By law of momentum

1500×10 = 1000×13+500xv

3 × 10 = 2 × 13 + v

v = 30-26 = 4m/s

=76

its the unit of momentum
P=mv
p=kg m/s
and 
P is also equal to impulse which is 
F.t
alternate unit is 
Ns

Displacement can equal to distance but can never greater than distance

The acceleration due to gravity is always 9.8 m/s/s, regardless of the ball's velocity. A person drops a ball from rest, and the ball accelerates downward at a rate of 9.8 m/s2.

Initial velocity, $u=20m{s}^{-1}$
Acceleration due to gravity, $g=-10m{s}^{-2}$

At maximum height, velocity will be zero, (v = 0) as the ball will change the direction of motion. Let the maximum height be $H$.
Using third equation of motion,
${\mathrm{v2}}^{}={\mathrm{u2}}^{}+2aH$
$0={202}^{}+2\times (-10)\times H$
$H=20m$

Newton second law explain the concept of Force

F=ma

u = 4m/s           

v=0           
t=2sec
a=?

v=u+at
0=8+a(2)
a=−4m/s2
so,
F = ma
=4×4=16N

According to Newton's third law, the forces on the two objects are equal in magnitude and opposite in reaction. Such forces cause one object to gain momentum and the other object to lose momentum such that total momentum of the system remains conserved in absence of any external force.

Hence, newton's third law of motion leads to law of conservation of momentum.

Acceleration of the body must be zero i.e
a=0
because it is moving with constant velocity.
a=F/m
F=ZERO
because acceleration is zero

Momentum doesn’t change i.e. (2m)*(v/2). K.E decreases by half while P.E becomes twice the original value.

as we know
Slope of Work-Time Graph=Power
so 
According to Question: 
Power/t=5
so, P/2=5
P=10 watts

The most commonly used unit is Joules;
erg is also a unit of energy and it is equal to 10^-7 Joules. 

Energy = Power x time so the units are kWh (kilo Watt hour).

Apply law of momentum conservation

3mv = m*0 + 2mv'

v= 2v'/3

v' = 3v/2

friction is not a conservative force. A conservative force is path-independent and only depends on the object's location. Since the amount of work done by friction is dependent on the direction, it is non-conservative.

Work-energy principle is valid regardless of any non conservative force. A s long as we are using the work done by the resultant force the work energy theorem is valid. Hence work-energy theorem is valid in the presence ofall types of forces i.e External force, Internal force and Conservative force.

NOTE: it's a Recall Based MCQs (Just remember it)

Acceleration = Aω²sin ωt The phase difference between acceleration and velocity is π/2.

In one complete cycle, the particle comes back to the initial velocity. Displacement is zero, therefore average velocity is also zero.

In a SHM in one time period particle covers a distance equal to oabcd as shown in the figure below.

The distance traveled from o to a is equal to the amplitude of the motion i.e. A.

Also, distance traveled in path (oa = ab = bc = cd) = amplitude = A

Hence total distance covered by particle = distance traveled in path (oa+ab+bc+cd )= A+A+A+A = 4A

l=2λ/2
l=λ

3λ/2=L
λ=2L/3

For frequency of oscillation of wire n∝√T.

Here T is tension in the wire. In order to increase frequency twice, tension needs to be made 4 times.

So, new tension must be 4×10=40N

Video Solution:

In a stretched string only transverse wave can exist because compression and rarefraction is not possible in stretched string.

we can apply Doppler's effect to both Light waves and Sound waves

Since there is no no relative motion between the listener and source, hence actual frequency will be heard by listener.

At the nodes, the magnitude of the slope of the waveform is maximum.

Thus, the value of load to stretch the string will be maximum, so strain will be maximum at nodes.

Amplitude is minimum at the nodes.
Strain is minimum at the anti-nodes.

Nodes (N): The points where the amplitude is minimum are called nodes.
The distance between two successive nodes is λ/2.
Nodes are at permanents rest.
At nodes air pressure and density both are high.
Antinodes (A): The points of maximum amplitudes are called antinodes.

The distance between two successive nodes is λ/2.
At nodes air pressure and density both are low.
The distance between a node (N) and adjoining antinode (A) is λ/4.

