Syllabus - EXAM, Recruitment, Test, CTET, UGC

Friday, January 27, 2012

UPSC Civil Service Syllabus Mathematics (Optional Subjects)

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Syllabus of Examination - UPSC Civil Service

Mathematics (Optional Subjects)

Paper-I

(1) Linear Algebra: Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; Linear transformations, rank and nullity, matrix of a linear transformation.
Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices and their eigenvalues.

(2) Calculus: Real numbers, functions of a real variable, limits, continuity, differentiability, mean-value theorem, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange's method of multipliers, Jacobian.
Riemann's definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes.

(3) Analytic Geometry: Cartesian and polar coordinates in three dimensions, second degree equations in three variables, reduction to canonical forms, straight lines, shortest distance between two skew lines; Plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties.

(4) Ordinary Differential Equations: Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut's equation, singular solution. Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution.
Second order linear equations with variable coefficients, Euler-Cauchy equation; Determination of complete solution when one solution is known using method of variation of parameters.
Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients.

(5) Dynamics & Statics: Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; Work and energy, conservation of energy; Kepler's laws, orbits under central forces.
Equilibrium of a system of particles; Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions.

(6) Vector Analysis: Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in cartesian and cylindrical coordinates; Higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.

Paper-II

(1) Algebra: Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem.
Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields.

(2) Real Analysis: Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series.
Continuity and uniform continuity of functions, properties of continuous functions on compact sets.
Riemann integral, improper integrals; Fundamental theorems of integral calculus.
Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima.

(3) Complex Analysis: Analytic functions, Cauchy-Riemann equations, Cauchy's theorem, Cauchy's integral formula, power series representation of an analytic function, Taylor’s series; Singularities; Laurent's series; Cauchy's residue theorem; Contour integration.

(4) Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality.
Transportation and assignment problems.

(5) Partial differential equations: Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasilinear partial differential equations of the first order, Cauchy's method of characteristics; Linear partial differential equations of the second order with constant coefficients, canonical form; Equation of a vibrating string, heat equation, Laplace equation and their solutions.

(6) Numerical Analysis and Computer programming: Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods. Newton's (forward and backward) interpolation, Lagrange's interpolation.
Numerical integration: Trapezoidal rule, Simpson's rules, Gaussian quadrature formula.
Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods.
Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers.
Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms.
Representation of unsigned integers, signed integers and reals, double precision reals and long integers.
Algorithms and flow charts for solving numerical analysis problems.

(7) Mechanics and Fluid Dynamics: Generalized coordinates; D' Alembert's principle and Lagrange's equations; Hamilton equations; Moment of inertia; Motion of rigid bodies in two dimensions.
Equation of continuity; Euler's equation of motion for inviscid flow; Stream-lines, path of a particle; Potential flow; Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.

Note : Details here are of informatory in nature. And you are advised to verify details and from any UPDATES from UPSC / Emploment News Paper

Union Public Service Commission

SYLLABI FOR THE EXAMINATION PART-B
MAIN EXAMINATION

GEOLOGY

PAPER - I

1. General Geology: The Solar System, Meteorites, Origin and interior of the earth and age of earth; Volcanoes- causes and products, Volcanic belts ; Earthquakes - causes , effects , Seismiczones of India; Island arcs ,
trenches and mid - oceanridges; Cont inental dr i f ts; Seaf loor spreading, Plate tectonics; Isostasy.

2. Geomorphology and Remote Sensing: Basic concepts of geomorphology ; Weathering and soil formations; Landforms, slopes and drainage; Geomorphic cycles and their interpretation; Morphology and its relation to structures and lithology; Coastal geomorphology; Applications of geomorphology in mineral prospecting, civil engineering ; Hydrologyand environmental studies; Geomorphology of Indian subcontinent. Aerial photographs and their interpretationmerits and limitations; The Electromagnetic spectrum; Orbiting satellites and sensor systems; Indian Remote Sensing Satellites; Satellites data products; Applications of r e m o t e s e n s i Geographic Information Systems (GIS) and Global Positioning System (GPS) - its applications.

