and glycerol are heated together, glycerol acts as a dehydrating agent and facilitates the breakdown of oxalic acid, resulting in the formation of formic acid and carbon dioxide.

Hence, the correct answer is option d. Formic acid

A meta directing group is a substituent that directs incoming electrophiles to the meta position relative to itself on an aromatic ring. The –COOH (carboxyl) group is an electron-withdrawing group and is a strong meta director. On the other hand, –NH2 (amino) and –OH (hydroxy) are electron-donating groups and are ortho/para directors. The –R (alkyl) group is also an electron-donating group and directs to the ortho/para positions.

Hence, the correct answer is option c. –COOH

Dichlorobenzene can have chlorine atoms substituted at different positions on the benzene ring. The three possible position isomers are:

1,2-Dichlorobenzene (ortho)

1,3-Dichlorobenzene (meta)

1,4-Dichlorobenzene (para)

Hence, the correct answer is option b. 3

Terylene, also known as polyethylene terephthalate (PET), is a condensation polymer formed by the reaction of terephthalic acid and ethylene glycol, releasing water as a byproduct. Polyethene, PVC (polyvinyl chloride), and Teflon (polytetrafluoroethylene) are all addition polymers.

Hence, the correct answer is option b. Terylene

Penicillin is an antibiotic drug that is used to treat bacterial infections. It works by inhibiting the synthesis of bacterial cell walls, leading to the destruction of the bacteria.

Hence, the correct answer is option c. Antibiotic drug

Enzymes are biological catalysts that speed up chemical reactions in living organisms. They are composed of proteins, which are chains of amino acids folded into specific shapes necessary for their catalytic activity.

Hence, the correct answer is option b. Proteins

Uracil is a nitrogenous base that is found only in RNA. In RNA, uracil replaces thymine, which is found in DNA. The other bases (adenine, guanine, and cytosine) are found in both DNA and RNA.

Hence, the correct answer is option c. Uracil