SOLVED PAPER OF MPPSC FOREST RANGER AND ASSISTANT CONSERVATOR OF FOREST EXAM 2008:

1. Green colour of leaves is due to the presence of—
(A) Iron
(B) Chlorophyll
(C) Etiolin
(D) None of these
Ans : (B)

2. Purity of Milk is measured by—
(A) Hydrometer
(B) Manometer
(C) Lactometer
(D) Thermometer
Ans : (C)

3. Who invented Dynamite ?
(A) Neil Bohr
(B) Alfred Nobel
(C) Homi Bhabha
(D) Lord Chelmsford
Ans : (B)

4. In which state is Khajuraho situated ?
(A) Rajasthan
(B) Madhya Pradesh
(C) Orissa
(D) Maharashtra
Ans : (B)

5. World’s largest bird, which can run very fast, is—
(A) Ostrich
(B) Emu
(C) Kiwi
(D) Penguin
Ans : (A)

6. How many Judges are there in International Court of Justice ?
(A) 11
(B) 10
(C) 15
(D) 9
Ans : (C)

7. In which year the man first landed on Moon ?
(A) 1968
(B) 1969
(C) 1970
(D) 1971
Ans : (B)

8. Radar was invented by—
(A) J. L. Baird
(B) Graham Bell
(C) George Eastman
(D) R. W. Watt
Ans : (D)

9. Which country’s currency is ‘Kyat’ ?
(A) Thailand
(B) Malaysia
(C) Myanmar
(D) Israel
Ans : (C)

10. Pituitary gland is present—
(A) Below the brain
(B) Above the brain
(C) Inside the brain
(D) Not near the brain
Ans : (A)

11. Manas Wildlife Sanctuary is located in which state ?
(A) Gujarat
(B) Madhya Pradesh
(C) Assam
(D) Uttar Pradesh
Ans : (C)

12. Rajghat Dam is situated on which river ?
(A) Chambal
(B) Sutlej
(C) Betwa
(D) Narmada
Ans : (C)

13. Which is the largest continent of the world ?
(A) Australia
(B) Asia
(C) North America
(D) Africa
Ans : (B)

14. Salim Ali was associated with ?
(A) Horology
(B) Entomology
(C) Ornithology
(D) Parasitology
Ans : (C)

15. Trachoma is the disease of which organ ?
(A) Throat
(B) Eyes
(C) Liver
(D) Lungs
Ans : (B)

16. Which gas is used in preparation of Soda Water ?
(A) Carbon monoxide
(B) Chlorine
(C) Carbon dioxide
(D) Carbon
Ans : (C)

17. ‘Universal Donor’ belongs to blood group—
(A) O
(B) A
(C) B
(D) AB
Ans : (A)

18. Viruses lack—
(A) Proteins
(B) Enzymes
(C) Nucleic Acids
(D) Tentacles
Ans : (B)

19. Mammal which can fly—
(A) Whale
(B) Bat
(C) Snake
(D) Hen
Ans : (B)

20. Which king constructed the ‘Sanchi Stupa’ ?
(A) Bimbisara
(B) Ashoka
(C) Pushyamitra Shung
(D) Kanishka
Ans : (B)

21. In which state is the Kudremukh Iron Ore Scheme situated ?
(A) Kerala
(B) Karnataka
(C) Tamil Nadu
(D) Maharashtra
Ans : (B)

22. In which country is Angle Waterfall situated ?
(A) America
(B) Venezuela
(C) Canada
(D) Australia
Ans : (B)

23. Which country is called the ‘Land of Setting Sun’ ?
(A) Japan
(B) Indonesia
(C) Britain
(D) New Zealand
Ans : (C)

24. How much % of Nitrogen is present in Atmosphere ?
(A) 10%
(B) 33%
(C) 50%
(D) 78%
Ans : (D)

25. The iron ore mined from Belaidila is exported to which country ?
(A) Japan
(B) Russia
(C) England
(D) Iran
Ans : (A)

26. Which River flows between the Vindhya and Satpura mountain ranges ?
(A) Godavari
(B) Narmada
(C) Tapti
(D) Chambal
Ans : (B)

27. In which state cashew production is the highest ?
(A) Maharashtra
(B) Goa
(C) Kerala
(D) Karnataka
Ans : (C)

28. Which of the following is not a fresh water fish ?
(A) Cod
(B) Eel
(C) Salmon
(D) Trout
Ans : (A)

29. Scientific study of fishes is called—
(A) Herpetology
(B) Lepidopteriology
(C) Ichthyology
(D) Ornithology
Ans : (C)

30. In which state the Dafla and Sinhpo tribes are found ?
(A) Himachal Pradesh
(B) Madhya Pradesh
(C) Andhra Pradesh
(D) Arunachal Pradesh
Ans : (D)

31. The most important reason for population explosion in India is—
(A) Urbanisation
(B) Increase in birth-rate
(C) Decrease in death-rate
(D) Improvement in health facilities
Ans : (D)

32. How much percentage of Protein is present in Soyabean ?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
Ans : (B)

33. What is Kharpatwar ?
(A) Harmful and unwanted (Weeds) plants grown in cultivated crops
(B) Unwanted plants on Soil
(C) Harmful grass in Rice Harvest
(D) Useless grass on agricultural land
Ans : (A)

34. Central Rice Research Institute is located at—
(A) Chennai
(B) Cuttak
(C) Kolkata
(D) Rajendranagar
Ans : (B)

35. In India which harvest in highest average product per Hectare ?
(A) Maize
(B) Wheat
(C) Bajra
(D) Rice
Ans : (D)

36. At present how many states and centrally administered territories are there in Indian Union ?
(A) 25, 8
(B) 24, 8
(C) 28, 7
(D) 26, 8
Ans : (C)