3. Structural Geology: Principles of geologic mapping and map reading, Projection diagrams, Stress and strainellips oidandstress- strain relationships of elastic, plastic and viscous materials; Strain markers in deformed rocks; Behaviour of minerals and rocks under deformation conditions; Folds and faults classification and mechanics; Structural analysis of folds, foliations, lineations, joints and faults, unconformities; Time-relationship between crystallization and deformation

Note : Details here are of informatory in nature. And you are advised to verify details and from any UPDATES from UPSC / Emploment News Paper

UPSC CSE Syllabus for HISTORY - MAIN EXAMINATION

Latest Updated Exam / Guess Papers - http://syllabus123.blogspot.com/

Union Public Service Commission (Civil Service Commission)

SYLLABI FOR THE EXAMINATION PART-B
MAIN EXAMINATION

HISTORY

PAPER - I

1. Sources: Archaeological sources: Exploration , excavation , epigraphy , numismatics, monuments Literary sources: Indigenous : Primary and secondary ; poetry , scientific literature , literature , literature in regional languages, religious literature. Foreign accounts: Greek, Chinese and Arab writers.

2. Pre-history and Proto-history: Geographic alfactors; hunting and gather ing (paleol i thic and mesol i thic) ; Beginning of agriculture (neolithic and chalcolithic).

3. Indus Valley Civilization: Origin, date, extent, characteristics, decline, survival and significance, art and architecture.

4. Megalithic Cultures: Distribution of pastoral and farming cultures community life, Settlements, Development of agriculture, Crafts, Pottery, and Iron industry.

5. Aryans and Vedic Period: Expansions of Aryans in India. Vedic Period: Religious and philosophic literature; Transformation from Rig Vedic period to the later Vedic period; Political, social and economical life; Significance of the Vedic Age; Evolution of Monarchy and Varna system.

6. Period of Mahajanapadas: Formation of States (Mahajanapada) : Republics and monarchies; Rise of urban centres; Trade routes; Economic growth; Introduction of coinage; Spread of Jainism and Buddhism; Rise of Magadha andNandas. Iranian and Macedonian invasions and their impact.

7. Mauryan Empire: Foundation of the Mauryan Empire , Chandragupta, Kautilya and Arthashastra; Ashoka; Concept of Dharma; Edicts; Polity, Administration; Economy; Art, architecture and sculpture; External contacts; Religion; Spread of religion; Literature. Disintegration of the empire; Sungas and Kanvas.

Note : Details here are of informatory in nature. And you are advised to verify details and from any UPDATES from UPSC / Emploment News Paper

