2069- Entrance Questions

• a. although: "Although his project was not completed, he was given permission to leave." This option shows a contrast correctly.
• b. in spite of: "In spite of his project was not completed, he was given permission to leave." This option is grammatically incorrect because "in spite of" should be followed by a noun or gerund.
• c. as it: "As it his project was not completed, he was given permission to leave." This does not make sense contextually.
• d. despite: "Despite his project was not completed, he was given permission to leave." This is grammatically incorrect; it should be "Despite his project not being completed".

a. but also: This should be used in a "not only... but also" structure.

b. both: This should be followed by "and", e.g., "both hard working and friendly".

c. as well as: "Rajendra is hard working as well as friendly." This is grammatically correct and indicates both qualities.

d. not only: This should be used in a "not only... but also" structure.

• a. have come: This is the correct form because "more than one hundred people" is plural.
• b. has come: Incorrect, as "has" is singular.
• c. is coming: Incorrect, as it is singular and also in present continuous tense which doesn't fit the context as well as "have come".
• d. was coming: Incorrect, as it is past continuous and also singular.

• a. as well as: "Mr. Thakuri speaks both Nepali as well as Maithili very perfectly." This is incorrect because "both" is typically paired with "and," not "as well as."
• b. and also: "Mr. Thakuri speaks both Nepali and also Maithili very perfectly." This is somewhat redundant and less commonly used.
• c. and: "Mr. Thakuri speaks both Nepali and Maithili very perfectly." This is the correct and most natural pairing.
• d. with: "Mr. Thakuri speaks both Nepali with Maithili very perfectly." This does not make sense in this context.

• a. discussion: "Reading, observing, teaching and discussion are good ways to gain knowledge." This is correct as it maintains parallel structure with the other nouns in the list.
• b. discussing: This is a gerund, but it breaks the parallel structure as the other items are nouns.
• c. to discuss: This infinitive form does not match the noun forms of the other items.
• d. discusing: This is a misspelling of "discussing" and is incorrect for the same reason as option b.

• a. an: Incorrect, "an" is used before words that start with a vowel sound, and "Narayanghat" starts with a consonant sound.
• b. a: Incorrect, "a" is used before singular, countable nouns that begin with a consonant sound, but place names typically do not require this article.
• c. the: Correct, specific places often use "the," especially when they are unique or well-known.
• d. no article: Incorrect, the sentence sounds incomplete without "the."

• a. with: Incorrect, "concerned with" can be used, but it doesn't fit as naturally here.
• b. for: Incorrect, "concerned for" suggests concern for people, not about a topic or issue.
• c. about: Correct, "concerned about" is the proper phrase when discussing worry or concern over a topic.
• d. of: Incorrect, "concerned of" is not a correct phrase in English.

• a. by; for: Incorrect, "for" does not make sense in this context.
• b. by; with: Correct, "by a robber" indicates the agent, and "with a gun" indicates the instrument used.
• c. in; for: Incorrect, these prepositions do not fit the context.
• d. with; for: Incorrect, "with a robber" and "for a gun" are incorrect.

• a. has: Correct, "the fear" is the subject, which is singular, so "has" is appropriate.
• b. have: Incorrect, "have" is plural and does not agree with the singular subject "the fear."
• c. was: Incorrect, "was caused" would be correct, but here "has" fits better.
• d. has been: Incorrect, "has been" would require a different sentence structure.

• a. cutting: Correct, this form is commonly used in English.
• b. to cut: Incorrect, this form does not fit the sentence correctly.
• c. to be cut: Correct, this is another grammatically correct way to express the need for the grass to be cut.
• d. both a and c: Correct, both "cutting" and "to be cut" are grammatically correct in this context.

• a. at: Incorrect, "at this evidence" is not a standard English phrase.
• b. by: Correct, "by this evidence" means based on this evidence.
• c. from: Incorrect, "from this evidence" could work but it’s less common than "by" in this context.
• d. in: Incorrect, "in this evidence" does not make sense in this context.

• a. at: Incorrect, "object at" is not a standard English phrase.
• b. about: Incorrect, "object about" is not correct usage.
• c. in: Incorrect, "object in" is not a standard English phrase.
• d. to: Correct, "object to" is the correct preposition to use with "object."