37. In Rajya Sabha elected members of which state are in greatest number ?
(A) Andhra Pradesh
(B) Madhya Pradesh
(C) Bihar
(D) Uttar Pradesh
Ans : (D)

38. So far who has won the Lok Sabha seat with highest number of votes ?
(A) Indira Gandhi
(B) Jawahar Lal Nehru
(C) Ram Vilas Paswan
(D) P. V. Narsimha Rao
Ans : (D)

39. Which state in India first started Employment Guarantee Programme ?
(A) West Bengal
(B) Gujarat
(C) Kerala
(D) Maharashtra
Ans : (D)

40. Breeder Seed is which stage of Seed Production Cycle ?
(A) Second
(B) First
(C) Third
(D) Fourth
Ans : (B)

41. Which is the biggest Trade Union of India ?
(A) BMS
(B) CITU
(C) INTUC
(D) AITUC
Ans : (A)

42. Steel Ball floats on mercury, because—
(A) Nothing can sink in mercury
(B) Density of mercury is higher than steel
(C) Density of steel is higher than mercury
(D) Ball can not float
Ans : (B)

43. Sun Light takes……time to reach the earth.
(A) 8 seconds
(B) 8 years
(C) 8 minutes
(D) 4 minutes
Ans : (C)

44. pH value of pure water is—
(A) 14
(B) 2
(C) 7
(D) 9
Ans : (C)

45. It burns with blue flame—
(A) Nitrogen
(B) Hydrogen
(C) Sulphur dioxide
(D) Carbon monoxide
Ans : (A)

46. Deficiency of which vitamin causes Night Blindness ?
(A) Vitamin A
(B) Vitamin B1
(C) Vitamin C
(D) Vitamin D
Ans : (A)

47. Which organ of body is affected first by Nuclear Radiation ?
(A) Liver
(B) Lungs
(C) Bone Marrow
(D) Brain
Ans : (C)

48. How many chromosomes are there in a Bacteria ?
(A) One
(B) Two
(C) Many
(D) Not even one
Ans : (A)

49. Whose milk contains highest protein content ?
(A) Cow
(B) Goat
(C) Sheep
(D) Buffalo
Ans : (C)

50. With which area Dr. V. J. Curian is connected ?
(A) Animal Husbandry
(B) Milk Development Industry
(C) Plant Protection
(D) None of the above
Ans : (B)

51. Find out that smallest number which is fully divisible by 6, 10, 15 and 18—
(A) 800
(B) 900
(C) 1,000
(D) 1020
Ans : (B)

52. When is ‘World Health Day’ celebrated ?
(A) 12 December
(B) 7 April
(C) 10 October
(D) 23 May
Ans : (B)

53. Which world renowned Mountain peak is called ‘Sagar Matha’ ?
(A) Everest
(B) Nanda Devi
(C) K2
(D) Kanchenjunga
Ans : (A)

54. In India, which city is called ‘Sun City’ ?
(A) Puri
(B) Kohima
(C) Jodhpur
(D) Kanyakumari
Ans : (C)

55. In which area is Bhatnagar Prize given ?
(A) Sports
(B) Film
(C) Science and Technology
(D) Literature
Ans : (C)

56. How many spokes (Tilian) are there in the wheel in India’s National Flag ?
(A) 20
(B) 22
(C) 24
(D) 25
Ans : (C)

57. Which of the following separates Daman from Diu ?
(A) Mahi River
(B) Rann of Kachha
(C) Narmada River
(D) Gulf of Khambhat
Ans : (D)

58. Of the following countries which is situated in the ‘Horn of Africa’ ?
(A) Tunisia
(B) Somalia
(C) Kenya
(D) Sudan
Ans : (B)

59. World’s Wild Ass is found only in—
(A) Rann of Kachchh
(B) Chhota Nagpur
(C) Ladakh
(D) Sunderbans
Ans : (A)

60. Indian Space Research Institute’s Satellite Tracking and Ranging Station is located at—
(A) Kawalur
(B) Hassan
(C) Sriharikota
(D) Ahmedabad
Ans : (B)

61. What is the name of India’s first fast breeder Neutron Reactor located at Kalpakkam ?
(A) Apsara
(B) Dhruv
(C) Poornima
(D) Kamini
Ans : (D)

62. Of which famous woman’s ‘autobiography’ is ‘Golden Girl’ ?
(A) Amrita Shergil
(B) P. T. Usha
(C) Lata Mangeshkar
(D) Nargis Dutt
Ans : (B)

63. What is Tejas ?
(A) Ultramodern Radar
(B) Ultramodern Fighter Battleship
(C) Light Combat Aeroplane
(D) Remote Sensing System
Ans : (C)

64. Sharda Act is related to—
(A) Child Marriage
(B) Sati Pratha
(C) Widow Remarriage
(D) Child Killings
Ans : (A)

65. Out of the following which is concerned with ‘Al Nino’ ?
(A) Labrador Current
(B) Benguela Current
(C) Humboldt Current
(D) Kuro Shiwo Current
Ans : (C)

66. Which separates the main land of India from Rameshwaram Island ?
(A) Pamban Channel
(B) 9thChannel
(C) 10thChannel
(D) Palk Strait
Ans : (A)

67. What are the main constituents of Biogas ?
(A) Methane + Carbon dioxide
(B) Nitrogen + Butane
(C) Ethane + Butane
(D) Carbon dioxide
Ans : (A)

68. Who gave the name, ‘Indian National Congress’ ?
(A) Dadabhai Naoroji
(B) A. O. Hume
(C) W. O. Bannerji
(D) Dufrin
Ans : (A)

