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Basalt is the best example of volcanic igneous rocks. 

Mineral is a natural inorganic substance which has certain chemical and physical properties.

Feldspar and silica covers largest area of the Earth’s crust. 

The erupted solid particles consist of large rock fragments as well as small angular rock pieces. Cinder as they are called is deposited around the vent to form cinder cone.

Sand stone is an example of metamorphic rocks.

Bauxite, mica

The Magma from the interior of the earth finds its way towards the surface through a passage. When it is able to reach the surface, it cools and solidifies, and a vertical or highly inclined feature is formed, and such a features is called dyke.

Mt. Vesuvius, Mt. krakatau and Mt. Pelean Volcanoes are called ‘Super Volcanoes.

Correct option is (A) Mass

A volcanic cone composed of alternative layers of ash, cinder and lava is called composite cone. This results from the accumulation of materials over a long period of time from a number of eruptions. This type of cone is the most common volcanic feature. Fujiyama of Japan and Mt. Etna of Sicily are examples of this type of cone.

Sedimentary rocks are associate with fossils.

Metamorphic rocks are the example of Marble.

The acid lava, which is vicious, solidifies quickly and blocks the vent. This stands up as a steep-sided cone called spine or plug. 

Intrusive rocks are formed by the cooling of the magma deep inside the crust of the earth and its solidification under great pressure.

A Geyser is a hot spring form which a column of hot water and stream are alternatively ejected to a great height.

In ancient times, Greeks believed that volcanic eruptions were due to anger of Goddess ‘Vulcan’, living under the Mt.Vulcan (Lipari Islands near Sicili of Italy). People thought that volcano was the mountain of fire. Causes of Volcano: The volcanic eruptions are closely associated with various causes.

• Gases and water vapour formed due to heating of underground water. 
• Movement and breaking of major and minor plates of the Earth. 
• Ascent of magma forced by excess pressure. 
• The temperature inside the Earth increases with the increasing depth 1°C per 32m). 
• Formation of magma because of increase in temperature and reduction in pressure.

Effects of volcanoes: 

• Volcanoes are natural hazard and disaster which cause extensive damage to life and property. 
• Volcanoes cause damage to agricultural fields, industries, dwellings, buildings, roads, railways, airports, dams, reservoirs etc. 
• Volcanoes cause diversion of river course and flooding of water. 
• Volcanic dust, ash and smoke cause air pollution. 
• Volcanic eruption sometimes produce seismic waves.

Hot springs or thermal spring’s are more common. The water sinks deep inside where the rocks are heated. The heated water rises to the surface without any explosion. Such springs contain dissolved minerals which are of medicinal value. They can be also used to generate electricity. Iceland has thousands of hot springs.

Intrusive land forms occur when lavas solidified within the earth’s crust and gives rise to various shapes or forms intrusive landforms are formed along the bedding planes of sedimentary rocks.

Laccolith is a large mound of igneous rock formed along a bedding plane in the sedimentary rock layers.

The shape of lava dome is determined by the nature of lava. The highly fluid basic lava builds up shield dome with gently rising slopes, and flattened top. The basic lava, which is highly viscous, builds up dome with a great height and steep slope.

Acidic lava is highly viscous, contains high percentage of silica. If flows slowly and solidifies quickly. Hence deposition occurs only around the craters with steep slopes called domb shaped volcano.

It is composed of iron and magnesium, black inn colour and highly fluid, when it is poured out from the volcano, it flows for a long distance and forms

Batholith is a very large dome -shaped intrusion of igneous rock. It is exposed to the surface only after considerable erosion.

∵Each child gets = 5sweets
Therefore, 24 children will get 24 x 5 = 120 sweets Total number of sweets =120
If the number of children is reduced by 4, then children left = 24 – 4 =20
Now each child will get sweets = 120/20=6 sweets

Three types of volcanic materials are distinguished as Liquid, sold and gaseous materials.

1. The liquid material: Lava is the most important liquid material ejected by volcanoes. The molten rock material is called “Magma” below other earth’s surface, while it is called lava when it reaches the earth’s surface. There’are two main types of lava-acid lava and basic lava.

2. Solid materials: It consists of volcanic dust, volcanic ash, cinder, volcanic bombs and large angular fragments. The finest particles thrown out by volcanoes are called ‘volcanic dust’. They are grey in color and very light in weight. The molten lava shoots up to the sky at the time of explosion.

Then it cools and solidifies into round mass before falling to the earth. It is called “volcanic bomb’. Small lava fragments are thrown out by a volcano during eruption and are known as “lapilli or pumice’. These are angular in shape and as big as finger joints. The smaller fragments of lava smaller than lapilli are like peas and are called “volcanic ash” or ‘Cinder’. The solid angular fragments which are bigger than lapilil are known as ‘Breccia’.

