2072 Entrance Questions

The correct answer is c. seat, sit.

Explanation:

In American English pronunciation, both "seat" and "sit" have the same vowel sound /iː/.

The vowel sound in "seat" and "sit" is represented by the same IPA symbol /iː/ (the long 'ee' sound).

Therefore, option c (seat, sit) is the pair that has the same vowel sound.

The correct answer is b. falling.

Explanation:

Tone in linguistic terms refers to the pitch pattern of a sentence.

In the sentence "I saw a black bird," the natural intonation pattern in English typically falls towards the end of the sentence.

This falling intonation is common in declarative sentences where the speaker's voice tends to lower towards the end to indicate completion.

Therefore, option b (falling) is the correct answer because the sentence "I saw a black bird" ends on a falling tone.

The word "joy" has the same initial consonant sound as the word c. gesture.

Explanation:

The initial consonant sound of "joy" is /dʒ/ (like the 'j' sound in "jump").

Similarly, the word "gesture" also starts with the consonant sound /dʒ/.

Therefore, the correct answer is option c (gesture), as both "joy" and "gesture" share the same initial consonant sound /dʒ/.

The correct answer is a. Three.

Explanation:

Syllables are distinct units of sound in a word. To determine the number of syllables in "pleasurable," we break it down into its phonetic components: pleasurable /ˈplɛʒərəbəl/.

Counting the syllables: pleasurable has three syllables: plez-uh-ruh-bul.

Therefore, the correct answer is option a (Three).

The word "omniscient" refers to having complete or unlimited knowledge, awareness, or understanding; it is often used to describe a deity or a being with infinite knowledge.

Let's see the option

Omnipresent" (option a) refers to being present everywhere at the same time.

"Omnipotent" (option b) refers to having unlimited power or authority.

"Fatalist" (option c) refers to a person who believes that events are predetermined and inevitable.

"Omniscient" (option d) specifically means having complete knowledge or awareness of everything.

The correct answer is option d. omniscient.

"Aspiration" means a strong desire or ambition to achieve something. "Yearning" similarly conveys a strong longing or desire, making it a synonym for "aspiration."

The correct answer is option b. yearning

"Hypocrisy" refers to pretending to have qualities or beliefs that one does not actually possess. The opposite of this insincerity or deceitful behavior is "sincerity," which means honesty, genuineness, and being true to oneself.

The correct answer is option c. Sincerity

"He died of neglect" indicates the cause of death was neglect (lack of care). "She died in a train accident" specifies the location or circumstance where the death occurred (train accident).

The correct answer is option d. of,in

When asking who someone accompanied, the correct preposition to use with "go" is "with." Therefore, the complete sentence would be "Who did you go with?"

The correct answer is option b. with

Let's fill in the missing vowels:

defin_te: definite

po_gnant: poignant

exist_nce: existence

The missing vowels are "i" and "e," which are correctly represented in option a (e-i-e).

The correct answer is option a. e-i-e

The correct answer is d. over.

Explanation:

The sentence implies that the plane passed above or higher than the speaker's head. The correct preposition to use in this context is "over." Therefore, the correct completion of the sentence is "The plane flew over my head."

The correct answer is a. are.

Explanation:

"You and I" is a compound subject consisting of two persons (you and I). In English grammar, when the subject is a compound noun or pronoun joined by "and," the verb that follows should be plural. The correct form of the verb "to be" (working) that agrees with a plural subject is "are." Therefore, the correct sentence is "You and I are working."

The correct answer is c. change the possible defeat into a victory.

Explanation:

The expression "turn the tables" means to reverse a situation, typically from a position of disadvantage or potential defeat to one of advantage or victory. In the context of the sentence "He has turned the table on his enemy," it suggests that he has managed to change the situation around, possibly from being at a disadvantage to now being in a position of advantage or victory over his enemy.

The correct answer is b. conservative.

Explanation:

Conservative refers to being opposed to great or sudden change. It suggests a preference for maintaining the status quo or traditional values rather than embracing radical changes.

The correct answer is c. vice.

