Jee Adv Sample TestPaper ResoNET-2016

8/18/2019 Jee Adv Sample TestPaper ResoNET-2016

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Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-324005

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Index

The sample test papers are only for reference and guidance. The sample papers given in the booklet are actually the papers of previousyear's ResoNET conducted by Resonance for its various courses.

Note : Resonance reserves the right to change the pattern of selection test (ResoNET). Pervious year papers do not guarantee that thepapers for this year selection test will be on the same pattern. However, the syllabus of the test paper will be equivalent to the syllabusof qualifying school/board examination and as given on page no. 4.

For More Practice of RESONANCE NATIONAL ENTRANCE TEST (ResoNET) - 2016

Resonance selection test papers of last few years with answer key, hints & solutions are available on demand. Following sets ofPractice Test Papers (PTPs), in hard copy, are available with us :

S.No.

Sample Paper

Code Detai l s of PTPs Co urse (Code) Target Rem a rk

1 Set-A 10 Papers S et for Class-X Appearing/Passed s tudentsVIKAAS (JA) &

VIPUL (JB)JEE(Main + Advanced) 2018

Ans wer k ey ,

Hints & Solutions

2 Set-B 10 Papers Set for Class-XI Appearing/Passed students VISHWAAS (JF) JEE(Main + Advanced) 2017 Only Answer key

3 Set-C 10 Papers S et for Class-XII Appearing Pass ed studentsVISHESH (JD) &

VIJAY (JR)JEE(Main + Advanced) 2017

Ans wer k ey ,

Hints & Solutions

Interested students may collect the same from Resonance Study Centres or Corporate Office at Kota (at Plot No. A-46, A-52, Near CityMall, Jhalawar Road, Reception) by paying an additional fees of Rs.300/- only per set. Any of the above Practice Test Papers (PTPs)sets may be procured through post / courier from 'Resonance Eduventures Ltd' by sending a Bank Demand Draft (DD) of Rs. 300/- infavour of 'Resonance' and payable at Kota. A student may send the request application on plain paper along with prerequisite fees tothe institute to collect any of the sets of Practice Test Papers (PTPs). Please, mention clearly your name and roll number (ApplicationForm No.) on the back of the DD and which set of Practice Test Papers (Set A, B or C) is required by you in the request application.Resonance Selection Test Papers of last few years with Answer key, Hints & Solutions are available on demand. ResoNET Papers are

available Online too.ResoNET Online Practice Test Papers (OPTPs) :

S. No. Details of OPTPs Course Code Target Fee(Taxes included)

1 3 Tests for Class-X Appearing/Passed students VIKAAS (JA) & VIPUL (JB) JEE(Main + Advanced) 2018 Rs. 300/-

2 6 Tests for Class-X Appearing/Passed students VIKAAS (JA) & VIPUL (JB) JEE(Main + Advanced) 2018 Rs. 500/-

3 3 Tests for Class -XI Appearing/Passed students VISHWAAS (JF) JEE(Main + Advanced) 2017 Rs. 300/-

4 6 Tests for Class -XI Appearing/Passed students VISHWAAS (JF) JEE(Main + Advanced) 2017 Rs. 500/-

5 3 Tests for Class-XII Appearing/Passed students VISHESH (JD) & VIJAY (JR) JEE(Main + Advanced) 2017 Rs. 300/-

6 6 Tests for Class-XII Appearing/Passed students VISHESH (JD) & VIJAY (JR) JEE(Main + Advanced) 2017 Rs. 500/-

Students can buy these Online Test papers at http://elpd.resonance.ac.in

Sample Test Paper (STP) For ResoNET-2016

© Copyright reserved 2016-17.All rights reserved. Any photocopying, publishing or reproduction of full or any part of this material is strictly prohibited. This material belongs to only the applicants of RESONANCE for its

various Selection Tests (ResoNET) to be conducted for admission in Academic Session 2016-17. Any sale/resale of this material is punishable under law. Subject to Kota Jurisdiction only.

S.No. Contents TargetPage

No.