Wednesday, January 25, 2012

CBSE MODEL TEST PAPER – 2012 Class – X Subject – Science

CBSE MODEL TEST PAPER – 2012

Subject – Science
Class – X
Time allowed: 3 hrs.] [MM: 80
General Instructions:
1. The question paper comprises of two sections, A and B. You
are to attempt both the sections.
2. All questions are compulsory.
3. There is no overall choice. However internal choice has
been provided in all the three questions of five marks category.
Only one option in such question is to be attempted.
4. All questions of section A and all questions of section B are
to be attempted separately.
5. Question numbers 1 to 4 in section A are one mark questions.
These are to be answered in one word or one sentence.
6. Question numbers 5 to 13 are two mark questions, to be
answered in about 30 words each.
7. Question numbers 14 to 22 are three mark questions, to be
answered in about 50 words each.
8. Question numbers 22 to 25 are five mark questions, to be
answered in about 70 words each.
9. Question numbers 26 to 41 are multiple choice questions
based on practical skills. Each question is of one mark.
You are to select one most appropriate response out of the
four provided to you.
Section – A
Q.1 What would be the electron dot structure of a molecule of
sulphur which is made up of eight atoms of sulphur?
Q.2 When a red rose is seen in green light, explain the colour
it will appear to be.
Q.3 Which of the following belong to the same trophic level?
Grasshopper, frog, grass, lizard
Q.4 How does O3 layer of atmosphere protect the human on earth?
Q.5 Three elements A,B and C have 3,4 and 2 electrons
respectively in their outermost shell. Give the group number
to which they belong in the Modern Periodic Table.
Also give their valencies.
Q.6 Identify the elements with the following property and
arrange them in increasing order of their reactivity.
a. An element which is a soft and reactive metal.
b. The metal which is an important constituent of limestone
c. The metal which exists in liquid state at room temperature.
Q.7 What are different methods of contraception? Which technique
of contraception may be effective to prevent sexually
transmitted diseases?
Q.8 A) In the human body what is the role of:
i) Seminal vesicles and ii) Prostate gland.
B) List two functions performed by testes in human beings.
Q.9 An object 3.0cm high is placed at a distance of 24cm in
front of a convex lens of focal length 16cm. Find the position,
nature and size of the image formed. (v = + 48cm, hi
= - 6 cm, the image is real, inverted and larger in size)
Q.10 What is meant by ‘dispersion of white light? Draw a
ray diagram to show dispersion of white light by a glass
prism. Why do we get different colours of light.
Q.11 Write the function of the following parts of human eye:
a) Iris b) Ciliary muscles
c) Pupil d) Eye lens.
Q.12 Define fossil fuels. Give two examples. Write two steps to
conserve fossil fuels.
Q.13 Briefly mention their contribution (any two)
a. Local people in Sal forests management in West
Bengal in 1980s
b. Woman folk of village Reni Gharwal in Himalayas in 1970s.
c. Bishnoi community of Rajasthan in conservation .
Q.14 a) Why does carbon form largest number of compounds?
b) Why are some of these called saturated and other
unsaturated compounds?
c) Write the names of the compounds:
i) CH3CH2Br
ii) H H H H
I I I I
H C C C C C C H
I I I I
H H H H
Q.15 Table given shows a part of the periodic table:
H He
Li Be B C N O F Ne
Na Mg Al Si P S Cl Ar
Using the table explain why
a. Li and Na are considered as active metals?
b. Fluorine is more reactive than chlorine?
c. Atomic size of Mg is less than that of Na?
Q.16 a) Draw the structure of a flower and label any four
parts of it.
b) Give one example to each. Vegetative propagation
done by: a) roots, b) stems, c) leaves
Q.17 Mendel studied the inheritance pattern of traits in
pea plants. According to this study he obtained 9:3:3:1
ratio for certain traits in progeny of F2 generation. Based
on it, answer the followinga.
Which traits did he study? Give the representation.
b. What was the trait of progeny of F1?
c. What rule does this inheritance pattern suggest?
Q18 a) What is genetic drift?
b) How do genetic drift, mutation and natural selection play
a dominant role in the process of evolution?
Q.19 a) What is variation?
b) Describe the role of variations in providing survival and
advantage to the organism of a species.
Q.20 a) Define refractive index of a medium.
b) Light enters from air to glass plate. If the speed of light
in vacuum is 3 ×108 m/s and the speed of light in glass is
2 × 108 m/s, what is the refractive index of glass?
Q.21 Draw a ray diagram in each of the following cases to
show the position and nature of the image formed when
the object is placed:
i) Between optical centre and principal focus (F) of a convex
lens.
ii) at 2F of a convex lens.
Q.22 a) Define far point of eye and write its value for a person
of normal vision.
b) The far point of a myopic person is 80cm in front of
the eye. What is the power of the lens required to correct
the problem?
Q.23 a) Classify the following as alkane, alkene and alkyne:
CH4, C2H4, C3H4, C4H10, C2H2
b) What is substitution reaction? Which of the above compounds
undergo substitution reaction?
c) What happens when methane burns in air? Write chemical
equation.
d) Write the structure of the alcohol used in bear, whisky,
wine etc.
Or
a) Explain the given reactions with example –
i) Oxidation reaction
ii) Combustion reaction
iii) Hydrogenation reaction
b) Why detergents are better cleansing agents than
soaps? Explain.
Q.24a) What is budding? Explain by a series of labeled
sketches the manner in which reproduction occurs in Hydra.
b) Brophyllum reproduces asexually by vegetative propagation.
State two advantages Bryophyllum gets because
of this type of reproduction.
c) Give major difference between self pollination and cross
pollination.
Or
a) What is normal period of menstrual cycle in human
females? Why does menstruation occur?
b) Draw a labeled diagram of human female reproductive system.
c) Define the terms i) Placenta ii) Parturition