69. Which of the following gas produces ‘Green House Effect’ ?
(A) CO
(B) CO2
(C) Nitrogen
(D) Nitric oxide
Ans : (B)

70. Which of the following is not a Free Trade Zone ?
(A) Kandla
(B) Falta
(C) Santacruz
(D) Pondicherry
Ans : (D)

71. Which of the following connects the Sikyang Province of China and Pakistan Occupied Kashmir (POK) ?
(A) Siachin road
(B) Silk road
(C) Goodwill road
(D) Karakoram road
Ans : (D)

72. Starting from evening 8 O’clock to 2 O’clock at night how many times the hands of the clock shall make right angle ?
(A) 6
(B) 8
(C) 11
(D) 7
Ans : (C)

73. Who constructed the Jagannath Temple at Puri ?
(A) Narsingh Burman
(B) Parmeshwar Burman
(C) Antburman Chodgang
(D) Aadityaburman Chodgang
Ans : (C)

74. In which of the following the ‘Gayatri Mantra’ is included ?
(A) Samveda
(B) Rigveda
(C) Yagyavalkya
(D) Aitareya Upanishad
Ans : (B)

75. Enzymes are made mostly of the following—
(A) Fats
(B) Protein
(C) Carbonic acids
(D) Carbohydrate
Ans : (B)

76. Out of the following Shiv Samudram water-fall is situated on which River ?
(A) Tungabhadra River
(B) Narmada River
(C) Kaveri River
(D) Chambal River
Ans : (C)

77. In India which of the following has the longest Railway Division ?
(A) Eastern Railway
(B) Western Railway
(C) Northern Railway
(D) Central Railway
Ans : (D)

78. When was life originated on Earth ?
(A) 300 mllion years ago
(B) 3500 million years ago
(C) 1000 million years ago
(D) 4500 million years ago
Ans : (B)

79. What is an Atomic Reactor ?
(A) A Reservoir of Heavy Water
(B) Atomic furnace in which nuclear fission produces heat
(C) A Chemical Reservoir
(D) An Atom Bomb
Ans : (B)

80. In Datia (M.P.) ‘Kudau Singh Music School’ was started in his memory. Kudau Singh was associated with which area of music ?
(A) Bansuri
(B) Tabla
(C) Sitar
(D) Mridang and Pakhawaj
Ans : (D)

81. What is Param 10,000 ?
(A) Radar
(B) Surface to Surface missile
(C) Surface to Air missile
(D) Computer
Ans : (D)

82. In Madhya Pradesh Panna is associated with—
(A) Copper
(B) Gold
(C) Diamond
(D) Mica
Ans : (C)

83. Who was the first Caliph ?
(A) Imam Husain
(B) Abu Bakr
(C) Sulaiman
(D) Constantine
Ans : (B)

84. India is the Chief Exporter of—
(A) Coffee
(B) Mica
(C) Silk
(D) Jute
Ans : (B)

85. Who wrote ‘Arthashashtra’ ?
(A) Bana Bhatta
(B) Kalidas
(C) Kautilya
(D) R. K. Narayan
Ans : (C)

86. Who wrote the book ‘Wings of Fire’ ?
(A) Jawaharlal Nehru
(B) Kuldeep Nayar
(C) A. P. J. Abdul Kalam
(D) J. B. Kriplani
Ans : (C)

87. Which is the National Anthem of India ?
(A) Vande Mataram
(B) Jana Gana Mana
(C) Sare Jahan Se Achchha Hindostan Hamara
(D) Jhanda Uncha Rahe Hamara
Ans : (B)

88. ‘Kiwi’ is the inhabitant of ?
(A) South Africa
(B) Indonesia
(C) Hungary
(D) New Zealand
Ans : (D)

89. Shambhu Maharaj was connected with—
(A) Painting
(B) Kathak dancing
(C) Film Music
(D) Photography
Ans : (B)

90. Who discovered Bacteria ?
(A) Jenner
(B) Leeuwenhock
(C) Linnaeus
(D) Ronald Ross
Ans : (B)

91. After India became independent who suggested that ‘Indian National Congress’ should be dissolved ?
(A) C. Rajgopalachari
(B) Mahatma Gandhi
(C) Acharya Kriplani
(D) Jai Prakash Narayan
Ans : (B)

92. Of the following dances which one is performed by single person ?
(A) Kuchipudi
(B) Bharat Natyam
(C) Odissi
(D) Mohiniattam
Ans : (D)

93. Who called ‘Britain is a nation of shop-keepers’ ?
(A) Mussolini
(B) Hitler
(C) Napoleon
(D) Garibaldi
Ans : (C)

94. Who founded, ‘Servants of India Society’ ?
(A) Pandit Hridaya Nath Kunjru
(B) Gopal Krishna Gokhale
(C) Bal Gangadhar Tilak
(D) Shriniwas Shastri
Ans : (B)

95. In which country were the 2008 Olympic Games held ?
(A) China
(B) Australia
(C) Spain
(D) England
Ans : (A)

96. Who was the first Indian Woman to swim across the English Channel ?
(A) Kamaljit Sandhu
(B) Rita Faria
(C) Arti Saha
(D) Shanta Rangaswami
Ans : (C)

97. When was the India’s Communication Satellite INSAT-C3 was launched from Kourou in French Guiana ?
(A) February 28, 2000
(B) May 26, 1999
(C) March 22, 2000
(D) January 24, 2002
Ans : (D)

98. Which country is called the ‘Playground of Europe’ ?
(A) France
(B) Scotland
(C) Netherland
(D) Switzerland
Ans : (D)

99. When was the United Nations Organisation founded ?
(A) October 20, 1945
(B) June 16, 1945
(C) November 11, 1944
(D) October 24, 1945
Ans : (D)

100. Keil Canal links the following—
(A) North Sea and Baltic Sea
(B) Pacific Ocean and Atlantic Ocean
(C) Mediterranean Sea and Red Sea
(D) Mediterranean Sea and Black Sea
Ans : (A)