First Law of Thermodynamics:

• The change of internal energy is a path independent function and depends upon the initial and final position.
• Mathematically, Change in the heat is given as 

ΔU = Q - W

Q is net heat transfer, w is work done on the system.​

Heat Transfer:

When the temperature is increasing, then the change in heat is positive. If the temperature is decreasing then the change in heat is negative.

Work done: Work is done when there is a change in volume. It is positive when the volume is increasing.

Explanation:

The First Law of Thermodynamics is:

ΔU = Q - W

Where:
ΔU = change in internal energy
Q = heat added to the system
W = work done by the system

This law states that energy can neither be created nor destroyed, only transformed from one form to another. This is the principle of conservation of energy.

The $P-V$ diagram of adiabatic process, isothermal process and isobaric process are shown in (figure).

Work done in process= area enclosed by $P-V$ diagram with volume axis.
Since area under the curve is maximum for adiabatic process, so work done on the gas will be maximum for adiabatic process.

Internal energy depends only on the initial and final states of temperature and not on the path. 

In a cyclic process, as initial and final states are the same, change in internal energy is zero (ΔE = 0).

Hence E is ΔU, the change in internal energy.

ΔQ = ΔU + ΔW

ΔW = ΔQ - ΔU

= 410 - 40 = 370 J

Pili or fimbriae are protein structures that extend from the bacterial cell envelope for a distance up to 2 μm. They function to attach the cells to surfaces

the oxygen producing bacteria is cyanobacteria. in the beginning of great transition that changed the condition on earth permanently. cyanobacteria raised the level of oxygen from 1% to 21%

In alpha protobacteria many species are associated with eukaryotic hosts such as symbiotic association of rhizobium species with the roots of leguminous plants for the fixation of atmospheric nitrogen

Most capsules are hydrophilic (“water-loving”) and may help the bacterium avoid desiccation (dehydration) by preventing water loss. Capsules can protect a bacterial cell from ingestion and destruction by white blood cells (phagocytosis).

Methanogens are microorganisms that thrive in strict anaerobic (oxygen-free) environments, such as the digestive tracts of animals, wetlands, and deep-sea sediments. They produce methane gas (CH4) as a metabolic byproduct in the absence of oxygen

The outer tissue of the cambium develops into the phloem tissue, which is responsible for the transport of sugars and other organic compounds throughout the plant. Phloem tissue is composed of several different types of cells, including sieve tube elements, companion cells, fibers, and parenchyma cells.

The guard cells in monocots may be elongated or dumbbell-shaped, and they are typically surrounded by two subsidiary cells, which help to regulate the opening and closing of the stomata.

Chlorosis in plants can be caused by the deficiency of various nutrients, including nitrogen (N) and magnesium (Mg).

Nitrogen is an essential macronutrient that is required by plants for various physiological functions, including the production of chlorophyll. When plants lack sufficient nitrogen, they cannot produce enough chlorophyll, which leads to the yellowing of leaves.

Magnesium is also a macronutrient that is required by plants for the proper functioning of chlorophyll. Magnesium is a central atom in the chlorophyll molecule, and its deficiency can lead to the yellowing of leaves.

The inner wall of guard cells in plants is generally thick and non-elastic. This feature helps maintain the shape and turgidity of the guard cells, which is essential for their role in regulating the opening and closing of stomata.

In dicot plants, the guard cells are typically kidney-shaped. These kidney-shaped guard cells surround the stomata, which are small openings in the leaf epidermis.

The first vaccine was developed by Edward Jenner, an English physician, in 1796.

Jenner is credited with developing the first vaccine for smallpox, a highly infectious and deadly disease that killed millions of people over the centuries. Jenner observed that milkmaids who had contracted cowpox, a less severe disease, seemed to be protected from smallpox. He tested his theory by inoculating a young boy with cowpox and then exposing him to smallpox. The boy did not develop smallpox, and Jenner concluded that cowpox could protect against smallpox.

Rheumatoid arthritis is an autoimmune disease that causes chronic inflammation in the joints and other parts of the body.In rheumatoid arthritis, the immune system mistakenly attacks the body's own tissues, particularly the synovial membrane that lines the joints. This leads to inflammation, which can cause pain, swelling, stiffness, and reduced mobility in the affected joints

The BCG vaccine is a live attenuated vaccine.

