Let see from the option

a. What is your name?

This is a questions, not a statement

b. 100 is a number

It is true;100 is a number so, it is a statement

c. Pokhara is far away

Whether it is true or false it depends on the location

d. Fewa lake is in Kathmandu

It is false because fewa lake is in Pokhara not in Kathmandu

Hence, the correct answer is option b. 100 is a number.

Given,

| x-5 | = 7  we have to find the value of x

As we know that, modulus represents -ve & +ve

taking +ve                                       -ve

+(x-5)=7                                         -(x-5)=7

x=7+5                                            -x + 5 =7

x=12                                             -x=7-5

-x=2

x=-2

Hence, the correct answer is option a. {12,-2}

Given,

f(x)=y=3x-2----------------(i) for x ε R, then f¯¹(7)=?

interchanging x & y, then

y=3x-2

y+2=3x

x=(y+2)/3

f¯¹(x)=(x+2)/3 ---------------(ii)

but we have to find the value of f¯¹(7) for that put x=7 in equation(ii)

f¯¹(7)=(7+2)/3

f¯¹(7)=9/3 = 3

Hence, the correct answer is option c. 3

Given,

f(x)=y= √(x-3) --------------(i)

Domain of f(x) is

inside the square root x-3 must be non-negative because the square root of a negative number is not defined.

x-3≥0

x≥3

Domain of f(x) is [ 3,∞)

Range of f(x) is

f(x)=√(x-3) will produce non-negative value because the square root function always return a non-negative result for non-negative inputs.

if we put x=3 into f(x)

f(3)=√(3-3) = √0 = 0 which is smallest value

If we increase the value of x, x-3 also increase thus √(x-3) also increase

example;

let x=7(which is increases from previous one i.e x=3)

7-3=4(which is increases from previous one i.e x=0

√4 = 2(which is increases from previous one i.e x=0)

There is no upper bound to the value of f(x) because as x->∞ , √(x-3) ->∞

Range of the function,

f(x)=√(x-3) is all non-negative real numbers i.e [0,∞)

Hence, the correct answer is option b.[0,∞)

Given,

f(x)= y=x^4 + 5

From the option

b. x-axis: If the equation of the curve does not change when y is change to -y then,curve is symmetrical about x-axis

so,

-y= x^4 + 5

-y= -(-x^4 - 5)

y= -x^4 - 5 ≠ f(x)

so, it is incorrect

d. y-axis: If the equation of the curve does not change when x is change to -x then, curve is symmetrical about y-axis

so,

y= (-x)^4 + 5

y= x^4 + 5 = f(x)

so, it is correct option

Hence, the correct answer is option d. y-axis

Given,

a,b,c,d,............are in G.S let common ratio be r

b=ar

c=br=ar*r=ar^2

d=cr=ar^2 * r= ar^3

1/a, 1/b, 1/c, 1/d

(1/b) / (1/a) = (1/ar) / (1/a) = 1/r

(1/c) / (1/b) = (1/ar^2) / (1/ar) = 1/r

(1/d / (1/c) = (1/ar^3) / (1/a^2) = 1/r

so,1/a, 1/b, 1/c, 1/d are in G.S

Hence, the correct answer is option a. G.S

Note; If a,b,c are any three  number in G.S then a/b = c/b

If A is a square matrix, then the matrix A+A^T is Symmetrix matrix

Note; A+A^T, AA^T,(A^T)A, A^2 are symmetric matrices for a square matrix

Hence, the correct answer is option b. symmetric

Given,

one root is 1/(3+√5)

α={1/(3+√5)} x {(3-√5)/(3-√5) }

α= {(3-√5)/(3)^2-(√5)^2 }

α= (3-√5)/(9-5)

α= (3-√5)/4

another root be(β) = (3+√5)/4

Sum of roots(α+β)={ (3-√5)/4 } + { (3+ √5)/4 } = (3-√5 +3+√5) / 4 =6/4 = 3/2

product of roots(α.β)={ (3-√5)/4 } x { (3+ √5)/4 } = (9-3√5 +3√5+(√5)^2) / 4^2 =(9-5)/16 = 4/16 = 1/4

now, the quadratic equation is

x^2- (α+β)x + α+β=0

x^2-3/2 * x + 1/4 =0

4x^2 - 6x + 1 = 0

Hence, the correct answer is option d. 4x^2 - 6x + 1 = 0

Given,
{(i-1) / (i+1) } ^ k
let see from the option,
a. 2
then,
={(i-1) / (i+1) } ^ 2
={(i-1)^2 / (i+1)^2 }
={(i^2 - 2i + 1 )/ (i^2 + 2i + 1) }               we know, i^2 =-1
={(-1 - 2i + 1 )/ (-1 + 2i + 1) }
= -2i/2i
= -1
which is negative no need to check other option it is the smallest number
Hence, the correct answer is option a. 2

Given,

distance is √2 units and

the line is x+y=1

x+y-1=0

From option

a. (0,-1) and (0,-3)

finding the distance using both point

at point (0,-1)                                                      at point (0,-3)

d=| ( 1*0 + 1*(-1) - 1 ) / (√1^2 + 1^2) |           =   | ( 1*0 + 1*(-3) - 1 ) / (√1^2 + 1^2) |

=| ( 0 - 1 - 1 ) / (√2) |                                        =    | ( 0 - 3 - 1 ) / (√2) |

=| -2 / (√2) |                                                      =  4 /√2

=(√2 * √2 ) / √2

=√2

Here, only (0,-1)  gives distance √2 which is same as in questions but not other point i.e (0,-3). so, it is incorrect option

Likewise

d. (0,-1) and (0,3)

finding the distance using both point

at point (0,-1)                                                      at point (0,3)

d=| ( 1*0 + 1*(-1) - 1 ) / (√1^2 + 1^2) |           =   | ( 1*0 + 1*(3) - 1 ) / (√1^2 + 1^2) |

=| ( 0 - 1 - 1 ) / (√2) |                                        =    | ( 0 + 3 - 1 ) / (√2) |

=| -2 / (√2) |                                                      =  2 /√2

=(√2 * √2 ) / √2                                                =(√2 * √2 ) / √2

=√2                                                                   =√2

Here, both points  (0,-1) and (0,3)  gives same distance √2 which is same as in questions  so, it is correct option

Hence, the correct answer is option d. (0,-1) and (0,3)

Given,

kx^2 + xy - y^2 + 2x - y = 0 comparing with ax^2 + 2hxy + by^2 + 2gx +2fy+c = 0 then,

a=k, b= -1, c=0, 2h=1                 2f= -1

h=1/2               f= -1/2

For general equation

ax^2 + 2hxy + by^2 + 2gx +2fy+c = 0 represent a pair of straight line is

abc + 2fgh- af^2- bg^2 - ch^2 =0

or, k*(-1)*0 + 2*(-1/2)*1*1/2 - k*(-1/2)^2 - (-1)*(1)^2 - 0*(1/2)^2 = 0

or, -1/2 -k/4 +1 =0

or,  -2-k+4=0

or, -k+2=0

or, -k= -2

k=2

Hence, the correct answer is option b. 2

Given,

the direction cosines of lines are 2,3,-6 and represented by l, m and n

l^2 + m^2 + n^2 =1

l=2/ (√ 2^2 + 3^2 + (-6)^2 )   =2/√4+9+36  = 2/√49  = 2/7

m=3/7

n= -6/7

The direction cosines of the lines are (2/7 , 3/7, -6/7 )

Hence, the correct answer is option d. (2/7 , 3/7, -6/7 )

For the vector to be linearly independent, the only solution to the equation xp+ yq+ zr = 0 must be x=0, y=0,z=0