101. Name the Indian State having the least population—
(A) Sikkim
(B) Nagaland
(C) Goa
(D) Tripura
Ans : (A)

102. The Hijri Era (Calendar) started in—
(A) 570 A.D.
(B) 1129 A.D.
(C) 622 A.D.
(D) 712 A.D.
Ans : (C)

103. Which of the following is the indicator of Air Pollution ?
(A) Cycas
(B) Algae
(C) Bryophytes
(D) Lichens
Ans : (D)

104. During Dehydration from human body the substance which is usually lost is—
(A) Sugar
(B) Sodium Chloride
(C) Calcium Phosphate
(D) Potassium Chloride
Ans : (B)

105. Where is the Test Tube Baby (Egg) fertilised ?
(A) Outside the body of mother
(B) In the Test Tube
(C) In the Testis of man
(D) It does not take place
Ans : (B)

106. The well known discussion between Nachiketa and Yama is narrated in—
(A) Kathopanishad
(B) Kenopanishad
(C) Mundakopanishad
(D) Chhandogyopanishad
Ans : (A)

107. Haemophilia is a genetic diseases which is caused by—
(A) Fall in Haemoglobin level
(B) Rheumatic Heart
(C) Absence of clotting of blood
(D) White blood cells become less in number
Ans : (C)

108. In Indian Constitution in which ‘Schedule’ there is mention of antidefection laws ?
(A) 10th Schedule
(B) 8th Schedule
(C) 2nd Schedule
(D) 5th Schedule
Ans : (A)

109. In British period in India fast development of Industries did not take place, because—
(A) Absence of Natural Resources
(B) Absence of Foreign Capital
(C) Absence of Heavy Industries
(D) Wealthy people were disinterested in Industries
Ans : (B)

110. When ants bite they inject in human body, this substance which causes pain—
(A) Glacial acetic acid
(B) Formic acid
(C) Methanol
(D) Stearic acid
Ans : (B)

111. Out of the following pairs of States and Tribes which pair is not correct ?
(A) Assam—Miri
(B) Arunachal Pradesh—Apatani
(C) Madhya Pradesh—Lebada
(D) Nagaland—Konyak
Ans : (C)

112. Out of the following which acts as Biofertilizer for better Rice Harvest ?
(A) Rhizobium sp.
(B) Azotobacter sp.
(C) Blue Green Algae
(D) Kawak Mul Kawak
Ans : (C)

113. Song (Rag) which is sung in the morning, is—
(A) Bhoopali
(B) Todi (Bhairavi)
(C) Darbari
(D) Bhimpalasi
Ans : (B)

114. Which is the correct sequence in order of ascending atomic weights of Hydrocarbons ?
(A) Propane, Butane, Ethane, Methane
(B) Methane, Ethane, Propane, Butane
(C) Butane, Propane, Ethane, Methane
(D) Butane, Propane, Methane, Ethane
Ans : (B)

115. Antigen is important for human body because it—
(A) Destroys harmful germs
(B) Is useful in treatment of poisons
(C) Reduces the body temperature
(D) Produces the antibodies
Ans : (D)

116. Night on Venus shall be of how many days ?
(A) 180 Earth days
(B) 135 Earth days
(C) 118 Earth days
(D) 50 Earth days
Ans : (C)

117. Who is associated with Discovery of Cristal Dynamics ?
(A) J. C. Bose
(B) C. V. Raman
(C) C. Ramanujam
(D) H. J. Bhabha
Ans : (B)

118. When an air bubble rises from the bottom of the lake and rises to the surface, its shape shall—
(A) Grow bigger
(B) Become smaller
(C) No change
(D) Become saucer shaped
Ans : (A)

119. Total internal reflection takes place when the ray of light passes through—
(A) Air to glass
(B) Water to glass
(C) Air to water
(D) Diamond to glass
Ans : (D)

120. In liquor poisoning which results in blindness the dangerous substance is—
(A) Methyl alcohol
(B) Ethyl alcohol
(C) Emyl alcohol
(D) Benzyl alcohol
Ans : (A)

SOME MATHEMATICAL TERMS: (S-Z)

S

Scalene Triangle
Scalene Triangle is a triangle, wherein, all the sides of the triangle are unequal or of different lengths.

Scalar
A scalar is the one with magnitude, but with no definite direction. Examples of scalars are length, temperature and mass. Mathematically, a scalar is said to be any real number or any quantity that can be measured by using a single real number.

Solid Geometry
Solid geometry is a term used for the surfaces and solids in space. It includes the study of spheres, cones, pyramids, cylinders, prism, polyhedra, etc. It also involves the study of related lines, shapes, points and regions.

Segment
A segment constitutes all points between two given points, including those two points.

Segment of a Circle
Segment of a circle is any internal region of a circle, that is bounded by an arc or a chord.

SAS Similarity
SAS similarity is side-angle-side similarity. When two triangles have corresponding angles as congruent and corresponding sides with equal ratios, the triangles are similar to each other.

SSS Congruence
When two triangles have corresponding sides congruent, the triangles are said to be in SSS congruency.

Semicircle
Semicircle is a half circle, with a 180 degree arc.

Spherical Trigonometry
Spherical trigonometry is a term used for the study of triangles on the surface of any sphere. The sides of these triangles are arcs of great circles. This study is useful for navigation purposes.

Solving Analytically
A technique of solving a mathematics problem, by using numeric or algebraic methods. This technique does not involve the use of a graphic calculator.

Solve Graphically
A technique of solving a mathematics problem, by using graphs and picture. Graphic calculators are used to solve a problem graphically.

Spheroid
Spheroid actually refers to an oblate spheroid. But, in some cases, it refers to an ellipsoid that looks more or less like a sphere.

T

Takeout Angle
The angle cut out from a piece of paper, so that the paper can be rolled into a right circular cone is called as the takeout angle.