1 How to Prepare for the Resonance National Entrance Test (ResoNET)-2016 ResoNET 2016 2

2 General Instructions for the Examination Hall ResoNET 2016 33 Syllabus for ResoNET-2016 ResoNET 2016 4

4Sampl e Test Paper- I : For Class-X Appearing/Passed students (Moving from Class-X to

Class-XI ) For the students applying for VIKAAS (JA) & VIPUL (JB) CoursesJEE(Main + Advanced) 2018 9

5Sampl e Test Paper-I Answer key & Hints & Solutio n : For Class-X Appearing/Passed s tudents

(Moving from Class-X to Class-XI ) For the students applying for VIKAAS (JA) & VIPUL (JB) CoursesJEE(Main + Advanced) 2018 18

6Sampl e Test Paper-II : For Class-XI Appearing / Passed students (Moving from Class-XI to Class-

XII).For the students applying for VISHWAAS (JF) CourseJEE(Main + Advanced) 2017 25

7Sampl e Test Paper-II Answer key & Hints & Solution : For Class-XI Appearing / Passed students

(Moving from Class-XI to Class-XII).For the students applying for VISHWAAS (JF) CourseJEE(Main + Advanced) 2017 42

8Sampl e Test Paper-III : For Class-XII Appearing / Passed students (Moving from Class-XII to Class-

XIII) For the students applying for VISHESH (JD) & VIJAY (JR) CoursesJEE(Main + Advanced) 2017 52

9Sampl e Test Paper-III Answer key & Hints & Solutio n : For Class-XII Appearing / Passed students

(Moving from Class-XII to Class -XIII) For the students applying for VISHESH (JD) & VIJAY (JR) Courses

JEE(Main + Advanced) 2017 68

10 Sample ORS Answer Sheet for Resonance National Entrance Test (ResoNET)-2016 ResoNET 2016 79


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HOW TO PREPARE FOR THE RESONANCE NATIONAL ENTRANCE TEST (ResoNET) - 2016

For Class-X appearing students (Class-X to Class-XI Moving) :

Study thoroughly the books of Science (Physics & Chemistry) and Maths of ClassesIX & X. (NCERT & Respective Board)

For Class-XI appearing st udent s (Class-XI to Class-XII Moving):

1. Study thoroughly the books of Physics, Chemistry and Maths of Class XI (Respective

Board).

2. Refer to the following books (only Class-XI syllabus) to increase the level of competence:

For Physics : Concepts of Physics by H.C. Verma Vol. I & II, NCERT Books

For Chemistry : NCERT Books(XI & XII), A text book of Physical Chemistry

(8th Edition), Shishir Mittal, Disha Publications, Concise Inorganic

Chemistry, J.D. Lee, Wiley-India Edition, Vogel’s Qualitative Analysis for

the JEE (7th Edition), G. Svehla & Shishir Mittal, Pearson Education,Organic

Chemistry : Clayden, Greeves, Warren and Wothers, Oxford University,

A guide book to Mechanism In Organic Chemistry (6th Edition), Peter Sykes,

Pearson Education

For Maths : Higher Algebra By Hall & Knight; Co-ordinate Geometry By

S.L. Loney ; Plane Trigonometry By S.L. Loney, Problem book in high school

by A.I.Prilepko

Fo r Class-XII appearing st ud en ts (Class-XII to Class-XIII Moving ):

1. Study thoroughly the books of Physics, Chemistry and Maths of Classes XI & XII

(Respective Board).

2. Refer to the following books (Class-XI & Class-XII syllabus) to increase the level of

competence :

For Physics : Concepts of Physics by H.C. Verma Vol-I & II

For Chemistry : Physical Chemistry By R.K. Gupta, Organic Chemistry By

Morrison & Boyd, Organic Chemistry By I. L. Finar, Inorganic Chemistry By J.D.

Lee, Objective Chemistry By Dr. P. Bahadur

For Maths : Higher Algebra By Hall & Knight; Co-ordinate Geometry By S.L.

Loney; Plane Trigonometry By S.L. Loney, Differential Calculus By G.N. Berman;

Integral Calculus By Shanti Narayan; Vector Algebra By Shanti Narayan ;

A Das Gupta (subjective).

Note : For further practice, a set of several Practice Test Papers (PTPs) of Resonance may beprocured from the institute. For this, the details are available on Page No.1.