3. Gaseous Material: A variety of gaseous mixture comes out of a volcano, accompanied by liquid and solid materials, e.g. Vapour, hydrogen, carbon dioxide, sulphur, ammonium chloride etc. But vapour or steam is the most important. Sometimes huge amount of steam is thrown out to form dark clouds above the crater, like a ‘cauliflower’ in shape, it may bring heavy downpour of rain.

An extensive elevated land made up of depositional lava called lava plateau.

Volcanic bombs, dust, pumice, Scoria, Volcanic ash, cinder and rock fragments.

landforms are formed by the accumulation and solidification of lava and other material ejected by volcanoes eg: volcanic cones, crater etc.

The rock which are formed by the cooling and solidification of magma or lava on the surface of the earth re known as “Extrusive Igneous rocks”. These rocks are also called volcanic rocks, as they are formed during volcanic eruption. No crystals are formed in these rocks due to rapid cooling of lava; basalt is typical example of this kind of rock. ‘

These are intermediate rocks between the extruded volcanic rocks and the deep plutonic rocks. They are formed due to cooling and solidification of magma in cracks, pores, crevices etc.

The perpendicular bisector of the line joining A and B is the locus of the point which moves such that it is equidistant from A and B. 

By data we have A = (3, -2), B = (4, 1) 

Let P(x, y) be any point on the perpendicular bisector Thus we have PA = PB = PA² = PB² 

=> (x – 3)² + (y + 2)² = (x – 4)² + (y – 1 )²

⇒ x² + 9 - 6x + y² + 4 + 4y = x² + 16 - 8x + y² + 1 - 2y

⇒ -6x + 4y + 13 = -8x – 2y + 17 

⇒ 2x + 6y – 4 = 0. 

⇒ x + 3y – 2 = 0 is the equation of the locus of a point.

Let A = (-5, 7) and B = (-3, 1) and P(y, b) be any point of the locus 

By data PA = 2PB = PA² = 4PB² ⇒ (x + 5)⁵ + (y – 7)² 

= 4[(x + 3)² + (y – 1)²] 

⇒ x² + 10x + 25 + y² + 49 – 14y 

= 4(x² + 9 + 6x + y² + 1 – 2y) 

= 4x² + 36 + 24x + 4y² + 4 – 8y 

= 3x² + 3y² + 14x + 6y – 34 = 0 

which is the equation as to the locus.

A sequence of non-zero terms is called a geometric progression if the ratio of any term to its preceding term is constant. This constant is called common ratio and is denoted by ‘r’ 

Let a be the first term and (r ≠ 0) be the common ratio of a G.P. Then general term of G.P.is T_n = a . r^n-1

Note: 

Terms in G.P.are in the form a, ar, ar² , ar^n-1, 

No term in G.P.can be zero. 

Three terms a,b,c are in G.P.

if b/a = c/b i.e b² = ac, abc ≠ 0

The general form of a GP is a, ar, ar², ar³ and so on. The nth term of a GP series is

 T_n = ar^n-1, 

where, a = first term and r = common ratio = T_n/T_n-1 .

 The sum of infinite terms of a GP series, S_∞= a/(1-r) 

where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.

Let ‘a’ be the first term and ’r’(≠) be the common ratio of the given G.P.The general teams of G.P. If S_n denotes the sum of ‘n’ terms, then,

S_n = a((1 - rⁿ)/(1 - r)) r ≠ 1

This can also written as

S_n = a((rⁿ - 1)/(r - 1))

Note: (1) S_n = a + ar + ar² +….. +ar^n-1 

(2) If r = 1, then Sn = a + a + a +……………+a – na 

(3) If r = 1, then formulas for S_n fail 

(4) If r < 1, then use  S_n = a((1 - rⁿ)/(1 - r))

(5) If r > 1, use  S_n = a((rⁿ - 1)/(r - 1))

(6) Sum of an infinite G.P.,a + ar + ar²  + ..... is a/(1 - r), - 1 r < 1

(7) If a, b, c are in G.P.then ‘b’ is the G.M. (geometric mean) between a and c, then b²  = ac ⇒ b = √ac

(8) If A and G are A.M. and G.M. of two given distinct positive real numbers, then relation between A and G is A > G.

Sum of G.P. up to n terms if 1^st term is a and

the common ratio is r.

Sn =a.(1-rⁿ)/(1-r)………….(1) while r < 1 .

or

Sn =a.(r^n-1)/(r - 1)………(2) while r > 1 .

Sum up to infinite terms = a/(1-r).