The BCG vaccine, which stands for Bacille Calmette-Guérin, is a vaccine that is used to protect against tuberculosis (TB). It is made from a weakened form of Mycobacterium bovis, which is a related bacterium to the one that causes TB in humans.

During apoptosis, the infected cell undergoes controlled self-destruction, which helps eliminate the intracellular virus and limits the infection's progression.

Natural killer (NK) cells are a type of lymphocyte, a white blood cell involved in the immune system. They recognize and eliminate infected or abnormal cells, such as cancer cells and virus-infected cells. NK cells are part of the innate immune response and act as a rapid defense mechanism.

When someone gets a splinter or cut, neutrophils are attracted to the site of injury by a process called "chemotaxis." Chemotaxis is the movement of cells, particularly white blood cells like neutrophils, in response to chemical signals released by damaged tissues or pathogens.

monocytes are a type of white blood cell that is released from the bone marrow. They are a crucial part of the immune system and play a role in defending the body against infections and other foreign invaders

esterase, phosphatase and peptidases are the example of hydrolases

a heterogenous group of enzyme which convert one isomer into another isomeric form is called isomerase. e.g mutase

hexokinase is the first enzyme used in glycolysis.Hexokinase is a protein which is classified under the main grouping of atransferase enzyme

first enzyme was discovered by Anselme Payen in 1833 and the enzyme was carbohydrate digesting enzyme called diastase

Sea urchins belong to the phylum Echinodermata, which also includes other familiar marine animals such as starfish, sand dollars, sea cucumbers, and brittle stars. Echinoderms are characterized by their unique radial symmetry, which is usually pentaradial in adults, as well as their endoskeleton of calcareous plates or ossicles.

Glochidium larva is a specialized larval stage that is present in some species of freshwater mussels, which are a type of bivalve mollusk. The glochidium larvae of these mussels attach themselves to the gills or fins of a suitable fish host and then develop into a juvenile mussel. However, not all mollusks have glochidium larvae. The presence of glochidia is a characteristic feature of some freshwater mussels, and other types of mollusks have different types of larval stages

only mammals have non nucleated RBC's while fish, amphibians, reptiles and birds have nucleated RBC's

The body of echinoderms may be

1. flattened like biscuit for example cake urchin
2. star shaped with short arms for example star fish
3. globular for example sea urchin

so option d all of these will be correct

Animals of the phylum Cnidaria, formerly known as Coelenterata, are typically included in the grade Radiata. Radiata is a grade that describes animals with radial symmetry, which includes organisms like jellyfish, corals, and sea anemones.

Parazoa are simple, multicellular animals thought to have evolved from protozoa. They include organisms like sponges and placozoans, characterized by a lack of true tissues and organs, making them some of the most primitive multicellular animals

Explanation:

Hodgkin's disease, or Hodgkin's lymphoma, can indeed result in the enlargement of lymph nodes in various parts of the body, including the neck. Enlarged lymph nodes in the neck are a common symptom of Hodgkin's disease

Explanation:

Large lymphatic vessels that collect lymph from smaller lymphatic vessels are typically referred to as "lymphatic trunks." These lymphatic trunks converge and eventually form the two main lymphatic ducts in the body: the thoracic duct and the right lymphatic duct

Explanation:

lymph nodes in the axillary region are located in the underarm or armpit area. These axillary lymph nodes are an essential part of the lymphatic system and play a crucial role in filtering and draining lymph from the upper extremities

Explanation:

Lymph vessels have masses of connective tissue called "lymph nodes" at certain points along their course. Lymph nodes are small, bean-shaped structures that are part of the lymphatic system.

lymphatic ducts were first discovered in liver

The ventricles of the heart are the lower chambers, and they are larger and thicker-walled compared to the atria. The left ventricle is typically thicker and more muscular than the right ventricle because it pumps oxygenated blood to the body's systemic circulation, which requires more force.