Tan
The trigonometric function known as the tangent function, gives the ratio of opposite and adjacent side of a triangle.

Tan^-1
The angle that has tangent equal to 1, therefore, tan^-1 = 45º. In radians tan^-1 = Π/4

Tangent Line
A tangent line touches the curve instead of just crossing it. A tangent line can also be defined as a line that intersects the differential curve at a point.

Tautochrone
Tautochrone is a Greek word that means at the same time. Tautochrone has a shape of cycloid hanging downwards. The peculiar feature of a tautochrone is that a bead sliding down the frictionless wire will always take the same time irrespective of the fact that how high or low is the release point.

Taylor Polynomial
The Taylor polynomial is a partial sum of Taylor series. Using the Taylor's polynomial a function can be approximated to a very close value provided the function possess sufficient number of derivatives.

Taylor Series
Taylor series is given by: f(a) + f'(a)(x - a) + f''(a)/2(x - a)² + f'''(a)/3(x – a)³+.........+ fⁿ(a)/n(x – a)ⁿ.

Term
The parts of a mathematical sequence or operations separated by addition or subtraction.

Tetrahedron
Tetrahedron is a polyhedron with four triangular faces. It can be viewed as a pyramid with triangular base.

Three Dimensional Coordinates
The right handed system of coordinates that is used to locate a point in the three dimensional space.

Torus
If we revolve a circle (In 3-D) about a line that does not intersect the circle, then the surface of revolution creates a doughnut shaped figure called as torus.

Transpose of a Matrix
The matrix which is formed by turning all the rows of the matrix into columns or vice-versa.

Transversal
A line that cuts two or more parallel lines.

Trapezium
A quadrilateral with one pair of parallel sides is referred to as trapezium.

Triple (Scalar) Product
Multiplication of vectors using dot product.
If a, b and c are three vectors then triple scalar product is a. (b x c)

Trivial
Trivial solutions are the simple and obvious solutions of a equation. For example, consider the equation x + 2y = 0, here x= 0, y =0 are the trivial solutions and x = 2, y = -1 are the non-trivial solutions.

Truncated Cone or Pyramid
A cone or pyramid whose apex is cut off by intersecting plane. If the cutting plane is parallel to the base it is called as the frustum.

Truncated Cylinder or Prism
A cylinder or prism that is cut by a parallel or oblique plane to the bases. The other base remains unaffected by the cutting of the base.

Truncating a Number
A method of approximation wherein the decimals are dropped after a certain point instead of rounding. For example, 3.45658 would be approximated to 3.4565.

Twin Primes
Prime numbers that have a difference of two between each other. For example, 3 and 5.

U

Unbounded Set of Numbers
Unbounded set of numbers can be defined as the set of numbers which is not bounded, either by a lower bound or by an upper bound.

Under determined System of Equations
Under determined System of Equations is defined to be a linear system of equations, wherein the equations are comparatively less than the variables. The system might be consistent or inconsistent. This depends upon the equations in it.

Uniform
Uniform means same, constant, or in the same pattern.

Undecagon
A polygon having 11 sides is called undecagon.

Unit Circle
Unit circle is defined to be a circle with radius one and is centered at the origin on the x-y plane.

Uncountable
Uncountable is a set that has comparatively more elements than the set of integers. It is an infinite set, in which one cannot put its elements into a one-to-one correspondence with its set of integers.

Upper Bound of a Set
Upper bound of a set is defined to be a number which is greater than or equal to all the elements present in a set. For instance, 4 is a upper bound of the interval [0,1], similarly 3,2 and 1 also are the upper bounds of this interval.

u-Substitution
u-Substitution is a method of integration, that necessarily involves the use of the chain rule in its reverse form.

Union of Sets
Union of sets is defined as the combination of the elements of two sets or more than that. The union is denoted by the U symbol.

Unit Circle Trigonometry Definitions
Unit circle trig definitions is the set of all the six trigonometry functions such as the sine, cosine, tangent, cosecant, secant, and cotangent.

V

Variable
The independent quantity in an algebraic expression is called as variable.

Varignon Parallelogram of a Quadrilateral
The parallelogram formed by joining the midpoints of the adjacent sides of any quadrilateral.

Vector
A quantity drawn as an arrow that has both magnitude and direction.

Vector Calculus
The problems involving calculus principles (derivatives, integrals etc) of the three dimensional figures.

Venn Diagrams
Venn diagrams are the pictorial representation of the set operations.

Verify a Solution
We verify a solution by putting the obtained values of the variables and checking if those values satisfy the expression.

Vertex
For a triangle, the meeting end of two sides is called a vertex.

Vertex of an Ellipse
The points on the ellipse where the ellipse takes a sharp turn. Mathematically, vertices of an ellipse are the points that lie on the line through the foci (or the major axis)

Vertex of a Hyperbola
The points at which the hyperbola takes its sharpest turns. Vertices of a hyperbola are the points that lie on the line through the foci.

Vertex of a Parabola
The point at which the hyperbola takes a sharp turn. The vertex of a parabola lies midway between the focus and directrix.

Vertical Angles
Vertical angles are the opposite angles that are formed due to the intersection of two lines.

Vertical Compression
Vertical shrinking of a geometrical figure is called as vertical compression.

Vertical Dilation
Enlargement of a geometrical figure vertically is called as vertical dilation.

Vertical Line Equation
The equation x = a is called the vertical equation of line.

Vertical Line Test
It is used to test if a relation is a function. It is a fact that if a vertical line cuts the graph of a relation at more than one point then the given relation is not a function.

Vertical Reflection
A reflection in which a plane figure is vertically flipped. For a vertical reflection the axis of reflection is always horizontal.

Vertical Shift
Shifting a geometrical figure vertically is called as vertical shift.

