Definition
A group of words that makes complete sense is called a sentence.
(i) American President visited India.
(ii) Indian history goes back to thousands of years. The lines given above make complete sense. Therefore, they are sentences.

Some Important Analogy
Quantity and unit
1. Mass : kilogram 11. Current: Ampere
2. Force : Newton 12. Luminosity : Candela
3. Energy : Joule 13. Pressure : Pascal
4. Resistance : Ohm 14. Area : Hectare
5. Volume :Litre 15. Temperature : Degrees.
6. Angle : Radian 16. Conductivity: Mho
7. Power: Watt 17. Magnetic field : Oersted
8. Potential: Volt 18. Length : Metre
9. Work: sJoule
10. Time : Second
Individual and group
1. Cattle : Herd 7. Sheep : Flock
2. Flowers: Bouquet 8. Riders : Cavalcade
3. Grapes : Bunch 9. Bees : Swarm
4. Singer: Chorus 10. Man : Crowd
5. Artist: Troupe 11. Soldiers : Army
6. Fish : Shoal 12. Nomads : Horde
13. Sailors : Crew
Male and female
1. Dog : Bitch 6. Drone : Bee
2. Stag : Doe 7. Gentleman : Lady
3. Son: Daughter 8. Nephew : Niece
4. Lion : Lioness 9. Tiger : Tigress
5. Sorcerer: Sorceress 10. Horse : Male
Individual and class
1. Man : Mammal 5. Whale : Mammal
2. Ostrich : Bird 6. Rat: Rodent
3. Snake : Reptile 7. Lizard : Reptile
4. Butterfly: Insect
Study and topic
1. Seismology : Earthquakes 18. Entomology : Insects
2. Botany : Plants 19. Zoology : Animals
3. Onomatology : Names 20. Occultism : Supernatural
4. Ethnology : Human Races environment 21. Ecology: Organisms and
5. Ontology : Reality 22. Virology : Viruses
6. Herpetology: Amphibians 23. Malacology : Molluscs
7. Pathology : Diseases 24. Paleontology : Fossils
8. Astrology: Future 25. Pedology : Soil
9. Anthropology: Man 26. Taxonomy : Classification
10. Paleography : Writing 27. Orography: Mountains
11. lchthyology : Fishes 28. Selenography: Moon
12. Semantics : Language 29. Eccrinology : Secretions
13. Nephrology: Kidney 30. Histology : Tissues
14. Microbiology: microscopic organisms 31. ORNITHOLOGY : Bird
15. Hematology : Blood 32. Cardiology : Heart
16. Craniology : Skull 33. Phycology : Algae
17. Mycology : Fungi 34. Bryology : Bryophytes
35. Ornithology : Birds
Part and whole
1. Pencil : Lead 5. Room : Window
2. House : Kitchen 6. Aeroplane : Cockpit
3. Fan : Blade 7. Book: Chapter
4. Class : Member 8. Pen : Nib
Word and intensity
1. Wish : more...

Introduction
Analogy' means 'Equivalence'. In questions based on analogy, a particular relationship is given and another similar relationship has to be identified from the alternatives provided. Analogy tests are therefore meant to test a candidate's overall vocabulary, power of reasoning and abiliy to think concisely and accurately. Below are given some common relationships which will help you to know analogies better.