Explanation:

The myocardium is the middle layer of the heart wall and consists of specialized cardiac muscle cells responsible for contracting and pumping blood throughout the body. These muscle fibers in the myocardium are responsible for the heart's rhythmic contractions

Explanation:

The myocardium is the layer of the heart that contains the contractile element of the heart. It is made up of specialized cardiac muscle cells (cardiomyocytes) responsible for the contraction of the heart

The heart has three main layers: the outermost epicardium, the middle myocardium (which is responsible for pumping blood), and the inner endocardium. The endocardium is a smooth, thin, and delicate lining that covers the heart's chambers and valves

The human heart is found in the thoracic cavity . The heart is positioned slightly to the left of the midline, so it is more commonly felt and heard on the left side of the chest. It is located between the two lungs and sits behind the sternum (breastbone)

Membrane carbohydrates play a crucial role in endocytosis, pinocytosis, and phagocytosis by serving as recognition and signaling molecules. 

in cytosol some large molecules form colloidal solution which is of two type i-e sol (non -viscous) or gel ( jelly like or viscous). often the outer region of cytoplasm is more gel like 

membrane proteins makes plasma membrane selectively permeable barrier that select materials according to the cell's need

the secondary wall follows the order of  primary wall in development. it is laid down inside the primary wall

primary cell wall is the first wall formed in a developing cell. it is usually 1-3μm in thickness. more or less elastic and extendable , crystalline and optically active

Cellulose and chitin are indigestible polysaccharides for humans due to their complex structures.Both lack the specific enzymes needed for efficient breakdown in the human digestive system.

Explanation:

sucrose is hydrolyzed into its constituent monosaccharides, glucose and fructose. This hydrolysis reaction involves breaking the glycosidic bond that connects the glucose and fructose molecules in sucrose

Explanation:

• Oligosaccharides are carbohydrates made up of 2 to 10 monosaccharide units.

• The most common type of oligosaccharides are disaccharides, which are composed of two monosaccharides joined by a glycosidic bond.

Examples of common disaccharides:

• Sucrose = Glucose + Fructose

• Lactose = Glucose + Galactose

• Maltose = Glucose + Glucose

Explanation:

Protoplasm cannot survive if its water content is reduced as low as 10%

Explanation:

Carbohydrates are called "hydrated carbon" due to their composition of carbon, hydrogen, and oxygen in a 2:1 ratio, similar to water. They are also referred to as "polyhydroxy aldehydes and ketones" because they contain multiple hydroxyl groups (-OH) and either an aldehyde or ketone functional group, defining their chemical structure. 

Van Niel used the similarities between the process of photosynthesis in plants and in green and purple sulfur bacteria to propose that the oxygen produced by plants came from water.

HIV is surrounded by a coat of lipoprotein known as the viral envelope or membrane. This envelope is derived from the host cell membrane as the virus buds out of the infected cell during its replication cycle.the envelope is studded with viral glycoproteins, including gp120 and gp41, which are essential for attaching to and fusing with host cell receptors during the process of viral entry.

The core of the HIV virus is formed from a protein called p24 (also known as the Capsid protein). The p24 protein is a product of the gag gene of HIV, and it plays a central role in the structure and function of the viral core.

Explanation:

HIV (Human Immunodeficiency Virus) replicates using a process that involves the conversion of its RNA genome into DNA. This conversion is carried out by an enzyme called reverse transcriptase.

Explanation:

HIV (Human Immunodeficiency Virus) is a retrovirus, and its structure includes various proteins. One of these proteins is p17, also known as the HIV Matrix protein.

Tobacco mosaic virus (TMV; Tobamovirus, Virgaviridae) is a rodlike virus with a length of 300 nm and diameter of 18 nm.

HINT: The rate of reaction is affected by all these factors.

HINT: Use general expression for second order kinetics.

STEP 1:  The reaction X → Y follows second order kinetics.

Rate = k[X]²

STEP 2: If concentration of X increases 3 times i.e. [X'] = [3X]

Rate = k [X']² = 9 K[X]²

Hint: Intermediate formed in the first reaction and consumed in the second reaction

An intermediate is a molecule that is formed from two or more reactants and then reacts further to give products. An intermediate may be an unstable molecule (a reactive intermediate) or a highly stable molecule. 

Intermediate consumed in the reaction. It cannot be mentioned in the final reaction equation.  

O atom is an intermediate because it forms in the first reaction and is consumed in the second reaction.

 Due to the see-saw shape of SF₄,  $\mu$  0 . All other molecules have zero dipole moment.

Conditions for Writing Resonating Structures: 

(i) The contributing structures should have same atomic positions. 

