NTSE Syllabus for SAT: Mathematics, Science and Social Science (Download PDF)


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Integers: Question: If X2+X-1=0X0, thenX2+1X2 is a Real numbers. Question: If x and y are two positive real numbers such that their sum is one, then the maximum value of 44xy+xy is.

Question: If the roots of px+2qx+r=2 and qx-2prx+q=o are simultaneously real, than

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Prime numbers

Question: Out of the five digits numbers forn1ed by using digits 1,2, 3,4 and 5, how many are prime numbers?


Question: One of the factors of x + 10x - 27 is

Question: If x −a is a factor of x3 −3 × 2 a + 2a2 x + b then the value of b is:


Question: The HCF of two expressions p and q is 1. Their LCM is:

Simplification of Numerical Expressions

Question: The unit’s digit of the product 31001×71002×131003 is

Sequence and series

Question: The sum 11+12+14+21+22+24+31+32+34+. . +991+992+994lies between

Rational Numbers

Question: If x=11+2, then the value ofx2+2x+3is:

Direct and Inverse Variation

Question: A man can row three quarters of a km against the stream in 11 1 4 minutes and return in 1 7 2 minutes. The speed of the man in still water is:

Linear Equations in Two Variables

Question: If x+y=1thenx3+y3+3xy=

Question: For the equation 3x2+px+3=0 if one of the roots is the square of the other then p =

Statistics and Probability

Question: The probability that a leap year selected will have 53 Sunday is

Question: In a class of boys and girls, a student is chosen at random. If the probability that a boy is chosen is of the probability that a girl is chosen, the ratio of the number of boys to the total number of students is the class is

Question: A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blue and 1 is black?

Question: A number is selected at random from first 50 natural numbers. The probability that selected number is a multiple of 3 or 4 is:


Question: ABCD is a rectangle such that AC + AB = 5 AD and AC – AD = 8, then the area of rectangle ABCD is

Question: In the figure, DB is a diagonal of rectangle ABCD and line through A and line m through C divide DB in three equal parts each of length 1 cm and are perpendicular to DB Area (in 2 cm) of rectangle ABCD is

Square Roots and Cube Roots

Question: Out of all the divisors of256, the number of divisors which are not perfect squares is

Trigonometry function:

Question: cotA+CosecA-1cotA-cosecA+1is equal to

Question: tanθ+cotθtanθ-cotθ=2

Identities and equation

Question: If cosec39°=x, the value of1cosec251°+sin239°+tan251°-1sin251°sec239°is

Question: If secθ+tanθ=2, 0° < θ < 90°, then the value of cosec2θ+cot2θ is

Height and distance

Question: A balloon of radius r makes an angle α at the eye of an observer and the angle of elevation of its centre is β. The height of its centre from the ground level is given by:

Question: From the top of a light house the angles of depression of two ships on the opposite sides of it are the observed to be α and β. If the height of the light house be h meters and the line joining the ships passes through the foot of the light house, the distance between the ships is:

Question: A person travels at a speed of 24km/hr and reaches a town in 32 hours. How time does he take cover the same distance if his speed is 32km/h?


Question: In the figure, the area of square 2 ABCD is 4 cm and E any point on AB. F, G, H and K are the mid point of DE, CF, DG, and CH respectively. The area of KDC is

Parallel and Transverse lines

Question: The ratio in which the line 3x+y9=0 divides the line segment joining points (1, 3) and (2, 7) is:

Triangles and circles

Question: The distance between the centre of the two circles of radii r1andr2 is d. they will touch each other internally if

Question: The radii of two circles are 9 cm and 12 cm. The circumference of a circle whose area is equal to sum of the areas of the two circles is:

Question: In ΔABC, segment AD ⊥ BC, If BD = x units, then x is:

Question: The value (s) of a for which area of triangle, whose vertices are A (a, 2a), B (–2,6) and C (3,1) is 10 square units, are

Question: The ratio of the length of a side of an equilateral triangle and its height is:


Question: Algebraic Expressions and Identities including Factorization

Question: 22+632+3+2+3+2-3

Linear Equations in One Variable:

Question: If x - x - 1 = 0, then the value of 3 x - 2x + 1 is

Polynomials and linear equations in one and two variable

Question: If α and β are the zeroes of the polynomial fx=x2-5x+k such that α=1, then value of k is:

Arithmetic Progressions

Question: The first and last terms of an A. P. of n terms is 1, 31respectively. The ratio of 8th term and n2th term is 5: 9, the value of n is:

Question: How many terms of the A. P. 3, 6, 9, 12, 15. . must be taken to make the sum 108?


Area of plane figures

Question: The perimeters of a regular hexagon and a square are equal. The ratio of the area of the square to the area of the hexagon is

Surface area

Question: If V be the volume and S the surface area of a cuboid of dimensions a, b and c, then 1 V is equal to:

Cuboids and cylinder

Question: The diameter of a right circular cylinder is decreased by 10%. The volume of cylinder remains the same then the percentage increase in height is:


Question: Simple interest for 3 years on an amount is Rs. 3000/- and compound interest on the same amount at the same rate of interest for 2 years is Rs. 21 00/-. What is the rate of interest?