• a. about: Incorrect, "worked about the answer" does not convey the correct meaning.
• b. over: Incorrect, "worked over the answer" implies reviewing but not necessarily solving it.
• c. among: Incorrect, "worked among the answer" does not make sense.
• d. out: Correct, "worked out the answer" means to figure out or solve the answer.

• a. history: When adding "ic," it becomes "historic," which is a valid adjective.
• b. athlete: When adding "ic," it becomes "athletic," which is a valid adjective.
• c. artist: When adding "ic," it becomes "artistic," which is a valid adjective.
• d. success: When adding "ic," it would become "successic," which is not a valid word.

• a. spectacular: This is an adjective describing something impressive.
• b. marvel: This can be a verb meaning to be filled with wonder or astonishment.
• c. comparable: This is an adjective meaning able to be compared.
• d. peculiar: This is an adjective meaning strange or unusual.

• a. provided: Can take prefixes like "un-" (unprovided) or "re-" (reprovided).
• b. poisonous: Can take prefixes like "non-" (nonpoisonous).
• c. protected: Can take prefixes like "un-" (unprotected).
• d. detected: Can take prefixes like "un-" (undetected).

• a. will come: Incorrect, we do not use future tense in the subordinate clause after "before."
• b. would come: Incorrect, this is conditional and does not fit the context.
• c. could come: Incorrect, this indicates ability rather than a future action.
• d. comes: Correct, present simple tense is used for future events in time clauses.

• a. is: Incorrect, "is" is singular and "memoranda" is plural.
• b. was: Incorrect, "was" is singular and "memoranda" is plural.
• c. has been: Incorrect, "has been" is singular and "memoranda" is plural.
• d. have been: Correct, "have been" is plural and matches the plural subject "memoranda."

• a. scissors: Correct term for a cutting tool.
• b. tweezers: Correct term for a tool used to pick up small objects.
• c. forceps: Correct term for a medical instrument used in surgeries.
• d. pincers: Incorrect term if intended to refer to the plural form of the tool; it should be "pincer."

• a. amnesia: Incorrect, this refers to memory loss.
• b. insomnia: Incorrect, this refers to difficulty sleeping.
• c. anemia: Correct, this refers to a lack of red blood cells or hemoglobin in the blood.
• d. epicurean: Incorrect, this refers to a person devoted to sensual enjoyment, especially that derived from fine food and drink.

• a. lawyer: Incorrect, a lawyer is a profession and does not specifically imply a well-experienced person.
• b. cosmopolitan: Incorrect, a cosmopolitan person is someone familiar with and at ease in many different countries and cultures.
• c. veteran: Correct, a veteran is someone with a lot of experience in a particular field, often used for someone experienced in a profession or military.
• d. teacher: Incorrect, while a teacher can be experienced, the word "teacher" itself does not specifically imply a well-experienced person.

• a. that: Correct, "the doubt that Gita will come" is the proper phrase to express uncertainty about Gita's arrival.
• b. if: Incorrect, "the doubt if Gita will come" is not grammatically correct in this context.
• c. when: Incorrect, "when" does not fit well with "the doubt."
• d. why: Incorrect, "why" does not fit with "the doubt."

• a. adverb: Correct, "fast" modifies the verb "walk," describing how they walk.
• b. adjective: Incorrect, an adjective modifies a noun, but "fast" is modifying the verb "walk" in this sentence.
• c. preposition: Incorrect, a preposition shows the relationship between a noun (or pronoun) and other words in a sentence.
• d. demonstrative adjective: Incorrect, demonstrative adjectives are "this," "that," "these," and "those."

• a. I was heard to sing a song.: Correct, this is the proper passive form where the infinitive "to sing" is used correctly.
• b. I was heard sing a song.: Incorrect, the infinitive "to sing" is missing.
• c. I was heard singing a song.: Incorrect, while grammatically correct, it changes the meaning to continuous action.
• d. I was heard to sing a song by them.: While this is grammatically correct, it's more formal and less commonly used. The correct answer focuses on the more natural passive construction.

• a. He said that congratulations.: Incorrect, this is incomplete and not a proper sentence.
• b. He congratulated me.: Correct, this is the proper way to report the speech indirectly.
• c. He congratulated that I passed.: Incorrect, this structure is awkward and not grammatically correct.
• d. He said that I deserved congratulations.: Incorrect, although grammatically correct, it adds information ("I deserved") that wasn't in the original sentence.