(ii) These structures should have same number of unpaired electrons. 

(iii) These structures should have nearly same energy. 

(iv) These structures should be written such that negative charge is present on an electronegative atom and positive charge is present on an electropositive atom. 

(v) In contributing structures, like charges should not reside on adjacent carbon.

(vi) Hybrid structure is least energetic.

HINT: Central atom octet is not complete in electron - deficient species.

$N^{}{H}_3,P^{}{H}_3$ - electron-rich species, because the central atom has the lone pair. Nitrogen in ammonia and phosphorus in ${\mathrm{PH}}_3$ are central atoms and their octet is complete.

${\mathrm{CH}}_3-{\mathrm{CH}}_3$ is a Covalent neutral molecule and carbon octet is also complete .

But in the case of ${\mathrm{BH}}_3$ boron octet is not completed, it has only 6 electrons in its valence shell. So, it is an electron-deficient species.

HINT: For the same n value, the strength of overlapping is p-p > s-p > s-s

Bond strength depends upon two factors :

(i) Size of orbitals (ii) Extent of overlapping

Thereby, σ bond is always stronger than π bonds. The smaller the size of orbitals, stronger is
the bond.

When the n value is the same then p-p overlapping is stronger than s-p and s-s.

The order of bond strength can be explained on the basis of the fact that the more the area of overlap, the higher will be the strength. Since the p orbital has directional property, p – p overlap provides more area for overlap for the same internuclear distance.

In H-bonding, a hydrogen atom should be attached to a more electronegative atom.

In ${\mathrm{CH}}_{3}F$, hydrogen bonding did not occur because hydrogen is attached to a carbon atom and carbon atom is not an electronegative element.

Among H2O,H2S,H2Se and H2Te, the one with the highest boiling point is H2O because of intermolecular hydrogen bonding which leads to molecular association and leads to higher energy for boiling.

Causes of deviations from ideal behaviour is due to the following assumptions:

$\left(1\right)$. Volume occupied by gas molecules is negligible as compared to volume occupied by the gas.

$\left(2\right)$. The forces of attraction between gas molecules are negligible.

A real gas behaves as an ideal gas at low pressures and high temperature.

only in ISOTHERMAL PROCESS the temperature is constant hence boyle's law is valid.

The beans are cooked earlier in a pressure cooker because the boiling point increases with increasing pressure. That means food can cook at much higher temperature and since cooking reaction speeds up at higher temperatures, food cooks faster.

Hint: Gap in transition line should be low and transittion should be from lower to higher.

VIDEO EXPLANATION:

As we go up in hydrogen spectrum, the energy differences decrease and wavelength increases.

Absorption line in the spectra arises when energy is absorbed i.e., electron shifts from lower to higher orbit, out of option 1 and 2, 2 will have the lowest frequency as this falls in the Paschen series.

The higher the value of (n + l) for an orbital, the higher is its energy.

However, if two different types of orbitals have the same value of (n + l), the orbital with the lower value of n has lower energy.

Therefore, decreasing order of energy of the given orbitals is 5f > 6p > 5p > 4d.

Only 1s orbital is present in 1st shell.
Only 2s,2p orbitals are present in 2nd shell.
Only 3s, 3p,3d orbitals are present in 3rd shell.
Only 4s, 4p,4d and 4f orbitals are present in 4th shell.
So 1p and 3f do not exist

Magnetic orbital quantum number

• It is denoted by ml.
• It gives information about the spatial orientation of the orbital with respect to the standard set of co-ordinate axis.

The explanation for the incorrect option

• Azimuthal quantum numbers tell about the shape of the orbital.
• The spin quantum number denotes the orientation of the spin of the electron.
• The principal quantum number determines the size and to large extent the energy of the orbital.

Maximum number of electrons in a subshell of an atom can be determined by which of the following formula 4l + 2

Hint: Draw the orbital diagram and find the number of unpaired electron.

In this type of electronic configuration the number of unpaired electrons are 3. The orbital diagram is as follows:

n = main energy level
l= subshell
If n = 4 and l = 3, the subshell is 4f. In f subshell, there are 7 orbitals and each orbital can accommodate a maximum of two electrons, so, maximum no. of electrons in 4f subshell = 7 x 2 = 14.