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

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**Integers: ****Question: **If ${X}^{2}+X-1=0\phantom{\rule{0.2em}{0ex}}\left(X\ne 0\right),\phantom{\rule{0.2em}{0ex}}then\phantom{\rule{0.2em}{0ex}}{X}^{2}+\frac{1}{{X}^{2}}$ 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 $44\phantom{\rule{0.2em}{0ex}}x\phantom{\rule{0.2em}{0ex}}y\phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}xy\phantom{\rule{0.2em}{0ex}}i\mathrm{s.}$

**Question: **If the roots of $p\phantom{\rule{0.2em}{0ex}}x\phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}2qx\phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}r\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}2$ and $qx\phantom{\rule{0.2em}{0ex}}-2\phantom{\rule{0.2em}{0ex}}pr\phantom{\rule{0.2em}{0ex}}x\phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}q\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}o$ are simultaneously real, than

NTSE SAT Exam Last Minute Guidelines & Quick Revision

Dr. Manishika Jain, NTSE Scholar explains NTSE SAT Last Minute Guidelines & Quick Revision

**Prime numbers**

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

**Factors**

**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:

**HCF and LCM**

**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 ${3}^{1001}\times {7}^{1002}\times {13}^{1003}$ is

**Sequence and series**

**Question: **The sum $\frac{1}{1+{1}^{2}+{1}^{4}}+\frac{2}{1+{2}^{2}+{2}^{4}}+\frac{3}{1+{3}^{2}+{3}^{4}}+\dots \dots ..+\frac{99}{1+{99}^{2}+{99}^{4}}\phantom{\rule{0.2em}{0ex}}$lies between

**Rational Numbers**

**Question: **If $x=\frac{1}{1+\sqrt{2}}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.2em}{0ex}}$then the value of$\phantom{\rule{0.2em}{0ex}}{x}^{2}+2x+3\phantom{\rule{0.2em}{0ex}}is:$

**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+\phantom{\rule{0.2em}{0ex}}y=1\phantom{\rule{0.2em}{0ex}}then\phantom{\rule{0.2em}{0ex}}{x}^{3}+{y}^{3}+3xy=\dots $

**Question: **For the equation $3{x}^{2}+px+3=0$ 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:

**Parallelogram**

**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: **$\phantom{\rule{0.2em}{0ex}}\frac{\mathrm{cot}\u2006A+CosecA-1}{\mathrm{cot}\u2006A-cosecA+1}\phantom{\rule{0.2em}{0ex}}$is equal to

**Question: **$\frac{\mathrm{tan}\u2006\theta +\mathrm{cot}\u2006\theta}{\mathrm{tan}\u2006\theta -\mathrm{cot}\u2006\theta}=2\phantom{\rule{0.2em}{0ex}}$

**Identities and equation**

**Question: **If $cosec\phantom{\rule{0.2em}{0ex}}39\xb0=x,\phantom{\rule{0.2em}{0ex}}$the value of$\phantom{\rule{0.2em}{0ex}}\frac{1}{cose{c}^{2}51\xb0}+si{n}^{2}39\xb0+ta{n}^{2}51\xb0-\frac{1}{si{n}^{2}51\xb0se{c}^{2}39\xb0}\phantom{\rule{0.2em}{0ex}}$is

**Question: **If $\mathrm{sec}\u2006\theta +\mathrm{tan}\u2006\theta =2,\phantom{\rule{0.2em}{0ex}}0\xb0<\theta <\phantom{\rule{0.2em}{0ex}}90\xb0\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.2em}{0ex}}$ then the value of $cose{c}^{2}\theta \phantom{\rule{0.2em}{0ex}}+{\mathrm{cot}}^{2}\u2006\theta $ 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 $\alpha $ and $\beta $. 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 $24\phantom{\rule{0.2em}{0ex}}km/hr$ and reaches a town in 32 hours. How time does he take cover the same distance if his speed is $32\phantom{\rule{0.2em}{0ex}}km/h$?

**Angles**

**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 $3x\phantom{\rule{0.2em}{0ex}}+\phantom{\rule{0.2em}{0ex}}y\phantom{\rule{0.2em}{0ex}}\u2013\phantom{\rule{0.2em}{0ex}}9\phantom{\rule{0.2em}{0ex}}=\phantom{\rule{0.2em}{0ex}}0$ divides the line segment joining points $(1,\phantom{\rule{0.2em}{0ex}}3)$and $(2,\phantom{\rule{0.2em}{0ex}}7)$ is:

**Triangles and circles**

**Question: **The distance between the centre of the two circles of radii ${r}_{1}\phantom{\rule{0.2em}{0ex}}and\phantom{\rule{0.2em}{0ex}}{r}_{2}$ 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:

**Algebra: **

**Question: **Algebraic Expressions and Identities including Factorization

**Question: **$\frac{2\left(\sqrt{2}+\sqrt{6}\right)}{3\left(\sqrt{2}+\sqrt{3\phantom{\rule{0.2em}{0ex}}}\right)}+\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}$

**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 $f\left(x\right)={x}^{2}-5x+k$ such that $\alpha \phantom{\rule{0.2em}{0ex}}\u2013=1$, then value of k is:

**Arithmetic Progressions**

**Question: **The first and last terms of an A. P. of n terms is $1,\phantom{\rule{0.2em}{0ex}}31\phantom{\rule{0.2em}{0ex}}$respectively. The ratio of ${8}^{th}$ term and ${\left(n\phantom{\rule{0.2em}{0ex}}\u20132\right)}^{th}\phantom{\rule{0.2em}{0ex}}$ term is $5\phantom{\rule{0.2em}{0ex}}:\phantom{\rule{0.2em}{0ex}}9$, the value of n is:

**Question: **How many terms of the $A.P.\phantom{\rule{0.2em}{0ex}}3,\phantom{\rule{0.2em}{0ex}}6,\phantom{\rule{0.2em}{0ex}}9,\phantom{\rule{0.2em}{0ex}}12,\phantom{\rule{0.2em}{0ex}}15\dots \dots ..$must be taken to make the sum 108?

**Mensuration: **

**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:

**Interest: **

**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: **

**Physics: **

**Gravity**

**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:

**Measurements**

**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 40
^{o}, 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

**Chemistry: **

**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**

**Biology: **

**Air, Water, Soil**

**Micro-organisms**

- 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**

- 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: **

**History: **

**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

**Geography: **

**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?

**Biosphere**

**Atmosphere**

Which of the following is not a nuclear power station?

**Agriculture**

- 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:

**Population**

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

**Civics: **

**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?

**Judiciary**

- 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:

**Economics: **

**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 6
^{th}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

-Examrace Team