Hence, the correct answer is option c x=0, y=0, z=0

Given,

Once dice has=6 face

Two dices has = 6*6 = 36

the pairs that gives the sum which are less than 4 are {(1,1),(1,2),(2,1)}

probability of getting the sum less than 4 is

P(Sum less than 4) = Number of favourable outcomes / Total number of possible outcomes = 3/36 = 1/12

Hence, the correct answer is option b. 1/12

Given,

y=x^4 - 6x^2 +8x---------(i)

differentiate equation(i) with respect to x

y' = 4x^3 - 12x +8 ----------(ii)

again, differentiate equation(ii) with respect to x

y'' = 12x^2 - 12

for point of inflection

y'' = 0

12x^2 - 12 = 0

12(x^2 - 1)=0

x^2 - 1=0

x=1,-1

Hence, the correct answer is option c. 1,-1

Given,

Force(F)= 10N

Angle of inclination with the horizontal(θ)=45°

for vertical component of a force(Fy)=?

we know that,

Fy=Fsinθ

=10 x sin 45°

=10 x 1/√2

=(5 x 2) / √2

=(5 x √2 x √2) / √2

Fy=5√2N

The resolved part of the force in the vertical direction is 5√2N

Hence, the correct answer is option c. 5√2N

Given,

Initial Velocity(vo)=20 m/s

Inclination of the plane(θ)=30°

Acceleration due to gravity(g)=10 m/sec^2

The component of gravitational acceleration acting down the inclined plane is

a=gsinθ

a=10 x sin 30

a=10 x 1/2

a=5m/s^2

The ball is projected up the incline so, this acceleration will act as a deceleration.

We can use the kinematic equation to find the distance travelled before the ball comes to the rest.

v^2 = (u0)^2 + 2ad

or, 0 = (20)^2 + 2 x (-5) x d    ( where acceleration will be negative due to deceleration)

or, 0 = 400 - 10d

or, 10d = 400

d= 400/10 = 40m

Hence, the correct answer is option d. 40m

Let's see from the given option

a. Energy: The unit of energy is the joule (J). But we have to find the joule x second so, it is incorrect answer

b. Momentum: The unit of momentum is kilogram meter per second (kg m/s).But we have to find the joule x second so, it is incorrect answer

c. Angular momentum: The unit of angular momentum is joule second (J x S).This is because angular momentum is defined as the product of moment of inertia and angular velocity.

d. Power: The unit of power is the watt (W), which is equivalent to joules per second (J/s) but But we have to find the joule x second so, it is incorrect answer

Hence, the correct answer is option c. Angular momentum

Given equation F=q(v×B) describes the force F on a charged particle moving with velocity v in a magnetic field B, known as the Lorentz force equation

In this equation:

$\mathbf{F}$ is the force on the particle.

q is the charge of the particle.

v is the velocity of the particle.

B is the magnetic field.

v×B represents the cross product of the velocity and the magnetic field vectors

The cross product v×B yields a vector that is perpendicular to both v and B. Therefore, the resulting force $\mathbf{F}$ is also perpendicular to both $\mathbf{v}$ and $\mathbf{B}$.

Hence, the correct answer is option c. perpendicular to both v and B.

To determine the height at which the two balls collide, we need to analyse their motions. Let's denote the time of collision after the first ball is shot as $t$. Given that the second ball is shot 2 seconds later, its time of travel until collision is t−2.

Motion of the first ball:

The equation for the height h1 of the first ball after $t$ seconds is:

h1​=v0​t−1/2​gt^2

where v0=40 m/s (initial velocity) and $10$ m/s^2 (acceleration due to gravity).

Motion of the second ball:

The equation for the height h2 of the second ball after t−2 seconds is:

h2​=v0​(t−2)−1/2​g(t−2)^2

Setting the heights equal:

Since the balls collide at the same height,

h1=h2​

40t−5t^2=40(t−2)−5(t−2)^2

40t−5t^2=40t−80−5(t^2−4t+4)

40t−5t^2=40t−80−5t^2+20t−20

40t−5t^2=40t−5t^2+20t−100

0=20t−100

$20t=100$

t=5 seconds

Height of collision:

Now, substituting t=5 seconds into the height equation for the first ball:

h1​=40(5)−1/2​⋅10⋅(5)^2

h1​=200−25⋅5

h1​=200−125

h1​=75 meters

Therefore, the two balls collide at a height of: 75m

Hence, the correct answer is option a. 75m

When a cricketer hits a cricket ball at an angle of 45° to the horizontal with kinetic energy $K$, we need to analyse the kinetic energy of the ball at the highest point of its path.

Initial Kinetic Energy:

The initial kinetic energy $K$ can be expressed as:

K=(1 x mv^2 )​/2

where $m$ is the mass of the ball and $v$ is its initial velocity.

Components of Velocity:

Since the ball is hit at an angle of 45°:

The horizontal component of the velocity is vx=vcos⁡(45°)=v/√2

The vertical component of the velocity is vy=vcos⁡(45°)=v/√2

Kinetic Energy at the Highest Point:

At the highest point of its path, the vertical component of the velocity vy​ becomes zero, and only the horizontal component vx remains.

The kinetic energy at the highest point is due to the horizontal component of the velocity:

K highest​=(1 x mvx^2 ) / 2

​where, vx=v/√2

K highest​=(1/2 x m) x (v/√2 ) ^2

K highest​=(1/2 x m) x (v^2/2 )

K highest​=(1/4 x m v^2) 

Since the initial kinetic energy $K$ is: (1 x mv^2 ) / 2

The kinetic energy at the highest point is half of this initial kinetic energy:

K highest​= (1/4 x m v^2) = K/2

Therefore, the kinetic energy of the ball at the highest point of its path is:K/2

Hence, the correct answer is option b. K/2

When an object is at rest or stationary on a surface, the force of friction that prevents the object from moving is called static friction. Static friction can vary in magnitude up to a maximum value known as the limiting friction. This maximum value of static friction is what prevents the object from starting to move when a force is applied to it.

Static friction is the frictional force that exists between a stationary object and the surface it rests on.

The maximum value of static friction that can be exerted before the object starts to move is called limiting friction.

Limiting friction depends on the nature of the surfaces in contact and the normal force pressing the surfaces together.

Hence, the correct answer is option b. Limiting friction

India's Chandrayaan-3 mission successfully landing near the south pole of the Moon and its rover has confirmed the presence of hydrogen and oxygen. This information aligns with the findings from previous lunar missions and studies, where significant amounts of water ice (H2O) have been detected in the polar regions of the Moon.

Key points:

(i) Hydrogen and oxygen are fundamental components of water (H2O).

(ii) The detection of hydrogen and oxygen near the south pole of the Moon suggests the presence of water ice.

(iii) Water ice is crucial for future lunar exploration and potential habitation efforts, as it can be a vital resource for producing drinking water, breathable oxygen, and rocket fuel (hydrogen and oxygen can be split via electrolysis to produce hydrogen fuel and oxygen for life support and propulsion).

Hence, the correct answer is option b. Hydrogen and oxygen

When the girl drinks water from the lake while sitting in a boat, the displacement of water in the lake remains the same. This is due to the principle of displacement, which states that when an object (in this case, the boat with the girl) is placed in water, it displaces an amount of water equal to its own volume.

Key points to consider:

The girl drinking water from the lake does not change the total volume of water displaced by the boat in the lake.

According to Archimedes' principle, the buoyant force (or the weight of the water displaced) acting on the boat remains constant unless the volume of water displaced changes.

Therefore, the level of water in the lake will remain unchanged because the amount of water displaced by the boat (and thus the boat's weight) does not change when the girl drinks water.