Vertical Shrink
Vertical shrink is the shrink in which the plane figure is distorted vertically.

Vertical Stretch
Stretching the dimensions of a figure by a constant factor K in the vertical direction is called vertical stretch.

Vinculum
The horizontal line that is used in a fraction or radical.

W

Washer
The region between two concentric circles is called as washer. The radii of the two concentric circles different.

Washer Method
Washer method is used to determine the volume of solid of revolution.

Weighted Average
A type of arithmetic mean calculation in which one of the sets among the various sets of observation carries more importance than others (weight).

Whole Numbers
The numbers 0, 1, 2, 3, 4, 5....etc.

X

x-intercept
The point at which a graph intersects the x-axis.

x-y Plane
The plane formed by the x and y axis of the coordinate system.

x-z Plane
The plane formed by the x and z axis of the coordinate system.

Y

y-intercept
y-intercept is defined as a point where the graph intersects the y-axis.

y-z Plane
y-z plane is simply defined as the plane formed by the y-axis and z-axis.

Z

z-intercept
The point at which a graph intersects the z-axis.

Zero
Zero is a digit and plays a crucial role in mathematics. Zero is considered as a neutral number as it is neither positive nor negative. It is also an additive identity.

Zero Dimensions
When we talk of zero dimensions it means that no motion is possible without leaving that point.

Zero Matrix
A matrix all whose elements are zero.

Zero of a Function
If f(x) = 0, then the value of x which gives f(x) = 0, is called zero of a function.

Zero Slope
Any horizontal line has a slope equal to zero. A horizontal line has same y-coordinate so from the formula (y₂ - y₁)/(x₂ - x₁), we get the slope equal to zero.

Zero Vector
A vector with no magnitude and direction is called as a zero vector.

SOME MATHEMATICAL TERMS: (N-R)

N

n-dimensions
n-dimensions is the property of space that indicates that n mutually perpendicular directions for movement of any particle in that space is possible.

Natural Domain
It is an alternative term for domain. It is the range within which the function exists or has definite values. The term natural domain is used to signify that the domain is not restricted.

Natural Logarithm
When the logarithm of a number is taken with respect to the base e, then the logarithm is said to be natural logarithm. The natural logarithm is represented as ln a, where a is the number.

Natural Numbers
All integers greater than 0 are called natural numbers.

Negative Direction
The negatively associated data is often described in the form of a scatterplot. This way of describing natural numbers is known as negative direction.

Negative Exponent
A negative exponent is used to describe the reciprocal of the number. For example, 5^-2=1/5²

Negative Number
Any real number less than 0 is called a negative number.

Negative Reciprocal
The process of taking the reciprocal of a number and then its negative is called the negative reciprocal. For example the negative reciprocal of ¼ is -4.

Negatively Associated Data
If in a set of paired data, the value of one side increases with the decrease in the other, then the data is referred to as the negatively associated data.

Neighborhood
The neighborhood of any number a is the open interval containing the number. For example, the neighborhood of a can be written as (a + d, a - d).

n – gon
A polygon with n number of sides is called n – gon. For example, a hexagon can also be called 6-gon.

Not Adjacent
Two angles or lines are said to be not adjacent to each other, if they are not near to each other.

Nonagon
A polygon having nine sides is called a nonagon.

Noncollinear
The points that do not lie in a single line are said to be noncollinear points.

Non-Euclidean Geometry
To understand Non-Euclidean geometry we need to understant the parallel postulate. The paraller postulate states that for an given point say P and a line l, not passing through P, there is exactly one line that passes through P, which is parallel to l. The Non-Euclidean Geometry, thus refers to that branch of geometry that does not obey the parallel postulate principle. The hyperobolic geometry and elliptic geometry fall in the class of Non-Euclidean Geometry.

Nonnegative
Any quantity that is not less than zero is refered as nonnegative.

Nonnegative Numbers
The set of integers starting from 0 to infinity in the positive direction of the X-axis is referred to as whole numbers.

Non-overlapping sets
Two sets of numbers which do not have a single element in common are called non-overlapping sets.

Non real number
Any complex number of the form a + bi, where b is not equal to 0 is called a non real number. In other words, any number with an imaginary part is called non real number.

Nonsingular Matrix
Nonsingular matrix is also called Invertible Matrix. Any square matrix whose determinant is not 0 is called a nonsingular matrix.

Nontrivial
The solution of an equation is said to be nontrivial, if the solution does not include zeroes.

Nonzero
Any positive or negative number is a nonzero number.

Normalizing a vector
The process of finding out a unit vector parallel to the given vector and of unit magnitude is called normalization of the vector. The process is carried out by dividing the vector with its magnitude.

n th derivative
The process of taking the derivative of a function n times is called nth derivative. If the derivative of f(x) is taken n times, then its nth derivative will be represented as fⁿ(x).

n th Partial Sum
The sum of the first n terms in an infinite series is called the nth partial sum.

n th Root
The n th root of a number is the number which when multiplied with itself n times gives the number in question. The n th root of 5 can be represented as 5^1/n.

Null Set Any set with no elements in it is called a null set.

Number Line
A line representing all real numbers is called the number line.

Numerator
The top part of any fraction is called the numerator. In case of integers, the number itself is the numerator, as it is divided by 1.

O

Oblate Spheroid
If we revolve an ellipse about its minor axis then the 3 dimensional sphere obtained will be of the shape called oblate spheroid. Earth is an example of oblate spheroid.

Oblique
A line or a plane that is neither horizontal nor vertical but is tilted at some specific angle is called oblique.

Oblique Cone
An oblique cone is a cone in which the center of the base of the oblique cone is not aligned (not in line) with the center of the apex of the cone.

Oblique Cylinder
If the bases of the cylinder are not aligned just one above the other, it is called the oblique cylinder.