For simple harmonic motion, the displacement x as a function of time t can be expressed as:

x(t)=Acos⁡(ωt+ϕ)

where $A$ is the amplitude, $\omega$ is the angular frequency, and ϕ is the phase constant.

Given:

Time Period($12$ seconds

Angular frequency(ω)=2π/T=2π/12=π/6 rad/s

We need the time t when the displacement x(t)=A/2

A/2=Acos⁡(t*π/6 + ϕ)

cos⁡(t*π/6 + ϕ)=1/2​

The angle whose cosine is 1/2 is π/3 (or −π/3):

t*π/6+ϕ=±π/3

​ Assuming ϕ=0 for simplicity: t*π/6=±π/3​

t=±2 seconds

The positive solution is:

t=2 seconds

First, convert the velocity from km/hr to m/s:

64 km/hr=64×1000 m/3600 s

             =64000/3600 m/s  ≈17.78 m/s 

The total distance to be covered is the length of the train plus the length of the bridge:

Total distance=600 m+1000 m=1600 m

Time taken to cross the bridge:

t=Total distance/Velocity=1600 m/17.78 m/s≈90 s

Convert seconds to minutes:

90 s=1.5 minutes

The centripetal force F is given by:

F=(mv^2)/r

F=(1*v^2)/(0.5)

​ F=2v^2

Solving for v:

v^2 =F/2

V=√F/2

Therefore, the correct answer is: d. V=√F/2

A bolometer is an instrument that measures the power of incident electromagnetic radiation via the heating of a material with a temperature-dependent electrical resistance.

First, convert 14°F to Celsius (°C) using the formula:

T(°C)=5/9(T(°F)−32)

T(°C)=5/9(14−32)

T(°C)=5/9×(−18)

$T(°C)=-10$

Now, convert Celsius to Kelvin (K) using the formula:

T(K)=T(°C)+273T(K) 

T(K)=−10+273

$T(K)=263$

For a myopic eye, the corrective lens needs to bring the far point to infinity. The power P of the lens needed to correct myopia is given by:

P=−1/f​

where f is the focal length in meters. The far point for a myopic eye is given as 1.5 meters, so:

P=−1/1.5 m

​ P=−1/1.5 D

P=−0.67 D

Therefore, the correct answer is: d. -0.66 D

The critical angle (θc) is given by:

sin⁡(θc)=n2/n1​​

where n1 is the refractive index of glass and n2​ is the refractive index of water. Assuming typical values:

• Refractive index of glass, n1≈1.5
• Refractive index of water, n2≈1.33

Using the formula:

sin⁡(θc)=n2/n1=1.33/1.5=4/5 ​

Therefore, the critical angle is:

θc=sin⁡^−1(4/5)

thus, the correct answer is: b. sin⁡−1(4/5)

An open organ pipe can produce both odd and even harmonics. The fundamental frequency (first harmonic) of an open organ pipe is given by:

f1=v/2L​

where v is the speed of sound and L is the length of the pipe. The higher harmonics (overtones) are integer multiples of the fundamental frequency:

fn=n⋅f1​

where n=1,2,3,… Thus, an open organ pipe supports both odd and even harmonics.

Therefore, the correct answer is:

c. both odd and even harmonics

To determine what physical quantity is measured in watts per ampere, let's break down the units:

• A watt (W) is a unit of power.
• An ampere (A) is a unit of current.

The unit of power (W) divided by the unit of current (A) gives:

W/A​

Since power is the product of voltage (V) and current (I):

P=V⋅I

Solving for voltage (V):

V=P/I​

Thus, watt per ampere is the unit of electric potential (voltage).

Therefore, the correct answer is: a. electric potential

Resistivity (ρ) is a material property and is independent of the dimensions of the material, such as length and radius. The resistivity of a material is defined by its intrinsic properties and is given by:

R=ρL/A ​

where:

• $R$ is the resistance,
• ρ is the resistivity,
• L is the length,
• A is the cross-sectional area.

Since wires A and B are made of the same material, their resistivity is the same, regardless of their lengths or radii.