Let n be the unit vector in the direction of 2i - 3j + 6k 

∴ n = (2i - 3j + 6k)/√(2² + (-3)² + 6²) = (2i - 3j + 6k)/7 = (2/7)i - (3/7)j + (6/7)k 

Let r = xi + yj + zk be the position vector of any point (x,y,z) on the plane. Then the equation of the plane is

n.vector r = P

or, (xi + yj + zk).((2/7)i - (3/7)j + (6/7)k) = 5

or, 2x - 3y + 6z = 35 

a ∈ R, b ∈ R then ab² ∈ R 

∴ a * b ∈ R 

∴ * is a binary operation.

a ∈ Z⁺ , b ∈ Z⁺ , |a – b| ∈ Z⁺ 

∴ a * b ∈ Z⁺ 

∴ * is a binary operation.

a ∈ Z⁺ , b ∈ Z⁺ then a ∈ Z⁺ 

∴ a * b ∈ Z⁺ 

∴ * is a binary operation.

a * b = a – b,∀ a > be Q 

a * b = a – b * a = b – a 

a * b ≠ b * a 

hence not commutative 

(a * b) * c = (a – b) * c 

= a – b – c a* (b * c) 

= a* (b – c) = a – (b – c) 

= a – b + c ≠ (a* b) * c 

hence ≠ is not associative

a = 3, b = 2, 

a – b = 3 – 2= 1 

b-a = 2-3 = -1 

a – b ≠ b – a, 

hence not commutative 

a = 3, b = 2, c = 1 

(a * b) * c = (3 – 2) * 1 

= 1 * 1 = 0 

a*(b * c) = 3* (2 * 1) 

= 3*(2 – 1) = 3 * 1 

= 3 – 1 = 2 

(a * b) * c ≠ a * (b * c), 

hence * is not associative

a, b ∈ Q ⇒ a * b = a² + b² 

= b² + a² = b * a 

hence * is commutative 

(a * b) * c = (a² + b²) * c² 

= (a² + b²)² + c² 

a*(b * c) = a* (b² + c²) 

= a² + (b² + c²)² 

hence * is not associative

a ∈ Q, b ∈ Q 

a * b = ab + 1 

b * a = ab + 1 

∴ a * b = b * a, hence commutative 

( a * b )*c = (ab+1) *c 

= (ab + 1) c + 1 

= abc + c + 1 a*(b*c) 

= a* (bc + 1) 

= a (bc + 1) + 1 

= abc + a + 1 

∴ (a * b) *c * a* (b * c) 

hence * is not associative

a = Z⁺ , be Z⁺, 

a*b = 2^ab 

b * a = 2^ba = 2^ab 

a * b = b * a 

hence * is commutative 

(a * b) * c = 2^ab * c = 2^ab * c = 2^2al ’ ^x ‘ 

a*(b*c) = a* 2^ac = 2^a–2“ 

hence (a * b) * c * a * (b * c) 

∴ * is not Associative.

a ∈ Z⁺ , b ∈ Z⁺ , a * b = a^b 

b * a = b^a 

a * b ≠ b * a, 

hence * is not commutative 

(a * b) * c = ab * c = (a^b) c = a^bc 

a* (b * c) = a * b^c = (a)^bc 

(a * b) * c ≠ a* (b * c) 

hence * is not associative.

a * b = a + ab

b * a = b + ab

∴ a * b ≠ b * a, 

hence * is not commutative 

(a * b) * c = (a + ab) * c 

= (a + ab) + (a + ab) c 

= a + ab + ac + abc a* (b * c) 

= a * (b + bc) = a + a (b + bc) 

= a + ab + bca ≠ (a * b) * c 

hence * is not associative

(a, b) * (c,d) = (a + c, b + d) 

= (c + a, d + b) = (c, d) * (a, b) 

hence commutative 

[(a, b) * (c, d)] * (e, f) 

= (a + c, b + d) * (e, f) 

= (a + c + e, b + d + f) 

= (a, b) * [(c,d) * (e, f)] 

hence * is associative. 

Let (e, f) be the identity element of 

A (e, f) * (a, b) = (a,b) * (c, f) 

= (a, b) (a + e, b + 0) = (a, b) 

⇒ (e = 0, f = 0) ∉ N 

hence no identity element.

The following are the characteristics of Parliamentary System adopted by India:

1. The Parliament of India is composed of the President, Lok Sabha and Rajya Sabha. 

2. Fixed number of members of the Parliament are directly elected by the people. 

3. All political parties contest elections, which are held at regular intervals.

4. The party having majority in Lok Sabha or a coalition government comes into power. 

5. The leader of the majority party becomes the Prime Minister and he selects candidates to form the Council of Ministers. 

6. The Executive has to perform the responsibility of its individual ministerAship as well as the responsibility of the Legislature, for all their actions and policies.