Explanation:

In this context, "vice" refers to a moral fault or wickedness. Greed is considered a vice because it involves an excessive desire for material wealth or gain at the expense of others.

The correct answer is a. went off.

Explanation:

The phrase "went off" means that the gun fired unexpectedly or accidentally. It is commonly used to describe the unintentional discharge of a firearm.

The correct answer is d. lain.

Explanation:

To lie down means to recline or rest in a horizontal position. The correct past participle form of "lie" in this context is "lain." Therefore, the sentence should be "She has lain down for a rest."

The correct answer is d. -y.

Explanation:

The word "brother" can form the adjective "brotherly" by adding the suffix "-ly." Therefore, the correct answer is d. -y.

The correct answer is c. dis-.

Explanation:

The word "desirable" can form the opposite meaning by adding the prefix "dis-," resulting in "undesirable." Therefore, the correct answer is c. dis-.

The correct answer is a. Adjunct.

Explanation:

In the sentence "English teacher makes her class interesting," the word "interesting" describes the class and functions as an adjunct. An adjunct is a word or phrase that provides additional information about another element in the sentence without being essential to its meaning.

The correct answer is b. this evening.

Explanation:

Let's see from the option:

a. today afternoon: The correct phrase is "this afternoon."

b. this evening: This is a correct expression referring to the current evening.

c. the backside of a building: This phrase refers to the rear part of a building.

d. a worth seeing sight: The correct phrase is "a sight worth seeing."

Therefore, the correct answer that represents a grammatically correct and meaningful expression is b. this evening.

The correct answer is c. signaled.

Explanation:

To "beckon" means to signal someone to come nearer or to follow. Therefore, in this context, "she beckoned to enter the room" means she signaled or gestured for someone to enter the room.

The correct answer is d. hematophobia.

Hematophobia is the fear of blood. Let's see other options are:

a. chirophobia: fear of hands.

b. ergophobia: fear of work or functioning.

c. monomania: an obsession with a single subject or idea.

The correct answer is a. few.

Explanation:

"Few" indicates a small number of friends. When used without "a," it implies a negative connotation, suggesting not many friends due to his short temperament. The phrase "a few" would mean some friends, which does not convey the negative implication intended in the sentence.

The correct answer is b. I found him driving my car.

Explanation:

A passive sentence construction typically involves the subject being acted upon by the verb. In the sentence "I found him driving my car," the focus is on "him" (the object) being found driving the car by "I" (the subject). This makes it a passive construction.

Indeterminate means 0/0 , ∞/∞ and other soo

So for this questions we have give a/b which results must be indeterminate

So, check the given option which gives 0/0 which means the value of a & b must equal to 0 (i.e a=b=0)

The correct answer is option b.  𝑎 = 0, 𝑏 = 0

The notation (−∞, ∞) indicates a range of numbers that starts from negative infinity (−∞) and goes up to positive infinity (∞).

Let's see from the given option

Option a. {𝑥: − ∞ ≤ 𝑥 ≤ ∞}: This notation includes all real numbers from negative infinity to positive infinity, but the strict inequality (<) used in (−∞, ∞) means the endpoints are not included.

Option b. {𝑥: − ∞ < 𝑥 < 0}: This notation only covers real numbers less than zero.

Option c. {𝑥: − ∞ < 𝑥 < ∞}: This accurately represents the interval from negative infinity to positive infinity without including the endpoints.

Option d. {𝑥: 𝑥 ≥ 0}: This notation represents all real numbers greater than or equal to zero, which is not correct for the interval (−∞, ∞).

Hence the correct answer is option c. {𝑥: − ∞ < 𝑥 < ∞}.

Therefore, the correct answer that represents the set of all real numbers is c. {𝑥: − ∞ < 𝑥 < ∞}. This notation correctly signifies the entire range of real numbers without any exclusions at the endpoints.

Let's see from the given option

a. Bagmati is a River:This is a declarative statement asserting that Bagmati is indeed a river. It provides factual information.

b. 𝑥 > 0:This is a mathematical inequality stating that 𝑥 is greater than zero. While it is a statement, it is a mathematical condition rather than a factual assertion.

c. How old are you?:This is a question asking for information about someone's age. It is not a statement but an interrogative sentence.

d. 𝑦 > 0:Similar to option b, this is a mathematical inequality stating that 𝑦 is greater than zero. It is not a factual assertion but a mathematical condition.