Q.25 a) Find the focal length of a lens of power – 2.0 D. What

type of lens is this?

b) What is Snell’s law?

c) Differentiate between a real image and a virtual image.

Or
a) Define 1 dioptre of power of a lens.
b) Name the type of mirror used in solar furnace. Support
your answer with reason.
c) A convex lens forms a real and inverted image of needle
at a distance of 50cm from it. Where is the needle
placed in front of the convex lens if the image is equal
to the size of the object? Also find the power of the lens.
Section – B
Q.26 In the following two diagrams, which represents the correct
path of the light ray through a rectangular glass slab?
(I) (II)
a. I only b.II only c.Both I & II d.None of these
Q.27 According to the law of refraction, angle of incidence (i)
and angle of refraction (r) are related as –
a) i > r b) r > i
c) i = r d) (a) and (b) both
Q.28 A student obtained a blurred image of an object on a
screen using a concave mirror. In order to obtain a sharp
image on the screen he will have to shift the mirror.
a. towards the screen
b. away from screen
c. either towards or away from the screen depending upon
the position of the object.
d. to a position very far away from screen.
Q.29 Which of the following diagrams gives a correct picture:
(III) (IV)
a. I b. II c. III d. IV
Q.30 A child is standing in front of a magic mirror. She finds the
image of her head bigger, the middle portion of her body of
same size and that of the legs smaller. The following is the
order of combinations for the magic mirror from the top.
a) plane, convex and concave
b) convex , concave and plane
c) Concave, plane and convex
d) Convex, plane and concave
Q.31 A student added a piece of zinc metal to four different test
tubes containing different solutions viz. CuSO
ZnSO
change?
a) CuSO
4, AgNO3,4 and FeSO4. In which test tube he observed no4
b) AgNO
3
c) ZnSO
4
d) FeSO
4
Q.32 Ethanoic acid was added to sodium bicarbonate
solution and the gas evolved was tested with a burning
splinter. The following four observations were reported.
a. The gas burns with the pop sound and the flame gets
extinguished.
b. The gas does not burn but the splinter burns with a pop
sound.
c. The flame extinguishes and the gas does not burn.
d. The gas burns with a blue flame and the splinter burn
brightly.
The correct observation is reported in:
a. (i) only b. (ii) only c. (iii) only d. (iv) only
Q.33 Which of the following is alkene?
a) C
20H40 b. C20H42 c. C20H38 d. C20H41
Q.34 Which of the following statements about graphite and
diamond is true
a. They have same crystal lattice structure
b. They have same degree of hardness
c. They have same electrical conductivity
d. They can undergo same chemical reaction
Q.35 Pure acetic acid (100%) is called glacial acetic acid because:
a. It freezes to an ice like mass and floats on water like glaciers
b. It becomes ice and sinks in water
c. It is soluble in water
d. It is sour in taste
Q.36 Seedless plants like banana can be propagated by –
a. Vegetative reproduction
b. Fission
c. Sexual reproduction
d. All of these
Q.37 Which of the following can regenerate its lost body part.
a. Hydra
b. Spirogyra
c. Rhizopus
d. Planaria
Q.38 The process represented in the diagram below is the –
a. Formation of spores in Amoeba
b. Budding in yeast
c. Binary fission in Amoeba
d. Binary fission is paramecium s
Q.39 Ovary in human female reproductive system produces
a. Ovum
b. Hormone
c. Ovum and hormones
d. None of these
Q.40 Normal gestation period in humans is –
a. 3 months
b. 6 months
c. 9 months
d. 12 months
Q.41 Only one parent is needed fora.
Sexual reproduction
b. Pollination
c. Asexual reproduction
d. All of these