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GENERAL INSTRUCTIONS IN THE EXAMINATION HALL

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1. This booklet is your Question Paper. ¼;g iqfLrdk vkidk iz'u&i=k gS½

2. The Question Paper Code is printed on the top right corner of this sheet. ¼iz'u&i=k dksM bl i`"B

ds Åij nk; sa dk sus esa Nik gqvk gS½

3. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic

gadgets in any form are not allowed to be used. ¼[kkyh dkxt] fDyi cksMZ] y?kqx.kd lkj.kh] LykbM

:y] dSYd qysVj] eksckby ;k vU; fdlh bySDVªW kfud midj.k ds fdlh Hkh :i esa mi;ksx dh vkKk ugh a gS½

4. Write your Name & Appl ication Form Numb er in the space provided in the bottom of this

booklet. ( bl i`"B ds uhps fn;s x;s fjDr LFkku esa viuk uke o vko snu Q k We Z l a[; k vo'; Hkjs a½

5. Before answering the paper, fill up the required details in the blank space provided in the Objective

Response Sheet (ORS). ( iz'u&i=k gy djus ls igys] ORS&'khV esa fn;s x;s fjDr LFkkuksa esa iwNs x;s

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the blank space provided in the Objective Response Sheet (ORS) / Answer Sheet. ¼mÙkj&iqfLrdk

esa fn;s x;s fjDr LFkku esa vius iz'u&i=k dk dksM o viuk vko snu Q k We Z l a[; k Li"V :i ls Hkjuk uk Hkwysa½7. No rough sheets will be provided by the inv igilators. All the rough work is to be done in the blank

space provided in the question paper. ¼fujh{kd ds }kjk dksbZ jQ 'khV ugha nh tk;sxhA jQ dk;Z iz'u&i=k

esa fn;s x;s [kkyh LFkku esa gh djuk gS½

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QUESTION PAPER

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9. Marks distribution of questions is as follows. ¼iz'uksa ds izkIrkadks dk fooj.k fuEu izdkj ls gSA½

Correct Wrong Blank

1 to 20 35 to 42 47 to 54Only one correct

(dsoy ,d fodYi lgh)3 -1 0

21 to 24 43 to 46 55 to 58One or more than one correct Answer

(,d ;k ,d ls vf/kd fodYi lgh)4 0 0

25 to 32 Comprehensions (vuqPNsn) 4 0 0

33 to 34Matrix Match Type

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Marks to be awardedPart - I

(Mathematics)

Part - II

(Physics)

Part - III

(Chemistry)Type

Name : _________________________________ Application Form Number : _______________


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CLASS - X (CHEMISTRY)Basic : Cooling by evaporation. Absorption of heat. All things accupyspace, possess mass. Definition of matter ; Elementary idea about

bonding.

Solid, liquid and gas : characteristics-shape, volume, density;change of state - melting, freezing, evaporation, condensation,sublimation.

Elements, compounds and mixtures : Heterogeneous andhomogeneous mixtures; Colloids and suspension.

Mole concept : Equivalence - that x grams of A is chemically notequal to x grams of B ; Partical nature, basic units : atoms andmolecules ; Law of constant proportions ; Atomic and molecular masses;Relationship of mole to mass of the particles and numbers ;Valency ; Chemical formulae of common compounds.

At omi c st ructu re : Atoms are made up of smaller parti cles :electrons, protons, and neutrons. These smaller particles are present

in all the atoms but their numbers vary in different atoms.Isotopes and isobars.

Gradations in properties : Mendeleev periodic table.

Acids, bases and salts : General properties, examples and uses.Types of chemical reactions : Combination, decomposition,displacement, double displacement, precipitation, neutralisation,oxidation and reduction in terms of gain and loss of oxygen andhydrogen.

Extractive metallurgy : Properties of common metals ; Brief discussion of basic metallurgical processes.

Compounds of Carbon : Carbon compounds ; Elementary ideaabout bonding ; Saturated hydrocarbons, alcohols, carboxylic acids(no preparation, only properties).Soap - cleansing action of soap.

CLASS - X (MATHEMATICS)Number Systems :Natural Numbers, Integers, Rational number on the number line. Even- odd integers, prime number, composite numbers, twin primes,divisibility tests, Co-prime numbers, LCM and HCF of numbers.Representation of terminating/non-terminating recurring decimals, onthe number line through successive magnification. Rational numbersas recurring/terminating decimals. Ratio and proportions.