Based on the criteria that the question is asking for a statement (a declarative sentence that asserts something as true), option a. "Bagmati is a River" is the correct answer because it provides factual information about Bagmati being a river.

Therefore, the correct answer is a. Bagmati is a River.

The given equation is:

(2x - 1, -3) = (3, y + 3)

This equation represents a pair of coordinates being equated. The left side (2x - 1, -3) means the point with x-coordinate 2x - 1 and y-coordinate -3. The right side (3, y + 3) means the point with x-coordinate 3 and y-coordinate y + 3.

To find the values of x and y that satisfy this equation, we need to equate the corresponding components:

2x - 1 =3   &          -3 = y + 3

2x=3+1                   y=-3-3

2x=4.                      y= -6

x=2

Hence the value of x=2 & y= -6

The correct answer is option c. x=2, y= -6

Given,

f(x) = x , g(x) = x

Then,$(fog)(x)$ is defined as f(g(x))

f(g(x))=f(x)=x

Therefore, (fog)(x)=x

Hence, the correct answer is option a.x

The given equation is:

sin⁡(2x)=1, we need to find the values of x that satisfy this condition within the given options:

sin(2x)=1

We know that

$\sin \theta =1$ when θ=π/2+2nπ, where $n$ is any integer.

Then,

2x=π/2+2nπ

Divide both sides by 2:

x= π/4 + nπ

The correct answer is d. nπ+(−1)^n π/4, where $n$ is any integer. This form accounts for all possible solutions to sin⁡(2x)=1, as x can take values of the form $,\dots$ when $n$ is even (giving +π/4), and $\dots$ when $n$ is odd (giving - π/4).

𝑆𝑖𝑛(tan^−1 𝑥)

let, tan^−1 𝑥 = Θ

x=tanΘ

x= p / b (from Pythagoras theorem)

h=√ (p^2 + b^2 )

h= √ (x^2 + 1^2 )

h=x / √ (x^2 + 1 )

then,

=sinΘ

=p/h

=x / √ (x^2 + 1^2 )

=x / √ (x^2 + 1)

Hence, the correct answer is b. x / √ (x^2 + 1)

2p, p+8, 3p+1 are in A.P

As we know,

b-a=c-b

then,

(p+8)-(2p)=(3p+1)-(p+8)

p+8-2p=3p+1-p-8

-p+8=2p-7

8+7=2p+p

15=3p

p=5

The correct answer is a. 5

Given,

𝑥^2 +2 (𝑘 + 2)𝑥 + 9 𝑘 = 0 is comparing with a^2 + bx + c=0

then, a=1, b=2(k+2), c=9k

For equal roots

b^2 - 4ac =0

(2k + 4 )^2 - 4 x 1 x 9k =0

4k^2 +16k + 16 - 36k = 0

4k^2 - 20k +16 =0

K^2 - 5k + 4 = 0

K^2 - k(4+1) + 4 =0

K^2 - 4k - k + 4 =0

K(k-4) - 1(k - 4) = 0

(K-1)(K-4) =0

either,                         or,

(k-1) =0                   (k-4) =0

K=1                         k=4

Hence, the value of k is 4,1

The correct answer is option a. 4,1

Given,

=(1 + 𝜔 +𝜔^2)(1 + 𝜔 – 𝜔^2 ) ------------(i)

but we know (1 + 𝜔 +𝜔^2) = 0

then equation(i) become

=0 x (1 + 𝜔 – 𝜔^2 )

=0

The correct answer is option a. 0

the equation 𝑎𝑥^2+2h𝑥𝑦+𝑏𝑦^2=0, for the lines to be coincident, the condition ℎ^2 = 𝑎𝑏 must be satisfied.