Introduction
Sometimes an 'unseen passage' may be set and students may be asked to answer certain questions based on the passage. They can write good answers only
(i) When they fully grasp the meaning of the passage,
(ii) When they are able to express the meaning of the passage in their own simple, clear and direct English, and
(iii) When they clearly understand the questions asked.
Comprehension means 'Understanding' whatever you read and answering Question related to it. Answering question to a given passage depends actually on the following abilities of a student.
How good you are in understanding the meaning of the entire passage; in finding the answer in the passage; command you have in English Language.
Points to Keep in Mind While Doing Comprehension
1. Read the paragraph carefully and underline important points.
2. Read the questions one by one and try to find the answers in the paragraph.
3. Write answers in your own words.
4. Read the passage carefully two or three times, till your understand clearly (1) its subject and (2) what is said about the subject. Ask yourself, 'What is the main theme of the passage I am reading? What does the author say about that subject?
5. Read carefully the questions carefully, one by one, and try to understand them.
6. Now identify the part of the passage the question refers.
7. Do not add unnecessary details.
8. Finally write answers to the questions in your own words. Do not copy the language of the passage. The answer should be brief and to the point.
9. Revise your answers and examine them carefully
10. Be precise and to the point.
Passage
Read the following passage and answer the questions: The men who were governing Athens summoned Socrates to appear before them and to stand trial. His friends and pupils begged him to escape or to hide until the storm had blown over. But Socrates was no coward. He knew that he had done nothing wrong and that he had only taught what he believed to be just, true and honorable, and so he went to the court, an undersized, ugly old man, dust and travel-stained, but with a noble heart beating under the shabby garments which everyone knew so well. He made a powerful, dignified speech, answering every question, explaining that, although the Athenians knew it not, he was really their friend. He told them that they would gain nothing by taking away the last few years of his life, but that he was willing to die many deaths for what he believed to be right. The judges listened to him and condemned him to death. The old man made no complaint. He leaned on his staff, looking round the crowded court, "No evil can happen to a good man," he said, "either in life or more...

Line of symmetry
Line of symmetry is a line that divides a figure into two identical parts, each of which is the mirror image of the other. In the above figures the imaginary line is known as the line of symmetry, so the line of symmetry is the imaginary line along which we can fold the figures so that both the halves coin cide each other.
Note:

- A line of symmetry divides a figure into two equal halves.
- A figure can have more than one line of symmetry.
- A figure cannot have any line of symmetry.

Introduction
In our day to life we come across so many things around us which seems to be divided into two equal halves and both the halves look like in exact correspondence or position along an imaginary line. Take a look at the following figures.
If we fold these figures along an imaginary line, we will find that both the halves are mirror images of each other. The very common term used in our day to day life for these type of figures is "symmetry". So, symmetry occurs when one shape becomes exactly the same or both the figures overlap each other. Such types of figures are called symmetrical figures.

Volume of Geometrical Figures
A solid has capacity to acquire space.
The space occupied by a solid is called its volume. Sl unit of volume\[~={{m}^{3}}\]
If the volume of a cube is \[1{{m}^{3}},1{{m}^{3}}\] is the space occupied by a cube of sides 1m.
If the volume of the solid is 6 cm3 it means it occupies the space six times of the volume,\[~1c{{m}^{3}}\]
In the picture given below six shapes are combined to each other and length, width and height of every figure is 1 cm, therefore, the total length of the entire picture is 6 cm and width and height is 1cm, hence the volume of the entire picture is six times of the volume of every one.
Cube
The solid figure whose all sides or edges are equal is called cube. In the picture given below the edges of the cube are equal.
Features of the Cube
(i) A cube has 6 surfaces and shape of every surface is equal.
(ii) A cube has 12 equal edges called sides.
(iii) It has 8 vertices.
Therefore, formula the total surface area of Cube \[=6\times sid{{e}^{2}}\]
Lateral surface area of Cube \[=\text{ }4\times sid{{e}^{2}}\]
Volume of cube = side x side x side = \[{{\left( side \right)}^{3}}\]
Find the surface area of a cube whose side is 14 cm.
(a) \[1170c{{m}^{2~}}\]
(b) \[1175c{{m}^{2}}\]
(c) \[1176c{{m}^{2}}\]
(d) All of these
(e) None of these
Answer: (c)
Explanation
Side = 14 cm Surface area of a cube \[=6\times {{\text{(}side\text{)}}^{2}}\]
\[=6\times {{(14)}^{2}}c{{m}^{2}}\] \[=6\times 196\text{ }c{{m}^{2}}\]
\[=1176\text{ }c{{m}^{2}}\]
Cuboid
A solid made up of 6 rectangular surfaces is called cuboid. Match box is the example of a cuboid. In the picture given below I is length, b is breadth and h is the height of the cuboid.
Features of cuboid
(i) A cuboid has 6 rectangular surfaces.
(ii) It has 12 edges.
(iii) A cuboid has 8 vertices.
Therefore the total surface area of a cuboid = Sum of the surface area of its 6rectangular faces
\[=\text{l}\times b\text{ }+\text{l}\times b\text{ }+\text{ }b\times h+b\times h+\text{l}\times \text{ }h\text{ }+\text{ l}\times h\]\[=21b+2bh+21h\]
Therefore the total surface area of cuboid \[=2\left( lb+bh+lh \right)\]
Area of four walls of a cuboid = 2 (breadth \[\times \] height + length \[\times \] height)
Area of four walls of a cuboid \[=2(bh+Ih)\]
Area of four walls of a cuboid \[=2h(l+b)\]
The lateral surface area of a cuboid = The total surface area of four walls.
Volume of cuboid = length \[\times \] breath \[\times \] height \[=l\times b\times h=lbh.\]
more...