Let's see from the given option

Option a. Increase: Drinking water does not cause the lake's water level to rise.

Option b. Decrease: Similarly, drinking water does not cause the lake's water level to decrease.

Option d. May increase or decrease depending upon the weight of the girl: This is not correct because the displacement of water by the boat depends on its volume, not the weight of the girl.

Hence, the correct answer is option c.Remain unchanged.

Fire alarms typically work based on the principle of detecting smoke or heat, and in many cases, they utilize a detector that operates using the expansion of gas due to heat. This type of detector is commonly found in smoke alarms and fire detection systems.

Volume expansion of gas: When gas is heated, its molecules gain kinetic energy and move faster, causing them to exert greater pressure on their surroundings and thus expand in volume. This principle is utilized in fire alarms where a gas-filled chamber (such as in ionization smoke detectors) expands when exposed to heat or smoke, triggering the alarm mechanism.

Let's see from the given option

Option a. Volume expansion of solid: While solids do expand with heat, this principle is not typically used in fire alarms.

Option b. Volume expansion of water: Water expands when heated, but this principle is more relevant to issues like thermal expansion in pipes, not fire alarm systems.

Option d. Bimetallic bar which becomes curved on heating: Bimetallic strips curve due to differential expansion of two metals with different coefficients of thermal expansion. While this principle is used in some types of thermostats, it is not directly related to fire alarm systems.

Hence, the correct answer is option c. volume expansion of gas.

When relative humidity is high, the body's ability to cool itself through evaporation of sweat is significantly reduced. This is because high humidity means that the air already contains a high amount of moisture, making it harder for sweat to evaporate from the skin. As a result, the sensation of heat is more intense even if the actual air temperature is the same.

Key points to consider:

Relative humidity is a measure of how much moisture the air contains relative to the maximum amount it could hold at that temperature.

When relative humidity is high (close to 100%, as in 99%), sweating becomes less effective because the air is nearly saturated with moisture.

As a climber at the base camp of Mount Everest, where temperatures can be quite low, feeling the hottest would be more related to the humidity affecting the body's ability to cool down rather than the absolute temperature itself.

Lower relative humidity levels (like 50%, 30%, or 10%) would allow for more effective evaporation of sweat, which helps in cooling the body, thus reducing the sensation of heat.

Hence, the correct answer is option a. 99%

When using a microscope to focus on objects through a glass plate, the observed displacement in focus can be related to the refractive index of the glass.

Here are the key points to understand the solution:

1.Effect of glass plate on focusing:

When the microscope is initially focused on an ink mark (presumably beneath the glass plate), the microscope needs to be raised by 1 meter to focus properly.

When focusing on a scratch on the upper surface of the glass plate, an additional 2 meters of raising is required.

2. Relationship with refractive index:

The difference in raising the microscope (1 meter vs. 2 meters) is due to the thickness of the glass plate and the refractive index of the glass.

The refractive index (n) of the glass affects the apparent depth or position of the objects observed through it.

According to optics principles, if the thickness of the glass plate is t and the refractive index of the glass is n, the effective path length through the glass is not.

3.Calculation:

From the problem, the difference in focusing (1 meter vs. 2 meters) suggests that the thickness of the glass plate affects the microscope's focus due to refraction.

By comparing the given options, a refractive index of approximately 1.50 (option b) typically corresponds to the level of displacement mentioned (1 meter vs. 2 meters).

Hence, the correct answer is option b.1.50

When the aperture of a lens decreases, it affects several aspects of the image formation

Position of the image: The position of the image refers to where the image appears relative to the lens. A decrease in aperture (making it smaller) can affect the depth of field and the focus of the image. It can shift the apparent position of the image due to changes in how light rays converge after passing through the lens.

Size of the image: The size of the image refers to how large or small the image appears relative to the object being photographed. A smaller aperture can lead to changes in magnification and resolution, affecting the size of the image formed on the sensor or film.

Intensity of the image: The intensity of the image refers to the brightness or exposure of the image. While decreasing the aperture reduces the amount of light passing through the lens, it doesn't directly change the intensity of the image formed because exposure can be compensated by adjusting shutter speed or ISO sensitivity.

Since a decrease in aperture affects both the position (due to changes in focus and depth of field) and the size (due to changes in magnification and resolution) of the image formed by the lens, the correct answer is d. Both position and size of the image.

Hence, the correct answer is option d. Both position and size of the image.

Sound waves can propagate through rocks in both longitudinal and transverse forms, depending on the nature of the wave and the characteristics of the medium (in this case, the rock).

Longitudinal elastic wave:

In a longitudinal wave, the particles of the medium oscillate back and forth in the direction parallel to the direction of energy propagation.

Sound waves in rocks can generate longitudinal waves where compressions (regions of high pressure) and rarefactions (regions of low pressure) propagate through the rock parallel to the direction of the wave.

Transverse elastic wave:

In a transverse wave, the particles of the medium oscillate perpendicular to the direction of energy propagation.

While less common for sound waves in rocks, certain geological events or structures can generate transverse waves, also known as shear waves, where particles move perpendicular to the direction of the wave propagation.

Both longitudinal and transverse waves in rocks: Rocks, being elastic solids, can support both types of waves depending on the conditions. Longitudinal waves are more typical for sound propagation, but transverse waves can occur under specific circumstances (such as seismic events or in specific rock formations).

Stationary waves: Stationary waves are not typically how sound propagates through rocks. They are formed by the interference of two waves traveling in opposite directions and are more characteristic of specific resonant conditions rather than general sound propagation in rocks.

Hence, the correct answer is option c. Both longitudinal and transverse elastic wave.

When comparing a solid sphere and a hollow sphere with the same radius, both have the same surface area available for charge distribution. The charge storing capacity, or the amount of charge that can be held by an object, depends primarily on its surface area rather than its volume

Key points to consider:

1. Surface area and charge distribution:

The amount of charge that an object can hold depends on how much charge it can distribute over its surface.

Both the solid sphere and the hollow sphere with the same radius will have the same surface area exposed to the surroundings.

Therefore, they can hold an equal amount of charge because the charge resides on the surface of the object.

2. Effect of shape and volume:

While the volume of the hollow sphere is larger than that of the solid sphere (since it has a cavity inside), this extra volume does not contribute to the charge holding capacity directly.

In both cases, the charge resides on the outer surface, and the surface area of the spheres, which is the same in this scenario, determines the charge storing capability.

Let's see from the given option

Option a. Solid Sphere: While a solid sphere has a higher density of material compared to a hollow sphere, this does not affect the charge holding capacity as it is determined by the surface area.

Option b. Hollow Sphere: The presence of a cavity inside a hollow sphere does not increase its charge holding capacity beyond what its surface area allows.

Option d. Charge storing capacity depends upon surface temperature: Surface temperature can affect the conductivity and potential distribution of an object, but it does not directly determine the amount of charge an object can hold.

Hence, the correct answer is option c. Both will hold equal charges

To draw maximum current from a combination of cells, connecting them in parallel is the most effective method. Here’s why:

Parallel Connection: When cells are connected in parallel:

Each cell maintains the same voltage as it would individually.

The current capacity of the combination increases because the currents from each cell add together.

This configuration allows for the maximum total current output from the combination of cells.

Series Connection: When cells are connected in series:

The voltage of each cell adds up, resulting in a higher total voltage output.

However, the current remains the same across all cells in the series.

Drawing maximum current from series-connected cells is limited by the cell with the lowest capacity or internal resistance.

Mixed (Series-Parallel) or Both (a) & (b): While a mixed (series-parallel) configuration or using both series and parallel connections can provide a balance between voltage and current, when the goal is specifically to maximize current, parallel connection is the straightforward and effective choice.