Let's see the given option

a. ℎ^2 = 𝑎𝑏: This states that the squares of the coefficient ℎ must equal the product of coefficients 𝑎 and 𝑏. This condition ensures that the discriminant of the quadratic equation is zero, meaning the lines are coincident.

b. ℎ^2 > 𝑎𝑏: This would imply that ℎ^2 is greater than 𝑎𝑏, which does not guarantee that the lines are coincident. It suggests a different relationship between ℎ, 𝑎, and 𝑏.

c. ℎ^2 < 𝑎𝑏: Similarly, this does not ensure that the lines are coincident. It suggests a different relationship between ℎ, 𝑎, and 𝑏.

d. ℎ^2 > 0: This condition does not provide enough information about the coefficients 𝑎 and 𝑏 to determine if the lines are coincident. It simply states that ℎ^2 is positive.

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

Given equation is 𝑥^2 + 𝑦^2 =5 comparing with 𝑥^2 + 𝑦^2 =a^2

a^2=5

and given point is (x1,y1)=(2, 1)

using the formula of equation of tangent to the circle is;

X × X1 + Y × Y1 =a^2

X × 2 + Y × 1 = 5

2x + y = 5

Thus the correct answer is option c. 2x + y = 5

FOR SHORTCUT TRICK;

For the given point (2,1), if any of the options satisfy the condition where the left-hand side (LHS) of the equation equals the right-hand side (RHS), then that option is correct. In this case, option c satisfies this condition.

Given function is;

𝑦 =𝑥^3 – 𝑥^2------------(i) and we have to find 𝑑𝑦/𝑑𝑥 = 0  for that differentiate equation (i) with respect to x

dy= (3x^2 - 2x ) dx

dy/dx = (3x^2 - 2x )

According to the questions

dy/dx =0

(3x^2 - 2x ) =0

x(3x -2)=0

either,                            or,

x=0,                            (3x -2)=0

3x= 2

x=2/3

The value of x is 0, 2/3

Hence, the correct answer is option a. 0, 2/3

Given,

𝑦 = 𝑥^3 – 2𝑥 ------------(i)

for point of inflection

y" = 0----------(*)

Differentiate equation(i) with respect to x

y' = 3x^2 -2 ------------------(ii)

Again differentiate equation (ii) with respect to x

y" = 6x

Then equation(*) becomes

y" =0

6x = 0

x= 0

Hence, the correct answer is option a. 0

Given,

Force(F) = (2 𝑖 + 3 𝑗 - 4 𝑘) N

Time(t)=5 seconds

Displacement(s) = (3 𝑖 + 2j - 2 𝑘) m

work done by the force:

W=F⋅s=(2i+3j−4k)⋅(3i+2j−2k) = (2⋅3)+(3⋅2)+(−4⋅−2)=6+6+8=20 Joules

then power,

P=W / t = 20 Joules / 5 seconds = 4 Watts

Therefore, the correct answer is: a. 4

Given,

y1=A1sin⁡(ωt) and y2=A2cos⁡(ωt)

the trigonometric identity that relates sine and cosine:

cos(ωt)= sin(ωt+π/2) -----------(i)

then, by using equation (i)

y2=A2cos(ωt)= A2sin(ωt+π/2)

By comparing the arguments of the sine functions, we see that:

y1=A1sin(ωt) and y2=A2sin(ωt+π/2)

Thus, the phase difference between y1 and y2 is π/2.

Therefore, the correct answer is: c. π/2

To swim across the river by the shortest path, the man must aim upstream to counteract the river's current. Let's analyse the situation:

River Current: The river flows from west to east at 5 m/min.

Swimming Speed: The man can swim at 10 m/min in still water.

To achieve the shortest path (a straight line across the river from south to north), the man must swim in such a way that his resultant velocity is directed straight north. This means he must counteract the eastward component of the river's current.

Let's break it down into vector components:

Eastward Current: 5 m/min

Northward Swimming Speed: 10 m/min

The swimmer needs to swim at an angle θ such that the eastward component of his swimming cancels out the river's current.

Using trigonometry:

The swimmer's eastward component of speed must equal the river's speed.

Let θ be the angle east of north.