Information Source : Amar Ujala (26.1.12)
http://epaper.amarujala.com/pdf/2012/01/26/20120126a_014145.pdf

Saturday, January 21, 2012

X Mathematics Assignments Chapter: Probability

X Mathematics Assignments Chapter: probability

Directions for 1 – 4: State true or false

1. If the probability of a candidate winning an election is 80%, then the probability of the opponent winning the election is also 80%.

2. If two dice are thrown simultaneously then the total number of outcomes is 12.

3. A throws a coin twice and ‘B’ throws a similar coin thrice, the possibility of getting ‘all heads’ is more for ‘B’ than ‘A’.

4. The sum of the probability of an event happening and the same not happening is always the same. 1. F 2. F 3. F 4. F 5. An unbiased die is thrown. What is the probability of getting?

(i) an even number? (ii) a multiple of

5? (iii) an even number or a multiple of 3? (iv) a multiple of 2 and 3?

CBSE Math Test Paper - X Probability -6

CBSE Math Test Paper - X Probability -6
1. (1) A dice is thrown once. Find the probability of getting
(a) A number greater than 3 (b) A number less than 5

2. A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is
(a) Red (b) Black or white (c) Not black

3. A bag contains 4 red 5 black and 6 white balls. A ball is drawn from the bag a random. Find the probability that the ball drawn is
(a) White (b) Red (c) Not black (d) Red or white

4. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a queen nor a jack.

CBSE Math Test Paper - X Probability -1

CBSE Math Test Paper - X Probability -1

Section A MCQ. 1 Mark Each
Q.1 A fair dice is rolled. Probability of getting a number x such that 1 <=x<= 6, is
(a) 0 (b) > 1 (c) between 0 and 1 (d) 1

Q.2 A card is drawn from a well shuffled pack of 52 playing cards. The probability that the card is a red or a hearts is (a)1/3 (b)1/4 (c)1/2 (d)3/13

Q.3 The probability of getting a number between 1 and 25 which prime is
(a) 2/23 (b)9/23 (c)5/23 (d)None of these

CBSE I NCERT I IX SURFACE AREAS AND VOLUMES

CBSE I NCERT I IX SURFACE AREAS AND VOLUMES

Surface Area of a Cuboid and a Cube Surface Area of a Right Circular Cylinder
Surface Area of a Right Circular Cone Surface Area of a Sphere
Volume of a Cuboid Volume of a Cylinder
Volume of a Right Circular Cone Volume of a Sphere

Set Paper-1 Section A

1. The curved surface area of a right circular cylinder of height 14 cm is 88cm2. Find the diameter of the base of the cylinder.

2. Curved surface area of a right circular cylinder is 4.4m2. If the radius of the base of the cylinder is 0.7m, find its height.

3. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 21 cm.

4. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

5. Find the radius of a sphere whose surface area is 154cm2.

6. A matchbox measures 4cm x 2.5cm x 1.5cm. What will be the volume of a packet containing 12 such boxes?

7. A cubical water tank is 6m long, 5m wide and 4.5m deep. How many liters of water can it hold?

8. The capacity of a cubical tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.3m and 10m.

9. The height and the slant height of a cone are 21cm and 28 cm respectively. Find the volume of the cone.

10. If the volume of a right circular cone of height 9cm is 48π cm3, find the radius of the base. (Use π=3.14)

11. A triangle ABC with sides 5cm, 12cm and 13cm cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

12. Find the volume of a sphere whose surface area is 154cm2.

13. How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?

14. Find the amount of the water displaced by a solid spherical ball of diameter (i) 28cm (ii) 0.21m

15. Find the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel wad actually used, if 1/12 th of the steel actually used was wasted in making the tank.

Section B

16. A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine (in mm3) is needed to fill this capsule?

17. A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank.

18. The diameter of a metallic ball is 4.2cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3?

19. A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kilolitres?

20. The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28cm, find (i) height of the cone (ii) Slant height of the cone. (iii) Curved surface area of the cone.

21. A heap of the wheat is the form of a cone whose diameter is 10.5m and height is 3m. Find its volume. The heap is to be covered by congas to protect it from rain. Find the area of the canvas required.

22. The circumference of the base of a cylindrical vessel is 132 cm and height is 25 cm. How many liters of water can it hold?

23. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.\

24. A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?

25. A hemispherical bowl is made of steel, 0.25cm thick. The inner radius of the bowl is 5cm. Find the ratio of their surface areas.

26. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50per m2.

27. The floor of a rectangular hall has a perimeter 250m If the cost of painting the four walls at the rate of Rs 10per m2 is Rs 15000, find the height of the hall.

Section C

28. Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the titles is Rs 360 per dozen.

29. A plastics box 1.5 m long wide and 65 cm deep is to made. It is opened at the top. Ignoring the thickness of the plastics sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of the sheet for it, if a sheet measuring the box.

30. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm, wide and 25 cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all 12 edges?

31. Savitri had to make a model of cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25cm with a 2.5 cm radius? (Use π=22/7)

32. A metal pipe is 77 cm long. The inner diameter of a cross section is 4cm, the outer diameter being 4.4 cm. Find its (i) inner curved surface area. (ii) Outer curved surface area. (iii) Total surface area.

33. In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

34. The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding.

35. A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6m, find the cost of painting it, given the cost of painting is Rs 5 per 100cm2.

Test Paper -2 Questions Bank
1. An underground water tank is in the shape of cube of side 7 m. What will be its volume?
2. What will be volume of a box whose length 16 m, breadth 8 m and height is 5 m?
3. The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of our walls of room?
4. The volume of a cube is 27a3 . Find the length of its edge?
5. How much Aluminium sheet will be required to make a container with lid whose length is 13 m, breadth is 8 m and height is 4 m?
6. The volume of a cube is 1331 cm3 . Find the length of its edge?
7. The length of diagonal of a cube is 17.32 cm. Find the volume of that cube?
8. Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a cube. Find the volume of that cube?
9. Two cubes have edge 10 m. Their edges have been joined and form a cuboid. What will be the surface area of cuboid thus formed?
10. The total volume of a cube is 512 cubic cm. Find the side of a cube?