Oblique Prism
A prism whose bases are not aligned directly one above the other is called as oblique prism.

Obtuse Angle
An angle whose measure is more than 90º but less than 180º.

Obtuse Triangle
If one of the angles of a triangle is an obtuse angle then it is called as the obtuse triangle.

Octagon
A polygon with 8 sides is called octagon. It may have equal or unequal sides.

Octahedron
Octahedron is a polyhedron with 8 faces. An octahedron appears like two square based pyramids placed on one another. All the faces of an octahedron are equilateral triangles.

Octants
The eight parts into which the three dimensional space is divided by the co-ordinate axis.

Odd/Even Identities
Trigonometric identities show whether each trigonometric function is an odd or even function.
For example:
sin(-x) = sinx
cos(-x) = cosx
tan(-x) = tanx
csc(-x) = -cscx
sec(-x) = secx
tan(-x) = tanx
cot(-x) = -cotx

Odd Function
If the graph of a function is symmetric about x axis then the function is said to be an odd function. Alternately, an odd function satisfies the condition, f(-x) = -f(x).

Odd Number
The set of integers that are not a multiple of 2. For example, {1, 3, 5, 7, 9, ...)

One Dimension
A dimension of the space where motion can take place in only two directions, either backward or forward.

One-Sided Limit
Taking the limit of a term either from the left hand side or right hand side is called the one-sided limit.

One-to-One Function
A one-one function is type of function in which every element of the range corresponds to at least one element of the domain. A one-to-one function passes both the tests, the horizontal and vertical test.

Open Interval
A set interval excluding the initial and final numbers of the domain. For example in the interval of (2, 5) , 2 and 5 are the excluded from the set of numbers while performing any mathematical operation.

Operations on Functions
The operations on functions are as follows:
Addition: (f +g)(x) = f(x) + g(x)
Subtraction: (f - g) = f(x) – g(x)
Multiplication: (fg)(x) = f(x). g(x)
Division: (f/g)(x) = f(x)/g(x)

Order of a Differential Equation
The power on the highest derivative of a differential equation is called as the order of differential equation.

Ordered Pair
Two numbers written in the form (x,y) are called as the ordered pairs.

Ordinal Numbers
The numerical words that indicate order. The ordinal numbers are first, second, third etc,

Ordinary Differential Equation
A differential equation free of partial derivative terms.

Ordinate
The y coordinate of a point is usually called as the ordinate. For example, if P is a point (5,8) then the ordinate is the 8.

Origin
The reference point of any graph indicated by (0,0) in 2-D and (0,0,0) in 3-D.

Orthocenter
The point of intersection of three altitudes of a triangle is called orthocenter.

Orthogonal
Orthogonal means making an angle of 90º

Outcome
The result of an experiment, like throwing a dice or taking out a pack of cards from a set of cards.

Overdetermined System of Equations
An equation in which there are more equations than the number of variables involved.

P

Pi
Pie is defined as the ratio of circumference of a circle to its diameter. It is represented by the Greek letter Π. Many great mathematicians have done pioneering work in researching on the number pi like, Archimedes, Euler, William Jones etc, to name a few.

Point-Slope Equation of a Line
y – y₁ = m (x – x₁) is known as the point slope equation of a line, where m is the slope of the line and (x₁, y₁) represents a point on the line.
For example, equation of a line passing through (3,4) and making an angle of 45 degrees with the positive direction of x-axis is, y – 4 = 1(x – 3), here, (x₁, y₁) = (3,4) and slope = m = tan 45° = 1.

Polar Axis
The x axis is known as the polar axis.

Polar Conversion Formulas
The rules that are required to change the rectangular coordinates into polar coordinates are known as the polar conversion formulas.

Conversion Formulas
Polar to rectangular- x = rcosθ , y = rsinθ
Rectangular to polar- r²= x² + y²
Tanθ = y/x

Polar Curves
Spirals, lemniscates and limacones are the curves that have equations in polar form. Such types of curves with equations in the polar form are known as the polar curves.

Polar Integral Formula
Polar integral formula gives the area between the graph of curve r = r(θ ) and origin and also between the rays θ= α and θ= β (where α ≤ β).

Polygon
A closed figure bounded by line segments. The name of the polygon describes the number of sides of a polygon. Triangle, pentagon,hexagon etc are the examples of polygon.

Polygon Interior
All the points enclosed by a polygon is called as the polygon interior.

Polynomial Facts
An expression of the form, p(x) = a_nxⁿ + a_n-1x^n-1 +.............+ a₂ + a₁x + a₀ is called as the standard polynomial equation. Examples of polynomial equations are 3x + 2y² = 5 and 5x²+ 3y = 3.

Polynomial Long Division
Polynomial long division is useful method to express a n improper rational expression as the sum of a polynomial and a proper rational expression.

Positive Number
A real number greater than zero is known as a positive number.

Positive Series
A series that consists of only positive terms.

Postulate
A postulate is just like an assumption that is accepted to be true without proof.

Power
The number or variable (called as base) that is raised to the exponent is called as power.

Power Rule
Power rule is a formula that is used to find the derivative of power of a variable.

Power Series
A series that represents a function as a polynomial and whose power goes on increasing with every term. In other it has no highest power of x.
Power series in x is given by:
_n=0∑^n=∞a_nxⁿ + a₁x+ a₂x² + a₃x³ +......

Prime Numbers
A number that has one and the number itself as the factors. For example, 1, 2, 3, 5, 7, 11....

Probability
The likelihood of occurrence of an event is called as probability. It is one of the most researched areas of mathematics. There are some basic rules of probability:

• For any event A, 0≤ P(A) ≤ 1
• P = 1 for a sure event.
• P = 0 for an impossible event
• P (not A) = 1- P(A) or P(A^c) = 1 – P(A)

Proper Fraction
If the numerator of a fraction is less than the denominator then the fraction is said to be proper.