Perimeter and Area of Plane Figures
Perimeter of every figure is sum of its sides. The perimetre of a rectangular room is the sum of measurement of all sides where the area of a rectangle is the product of their sides. Therefore, the sum of the length of all the sides of a geometrical shape is called perimetre. Sl unit for measurement of perimetre is meter and Sl unit of area is square metre.
Perimeter and Area of Triangles
A triangle is one of the basic shapes of geometry. It has three vertices and three sides. Perimetre of triangle = Sum of the length of sides. Area of right angle triangle \[~=\frac{1}{2}\times Base\times Height\]
1. In the picture given below, ABC is a triangle whose sides are, AB, BC and AC. A perpendicular line AD is the height or altitude of the triangle. A square box at point D denotes the angle of \[{{90}^{o}}.\]
Perimeter of \[=AB+BC+CA.\]of its sides \[=AB+BC+CA.\] Area of \[\Delta ABC\,=\,\frac{1}{2}\times BC\times AD\] whereas BC is the base of the triangle and AD altitude.
Find the area and perimetre of the figure given below?
(a) \[8\text{ }c{{m}^{2}},15\text{ }cm\]
(b) \[~9\text{ }c{{m}^{2}},15\text{ }cm\]
(c) \[10\text{ }c{{m}^{2}},\text{ }8\text{ }cm\]
(d) All of these
(e) None of these
Answer: (b)
Explanation
Perimeter of \[\Delta ABC\]= Sum of its sides = AB + BC + CA= 4 cm + 6 cm + 5 cm = 15 cm Therefore, perimeter of \[\Delta ABC\text{ }=\text{ }15\text{ }cm\] Area of \[\Delta ABC=\frac{1}{2}BC\times AD\]whereas BC is the base of the triangle and AD is altitude. \[~\Delta ABC\text{ }=\text{ }9\text{ }c{{m}^{2}}\] The area of\[~\Delta ABC\text{ }=\text{ }9\text{ }c{{m}^{2}}\]
2. In the picture given below, a triangle has three equal sides, AB = BC = CA = a unit. Therefore, the triangle ABC is called equilateral triangle.
Perimeter of an equilateral triangle = AB + BC + CA \[=\text{ }Side\text{ }+\text{ }Side\text{ }+\text{ }Side\text{ }=\text{ }3\text{ }\times \text{ }Side\]
Therefore the perimetre of an equilateral triangle \[=3\times Side=\text{3}\times a\] Area of an equilateral triangle \[=\frac{\sqrt{3}}{4}\times {{(side)}^{2}}=\frac{\sqrt{3}}{4}\times {{a}^{2}}\]
Find the area of an equilateral triangle whose each side is 6 cm long?
(a) \[6\sqrt{3}\,\,c{{m}^{2}}\]
(b) \[8\sqrt{3}\,\,c{{m}^{2}}\]
(c) \[9\sqrt{3}\,\,c{{m}^{2}}\]
(d) All of these
(e) None of these
Answer: (c)
Explanation
The length of each side of the triangle is 6 cm therefore, it will be the equilateral triangle. Hence the area of the equilateral triangle =
\[\frac{\sqrt{3}}{4}\times {{(side)}^{2}}=\frac{\sqrt{3}}{4}\times 6\times 69\sqrt{3}\,\,c{{m}^{2}}.\]
Perimeter and Area of Parallelogram
Parallelogram is a quadrilateral more...