11. A rectangular box 14 cm long, 10 cm wide and 5 cm high is to be made with card-board. Find the area of card-board to make that box?
12. What will be the volume of a cylindrical tank whose radius is 7 cm and height is 5 cm?
13. How many solid spheres of 2/3 cm radius can be made from a solid sphere of 2 cm radius?
14. If the volume and surface area of a sphere is numerically same then what will be its radius?
15. The volume of a right circular cylinder is 392 π cm3 and its height is 8 cm. Find the radius?
16. The surface area of a sphere is 448 p cm2 . Find its radius?
17. What will be the edge of a cube? If its surface area is 324 sq cm .
18. The volume of a hemisphere is 144 π cm³. What will be its radius?
19. The curved surface area of a cone is 140 π cm². What will be the radius of cone whose slant height is 5 cm.
20. The radius of a solid sphere is 12 cm. How many sphere can be made from it of 6cm radius?
21. The volume of a cuboid is 840 cm³. If its length is 14 cm and breadth is 5 cm. Find the height of cuboid?
22. Four equal cubes have side 5 cm each. They are joined together edge to edge. What will be the surface area of cuboid thus formed?
23. The area of a rhombus is 56 cm2 and its diagonal is 7 cm. Find the length of other diagonal of the rhombus?
24. Find the maximum length of the rod that can be kept in cyboidal box of sides 30cm, 24cm and 18cm.
25. The curved surface area of a cylinder is 216 π . If its height is 18 cm then what will be its radius?
26. 60 circular plates of equal radius are placed on each other to form a cylinder. Find height of cylinder if thickness of each plate if 3/4 cm.
27. Curved surface area of a cone is thrice and curved surface area of the other. Slant height of
second cone is thrice the slant height of first. Find ratio of their radii.
28. A well of 2m diameter is dug 14m deep on the ground. Find the volume of earth taken out.
29. Volume of a solid sphere is 36πcm³ . Find its radius.
30. A boy recasted a cone of 4cm height and 27cm radius into a solid sphere. Find the radiusof the sphere.
Surface Area And Volume (Chapter-11) Answers
1. 343m³          2. 640m³          3. 396m²          4. 3a    5. 376m²          6. 11cm           7. 1000cm³                      8. 1728cm³          9. 1000m²        10. 8cm           11. 520cm²      12. 770cm²1                3. 2714. 3 units                15. 7cm            16. 112cm or 4 7cm                17. 9cm           18. 6cm1         9. 28cm           20. 8
21. 12cm   22. 450cm² 23. 16cm   24. √1800cm or 30 √2cm
25. 6cm 26. 45cm 27. 9:1 28. 44m³   29. 3cm 30. 9cm

CBSE: 10th Class Sample Test Paper - Coordinate Geometry

Q.1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).
Q.2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the ratio 3: 4.
Q.3. Show that the points (1, 1), (3, -2) and (-1, 4) are collinear.
Q.4. Find the centroid of the triangle whose vertices are (3, -5); (- 7, 4) and (10, - 2).
Q.5. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)
Q.6. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.
Q.7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

Heights and Distances : Class X Model Questions

1. The angle of elevation of the top of a tower, from a point on the ground and at a distance of 150 m from its foot,

is 30°. Find the height of the tower correct to one decimal place.

2. From a point P on the level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high,

how far is P from the foot of tower?

3. A kite is flying at a height of 75 meters from the level ground, attached to a string inclined at 60° to the horizontal. Find the length of the string to the nearest meter.

Arithmetic Progression Assignments for Class X CBSE Mathematics Sample Test Paper

Q. 1. Find the roots: (x + 2) / (x – 2) + (x – 2) / (x + 2) = 5/2, x ≠2, x≠ -2

Q. 2. Determine the values of p for which the quadratic equation: 2×2 + p x + 8 = 0 has real roots.

Q. 3. A shopkeeper buys a number of bananas for Rs. 600. If he had bought 10 dozen more bananas for the same amount, each dozen would have cost him Rs. 2 less. Find the number of bananas bought by him.

Q. 4. If the roots of the equation (c2 – ab)x2 – 2(a2 – bc) x + b2-ac = 0 are equal, prove that either a=0 or a3 + b3 + c3=3abc

Model Question Class X Quadratic Equations

1. Find the value of k for kx2 + 2x - 1 = 0, so that it has two equal roots

2. Find the value of k for k x2 - 2√ 5 x + 4 = 0, so that it has two equal roots.

3. If the roots of the equation (b - c) x2 + (c - c) x + (a - b) = 0 are equal, accordingly prove that 2b = a + c.

4. Find the discriminant of the quadratic equation 3x2– 4 √3 x + 4 = 0, and hence find the nature of its roots.

G.K. Questions [solved] – Kendriya Vidyalaya Sangathan ( Primary Teacher-PRT) held on 12-Feb-2011