NTSE Syllabus for science:



Conservation of energy

Magnetism and Electricity

While doing their experiment on finding the equivalent resistance of two resistors connected in series, the students A, B and C set up their circuits as shown. The correct set up is that of:

Commercial electric motors do not use:


Motion and Force

  • Area under acceleration – time graph gives change in velocity.
  • Two bodies with kinetic energies in the ratio 4: 1 are moving with equal linear momentum. The ratio of their masses is:
  • An apple falls from a tree because of gravitation between the earth and apple. If F1 is the magnitude of force exerted by the earth on the apple and F2 is the magnitude of force exerted by apple on earth, then:

Work and Energy

Light and Sound

  • A key of a mechanical piano is struck gently and then struck again but much harder this time. In the second case:
  • The intensity of sound wave gets reduced by 20 % on passing through a slab. The reduction in intensity on passing through two consecutive slabs is:
  • What is the angle of incidence when the incident ray is normal to the interface or boundary separating two media?
  • In an experiment with a rectangular glass slab, for an angle of incidence of 60o in air, angle of refraction is measured to be r1. When the glass slab is replaced by a hollow slab filled with water, angle of refraction is measured to be r2. Then:
  • If angle of minimum deviation through an equilateral prism is 40o, angle of incidence (being equal to angle of emergence) would be:

The Universe

Source of Energy

Solids, liquids and gases

  • Ice is floating on water in a beaker when ice completely melts then level of water in beaker
  • A body floats with 1 3 of its volume outside water and 3 4 of its volume outside another liquid. The density of the other liquid is:
  • A hydrometer floats with half of its stem outside water surface. It is now placed in alcohol (R. D = 0.8). The hydrometer floats


Mole Concept

  • Which of the following contains maximum number of molecules?
  • What mass of hydrogen and oxygen will be produced on complete electrolysis of 18g of water?
  • A cell will plasmolysis, if it is placed in:
  • Sample contains 3.01 × 1023 MgCO3 molecules

Acid, Bases, Salt:

  • Which of the following solution has the lowest pH value?
  • Which one of the following is not a base?
  • B (OH) 3 is boric acid.
  • A dilute Ferrous sulphate solution was gradually added to the beaker containing acidified Permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?

Periodic Classification of Elements

  • Which is the symbol of the element tungsten?
  • Which of the given element A, B, C, D and E with atomic number 2,3, 5,7, 10 and 30 respectively belong to the same period?

Metals and Non-Metals

Which of the following orders of atomic radii is correctly represented?

Structure of Atom

  • What are the electronic configurations of Na + and C − ions?
  • A sample of MgCO3 contains 3.01 × 1023 Mg2 + ions and 3.01 × 1023 2 C O 3 − ions. The mass of the sample is
  • It is due to greater screening effect in aluminium, its radii is greater than gallium.

Physical and Chemical Changes

In the double displacement reaction between aqueous potassium iodide and aqueous lead nitrate, a yellow precipitate of lead iodide is formed. While performing the activity if lead nitrate is not available, which of the following can be used in place of lead nitrate?

Which of the following represent saponification reaction?

. Hard water does not easily produce lather with soap because it contains:

Carbon and its Compounds:

  • A mixture of sulphur and carbon disulphide is:
  • Which of the following has shortest carbon-carbon bond length?

Fibers and Plastics

  • Which of the following may be isomer of aldehyde having general formula CnH2nO?
  • Aldehydes and ketones are functional isomers of each other belonging to family of carbonyl compounds with general molecular formula CnH2nO.

properties of chemical elements under dangerous conditions


Air, Water, Soil


  • Which one of the following is not an Annelid?
  • In Xerophytes, the rate of water loss get reduced due to covering of epidermis by:
  • The following blood vessel does not contain deoxygenated blood:


  • Reproduction is essential for living organisms in order to:
  • If salivary amylase is lacking in the saliva, which of the following functions in mouth cavity will be affect?

Life Processes

  • Which is correct sequence of air passage during inhalation?
  • If testa is removed from water soaked gram seed, the remaining structure is:

Heredity and Evolution

  • Some dinosaurs had feathers although they could not fly but birds have feathers that help them to fly. In the context of evolution this means that:
  • According to evolutionary theory, formation of new species is due to:
  • If, in a plant, red colour of the flower is dominant over white. A cross was made between a plant containing red flower and other with white flower. The cross yielded 50 % white flowered plant and 50 % red flowered plant. The genotype of the parent with red flower is:
  • Which one of the folio wing is not an adaptation for terrestrial life of cockroach?