Therefore, for drawing maximum current from a combination of cells, option b. parallel is the correct answer. This configuration allows each cell to contribute its full current capacity, resulting in the highest possible total current output from the combination.

Hence, the correct answer is option b. parallel

When two parallel wires carry currents in the same direction, they create magnetic fields around them according to Ampère's right-hand rule. These magnetic fields interact with each other, resulting in an attractive force between the wires. This force is due to the interaction of the magnetic fields generated by the currents flowing through each wire.

Key points to consider:

1. Magnetic fields and currents:

A current flowing through a wire generates a magnetic field around the wire.

When two wires carry currents in the same direction and are placed parallel to each other, the magnetic fields generated by these currents interact with each other.

The magnetic fields created by the currents in both wires will exert attractive forces on each other.

2. Nature of the force:

This attractive force between the parallel wires is purely magnetic in nature and is a manifestation of the Lorentz force law, which describes the force on a charged particle due to electromagnetic fields.

The force is not due to a potential difference (option a), mutual inductance (option b), or electric force (option c) between the wires but specifically arises from the magnetic fields interacting with each other.

Therefore, the correct answer is d. Magnetic forces between them, as this correctly identifies the physical phenomenon responsible for the attractive force observed between parallel wires carrying currents in the same direction.

Hence, the correct answer is option d. Magnetic forces between them

Given:

Emf (ε) = 2 volts

Initial current (I₁) = 3 A

Final current (I₂) = 2 A

Time interval (Δt) = 1 millisecond = 0.001 seconds

we can use the formula relating the induced electromotive force (emf), rate of change of current, and self-inductance:

E=−L x dI /dt -----------(i) 

for  dI /dt,

dI /dt= ( I₂ - I₁ ) / (Δt) =(2A-3A)/(0.001s) =−1000A/s

then equation (i) become

E=−L x dI /dt

or, 2= -L x (−1000A/s)

L= 2V/1000A/s

L=0.002H

Convert henries to millihenries (mH):

L=0.002H=2mH

Hence, the correct answer is option b.2 mH

Given:

Voltage across the inductance (V_L) = 60 volts

Voltage across the resistance (V_R) = 40 volts

Voltage across the capacitor (V_C) = 30 volts

The supply voltage (V_supply) can be calculated as:

𝑉 =√{(V_R)^2 +(V_L - V_C)^2 }

(since inductor and capacitor potentials are out of phase with each other)

𝑉 =√{(40)^2 +(60 - 30)^2 }

𝑉 =50 volts

Hence, the correct answer is option c.50 volts

The Earth's magnetic field is primarily generated by the motion of molten iron and nickel in its outer core. This motion creates electric currents through the process of convection and the Coriolis effect, known as the geodynamo process. The movement of these conductive materials generates electric currents, which in turn produce magnetic fields through the dynamo effect.

Key points to consider:

1.Geodynamo process:

The Earth's outer core is composed primarily of molten iron and nickel.

The rotation of the Earth and convective motion within the outer core generate electric currents.

These electric currents generate magnetic fields according to the principles of electromagnetism.

2. Cosmic rays and solar influence:

Cosmic rays and solar activity can interact with the Earth's magnetic field, affecting phenomena like auroras, but they do not generate the Earth's magnetic field itself.

Solar activity and cosmic rays can disturb the Earth's magnetic field temporarily, but they are not the primary source of its generation.

3. Buried magnetic dipole or induction by the Sun:

Option c (a strong magnetic dipole buried at the center of the Earth) is not correct. The Earth's magnetic field is not attributed to a single magnetic dipole buried within the Earth.

Option d (strong induction effect of the Sun) is also incorrect. While solar activity can influence the Earth's magnetic field, it does not create the Earth's magnetic field itself.

Hence, the correct answer is option a. Motion and distribution of materials in and around the Earth

When a free charged particle moves through a magnetic field, it experiences a force known as the magnetic Lorentz force. This force is given by:

F=qv×B

where:

𝐹  is the magnetic force acting on the particle,

𝑞 is the charge of the particle,

𝑣 is the velocity vector of the particle,

𝐵 is the magnetic field vector.

1.Force direction:

The direction of the magnetic force F is perpendicular to both the velocity vector v of the particle and the magnetic field B.

As a result, the magnetic force changes the direction of motion of the charged particle rather than its speed or energy directly.

2. Effect on speed and energy:

The magnetic force does not change the speed (option a) or the energy (option b) of the charged particle directly. Instead, it causes the particle's path to curve in a plane perpendicular to the magnetic field lines.

The kinetic energy of the particle remains constant if no other forces are acting on it besides the magnetic force.

3. Pressure and other considerations:

Option c, pressure, is not affected by the magnetic force on a single charged particle moving through a magnetic field.

The primary effect observed is the deflection or change in direction of motion of the charged particle due to the magnetic force.

Hence, the correct answer is option d. direction of motion

Therefore, the speed of the electron in the first excited state of a doubly ionized lithium atom is 1.5v

Hence, the correct answer is option c. 1.5v

"

Nuclear holocaust" refers to the catastrophic aftermath of a large-scale nuclear explosion or series of explosions. It involves the widespread destruction caused by the detonation of nuclear weapons, leading to devastating effects such as:

1. Massive loss of life: Immediate deaths due to the blast, heat, and radiation, followed by long-term health impacts from radiation exposure.

2. Environmental devastation: Severe damage to ecosystems, contamination of air, soil, and water with radioactive fallout.

3. Social and economic collapse: Disruption of essential services, displacement of populations, and breakdown of societal structures.

This term is used to describe the extreme consequences of nuclear warfare or a large-scale nuclear accident, highlighting the potential for global devastation and long-lasting effects on human civilization and the environment.

Hence, the correct answer is option d. After math of a nuclear explosion

While J. Robert Oppenheimer is most famously known for his role in the development of the atomic bomb during the Manhattan Project, his broader scientific contributions extended beyond just the bomb. However, focusing on the options provided:

Nuclear Reactor Physics (Option a): Oppenheimer made significant contributions to theoretical physics, including work on quantum mechanics and nuclear physics. Although he is most famously associated with the atomic bomb, his contributions also impacted the understanding and development of nuclear reactors, which utilize controlled nuclear reactions for energy production.

AK-47 Rifle (Option b) and Bullet Dynamics (Option c): These options are unrelated to Oppenheimer's work. They pertain to firearms and ballistics, which are not areas of expertise or contribution for Oppenheimer.

Design of Atom Bomb (Option d): This option is not entirely accurate in the context of the choices provided because Oppenheimer's direct involvement was more in the theoretical and leadership aspects of the atomic bomb project rather than the detailed design aspects.

Therefore, considering Oppenheimer's overall scientific career and the options provided, a. Nuclear Reactor Physics best represents his broader scientific contributions, which include significant work in nuclear physics beyond just the atomic bomb.

Hence, the correct answer is option a. Nuclear Reactor Physics

Hence, the correct answer is option b.70 seconds

This truth table corresponds to the AND gate. An AND gate outputs 1 only when both inputs are 1, and 0 otherwise. The table matches the behavior of an AND gate, where Y=A⋅B.

Hence, the correct answer is option d.AND gate

1. Electrons vs. Holes Mobility:

Electrons are the charge carriers in NPN transistors.

Holes are the charge carriers in PNP transistors.

Electrons have higher mobility compared to holes because electrons, being smaller and lighter particles, can move more quickly through a semiconductor material than holes, which are effectively the absence of electrons and move more sluggishly.