G.K. Questions [solved] – Kendriya Vidyalaya Sangathan ( Primary Teacher-PRT) held on 12-Feb-2011
1. For instant energy, athletes take :
a) Sucrose
b) Vitamin C
c) Sodium chloride
d) Milk
2. Which Sufi Saint’s Dargah is at Ajmer?
a) Salim Chishtib) Muinuddin Chisti
c) Baba Farid
d) Hazrat Nizamuddin
3. Through which one among the following materials does sound travel the slowest?
a) Air
b) Glass
c) Water
d) Wood
4. The wheel (chakra) in Indian National Flag contains how many spokes?
a) 12
b) 18c) 24
d) 26
5. In eye donation, which of the following parts of eyes is utilized?
a) Iris
b) Lewsc) Corena
d) Retina

G.K. Questions [solved] – Kendriya Vidyalaya Sangathan (TGT) held on 12-Feb-2011

1. Which of the following pairs is not correctly matched?
a) Kalinga Award – Popularization of Science
b) Barlong Award – Agriculture
c) David-Cohen Award – Literature
d) Pulitzer Prize – Progress in Religion
2. Which of the following characters was not a part of Shakespearian plays?
a) Julius
b) Brutus
c) Potter
d) Ariel
3. Which of the following international organizations is dedicated to the cause of wildlife conservation?
a) UNFPA
b) UNDP
c) UNESCO
d) WHO
4. Human Rights Day is observed on :
a) 10 October
b) 9 May
c) 10 December
d) 18 February
5. Railway coaches are made in the largest number at Integral coach factory, situated in:
a) Kapurthala
b) Perambur
c) Varanasi
d) Moradabad
6. Which of the following is not a necessary qualification for a state to become a member of United Nationas Organization? It should :
a) be a sovereign state
b) be a peace loving state
c) be a willing to discharge responsibilities under the UNO charter
d) guarantee human rights and freedom to its citizens
7. The imaginary line on the earth’s surface which closely follows 180o meridian, is called :
a) International date time
b) Tropic of Cancer
c) Equator
d) Prime Meridian

Syllabus - EXAM, Recruitment, Test, CTET, UGC

Friday, January 27, 2012

UPSC Civil Service Syllabus Mathematics (Optional Subjects)

Syllabus of Examination - UPSC Civil Service

Mathematics (Optional Subjects)

Paper-I

Paper-II

Suggested Reading:

UPSC CSE Syllabus for GEOLOGY - MAIN EXAMINATION

Union Public Service Commission

GEOLOGY

PAPER - I

UPSC CSE Syllabus for HISTORY - MAIN EXAMINATION

Union Public Service Commission (Civil Service Commission)

HISTORY

PAPER - I

Wednesday, January 25, 2012

CBSE MODEL TEST PAPER – 2012 Class – X Subject – Science

Saturday, January 21, 2012

X Mathematics Assignments Chapter: Probability

CBSE Math Test Paper - X Probability -6

CBSE Math Test Paper - X Probability -1

CBSE I NCERT I IX SURFACE AREAS AND VOLUMES

CBSE: 10th Class Sample Test Paper - Coordinate Geometry

CBSE: 10th Class Sample Test Paper - Coordinate Geometry

Heights and Distances : Class X Model Questions

Arithmetic Progression Assignments for Class X CBSE Mathematics Sample Test Paper

Arithmetic Progression Assignments for Class X CBSE Mathematics Sample Test Paper

Model Question Class X Quadratic Equations

Model Question Class X Quadratic Equations

Friday, January 20, 2012

G.K. Questions [solved] – Kendriya Vidyalaya Sangathan ( Primary Teacher-PRT) held on 12-Feb-2011

G.K. Questions [solved] – Kendriya Vidyalaya Sangathan (TGT) held on 12-Feb-2011

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