Food Production and Management

  • Which one is not major group of activities for improving crop yield can be classified as
  • The accumulation of non-biodegradable substances in a food chain in increasing amount at each higher trophic level is known as:

Diversity in Living Organisms

  • The barrier between the protoplasm and the outer environment in an animal cell is
  • Making antiviral drugs is more difficult than making anti bacterial medicines because:

Plant and Animal Nutrition

  • Photosynthesis is an important mode of autotrophic nutrition. The event which does not occur in photosynthesis is:
  • Spinal cord originates from:
  • Spinal cord is an extension of medulla oblongata
  • Phototropic and geotropic response of a plant is under control of following hormone:

Human Body

  • Pain centers in human brain differentiate between two stimuli on basis of: -
  • In which part of our body digestion of starch first of all starts?
  • Kidneys do not perform the function of:
  • During lack of oxygen in tissues of our body, the pyruvate is converted into lactic acid in:

Cellular Level of Organisation

  • A group of cells similar in forms, function and origin is known as
  • The complete breakdown of glucose in presence of oxygen in a cell takes place in
  • A plant cell differs from an animal cell in the absence of………. .

Some Common Diseases

Given below are the pairs of disease and causal pathogen. Which one of these is not a matching pair?

Our Environment

  • Population size is controlled by
  • Ozone bole was first observed over
  • Humus causes the soil to

Social science:


French Revolution

  • Jacobin Club was the most powerful political organisation in:
  • “When France sneezes, the rest of Europe catches cold”, who remarked these words?
  • The Tripartite Pact (1940) was signed by:

Industrial Revolution

  • Coal is non-renewable as well as non-recyclable resource.
  • Gutenberg was associated with:
  • Philanthropsis mainly work for:
  • The Vernacular Press Act (1878) was prepared to:

British Raj

  • The Jalianwala Bagh is located at
  • Socialist Parry was founded in:
  • Rashtriya Swayamsevak Sangh (RSS) was founded in:
  • Vallabhbhai Patel was born in Nadiad, Gujarat on:

Mughal Empire

  • The Lal Quila of DeU1i was built by the famous Mughal Emperor ________
  • Agra City was founded by

Maurya Empire

Early Medieval Period

Medieval Architecture and Culture

  • Who is the author of ‘Indulekha’ which was the first modern novel in Malayalam?
  • M. S. Swaminathan, the great scientist was awarded PADMA SRI by the Govt. of India in:
  • Hargovind Khurana, the great scientist was born on

Indian Freedom Struggle

Early States

Indus Valley Civilization

Jainism and Buddhism

Which of the following is not included in the teachings of Jainism?

Conquerors from Distant Lands

Popular Movements and Social Reforms

In which year was the Indian Forest Services set up?

Nationalism in Various Countries

Introduction and Sources of Ancient Indian History

Sun Yat Sen’s ideas became the basis of the political Philosophy of the

Vedic Period

The Upanishads are:

Jeevak, the first surgeon, was of:

World War I and II

New Empires and Kingdoms

A person who makes maps is called

World History

Universal Adult Franchise was firstly granted in:

UN and International Agencies

Which of the following statements about the international Court of justice is not correct?

The civil Court does not deal with:

Which of the following locations is not correct?

Name of the organization Location of Headquarter

(A) UNESCO Paris

(B) ILO Geneva

(C) FAO Brussels

(D) International Court of Justice the Hague


Water Resources

Which state of India has made roof top rain water harvesting compulsory to all houses:

Which of the following rivers of India flow through a rift valley?

Nagarjuna Sagar dam is on which river?



Which of the following is not a nuclear power station?


  • Who is known as the father of Green Revolution?
  • Milpa farming is practiced in:
  • Which country is largest producer of Rice in the world?
  • Flood occur frequently in the northern plains of India because of:

Resources and Development

Maharashtra state is ideal for cotton cultivation because:

Diversity and Livelihood

Internal Structure of the Earth and Rocks

Maps and Globe

Which continent of today is not a part of Gondwana land:

Natural Vegetation

Our Country – India

  • Which of the following rivers of India flow through a rift valley?
  • What is Overa?
  • Nagarjuna Sagar dam is on which river?

India and its Neighbors

Motion of the Earth

Climate – India and World

Rainfall in the Northern and North-Western parts of India in the month of October-November is caused mainly due to?

Why is there scanty rainfall in the Deccan Plateau?

Indian Physiographic Division

Drainage in India

Solar System

Major Domains and landforms

  • Milpa farming is practiced in:
  • Which country is largest producer of Rice in the world?
  • Flood occur frequently in the northern plains of India because of:


Which of the following is the working age group of the population?


Indian Constitution

  • Who was the Chairman of the Drafting Committee of Indian Constitution?
  • Indian Constitution Federation from:
  • What is Zero Hour?

Local and State Government

In the context of Panchayati Raj, which one of the following is true about Gram Sabha?


  • Amnesty International is an international organisation which works for
  • Name the Law which empowers the people to carry on democratic reforms:

Indian Government

  • Irrigation facilities should be improved urgently in India because:
  • In a parliamentary form of democracy:
  • Eligibility for a regional party to be recognized as a national party is:


Type of economies

  • Economic development of a country is measured on the basis of:
  • Entertainment Tax is an example of Indirect taxes
  • An example of Indirect Taxes is

Sectors of the Indian economy

Type of banks

Bank deposits

Role of banks in the system

Globalization and the Indian economy

  • Which summit of BRICS held in 2014?
  • The 6th summit of BRICS held in July 2014 in Brazil.
  • Which academy supports food security programme?

Consumer rights

  • COPRA is related to:

- Published/Last Modified on: November 1, 2018


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