Therefore, the correct answer is: b. equal to that of B

The impedance $Z$ of a series LCR circuit is given by:

Z=√(R^2+(XL−Xc)^2) ​

where:

• R is the resistance,
• XL=ωL is the inductive reactance,
• Xc=1/ωC​ is the capacitive reactance,
• ω(omega) is the angular frequency of the AC source.

When a capacitor is added in series, the capacitive reactance Xc​ affects the total impedance. The impedance depends on the relative magnitudes of XL  and Xc which in turn depend on the frequency of the AC supply. Therefore, the total impedance Z can increase or decrease depending on the frequency.

Thus, the correct answer is:

d. increases or decreases depending upon the frequency of a.c

Given:

E=X(emf of the cell)

$Y$ (potential difference across the external resistance)

R (external resistance)

The relationship between the emf $E$, internal resistance $r$, and external resistance R is given by:

E=V+Ir

X=Y+I⋅r

The current $I$ through the circuit can be found using Ohm's law:

I=Y/R ​

Substituting I into the emf equation:

X=Y+(Y/R)r 

X=Y+(Y​r)/R

X - Y = Yr/R

r=R(X−Y)/R​

Therefore, the correct answer is:

d. (X-Y)R/Y

The time period ($T$) of a charged particle in circular motion in a magnetic field is given by:

T=(2πm)/(qB) ​

Where:

$m$ is the mass of the particle,

$q$ is the charge of the particle,

B is the magnetic induction (magnetic field strength).

From this equation, it is evident that the time period $T$ is independent of the speed of the particle.

Therefore, the correct answer is:

a. speed

The kinetic energy (K) of the bullet is given by:

K=1/2mv^2

When the bullet is stopped, its kinetic energy is converted into heat energy (Q) which causes a rise in temperature:

Q=K

Q∝v^2

If the velocity is doubled (v→2v):

Q′∝(2v)^2=4v^2 

The rise in temperature is directly proportional to the heat energy absorbed. Therefore, if the velocity is doubled, the rise in temperature will be four times.

Therefore, the correct answer is:

c. 4 times

To find f(2), substitute $2$ into the function f(x):

f(2)=√(4−2^2)

f(2)=√(4−4​)

f(2)=0

Therefore, the correct answer is:

a. 0

The absolute value equation ∣x∣=2 implies that $x$ can be either 2 or -2. Thus, the solution set is: {2,−2}

Therefore, the correct answer is:

b. {-2, 2}

Since A is a subset of $B$ (A⊆B), every element of $A$ is also an element of $B$. Therefore, the intersection of A and $B$ is simply $A$:

A∩B=A

example;

A={ 1,3,5}

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

AnB={ 1,3,5} n {1,2,3,4,5,6}

={1,3,5}

=A

Therefore, the correct answer is:

b. A

A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself.

Let's analyse the options:

1: 1 is not considered a prime number because it only has one positive divisor (itself).

0: 0 is not a prime number because it is not greater than 1.

2: 2 is a prime number because it has exactly two distinct positive divisors: 1 and 2.

-1: -1 is not a prime number because prime numbers are defined only for positive integers greater than 1.

Therefore, the smallest prime number is:

c. 2

The curve y^2=4x is a parabola that opens to the right. It is symmetric about the x-axis because for every point (x,y)on the parabola, there is a corresponding point (x,−y) also on the parabola.

Therefore, the correct answer is:

b. X-axis

Given,

(xi-4)=13

(x*1-4)+(x*2-4)=13

x-4+2x-4=13

3x=13+8

x=21/3

x=7

To determine the type of matrix:

Symmetric Matrix: A matrix $A$ is symmetric if A= A^T

Skew Symmetric Matrix: A matrix A is skew symmetric if A=-A^T

Diagonal Matrix: A matrix is diagonal if all off-diagonal elements are zero.

Unit Matrix: A unit matrix (or identity matrix) has ones on the diagonal and zeros elsewhere.

For the given matrix A:

A=(1  3

      3   2)

The transpose A^T is:

A^T = (1    3​

             3   2​)

Since A= A^T, the matrix is symmetric.

Therefore, the correct answer is:

a. symmetric

To find the determinant of the matrix:

Using the property of determinants, if two rows (or columns) are identical or proportional, the determinant is zero.

