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a³ + 8b³ + 64c³ − 24abc 

= (a)³ + (2b)³ + (4c)³− 3 x a x 2b x 4c 

[Using a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)] 

= (a + 2b + 4c)(a² + (2b)² + (4c)² −a x 2b − 2b x 4c − 4c x a)

= (a+2b+4c)(a² +4b² +16c² −2ab−8bc−4ac)

Therefore, a³ + 8b³ + 64c³ − 24abc = (a+2b+4c)(a² +4b² +16c² −2ab−8bc−4ac)

17 + 6p = 9

Transposing 17 to R.H.S, we obtain

6p = 9 − 17

6p = −8

Dividing both sides by 6, we obtain

6p/6 = -8/6

p = -4/3

14y − 8 = 13

Transposing 8 to R.H.S, we obtain

14y = 13 + 8

14y = 21

Dividing both sides by 14, we obtain

14y/14 = 21/14

y = 3/2

= x³ − (2y)³ + (3z)³ − 3x x  x (−2y)(3z) 

= (x + (−2y) + 3z) (x² + (−2y)² + (3z)² −x(−2y)−(−2y)(3z)−3z(x))   [a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca)] 

= (x −2y + 3z)(x² + 4y² + 9 z² + 2xy + 6yz − 3zx)

The matter is made up of tiny particles, which are small beyond our imagination.

Anything in this world that occupies space and has mass is considered as matter.

The matter is made up of tiny particles, which are small beyond our imagination 

Matter exists in these states i.e. solids, liquids and gases.

²³C_3n = ²³C_2n+3

If ⁿC_x = ⁿC_y, then either x = y or x = n - y

∴ 3n = 2n + 3 or 3n = 23 – 2n – 3

∴ n = 3 or n = 4

आयत का क्षेत्रफल = 56 वर्ग सेमी = लम्बाई x चौड़ाई

56 = 1 x 56, 56 = 2 x 28, 56 = 4 x 14, 56 = 7 x 8

अतः आयत की लम्बाई और चौड़ाई = 1 सेमी x 56 सेमी, 2 सेमी x 28 सेमी, 4 सेमी x 14 सेमी, 7 सेमी x 8 सेमी.

(b) 15: 10: 6

Because,

= (1/x): (1/y) = 2: 3

Then, y : x = 2: 3

y = (2/3)x

= (1/y) : (1/z) = 3: 5

= z: y =3: 5

z = (3/5)y

x: y: z = x: (2/3)x: (3/5)y

= x: (2/3)x: (3/5) × (2/3)x

= x: (2/3)x: (2/5)x

= 15: 10: 6

(a) 3: 4: 5

Because,

Let (A/3) = (B/4) = (C/5) =k

= A = 3k, B=4k, C=5k

= A: B: C= 3K: 4K: 5K

A: B: C = 3: 4: 5

(c) 6: 4: 3

Because,

Let 2A=3B=4C=k

= A= (k/2), B=(K/3), C=(k/4)

= A: B: C= (K/2): (K/3): (K/4)

LCM of 2, 3 and 4 is 12

= [(K/2) ×12]: [(K/3) ×12]: [(K/4) ×12]

= 6: 4: 3

Hence, A: B: C = 6: 4: 3

(i) Let the fourth proportional to 1.5, 4.5 and 3.5 be x.

⟹1.5 : 4.5 = 3.5 : x

⟹ 1.5 × x = 3.5 × 4.5

⟹ x = 10.5

(i) Let the fourth proportional to 3a, 6a² and 2ab² be x.

⟹ 3a : 6a² = 2ab² : x

⟹ 3a × x = 2ab² × 6a²

⟹ 3a × x = 12a³b²

⟹ x = 4a²b²

1. Mortality is the death rate of a population. It gives a measure of the number of deaths in a particular population, in proportion to the size of that population, per unit of time. 

2. Mortality rate is typically expressed in deaths per 1,000 individuals per year. A mortality rate of 9.5 (out of 1,000) in a population of 1,000 would mean 9.5 deaths per year in that entire population or 0.95% out of the total. 

3. Absolute Mortality : The number of deaths under ideal conditions when there is no competition, and all the resources such as food and water are abundant, then it gives absolute mortality. 4

. Realized Mortality : The number of deaths under environmental pressures come into play gives realized mortality. 

5. It must be remembered that absolute mortality will always be less than realized mortality.

When we go up the altitude, beyond a particular height no tree are found and the vegetation comprise only of shrubs and herbs. The altitude beyond which no tree is seen is known as tree line.

1. Predators control the prey population but if a predator over exploits its prey, then the prey might become extinct. 

2. If prey species is not available, the predator will also starve and become extinct. Predators, therefore, do not kill the prey unnecessarily. They act as prudent.

Exponential .

1. The temperatures vary from subzero levels in polar areas and high altitudes, to about 50°C in tropical deserts during summer. 