The eastward component of his swimming speed is given by:

10sin⁡(θ)=5

sin(θ)= 5/10

θ=sin^−1(0.5)=$30º$

Therefore, the man should swim at an angle of 30° east of north to counteract the river current and achieve the shortest path directly across the river.

The correct answer is: b. 30° East of North

We know,

Surface Tension=Force/Length = [M^1 L T^−2] / [L] = [M^1 T^−2]

But in our questions we have to find the the dimension of surface energy:

[Surface Energy]=[Surface Tension]×[Area]=[M^1 T^−2] × [L^2]= [M^1 L^2 T^−2]

Therefore, the correct dimension for surface energy is: b. [M^1 L^2 T^−2]

The terminal velocity of a small spherical body falling in a viscous fluid can be determined using Stokes' law. According to Stokes' law, the terminal velocity vt of a spherical object falling through a viscous medium is given by:

vt=2r^2(ρs−ρf)g / 9η

where:

$r$ is the radius of the spherical body,

ρs is the density of the sphere,

ρf is the density of the fluid,

g is the acceleration due to gravity,

η is the dynamic viscosity of the fluid.

From this formula, it is clear that the terminal velocity vt is directly proportional to the square of the radius $r$. Therefore, the terminal velocity vt is proportional to r^2.

Thus, the correct answer is: d. r^2

The torque is defined as the rate of change of angular momentum:

τ=dL/dt

Given:

Initial angular momentum, L0

Final angular momentum, 4L0

Time interval, Δt=4 seconds

The change in angular momentum (ΔL) is:

ΔL=4L0−L0=3L0

Now, we use the formula for torque:

τ=dL/dt = 3L0 / 4seconds

So, the magnitude of the torque is:

τ=3L0/4

Therefore, the correct answer is: a. 3L0/4

Given,

Temperature of oxygen(To)=47ºC = (47+273)K=320K

According to the questions,

Crms(o)=Crms(H)

√(3RTo/M) = √(3RTH/M)  where, TH=temperature of hydrogen & To=Temperature of Oxygen

∴ To/Mo=TH/MH where, Mo=Molar mass of oxygen & MH=Molar mass of hydrogen

∴TH=T0.MH/M0=320×2/32=20K

The Temperature of Hydrogen is 20K

Hence, the correct option is c.20K

We know,

Entropy ($S$) is related to heat (Q) and temperature ($T$) through the formula:

ΔS=Q/T

Where:

$Q$ is the heat added or removed (with dimensions of energy),

$T$ is the absolute temperature.

Now, using the formula for entropy:

ΔS=Q/T = [M^1 L^2 T^−2] / [K] = [M^1 L^2 T^−2 K^-1]

Thus, the correct dimensional formula for entropy is: a. [M^1 L^2 T^−2 K^-1]

Given,

Side of the square plate = 2 units,

change in temperature(ΔT)=10ºC

linear expansivity of the material($\alpha )=x$

using the formula for the change in area (ΔA) due to thermal expansion is:

ΔA=2αAΔT --------(i)

Calculate the original area ($A$) of the square plate: A=side^2=2^2=4 units

Now equations(i) becomes,

ΔA=2αAΔT = 2× X × 4 × 10 =80X

Therefore, the correct answer is option: b. 80X

Given,

Initial power P1=2×10^5 Js^−1 m^−2 at T1=127ºC=(273+127)=400K

Final power P2=32×10^5 Js^−1 m^−2

we can use the Stefan-Boltzmann law, which states that the power radiated per unit area by a black body is proportional to the fourth power of its absolute temperature. Mathematically, this is expressed as:

P=σT4

where,

$P$ is the power radiated per unit area,

σ is the Stefan-Boltzmann constant,

T is the absolute temperature in Kelvin.

Using the Stefan-Boltzmann law, the ratio of the powers can be related to the ratio of the temperatures:

p2/p1=(T2/T1)^4

(32×10^5) / (2×10^5) =(T2/400)^4

16=(T2/400)^4

Taking the fourth root of both sides:

(16)^1/4 = (T2/400)

2=(T2/400)

T2=800K

But the given option all are in degree Celsius so we have to change it

Converting back to Celsius:

T2=800 K−273=527ºC

Therefore, the correct answer is: c. 527ºC

When a ray of light travels from one medium to another, such as from air to glass, several properties of the light can change due to the change in medium.