Here, the first and second rows are identical:

=0

Therefore, the correct answer is:

a. 0

The properties of these roots are:

ω^3(omega^3) =1

1+ω+ω^2=0 

We need to find the value of:

(1−ω)(1−ω^2)

Using the identity 1+ω+ω^2=0 , we can express ω+ω^2=−1

Expand the expression:

(1−ω)(1−ω^2)=1−ω−ω^2+ω⋅ω^2

Since ω⋅ω^2=ω^3=1:

1−ω−ω^2+1=2−(ω+ω^2)=2−(−1)=2+1=3

Therefore, the correct answer is:

d. 3

The magnitude (or modulus) of a complex number a+bi is given by:

∣a+bi∣=√(a^2+b^2) ​

For the complex number 2−3i:

∣2−3i∣=√( 2^2+(−3)^2 ) 

|2 - 3i| =√(4+9)

|2 - 3i| = √13​

Therefore, the correct answer is:

a. √13​

Given the values 1 and 2 in the options, check which option is equal. Use 1 in the first option. If LHS equals RHS, then check 2 in the same option you have chosen. If 2 is also equal, then the correct answer is the first option.

or you may solve this way too

To determine which quadratic equation has roots 1 and 2, we use the fact that if $a$ and b are the roots of the quadratic equation ax^2+bx+c=0 then:

x^2−(a+b)x+ab=0

For roots 1 and $2$:

a+b=1+2=3

ab=1⋅2=2

So the quadratic equation is:

x^2−3x+2=0

Therefore, the correct answer is:

a. x^2−3x+2=0

For Solving this Questions You  Can Directly use Calculator

or

you can solve in this way

The tan⁡^−1(1) is the angle whose tangent is 1. This angle is π/4 radians (or 45 degrees). Thus: tan⁡(tan⁡^−1(1))=1

Therefore, the correct answer is:

b. 1

The General solution of

cosθ=cosα

θ=2n∏±α

then cosx=1/2 is ∏/3

then general solution becomes

2n∏±∏/3

Therefore, the correct answer is:

c

The formula for the perpendicular distance from a point (x1,y1) to the line Ax+By+C=0

Distance=​∣Ax1​+By1​+C∣ / √ (A^2+B^2)

for the point (0,0)and the line x+y+1=0:

A=1,B=1,C=1,x1​=0,y1​=0

Distance= ​∣1*0​+1*0​+1∣ / √ (1+1)

|1| / √2

1/√2

Therefore, the correct answer is:

a

Given equation is;

x^2 + y^2 - 2x - 4y  +1 =0  comparing with x^2 + y^2 + 2gx + 2fy + c =0

then we get

2g=-2     &  2f=-4

g=-1             f=-2

then center becomes (h,k)=(-g,-f) = (-(-1),-(-2))=(1,2)

hence the correct option is

Equation of the tangent to the circle x^2 + y^2 =a^2 at any point (x1,y1) is

x*x1 + y*y1 =a^2

then

Given equation is

x^2 + y^2 = 10------(i)  at  point (x1,y1)=(2,3)

comparing equation (i) with  x^2 + y^2 =a^2

then a^2=10

using formula,

x*x1 + y*y1 =a^2

x*2 + y* 3=10

2x+3y=10 is the right answer

we are going to use this on formula

comparing with questions n=3 , a=2

then;

n*a^(n-1)

=3*2^(3-1)

=3*4

=12

the correct answer is

a.12

For Continuous

LHS=RHS

so,

x+2 = 2x

2= 2x-x

x=2

Hence the correct answer is b. x=2

Given,

X^2 + 3x-----(i) is1

then,

the derivative of equation (i) is;

2x + 3=1

2x=1-3

x= -2/2

x= -1

the correct answer is -1

Given,

x=2t + 1 and y=t^2

we have to find dy/dt

for that we have to differentiate y with respect to t

dy=2t dt

dy/dt=2t

the correct answer is 2t

Given curve is;

f(x)=x³ + 4x----(i)

for point of inflection

f“(x)=0 then

differentiate equation(i) with respect to x

f’(x)=3x^2 + 4 ------(ii)

again differentiate equation(ii) with respect to x

f“(x)=6x

for point of inflection

f“(x)=0  then

6x=0

x=0

then the correct answer is 0

Paraffins refer to a class of hydrocarbons that are saturated, meaning they contain only single bonds between carbon atoms. These compounds are also known as alkanes.