2. There are also seasonal changes in the temperature. 

3. Temperature also shows progressive decrease from the equator towards the poles and from plains to the mountain tops. 

4. Some unique habitats such as hot springs may show very high temperatures of about 80 to 100°C

5. In deep-sea hydrothermal vents average temperatures may rise up to 400°C.

1. Natality is the birth rate of a population. Due to increased natality the population density rises. 

2. Natality is a crude birth rate or specific birth rate. 

3. Crude birth rate : Number of births per 1000 population/year gives crude birth rate. Crude birth rate is helpful in calculating population size.

4. Specific birth rate : Crude birth rate is relative to a specific criterion such as age. E.g. If in a pond, there were 200 carp fish and their population rises to 800. Then, taking the current population to 1000, the birth rate becomes 800/200 = 4 offspring per carp per year. This is specific birth rate. 

5. Absolute Natality : The number of births under ideal conditions when there is no competition and the resources such as food and water are abundant, then it give absolute natality. 

6. Realized Natality : The number of births under different environmental pressures give realized natality. Absolute natality will be always more than realized natality.

To acclimatise in high altitude, the people have more haemoglobin/high RBC count to compensate for the low oxygen availability.

1. Mammals inhabiting colder regions have shorter snout, ears, tail and limbs to minimize the loss of body heat. This is called Allen’s Rule. 

2. Aquatic mammals such as whales and seals living in the polar seas, have a thick layer of fat which is called a blubber below their skin. 

3. Blubber acts as an insulator and thus helps to keep the body warm by reducing loss of body heat. 

4. Some animals like polar bears undergo hibernation and thus tide over the stressful winters.

The mammals are most successful animals on earth because they can maintain a constant body temperature with high range of tolerance whether in Antarctica or in Sahara desert.

Aerenchyma gives buoyancy to the aquatic plants due to presence of air chambers.

Algae (blue-green algae) and fungi together form lichen.

Mycorrhiza is a symbiotic association between a fungus and the roots of higher plants.

Cuscuta has lost its chlorophyll and leaves during evolution and thus it derives its nutrition from host plant, thus, it is a parasitic plant.

A. Haemophilia is caused due to the recessive gene on X chromosome. Y chromosome has no allele for this. If a male is X^hY, then he is haemophilic. If male inherits X^h from the mother, he will be haemophilic (with the genotype X^hY). If female inherits X^hX^h , one from the carrier mother and one from her haemophilic father, then she can be haemophilic.

B. Embryo has (trisomy of sex chromosome) XXY karyotype or Klinefelter’s syndrome. 

She was advised to undergo MTP since the child will have the following problems: 

i. male with feminine traits 

ii. gynaecomastia 

iii. underdeveloped testes 

iv. sterile

Cattle avoid browsing on Calotropis plants because it produces poisonous cardiac glycosides.

The cells of different organs of plants and animals need various necessary substances to carry out many metabolic activities and different type of waste products are created during these metabolic activities. So, transport of materials is necessary to supply the required substances and to remove the waste products.

The cells of different organs of plants and animals need various necessary substances to carry out many metabolic activities and different types of waste products are created during these metabolic activities. So, transport of materials is necessary to supply the required substances and to remove the waste products.

(d) capillaries

Centrosome, Lysosome.

(iii) under the fan

All living body is formed of cells. Cells are the structural and functional units of organisms.

Cell wall, large vacuole, plastids.

(i) A – Chloroplast

B – Mitochondrion

C – Ribosome

D – Vacuole

E – Nucleus

(ii) A – Photosynthesis 

B – Production, Storage and distribution of energy 

C – Protein synthesis

(iii) Genes are seen in the chromatin reticulum in the nucleus.

a. Plant Cell 

b. Endoplasmic reticulum 

c. Prokaryote 

d. Robert Brown 

e. Xanthophyll 

f. Endoplasmic reticulum

a. Amoeba; The others are prokary otes.

b. Lysosome; The others are present in both plant and animal cell.

c. Cell Membrane; Others are cell organelles

MJ. Schleiden and Theodor Schwann.

a. Endoplasmic reticulum – understand, marking

b. Nucleus – understand, marking

c. Mitochondrion – understand, marking

Simple Microscope

• Magnifies an object 2000 times its actual size
• Light source is used to see objects Electron Microscope
• Magnifies objects million times
• Electrons are utilized instead of light source.

There are certain organisms without a definite nucleus. In bacteria, cyanobacteria and mycoplasma, there is no nucleus. They are called prokaryotes.

But in the cells of Amoeba, animals and plants there is a well defined nucleus covered with membrane. These are known as eukaryotes.

1. Defend foreign particles.

2. Releases energy from the cells.

3. Synthesis biomolecules.

1. b. Golgi complex

2. c. Endoplasmic reticulum

3. a. Mitochondrion

The fictitious or imaginary force used to balance an actual or material force is called pseudo force, e.g., centrifugal force, F = \(\frac{-mv^2}{r}\) is a pseudo force. Pseudo forces do not have material sources, they are simply produced because of acceleration or rotation of the frame itself.

Coal and Petroleum.

The nearest point to the eye at which an object is visible distinctly is called the near point. (25 cm). 

The maximum distance up to which the normal eye can see things is called the far point (infinity).

The distance up to which normal eye can see clearly without putting any strain, on muscles of eye.