Let's see from the option

a. Wavelength decreases: This is correct. When light enters a denser medium like glass, its speed decreases, and consequently, its wavelength decreases. The relationship between speed, wavelength, and frequency is given by:

v=fλ

where v is the speed of light, $f$ is the frequency, and λ is the wavelength. Since the frequency remains constant when light enters a new medium, a decrease in speed results in a decrease in wavelength.

b. Wavelength increases: This is incorrect. The wavelength of light decreases when it enters a denser medium.

c. Speed increases: This is incorrect. The speed of light decreases when it enters a denser medium like glass.

d. Frequency decreases: This is incorrect. The frequency of light remains constant when transitioning between media.

Hence, the correct answer is option a. wavelength decreases

In a double slit interference experiment, white light (which is composed of all colors) produces a central white fringe at the point of zero path difference. The fringes around the central white fringe are colored due to the different wavelengths of the colors.

White light consists of colors with different wavelengths, with red having the longest wavelength and violet having the shortest. The fringe separation (fringe width) in an interference pattern is given by:

Δy=λD/d

where Δy is the fringe separation, λ is the wavelength of light, D is the distance between the slits and the screen, and $d$ is the distance between the slits.

Since fringe separation is proportional to wavelength, colors with shorter wavelengths will be closer to the central fringe, while those with longer wavelengths will be further away.

Violet has the shortest wavelength, followed by blue, green, and red.

Therefore, the color of the fringe nearest to the central white fringe is violet.

Hence the correct answer is option d. violet

The power of a convex lens changes when it is immersed in water compared to when it is in air,

we need to consider the lens maker's formula:

P=(nlens/nmedium−1)(1/R1−1/R21)

where:

$P$ is the power of the lens,

nlens is the refractive index of the lens material,

nmedium is the refractive index of the surrounding medium (air or water),

R1 and R2 are the radii of curvature of the lens surfaces.

When the lens is in air, nmedium=nair≈1. When the lens is in water, nmedium=nwater≈1.33.

Since the refractive index of the medium has increased (from 1 to 1.33), the term (nlens/nmedium−1) will decrease because nmedium is now larger. As a result, the power $P$ of the lens will decrease when the lens is immersed in water.

This effect will be the same for all colors, although the exact values of refractive indices vary slightly with wavelength (dispersion), the general trend of decreasing power holds true regardless of the color of light.

Hence, the correct answer is option b. Decrease for all colors

Given,

frequency(f)= 1000 Hz

speed of sound in the medium(v)=330 m/s

speed of the observer(vo)=10 m/s

speed of the source(vs)=10 m/s

Using the Doppler effect formula for sound,

When both the source and observer are moving towards each other, the formula for the observed frequency (f′) is:

f′=f{(v+vo)/(v−vs) }

f′=1000{(330+10)/(330-10) }

f′=1000(340/320)

f′=1000×1.0625

f′=1062.5Hz

Hence, the correct answer is option c. 1062.5Hz

For an open pipe (open at both ends), the fundamental frequency is given by:

fopen=v/2Lopen

For a closed pipe (closed at one end), the fundamental frequency is given by:

fclosed=v/4Lclosed

where:

$f$ is the frequency,

v is the speed of sound,

Lopen is the length of the open pipe,

Lclosed is the length of the closed pipe.

If both pipes resonate to the same tuning fork, their fundamental frequencies are equal:

fopen=fclosed

v/2Lopen = v/4Lclosed

4Lclosed=2Lopen

Lopen:Lclosed=2:1

Hence, the correct answer is option b. 2:1

The drift velocity of electrons in a copper wire changes when the radius of the wire is doubled, we need to understand the relationship between drift velocity and the dimensions of the wire.

The drift velocity (vd) of electrons in a conductor is given by the formula:

vd=I / nAe

where:

$I$ is the current,

n is the number of charge carriers per unit volume,

A is the cross-sectional area of the wire,

$e$ is the charge of an electron.