Alkanes have the general formula  CnH2n+2 and include well-known examples such as methane CH4  ethane C2H6  propane C3H8 and so on. They are characterized by being relatively less reactive compared to their unsaturated counterparts, the alkenes (which contain double bonds) and alkynes (which contain triple bonds).

Therefore, the correct answer is:
a. alkanes

Lassaigne's test is used to detect the presence of nitrogen in organic compounds. The test involves fusing the organic compound with sodium metal to convert any nitrogen present into sodium cyanide (NaCN). The fused mass is then treated with iron(II) sulphate and subsequently with sulfuric acid, resulting in the formation of iron(III) ferrocyanide (Fe4[Fe(CN)6]3​), also known as Prussian blue.

However, the green color mentioned in the question is due to the formation of a different complex when the organic compound contains both nitrogen and sulphur. This complex is sodium ferrocyanide ferricyanide (Na4[Fe(CN)5NOS],which forms a green coloration.

Therefore, the correct answer is:

c. Na4[Fe(CN)5NOS]

When aluminium carbide (Al4C3) reacts with water, it produces methane (CH4) and aluminium hydroxide (Al(OH)3​) as follows:

Al4C3+12H2O→3CH4+4Al(OH)3​

Therefore, the correct answer is:

d. CH4​

When aniline (C6H5NH2) reacts with benzaldehyde (C6H5CHO), it forms a Schiff base. The reaction involves the condensation of the amine group of aniline with the aldehyde group of benzaldehyde, resulting in the formation of an imine (Schiff base).

The reaction is as follows:

C6H5NH2+C6H5CHO→C6H5N=CHC6H5+H2O

Therefore, the correct answer is:

c. Schiff's base

Anti-knocking agents are compounds added to gasoline to reduce engine knocking and improve the octane rating of the fuel. Tetraethyl lead (Pb(C2H5)4​) was widely used as an anti-knocking agent in gasoline before it was phased out due to environmental and health concerns.

Therefore, the correct answer is:

a. Tetraethyl lead

When chloroform (CHCl3​) reacts with concentrated nitric acid (HNO3​), the product formed is chloropicrin (CCl3NO2). Chloropicrin, also known as nitrochloroform, is used as a pesticide and in chemical warfare as a tear gas.

The reaction can be represented as:

CHCl3+HNO3→CCl3NO2+H2O 

Therefore, the correct answer is:

b. chloropicrin

Tollen's reagent, also known as ammoniacal silver nitrate, is used to detect the presence of aldehydes. The reagent oxidizes aldehydes to carboxylic acids and, in the process, reduces silver ions to metallic silver, which deposits as a mirror on the inner surface of the reaction vessel.

Therefore, the correct answer is:

b. Tollen's reagent

Terylene, also known as Dacron, is a type of polyester. It is formed by the condensation polymerization of ethylene glycol and terephthalic acid. This makes it a condensation polymer.

Therefore, the correct answer is:

a. condensation polymer

Zinc blende is a mineral form of zinc sulphide. It is also known as sphalerite and is the chief ore of zinc.

Therefore, the correct answer is:

c. ZnS

Mohr's salt is a double salt of ferrous sulphate and ammonium sulphate with the formula (NH4)2Fe(SO4)2⋅6H2O. In this compound, iron is in the +2 oxidation state.

Therefore, the correct answer is:

d. +2

Acidic oxides are typically oxides of nonmetals that react with water to form acids or react with bases to form salts and water. Among the given options:

FeO (Iron(II) oxide) is a basic oxide.

CO2 (Carbon dioxide) is an acidic oxide.

CO (Carbon monoxide) is neutral.

CaO (Calcium oxide) is a basic oxide.

Therefore, the correct answer is:

b. CO2​

The ammonia (NH3) molecule has a trigonal pyramidal shape due to the presence of three hydrogen atoms bonded to a nitrogen atom and one lone pair of electrons on the nitrogen, causing the tetrahedral arrangement to become pyramidal.

Therefore, the correct answer is:

d. trigonal pyramidal

Orthophosphoric acid, commonly known as phosphoric acid (H3PO4), contains three hydrogen atoms that can be ionized, meaning it can donate three protons (H^+).