2. Performance Implications:Higher mobility of electrons leads to faster response times and better performance in high-frequency applications. This makes NPN transistors more efficient in switching and amplification applications.

3. Other Factors:

Low cost: Both NPN and PNP transistors can be manufactured at low costs; cost is not the main differentiating factor.

Low dissipation of energy: While energy dissipation is important, it is not the primary reason for preferring NPN over PNP.

Capable of handling larger power: NPN transistors are not necessarily capable of handling more power than PNP transistors; power handling depends more on the specific design and application.

Therefore, the primary reason for preferring NPN transistors over PNP transistors is the higher mobility of electrons compared to holes, which results in better performance characteristics.

Hence, the correct answer is option d. Electrons have high mobility than holes and hence high mobility of energy

From option

a. Antoine Laurent de Lavoisier:

Antoine Laurent de Lavoisier, a French chemist, is often referred to as the "Father of Modern Chemistry".

In 1789, Lavoisier formulated the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction. This principle laid the foundation for modern chemistry and helped to establish the concept that the total mass of reactants in a chemical reaction is equal to the total mass of the products.

b. Joseph Louis Proust:Joseph Louis Proust is known for his work on the Law of Definite Proportions (or Proust's Law), which states that a chemical compound always contains the same proportion of elements by mass.

c. John Dalton:John Dalton is famous for his atomic theory, which proposed that all matter is composed of atoms, indivisible and indestructible particles. He also contributed to the Law of Multiple Proportions.

d. Niels Bohr:Niels Bohr is known for his model of the atom, particularly for introducing the theory that electrons travel in specific orbits around the atom's nucleus and for his work on quantum mechanics.

Hence, the correct answer is option a. Antoine Laurent de Lavoisier

Expected vs. Actual Configuration:

Based on the aufbau principle, one might initially expect the electronic configuration of copper (Cu) to be [Ar] 3d^9 4s^2

However, the actual electronic configuration is [Ar] 3d^10 4s^1

Stability Considerations:

In transition metals, achieving a fully filled or half-filled d-subshell provides extra stability.

For copper, a fully filled 3d subshell (3d^10) is more stable than a partially filled one (3d^9).

This stability is due to the exchange energy and the overall lower energy state that results from a fully filled d-subshell.

Electron Configuration of Copper:

Copper (atomic number 29) has the following actual electronic configuration: [Ar] 3d^10 4s^1.

The single electron in the 4s orbital is paired with the completely filled 3d orbital, resulting in a more stable electronic arrangement.

Hence, the correct answer is option b. [Ar] 3d^10 4s^1

Definition of Electronegativity:

Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons.

It is a dimensionless quantity and is usually measured on the Pauling scale.

Electronegativity Trends in the Periodic Table:

Electronegativity increases across a period from left to right.

Electronegativity decreases down a group.

This trend occurs because as you move across a period, atoms have more protons, which increases their positive charge and attracts electrons more strongly. As you move down a group, the addition of electron shells increases the distance between the nucleus and the valence electrons, reducing the nucleus's pull on the electrons.

from the given option

Chlorine (Cl): Chlorine is very electronegative with a value of about 3.16 on the Pauling scale, but it is not the most electronegative element.

Oxygen (O): Oxygen has a high electronegativity of about 3.44 on the Pauling scale.

Fluorine (F): Fluorine is the most electronegative element with a value of 3.98 on the Pauling scale. This is because fluorine is at the top of the halogen group and has the highest ability to attract electrons in a bond.

Nitrogen (N): Nitrogen also has a high electronegativity of about 3.04 on the Pauling scale but is less than fluorine and oxygen.

Hence, the correct answer is option c. Fluorine

Valence Shell Electron Pair Repulsion (VSEPR) Theory:

VSEPR theory is used to predict the shape of molecules based on the repulsion between electron pairs around a central atom.

Electron pairs (bonding and lone pairs) repel each other and arrange themselves as far apart as possible to minimize repulsion.

Structure of Ammonia (NH3):

Central Atom: Nitrogen (N) is the central atom in NH3_33​.

Valence Electrons: Nitrogen has 5 valence electrons.

Bonding and Lone Pairs: In NH3​, nitrogen forms three single bonds with hydrogen atoms and has one lone pair of electrons.

Electron Pair Geometry:The electron pair geometry around nitrogen is tetrahedral because there are four regions of electron density (three bonding pairs and one lone pair).

Molecular Shape:

The molecular shape of NH3​ is determined by the positions of the atoms, ignoring the lone pairs.

The lone pair on nitrogen exerts a repulsive force that pushes the hydrogen atoms closer together, resulting in a trigonal pyramidal shape.

Bond Angles: The lone pair-bond pair repulsion is stronger than bond pair-bond pair repulsion, causing the H-N-H bond angles to be slightly less than the ideal tetrahedral angle of 109.5°. In NH3​, the bond angles are approximately 107°.

Hence, the correct answer is option d. pyramidal

Copper sulphate commonly exists as a hydrated compound with water molecules associated with it. The chemical formula for hydrated copper sulphate is:

Copper(II) sulfate pentahydrate: CuSO4⋅5H2O

Hydrated Form:

In this form, each copper sulfate molecule is associated with five water molecules.

This hydrated form is often called "blue vitriol" or "bluestone" due to its blue color.

Structure:

The five water molecules are coordinated to the copper ion and integrated into the crystal lattice of the compound.

Four of the water molecules are directly bonded to the copper ion, while the fifth is hydrogen-bonded in the crystal structure.

Importance of Hydration:

The hydration is crucial for the properties of the compound, including its color and crystalline structure.

When heated, the hydrated copper sulphate loses water molecules and turns into anhydrous copper sulphate (CuSO4​), which is white.

Hence, the correct answer is option a. 5.

Definition of Brass:

Brass is a metallic material composed of a combination of two or more elements, specifically copper and zinc.

It is created by melting and mixing these metals together, forming a solid solution when cooled.

Nature of Brass:

Alloy: An alloy is a mixture of two or more elements, where at least one of them is a metal. Alloys are designed to have specific properties that are different from their constituent elements.

Brass is specifically an alloy because it is made by combining two metals (copper and zinc) to achieve desired properties like increased strength, corrosion resistance, and workability.

Comparison with Other Options:

Metalloid: Metalloids are elements that have properties intermediate between metals and non-metals. Examples include silicon and arsenic. Brass is not an element, so it cannot be a metalloid.

Non-metal: Non-metals are elements that lack the properties of metals. Examples include carbon and sulphur. Brass is not a non-metal because it is a mixture of metals.

Alkali Metal: Alkali metals are elements found in Group 1 of the periodic table, such as lithium, sodium, and potassium. Brass is not an element, so it cannot be an alkali metal.

Hence, the correct answer is option b. alloy

The ring test is a qualitative test used to detect the presence of nitrate ions (NO3^-​) in a solution. During this test, the nitrate ion is reduced to nitric oxide (NO), which then reacts with ferrous sulphate (FeSO4) to form a brown ring.

The brown ring formed during the ring test for nitrate is due to the formation of the complex compound FeSO4.NO

Hence, the correct answer is option c. FeSO4.NO

Kipp's apparatus is a piece of laboratory equipment used for generating gases on demand through the reaction of a solid and a liquid. It is designed to safely and conveniently produce gases that are required in small quantities.

Usage:

Components of Kipp's Apparatus:

Three Chambers: The apparatus typically consists of three chambers. The upper chamber holds the solid reactant, the middle chamber collects the generated gas, and the lower chamber contains the liquid reagent.

Stopcock: A stopcock or valve is used to control the flow of the liquid reagent to the solid reactant.

Operation:

The liquid reagent is allowed to flow into the upper chamber where it reacts with the solid reactant, producing a gas.