For a cylindrical wire, the cross-sectional area $A$ is given by:

A=πr^2

If the radius ($r$) of the wire is doubled, the new radius r′ is:

r′=2r

The new cross-sectional area A′ is:

A′=π(r′)^2=π(2r)^2=4πr^2=4A

Now, substituting the new area A′ into the drift velocity formula:

vd′=I / nA′e = I / n4Ae = 1/4 x I / nAe = vd/4

Thus, when the radius of the copper wire is doubled, the drift velocity of electrons decreases by a factor of four.

Hence, the correct answer is option c. Decreases four times

In series the bulb with less power glows brightly and in parallel the bulb with more power glows brightly

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

Given

C=1 F

For a spherical capacitor with one conducting sphere and the other sphere at infinity, the capacitance C is given by:

C=4πϵ0R-----------(i)

where:

$C$ is the capacitance,

ϵ0 is the permittivity of free space (8.854×10^−12 F/m),

$R$ is the radius of the spherical conductor.

then equation(i) becomes

1=4πϵ0R

R=1/4πϵ0

R=1/(4π x 8.854×10^−12)

R≈1/111.265×10^−12

R≈8.99×10^9m

This value is much larger than the radius of the Earth (approximately 6.4×10^6 m)

Hence, the correct answer is option d. a sphere having radius of more than that of the Earth

Given:

Coil 1: N1=50 turns and f1=50 Hz

Coil 2: N2=100 turns and f2=150 Hz

The induced emf in a coil rotating in a magnetic field is given by the formula:

E=NABωsin(ωt)

where:

$N$ is the number of turns in the coil,

A is the area of the coil,

$B$ is the magnetic field strength,

ω is the angular velocity (in radians per second).

The angular velocity $\omega$ is related to the frequency f by:

ω=2πf

The induced emf in Coil 1 is:

E1=N1ABω1

E1=50⋅A⋅B⋅2π⋅50

E1=50⋅A⋅B⋅100π

E1=5000ABπ

The induced emf in Coil 2 is:

E2=N2ABω2

E2=100⋅A⋅B⋅2π⋅150

E2=100⋅A⋅B⋅300π

E2=30000ABπ

The ratio of the induced emf in Coil 1 to Coil 2 is:

E1/E2=5000ABπ/30000ABπ = 1/6

Hence, the correct answer is option c. 1:6

Given,

The galvanometer has a full-scale deflection of 100 mA (0.1 A) and a resistance Rg of 1 Ω.

The desired ammeter range is 0-1 A.

The shunt resistor Rs must be chosen so that when 1 A flows through the ammeter, only 0.1 A flows through the galvanometer, and the remaining 0.9 A flows through the shunt resistor.

Current through the galvanometer(Ig)=0.1A

Current through the shunt resistor(Is)=1A−0.1A=0.9A

Voltage across the galvanometer and shunt resistor (they are in parallel) (Vg)=Ig x Rg=0.1×1=0.1V

The voltage across the shunt resistor must also be 0.1 V since they are in parallel:

Vs=Is x Rs

0.1 = 0.9×Rs

Rs=0.1/0.9 = 1/9 ≈0.111Ω

Hence, the correct answer is option c. 0.111 Ω

Specific Charge of a Proton

Charge of a proton (qp): +e (where e=1.6×10^−19 C)

Mass of a proton (mp): 1.67×10^−27kg

The specific charge of a proton (SCp) is:

SCp=qp/mp=(1.6×10^−19 C)/(1.67×10^−27kg)

Specific Charge of an Alpha Particle

An alpha particle consists of 2 protons and 2 neutrons.

Charge of an alpha particle (qα): +2e (since it has 2 protons)

Mass of an alpha particle (mα):The mass of 2 protons and 2 neutrons

mα=2mp+2mn≈4mp

(The mass of a neutron mn is approximately the same as the mass of a proton mp)

The specific charge of an alpha particle (SCα) is:

SCα=qα/mα=2e/4mp = e/2mp