Therefore, the correct answer is:

c. tribasic acid

Epsom salt is a common name for magnesium sulphate heptahydrate.

Therefore, the correct answer is:

a. MgSO4⋅7H2O

The Ostwald process is an industrial process for the production of nitric acid.

Therefore, the correct answer is:

b. nitric acid

Electron affinity generally increases across a period and decreases down a group in the periodic table. Among halogens, fluorine has high electron affinity, but chlorine actually has the highest electron affinity due to less electron-electron repulsion in its larger atomic size compared to fluorine.

Therefore, the correct answer is:

a. chlorine

The molar mass of CO2​ is 44 g/mol. Therefore, 44 grams of CO2 is 1 mole of CO2​. One mole of any substance contains Avogadro's number of molecules, which is 6.023×10^23.

Therefore, the correct answer is:

a. 6.023 * 10^23 no of CO2 molecules

The molecular weight of potassium dichromate (K2Cr2O7​) is divided by the number of electrons lost or gained per formula unit during the redox reaction. In acidic medium, K2Cr2O7​ undergoes the following half-reaction:

Cr2​O7^2−​  +  14H^+  +  6e^− → 2Cr3^+  +  7H2​O

Here, 6 electrons are involved per molecule of potassium dichromate.

Therefore, the equivalent weight is:

Equivalent weight= (Molecular weight) / 6

The correct answer is:

b. Mol. wt/6

Given,

For a Deci normal solution(N) = 0.1(N/10)

Volume=100ml=0.1L

For sodium carbonate (Na2CO3):

Equivalent weight=Molar mass/number of equivalents=106g/mol

Using Formula

Weight=Normality × Volume in Litres × Equivalent weight

Weight =0.1×0.1L×106g/mol

Weight=1.06g

Therefore, the correct answer is:

a. 0.53 gm

Surface tension is the force per unit length. Therefore, its unit in the cgs system is dynes per centimetre.

Therefore, the correct answer is:

b. dynes. cm−1

This principle is known as Hund's rule. Hund's rule states that electrons will fill degenerate orbitals (orbitals with the same energy) singly and with parallel spins before pairing up in any one orbital. This minimizes the repulsion between electrons and is a way to achieve a more stable configuration.

Therefore, the correct answer is:

a. Hund's rule

Copper has an anomalous electron configuration. While we might expect the configuration to be [Ar]4s^2 3d^9 , copper actually adopts a configuration of [Ar]4s^1 3d^10. This is because a filled $d$ subshell (10 electrons) provides extra stability.

Therefore, the correct answer is:

b. [Ar] 4s^1 3d^10

Explanation:

[Ar] 4s^2 3d^9: This configuration is not correct for copper because it does not maximize the stability gained by having a completely filled $3d$ subshell.

[Ar] 4s^1 3d^10: This is the actual configuration of copper, which provides a more stable, lower-energy state.

The pH of a solution is defined as:

pH=−log[H^+]

Given the pH is 5.2, we can find the hydrogen ion concentration [H^+] by:

[H^+]=10^−(pH)

[H^+]=10^(−5.2) 

Calculating 10^(-5.2):

[H^+]≈6.3×10^−6 M

Therefore, the correct answer is:

b.6.3×10^−6 M

For a first-order reaction, the rate law is given by:

Rate=k[A]

The rate is measured in concentration per time (e.g., M/s), and the concentration is measured in M (moles per liter). For a first-order reaction:

[Rate]=M​/s

[A]=M

The rate constant k must therefore have units that will cancel out the concentration unit, leaving units of time inverse:

[K]=[Rate] / [A]

[K]=(M​/s)/M

[K]=1/s

[K]=s^−1

Therefore, the correct answer is:

a.s^−1

The enthalpy of formation (ΔH^∘ base f​) of a compound is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. This can be either positive or negative depending on whether the formation of the compound is exothermic or endothermic.

Therefore, the correct answer is:

c. can be positive or negative

Explanation:

Always positive: Incorrect, as some compounds release energy when formed (exothermic).

Always negative: Incorrect, as some compounds absorb energy when formed (endothermic).

Can be positive or negative: Correct, as it depends on the specific enthalpy change associated with the formation of the compound.

Unpredictable: Incorrect, as the enthalpy of formation can be determined experimentally or calculated.