Proper Rational Expression
A rational expression having degree of the numerator less than the degree of denominator.

Pythagorean Theorem
According to Pythagoras theorem, the sum of squares of the two arms or legs of a right angled triangle is equal to the sum of the square of the hypotenuse. If AB, BC and AC are the threes side of a right angled triangle taken in same order then AC² = AB² + BC² .
.

Q

Q1
Q1 or the first quartile is the median of the data which are less than the overall median. For example, consider a set of data, 3, 5, 7, 8, 9, 10. The median of this set of data is 7. 3, 5 are the only numbers less than the median. The median of the numbers 3 and 5 is 4, so the 1st quartile is 4.

Q3
Q3 or the third quartile is the median of the data which is more than the overall median. For example, if we consider a set of data, 2, 3, 5, 6, 8 the median is 5. Now, 6 and 8 are the numbers in this set that are greater than the overall median. These are called as Q3 or third quartile.

QED
QED stands for quod erat demonstrandum, which means "That which has to be proven".

Quadrangle
A polygon with four sides.

Quadrants
The four sections into which the x-y plane is divided by the x and y axis.

Quadratic
A two degree polynomial equation represented by the equation,
ax² + bx + c = 0, where, a ≠ o.

Quadratic Polynomial
Any polynomial of degree 2.

Quadrilateral
A closed figure bounded by four lines.

Quadruple
Four times any number or a value is called as quadruple.

Quartic Polynomial
A polynomial of degree four.
Example: ax⁴ + bx³ + cx² + dx + e = 0

Quintic Polynomial
A polynomial of degree 5
a⁵ + b³ + c

Quintiles
From a set of data, the 20th and 80th percentiles are called the quintiles.

Quintuple
Multiplying any number by a factor of 5.

R

Radian
It is the unit of measuring angles. For example, 180 º = Π radians, 45 º = Π/4 radians etc,

Radical
The designated symbol for the square root of any mathematical entity is called radical.

Radicand
The mathematical quantity whose nth root is taken. It is the number under the radical symbol.

Radius of a circle
The distance or the measure of the line segment between center of circle and any point on the circle is called the radius of the circle.

Range
The limit within which set of values reside. For example, the range of the function y = x² is [0, ∞] or {y|y ≥ o}

Ratio
The resultant quantity derived by dividing one number with the other.

Rational Exponents
The exponents which are composed of rational numbers are called rational exponents.

Rational Function
Given two polynomials, one divided by another, the resultant is expressed as a function, then it is called rational equation.

Rational numbers
The set of all ratios, made up of real numbers, which do not have zero as denominator.

Rational root theorem
All possible roots of a polynomial are provided by the rational root theorem.

Rationalizing Substitution
It is a method of integration capable of transforming a fractional integrand into more than one kind of root.

Rationalizing the Denominator
The process of adjusting a fraction is such a way that denominator becomes a rational number.

Ray
A line having only one end point and extending infinitely in the other direction is called a ray.

Real numbers
It is a set of all numbers consisting of positive, negative, rational, square root, cube root etc. Real numbers form the set of all the numbers on the number line.

Reciprocal Numbers
One divided by the given number is the reciprocal of the number.

Rectangle
A rectangle is a quadrilateral having all equal angles. They are equal to 90⁰.

Rectangle Parallelepiped
Rectangle Parallelepiped is a polyhedron where every face is a rectangle.

Recursive Formula
In a series of numbers, the next term in the series is calculated by a formula which uses previous terms in that same series. This term is called recursive term and the process is called recursive formula.

Reducing a fraction
When numerator and denominator, both have common factors, we cancel out all of them until no common factor remains.

Regular Octahedron
A polyhedron which has eight faces is called regular octahedron.

Regular Polygon
A regular polygon is one in which all angles and sides are are congruent to each other.

Regular Prism
Regular Prism is a prism in which all the face comprise of regular polygons.

Regular Pyramid
The pyramid who's base is made up of regular polygon is called regular pyramid.

Regular Right Prism
A regular right prism is one whose bases are made up of right polygons

Right Pyramid
Right Pyramid is a pyramid where base is a regular regular polygon and the apex is directly on top of the center of the base of polygon.

Regular Tetrahedron
Regular Tetrahedron is a pyramid where all the faces of the polygon are triangles.

Related Rates

The set of all the problems, where the changes in various rates are calculated by means of differentiation.

Relation
The ordered pair of entities which have some distinct abstraction between them is called a relation.

Relative Maximum
Relative maximum is a point in the graph which is at the highest point for that particular section.

Relative Minimum
Relative minimum is a point in the graph which is at the lowest point for that particular section.

Relative Prime
Those numbers which have the greatest common factors as prime numbers are called relative prime numbers.

Remainder
The number which is left over after the division as an undivided whole number is called remainder.

Residual
The measure of a line which is parallel to Y axis and one end of which is touching the data point is called residual.

Rhombus
The parallelogram having all equal sides is called rhombus.

Reimann Geometry
Reimann geometry is a type of geometry where all the lines are considered non parallel, intersecting and happening on the surface of the sphere.

Right Circular Cone
A right circular cone is a cone whose base is a circle and any radius is making right angle to the line segment from apex of the cone to center of the circle.

Right Circular Cylinder
Right circular cylinder cylinder whose bases is are circular.

Regular Hexagon
A hexagon with all sides equal to each other is called regular hexagon.

Rose Curve
The leaves of the curve which have complete symmetry over the center of the curve is called a rose curve.

Rotation
When figure is transformed according to a fixed point is called rotation (generally in same plane).

Rounding a Number
Without compromising the degree of accuracy to a large extent, the approximation of number to the nearest value is called rounding of the number