Introduction
There are different types of figures. Figures are classified by its shapes and sizes.area of a geometrical figure is its total surface area while the volume is the spaceoccupied by the object. Area and volume of everything can be obtained. In this chapter, we will learn about the area and volume of some common shapeswhich are also known as the geometrical figures.

Triangles
A triangle has three sides and three vertices. The sum of the three angles of a triangle is equal to 180° and one angle of a triangle \[={{180}^{o}}-\] (Sum of two angles).
In ABC, \[\angle A+\angle B+\text{ }\angle C={{180}^{o}}\]
In APQR, \[\angle P+\angle Q+\angle R={{180}^{o}}\]
Find the measurement of A if B and C are given when A, B and C are the angles of the triangle.
(a) \[~A={{180}^{o}}-(B+C)\]
(b) \[A={{180}^{o}}+(B-C)\]
(c) \[A={{180}^{o}}+C-B\]
(d) All of these
(e) None of these
Answer: (a)
Explanation
The sum of angles of the triangle \[={{180}^{o}}.\]
Hence, the angle \[A={{180}^{o}}-(B+C).\]
Exterior
Angle of a Triangle The angle between the produced side and its adjacent side of triangle is called exterior angle. The exterior angle is equal to the sum of two opposite interior angles of that triangle. In the picture given below the angles \[\angle ABD\] and \[\angle ACE\] are the exterior angles of the triangle.
Thus,
\[\angle ACE=\angle BAC+\angle ABC\]
\[\angle ABD=\angle BAC+\angle ACB\]
\[\angle CAF=\angle ABC\text{ }+\angle ACB\]
Find the measurement of the angles x and y from the picture given below.
(a) \[x={{80}^{o}}\]and\[y={{10}^{o}}\]
(b) \[x={{110}^{o}}\]and\[~y={{120}^{o}}\]
(c) \[x={{70}^{o}}\]and\[y={{90}^{o}}\]
(d) All of these
(e) None of these
Answer: (b)
Explanation
\[x\]and\[y\] are the exterior angle therefore,
\[x=\angle PRQ\text{ }+\angle PQR={{60}^{o}}+{{50}^{o}}={{110}^{o}}\]
\[y=\angle QPR+\angle PQR={{70}^{o}}+{{50}^{o}}={{120}^{o}}\]
Area of the Triangle
The area of a triangle is the area bounded by the sides of the triangle.
Heron's Formula To find the area of a triangle by Heron's Formula, First find the semi perimeter of a triangle by the following formula: \[s=\frac{a+b+c}{2}\] (Here "s" stands for half of perimeter or semi perimeter and a, b and c refers to 3 sides of the triangle) \[Area=\sqrt{s(s-a)(s-b)(s-c)}\]by heron's formulae.
If the sides of a triangle are 18 cm, 24 cm and 30 cm then find the area of the triangle.
(a) \[216c{{m}^{2}}\]
(b) \[210c{{m}^{2}}\]
(c) \[21c{{m}^{2}}\]
(d) All of these
(e) None of these
Answer: (a)
Explanation
Let sides A = 18 cm, B = 24 cm, C = 30 cm \[s=\frac{a+b+c}{2}=\frac{18+24+30}{2}=\frac{72}{2}=36\] \[Area=\sqrt{s(s-a)(s-b)(s-c)}\]by heron's formulae \[=\sqrt{36\left( 36-18 \right)\left( 36-24 \right)\left( 36-30 \right)}\] \[=\sqrt{36\times 18\times 12\times 6}\] \[=\sqrt{{{6}^{2}}\times 9\times 2\times 6\times 2\times 6}\] \[=\sqrt{{{6}^{2}}\times {{3}^{2}}\times {{2}^{2}}\times {{6}^{2}}}\] \[=\sqrt{{{(6\times 3\times 2\times 6)}^{2}}}=6\times 3\times 2\times 6=216\,c{{m}^{2}}\]
Area of the Right Angled
Triangle The area of a right angle triangle is the half of the Product of height and base. more...

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