The generated gas accumulates in the middle chamber and can be drawn off as needed.

Preparation of Hydrogen Sulphide (H2S):

Reaction: Hydrogen sulfide gas is commonly prepared using Kipp's apparatus by reacting iron(II) sulfide (FeS) with dilute hydrochloric acid (HCl).

                      FeS+2HCl→FeCl2​+H2​S

Process: In the apparatus, iron(II) sulphide is placed in the upper chamber, and dilute hydrochloric acid is placed in the lower chamber. When the acid is allowed to contact the iron(II) sulphide, hydrogen sulphide gas is produced.

From other option

Cl2​ (chlorine): Chlorine gas is typically prepared by other methods, such as the reaction of hydrochloric acid with potassium permanganate.

SO2​ (sulphur dioxide): Sulphur dioxide is often prepared by burning sulphur or heating sulphite compounds with an acid.

CO2 (carbon dioxide): Carbon dioxide can be produced by reacting a carbonate or bicarbonate with an acid, often done in simpler setups than Kipp's apparatus.

Hence, the correct answer is option is d. H2S (hydrogen sulphide).

Chlorophyll is the green pigment found in plants, algae, and cyanobacteria, which is crucial for photosynthesis. The central metal ion in the chlorophyll molecule is magnesium (Mg^2+). This magnesium ion plays a vital role in the chlorophyll molecule by coordinating with the nitrogen atoms of the porphyrin ring, helping to stabilize the structure and enabling it to effectively absorb light energy, which is then used to convert carbon dioxide and water into glucose and oxygen during photosynthesis.

Let's see from the option

Ca^2+ (Calcium): Calcium is not a part of the chlorophyll molecule but is important in other plant functions, such as maintaining cell wall structure and signaling.

Ba^2+ (Barium): Barium is not involved in chlorophyll or plant physiology in any known biological capacity.

Cu^2+ (Copper): Copper is essential for plant enzymes and is involved in photosynthesis, respiration, and other biochemical processes, but it is not a component of chlorophyll.

Hence, the correct answer is option a. Mg^2+.

The tetrahedral structure of carbon was independently proposed by Jacobus Henricus van 't Hoff and Joseph Achille Le Bel in 1874. They suggested that the four valence bonds of carbon are directed toward the corners of a regular tetrahedron. This concept was a ground breaking idea that explained the three-dimensional arrangement of atoms in organic molecules, particularly in explaining the phenomenon of optical activity in stereochemistry.

Let's see from the option

Linus Pauling: Linus Pauling made significant contributions to the understanding of chemical bonding and molecular structures, including the concept of hybridization, but he did not propose the tetrahedral structure of carbon.

Robert Corey: Robert Corey worked closely with Linus Pauling and made significant contributions to the understanding of protein structures, particularly the alpha helix and beta sheet, but he did not propose the tetrahedral structure of carbon.

James Watson: James Watson is best known for his role in the discovery of the double helix structure of DNA, not for proposing the tetrahedral structure of carbon.

Hence, the correct answer is option b. van't Hoff and Le Bel.

The Haber process, also known as the Haber-Bosch process, is an industrial method used for the synthesis of ammonia from nitrogen and hydrogen gases. This process was developed by Fritz Haber and later scaled up by Carl Bosch. The chemical reaction for the Haber process is:

N2​(g)+3H2​(g)↔2NH3​(g)

This reaction takes place at high temperatures (about 400-500°C) and high pressures (about 150-200 atmospheres) in the presence of an iron catalyst. The ammonia produced is primarily used for the manufacture of fertilizers, which are essential for modern agriculture.

Let's see from the option

Sulphuric acid: Sulphuric acid is produced by the Contact process, not the Haber process.

Nitric acid: Nitric acid is produced by the Ostwald process, which involves the oxidation of ammonia.

Sodium hydroxide: Sodium hydroxide is typically produced by the chloralkali process, which involves the electrolysis of sodium chloride (salt) solution.

Hence, the correct answer is option c. ammonia.

Benzene was first isolated by Michael Faraday in 1825. Faraday discovered benzene in an oily residue that remained from the production of illuminating gas, which was derived from whale oil. He identified it as a distinct hydrocarbon compound and named it "bicarburet of hydrogen," which was later named benzene.

Let's see from the option

Berzelius: Jöns Jacob Berzelius was a prominent chemist who developed the modern system of chemical notation and made significant contributions to chemical theory, but he did not isolate benzene.

Cavendish: Henry Cavendish was a British scientist known for his discovery of hydrogen and his research into the composition of water and air, but he did not isolate benzene.

Wöhler: Friedrich Wöhler is best known for his synthesis of urea, which was a significant milestone in organic chemistry, but he did not isolate benzene.

Hence, the correct answer is option d. Faraday

Prussian blue is a complex compound with the chemical formula Fe₄[Fe(CN)₆]₃. It is a dark blue pigment used in paints, inks, and dyes. Prussian blue is formed by the reaction of ferric ions (Fe³⁺) with ferrocyanide ions ([Fe(CN)₆]⁴⁻).

Let's see from the option

Na₄[Fe(CN)₆]: This is sodium ferrocyanide, which is a different compound and not Prussian blue.

Fe(CNS)₃: This is ferric thiocyanate, which is another different compound and not related to Prussian blue.

Na₂[Fe(CN)₅NO]: This is sodium nitroprusside, which is used as a medication and in analytical chemistry, but it is not Prussian blue.

Hence, the correct answer is option a. Fe₄[Fe(CN)₆]₃.

The Uranium series, or the uranium-radium series, which starts with uranium-238 (U-238) and ends with lead-206 (Pb-206), is characterized by isotopes with mass numbers that follow the pattern 4n+2. This series is one of the three classical radioactive decay series.

Let's see from the option

a. 4n: This is associated with the Uranium series (also known as the Uranium-radium series), but it was incorrectly listed in the previous responses. The correct designation for the Uranium series is $4n+2$.

c. (4n+1): This series is related to the Neptunium series, which begins with neptunium-237.

d. (4n+3): This series is related to the Actinium series, which starts with actinium-227.

Hence, the correct answer is option b. (4n+2)

Bakelite is a type of condensation polymer. It is made through the condensation polymerization of phenol and formaldehyde. In this process, phenol and formaldehyde react to form Bakelite, releasing water as a by product. This reaction results in a network polymer with strong, three-dimensional cross-linking, giving Bakelite its durable and heat-resistant properties.

Let's see from the option

a. Polystyrene: Polystyrene is a type of addition polymer, not a condensation polymer. It is produced by the polymerization of styrene monomers without the release of any by products.

b. Teflon: Teflon, or polytetrafluoroethylene (PTFE), is also an addition polymer. It is made from the polymerization of tetrafluoroethylene monomers and does not involve condensation or the release of by products.

d. Polyvinyl chloride (PVC): PVC is another addition polymer. It is made from the polymerization of vinyl chloride monomers without the release of by products.

Hence, the correct answer is option c. Bakelite.

Transition elements, which are the elements found in the d-block of the periodic table, are known for exhibiting a range of oxidation states. This property arises because transition metals have partially filled d orbitals, allowing them to lose different numbers of electrons and thus show multiple oxidation states. For example, iron can exist in the +2 and +3 oxidation states, and copper can exist in the +1 and +2 oxidation states.

Let's see from the option

a. exhibit inert pair effect: The inert pair effect is generally associated with post-transition metals (such as those in the p-block) and not with transition metals. It refers to the tendency of the s-electrons in the outermost shell to remain non-bonding or "inert" in heavier elements.

b. have low melting points: Transition metals generally have high melting points due to the strong metallic bonding caused by the presence of d electrons. For example, tungsten has one of the highest melting points of any metal.

c. do not show catalytic activity: Transition metals are well-known for their catalytic activity. Many transition metals and their compounds act as catalysts in various chemical reactions. For example, platinum and palladium are used in catalytic converters in cars to reduce emissions.