Polynomials :

Polynomial in one variable and its Degree. Constant, Linear, quadratic,cubic polynomials; monomials, binomials, trinomials, Factors andmultiplex. Zeros/roots of a polynomial/equation.Remainder theorem, Factor Theorem. Factorisation of quadratic andcubic polynomialsStandard form of a quadratic equation ax2 + bx + c = 0, (a 0).

Relation between roots and coefficient of quadratic and relationbetween discriminant and nature of roots.

Linear Equation :

Linear equation in one variable and two variable and their graphs.Pair of linear equations in two variables and their solution andinconsistency

Ar i thm et ic Pro gr ess io ns (AP) :

Finding the nth term and sum of first n terms.

Trigonometry :

Trigonometric ratios of an acute angle of a right-angled triangle,Relationships between the ratios.Trigonometric ratios of complementary angles and trigonometricidentities. Problems based on heights and distances.

Coordinate Geometry :

The cartesian plane, coordinates of a point, plotting points in theplane, distance between two points and section formula (internal).

Area of triangle. Properties of triangle and quadrilateral. (Square,Rectangle rhombus, parallelogram).

Geometry :

Lines :Properties of parallel and perpendicular lines.Triangle :

Area of a triangle, Properties of triangle, similarity and congruencyof triangles.Medians, Altitudes, Angle bisectors and related centres.Geometrical representation of quadratic polynomials.

Circle :

Properties of circle, Tangent, Normal and chords.

Mensuration :

Area of triangle using Heron’s formula and its application in findingthe area of a quadrilateral.

Area of circle ; Surface areas and volumes of cubes, cuboids,spheres (including hemispheres) and right circular cylinders/conesand their combinations.

Statistics :

Mean, median, mode of ungrouped and grouped data.

Probability :

Classical definition of probability, problems on single events.

Logarithm & exponents :

Logarithms and exponents and their properties.

Interest :

Problem based on simple interest, compound interest and discounts.

Mental Ability :

Problem based on data interpretation, family relations, Logical

reasoning.

Direct & Indirect variations :

Ratios & proportions, Unitary method, Work and time problems.

CLASS - X (PHYSICS)Mechanics : Uniform and non-uniform motion along a straight line ;Concept of distance and displacement, Speed and velocity,accelaration and relation ship between these ; Distance-time andvelcocity - time graphs.Newton’s Law of motion ; Relationship between mass, momentum,force and accelaration ; work done by a force ; Law of conserva-tion of energy.Law of gravitation ; acceleration due to gravity.Electricity and magnetism : Ohm’s law ; Series and parallel com-bination of resistances ; Heating effect of current.

Magnetic field near a current carrying straight wire, along the axisof a circular coil and inside a solenoid ; Force on current carryingconductor ; Fleming’s left hand rule ; Working of electric motor ;Induced potential difference and current

Electric generator : Principle and working ; Comparision of AC andDC ; Domestic electric circuits.

Optics : Rectilinear propagation of light ; Basic idea of concavemirror and convex lens ; Laws of refraction ; Dispersion.

CLASS - XI (CHEMISTRY)

Some Basic Concepts of Chemistry : Particulate nature of matter,

laws of chemical combination, Dalton’s atomic theory : concept of elements, atoms and molecules.

Syllabus of ResoNET 2016


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Atomic and molecular masses. Mole concept and molar mass ;percentage composition and empirical and molecular formula ;chemical reactions, stoichiometry and calculations based onstoichiometry.Structure of Atom : Discovery of electron, proton and neutron ;atomic number, isotopes and isobars.Thompson’s model and its limitations, Rutherford’s model and itslimitations, concept of shells and sub-shells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle,

concept of orbitals, quantum numbers, shapes of s, p, and d orbitals,rules for filling electrons in orbitals - Aufbau principle, Pauli exclusionprinciple and Hund’s rule, electronic configuration of atoms, stabilityof half filled and completely filleld orbitals.

Classif ication of Elements and Periodicity in Properties :Significance of classification, brief history of the development of periodic table, trends in properties of elements - atomic radii, ionicradii, inert gas radii, ionization enthalpy, electron gain enthalpy,electronegativity, valence.