Hence, the correct answer is option d. exhibit variable oxidation states.

Corrosive sublimate is the common name for mercury(II) chloride (HgCl₂). This compound is known for its high toxicity and corrosive properties. It is called "corrosive sublimate" because it can sublime, meaning it can transition directly from a solid to a gas without becoming liquid, and it is highly corrosive.

Let's see from the option

Hg₂Cl₂: This is mercury(I) chloride, also known as calomel. It is less corrosive and not referred to as "corrosive sublimate."

HgI: This is mercury(I) iodide. It is not associated with the term "corrosive sublimate."

HgO: This is mercury(II) oxide. It is a solid and does not have the sublimation property associated with "corrosive sublimate."

hence, the correct answer is option a. HgCl2

When ethanol (CH₃CH₂OH) reacts with potassium dichromate (K₂Cr₂O₇) in the presence of sulfuric acid (H₂SO₄), the ethanol is oxidized to acetic acid (CH₃COOH). The reaction proceeds through the intermediate formation of acetaldehyde (CH₃CHO), which is then further oxidized to acetic acid. This is a common reaction in organic chemistry where a primary alcohol is oxidized to a carboxylic acid.

The balanced chemical equation for the overall reaction is:

3 CH3​CH2​OH+K2​Cr2​O7​+4 H2​SO4​→3 CH3​COOH+K2​SO4​+Cr2​(SO4​)3​+7 H2​O

Let's see from the option

a. CH₃COCH₃: This is acetone, a ketone, which is not formed in this reaction. Ethanol cannot be oxidized to acetone directly.

c. HCHO: This is formaldehyde, which is not a product of ethanol oxidation. Formaldehyde is typically formed by the oxidation of methanol.

d. CH₃COOCH₂CH₃: This is ethyl acetate, an ester. Esters are not formed by the oxidation of ethanol with potassium dichromate in the presence of sulfuric acid.

Hence, the correct answer is option b. CH₃COOH

Formic acid is the simplest carboxylic acid, and its IUPAC name is methanoic acid. The name "methanoic acid" is derived from "methane," the simplest alkane, with the "-e" ending replaced by "-oic acid" to denote that it is a carboxylic acid.

Let's see from the option

a. ethanoic acid: This is the IUPAC name for acetic acid (CH₃COOH), which has one more carbon atom than formic acid.

b. propanoic acid: This is the IUPAC name for propionic acid (CH₃CH₂COOH), which has two more carbon atoms than formic acid.

d. butanoic acid: This is the IUPAC name for butyric acid (CH₃CH₂CH₂COOH), which has three more carbon atoms than formic acid.

Hence, the correct answer is option c. methanoic acid.

Ammoniacal silver nitrate solution, commonly known as Tollen's reagent, is a chemical reagent used to test for the presence of aldehydes. Tollen's reagent is prepared by dissolving silver nitrate (AgNO₃) in water, adding ammonia (NH₃) until the precipitate of silver oxide (Ag₂O) dissolves, forming a clear solution containing the diamminesilver(I) complex [Ag(NH₃)₂]⁺.

When Tollen's reagent is added to an aldehyde, the aldehyde is oxidized to a carboxylic acid, and the silver ions in the reagent are reduced to metallic silver, forming a characteristic silver mirror on the inner surface of the reaction vessel. This reaction does not occur with ketones, which makes Tollen's reagent a specific test for aldehydes.

Let's see from the option

a. Bayer's reagent: Bayer's reagent is a solution of potassium permanganate (KMnO₄) used to test for unsaturation (double bonds) in organic compounds.

b. Schiff's reagent: Schiff's reagent is used to detect aldehydes as well, but it consists of a solution of rosaniline dye decolorized by sulfur dioxide.

c. Fehling's solution: Fehling's solution is a mixture of copper(II) sulfate, sodium potassium tartrate, and sodium hydroxide, used to test for the presence of reducing sugars.

Hence, the correct answer is option d. Tollen's reagent.

When nitrobenzene is reduced in a neutral medium, the primary product is phenyl hydroxylamine (C₆H₅NH(OH)). This reduction typically involves partial reduction of the nitro group (-NO₂) to a hydroxylamine group (-NHOH).

Let's see from the option

b. aniline: Aniline (C₆H₅NH₂) is typically formed when nitrobenzene is reduced in acidic or strongly basic conditions, not in a neutral medium.

c. hydrazobenzene: Hydrazobenzene (C₆H₅NHNH₂C₆H₅) is generally formed under conditions involving prolonged reduction and is more likely to form in strongly basic or acidic media.

Hence, the correct answer is option a. phenyl hydroxylamine.

When a ketone reacts with a Grignard reagent (RMgX), the reaction typically proceeds through nucleophilic addition of the Grignard reagent to the carbonyl carbon of the ketone, forming a tertiary alcohol after hydrolysis.

Here is the general reaction mechanism:

1. The Grignard reagent (RMgX) adds to the carbonyl group of the ketone (R'COR'') to form an alkoxide intermediate.
2. The intermediate is then protonated during the acidic work-up (usually with water or dilute acid) to yield the tertiary alcohol.

The overall reaction can be represented as:

R2CO+R’MgX→R2C(OMgX)R’→R2​C(OH)R’

Let's see form the option

a. primary alcohol: A primary alcohol is typically formed when a formaldehyde (H₂CO) reacts with a Grignard reagent.

c. secondary alcohol: A secondary alcohol is formed when an aldehyde (RCHO) reacts with a Grignard reagent.

d. carboxylic acid: Carboxylic acids are not formed in this reaction. A carboxylic acid can be formed if carbon dioxide (CO₂) reacts with a Grignard reagent.

Hence, the correct answer is option b. tertiary alcohol.

Potassium permanganate (KMnO₄) is not considered a primary standard substance. A primary standard substance is a reagent that is pure, stable, non-hygroscopic, and has a known high molar mass. It should also be easy to weigh accurately. Primary standards are used in titrations to determine the concentration of solutions.

Here's why KMnO₄ is not a primary standard:

KMnO₄ (Potassium permanganate): It is not a primary standard because it is not stable in solution. KMnO₄ tends to decompose over time, and its solutions are also prone to reacting with organic material and other impurities, which can affect its concentration.

Let's see from the option

(COOH)₂ (Oxalic acid): Oxalic acid is a primary standard because it is available in a pure form, stable, and can be accurately weighed.

K₂Cr₂O₇ (Potassium dichromate): Potassium dichromate is a primary standard because it is pure, stable, and has a high molar mass. It is often used in redox titrations.

NaCl (Sodium chloride): Sodium chloride is a primary standard because it is available in a pure form, is stable, and can be accurately weighed.

Hence, the correct answer is option c. KMnO4

Molecularity of a reaction refers to the number of reactant molecules involved in an elementary step of a reaction. While molecularity is a theoretical concept that describes the mechanism of a reaction, it is not a factor that directly influences the rate of reaction in a practical sense. Instead, molecularity is a characteristic of the reaction mechanism and is determined by how the reaction proceeds on a molecular level.

Let's see from the option

a. Concentration: The concentration of reactants directly affects the rate of reaction. According to the rate law, the rate of reaction is proportional to the concentration of the reactants raised to some power. Generally, increasing the concentration of reactants increases the frequency of collisions between them, thereby increasing the reaction rate.

b. Temperature: Temperature significantly affects the rate of reaction. Increasing the temperature typically increases the reaction rate because it raises the kinetic energy of the molecules, leading to more frequent and more energetic collisions, which in turn increases the likelihood of reactant molecules overcoming the activation energy barrier.

c. Nature of reactants: The nature of the reactants, including their physical state, chemical properties, and bond strengths, influences the reaction rate. For example, reactions involving ionic compounds in aqueous solutions tend to proceed faster than those involving covalent compounds because ions in solution are more readily available to collide and react.

Hence, the correct answer is option d. molecularity

Intensive properties are characteristics of a substance that do not depend on the amount of matter or the size of the sample. These properties are intrinsic to the substance itself and remain constant regardless of the sample size.

Let's see from the option

a. Density: Density is defined as mass per unit volume (density = mass/volume). It is an intensive property because it does not change with the amount of the substance. For instance, the density of water remains 1 g/cm³ whether you have a small glass of water or a large tank of water.

b. Mass: Mass is an extensive property because it depends on the quantity of matter. The total mass of a substance increases with the size of the sample.

c. Volume: Volume is also an extensive property. It depends on the amount of matter present, and it increases with the quantity of the substance.

d. Enthalpy: Enthalpy is an extensive property because it is related to the total amount of matter in a system. The enthalpy of a system increases with the size of the system.

Hence, the correct answer is option a. density

Predicament refers to a difficult, unpleasant, or embarrassing situation.

Quandary means a state of perplexity or uncertainty, which is very similar in meaning to predicament.

Hence, the correct answer is option d. quandary

Preferment refers to the action of promoting or advancing someone to a higher position or rank.

Promotion means the act of raising someone to a higher position, which aligns closely with the meaning of preferment.

Hence, the correct answer is option c. promotion

Gainsay means to deny or contradict something.

Deny means to state that something is not true, which is the same as gainsaying.

Hence, the correct answer is option b. deny

Agnosticism is the belief that the existence or non-existence of God is unknown or unknowable.

Atheism is the belief that God does not exist.

Monism refers to the belief in the unity of everything into a single reality or substance.

Hence, the correct answer is option c. agnosticism

Nihilism is the belief that life is meaningless and rejects all religious and moral principles.

Morbid refers to an abnormal and unhealthy interest in disturbing and unpleasant subjects, especially death and disease. It can also mean related to or affected by disease.

Healthy is the opposite of morbid as it denotes a state of physical and mental well-being, free from illness or abnormal conditions.

Hence, the correct answer is option a. healthy

Sophism is a fallacious argument, often used to deceive or manipulate.

Pluralism is a belief in diversity or multiple perspectives.

Pacifism is the belief in avoiding violence and conflict.

Hedonism is the pursuit of pleasure as the highest good.

Hence, the correct answer is option d. sophism

Esteem means to regard someone with respect and admiration.

Insult means to speak to or treat someone with disrespect or contempt, which is the opposite of showing esteem.

Hence, the correct answer is option b. insult

Hold back means to restrain oneself or not reveal one's feelings or intentions. It fits the context of being unsure of how someone will react.

Hence, the correct answer is option a. Hold back

Clear off: This phrasal verb means to leave or go away from a place, often implying that you are removing yourself from it. In the context of telling children to take their football and "clear off," it means to go away from the area.

Clear up: This phrasal verb means to tidy or make something clear, which does not fit the context of leaving or going away.

Clear in: This is not a commonly used phrasal verb in this context. It does not fit the intended meaning of leaving.

Clear out: This phrasal verb generally means to remove or dispose of things from a place, which is not the most appropriate in the context of telling children to take their football and leave.

Hence, the correct answer is option b. clear off

Surrendered to means to give up or yield to someone.

Waited for means to stay in anticipation of something.

Hence, the correct answer is option b. to, for

From: Indicates movement or transition between one place and another.

For: Indicates the purpose of quick supervision and attending to business.

Hence, the correct answer is option c. from, for

At: Used to indicate focus or direction toward something, such as fault or errors.

The sentence would be: "Everybody winks at one's fault and laughs at others' errors."

Hence, the correct answer is option d. at, at

To carry the day means to achieve victory or success in a particular situation or contest. It implies winning or succeeding.

Hence, the correct answer is option a. to be victorious

Prosecution is pronounced as /ˌprɒsɪˈkjuːʃən/. The primary stress is on the fourth syllable, which is "cu".

Here’s how the stress pattern breaks down:

pro (unstressed)

si (unstressed)

cu (stressed)

tion (unstressed)

The primary stress is on "cu" in "prosecution," making the stress on the 4th syllable.

Hence, the right answer is option c. 4th syllable

"If only" is used to express a wish or a hypothetical situation that is not currently true but is desired. It implies that something would be better or different if the condition were met. In this case, it expresses a wish that the person would drive more slowly.

The sentence would be: "We will follow him if only he would drive more slowly."

Let's see from the option

a. in case: This is used to talk about a possible situation or condition that might happen, but it doesn’t convey the sense of a strong wish or hypothetical situation. For example, "Take an umbrella in case it rains."

b. even if: This is used to indicate that something will happen regardless of the condition. It does not convey a sense of wishing or desiring a condition to be true. For example, "I will go to the party even if it rains."

d. but for: This is used to express a condition that would have led to a different result. It implies that if not for a particular factor, something else would happen. For example, "But for his help, I would have failed."

Hence, the correct answer is option if only

a. Generative Pre-trained Transformer
This is because ChatGPT is based on a type of AI model called a Transformer, and it’s pre-trained on a large dataset to generate responses.

Hence, the correct answer is option a. Generative Pre-trained Transformer

MS-DOS is primarily a command-line interface operating system, where users interact with the system by typing text commands. It does not have a graphical user interface (GUI) or support multitasking in the modern sense. It also does not use a menu-driven interface as its primary method of interaction.

Hence, the correct answer is option a. Command Line Interface

a. Python
Python is widely used in AI and machine learning due to its simplicity and the extensive libraries available, such as TensorFlow, Keras, and PyTorch.

Hence, the correct answer is option a. Python

b. Landing safely on the moon's surface
AI is utilized in Chandrayaan-3 for navigating and safely landing on the moon's surface, ensuring the lander can adjust its trajectory and avoid obstacles.

Hence, the correct answer is option b. Landing safely on the moon's surface

c. Router
Routers operate at the network layer (Layer 3) of the OSI model and are responsible for directing data packets between devices on different networks.

Hence, the correct answer is option c. Router

Let's convert the given binary into decimal

=1011

=1 x 2^3 + 0 x 2^2  + 1 x 2^1 + 1 x 1^0

=8+0+2+1

=11

and for 1111

=1 x 2^3 + 1 x 2^2  + 1 x 2^1 + 1 x 1^0

=8+4+2+1

=15

Hence, the given binary code 1011 and 1111 of decimal value is 11 and 15

Hence, the correct answer is option c. 11 and 15

a. System file
The .BAT extension stands for batch file, which is a type of script file in DOS and Windows used to automate tasks. It can contain a sequence of commands for execution by the command interpreter.

Hence, the correct answer is option a. System file

b. Cripper is the correct answer.

Crippler is considered one of the earliest known computer viruses, appearing in the early 1980s. It is widely recognized as one of the first examples of a computer virus in the wild.

Let's see from the option:

Cripper: Released in the early 1980s, it is often cited as one of the first viruses.

Blaster: Also known as MSBlast or Lovsan, it was a significant worm that spread in 2003.

Sasser: A worm that appeared in 2004, following Blaster.

Mydoom: A worm that emerged in 2004, after Blaster and Sasser.

Hence, the correct answer is option b. Cripper