Chemical Bonding and Molecular Structure :Valence electrons, ionic bond, covalent bond, bond parameters, Lewisstructure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalentmolecules, VSEPR theory, concept of hybridization involving s, p and

d orbitals and shapes of some simple molecules,molecular orbital theory of homonuclear diatomic molecules (qualitativeidea only), hydrogen bond.

States of Matter : Gases and Liquids :Three states of matter, intermolecular interactions, type of bonding,melting and boiling points, role of gas laws in elucidating the conceptof the molecule, Boyle’s law, Charles’ law, Gay Lussac’s law,

Avogadro’s law, ideal behavior, empirical derivation of gas equation, Avogadro’s number ideal gas equation, deviation from ideal behaviour,Liquefaction of gases, critical temperature.Liquid State - Vapour pressure, viscosity and surface tension(qualitative idea only, no mathematical derivations)Thermodynamics :Concepts of system, types of systems, surroundings, work, heat,energy, extensive and intensive properties, state functions.First law of thermodynamics - internal energy and enthalpy, heatcapacity and specific heat, measurement of U and H, Hess’s lawof constant heat summation, enthalpy of bond dissociation,combustion, formation, atomization sublimation, phase transition, ion-ization, and dilution.Introduction of entropy as a state function, free energy change for spontaneous and non-spontaneous process, equilibrium.

Equilibrium : Equilibrium in physical and chemical processes,dynamic nature of equilibrium, law of mass action, equilibriumconstant, factors affecting equilibrium - Le Chatelier’s principle ;ionic equilibrium - ionization of acids and bases, strong and weakelectrolytes, degree of ionization concept of pH. Hydrolysis of Salts(elementary idea), buffer solutions, solubility product, common ioneffect (with illustrative examples).

Redox Reactions : Concept of oxidation and reduction, redox re-actions,oxidation number, balancing redox reactions, applications of redoxreaction.

Hydrogen : Position of hydrogen in periodic table, occurrence, iso-topes, preparation, properties and uses of hydrogen ; hydrides -ionic, covalent and interstitial ; physical and chemical properties of water, heavy water ; hydrogen peroxide - preparation, reactionsand structure ; hydrogen as a fuel.

s-Block Elements (Alkali and Alkaline Earth Metals) :Group 1 and Group 2 elements :General introduction, electronic configuration, occurrence, anomalousproperties of the first element of each group, diagonal relationship,trends in the variation of properties (such as ionization enthalpy,atomic and ionic radii), trends in chemical reactivity with oxygen,

water, hydrogen and halogens ; uses.

Preparation and properties of some important compoundsSodium carbonate, sodium chloride, sodium hydroxide and sodiumhydrogen carbonateCaO, CaCO

3, and industrial use of lime and limestone, Ca.

General Introduction to p-Block Elements :Group 13 elements : General introduction, electronic configuration,occurrence, variation of properties, oxidation states, trends in chemi-cal reactivity, anomalous properties of first element of the group ;Boron - physical and chemical properties, some important compounds; borax, boric acids, boron hydrides. Aluminium : uses, reactionswith acids and alkalies.Group 14 elements ; General introduction, electronic configuration,occurrence, variation of properties, oxidation states, trends inchemical reactivity, anomalous behaviour of first element. Carbon -catenation, allotropic forms, physical and chemical propeties ; usesof some important compounds : oxides.Important compounds of silicon and a few uses : silicon tetrachlo-ride, silicones, silicates and zeolites.

Principles of qualitative analysis : Determinantion of one anionand one cation in a given saltCations - Pb2 + , Cu2+, As3+, Al3+, Fe3+, Mn2+, Ni2 +, Zn2+, Co2+, Ca2+, Sr 2+,

Ba2+, Mg2+, 4NH

Anions - ,NO,SO,SO,S,CO –

2

– 2

4

– 2

3

– 2 – 2

3 –

3 – 2

42 – 3

4 – – – –

3 – 3 COOCHOC,PO,,Br ,Cl,NO,NO

(Note : Insoluble salts excluded)

Organic chemistry - Some Basic Principles and Techniques

General introduction, methods of purification, qualitative andquantitative analysis, classification and IUPAC nomenclature of organic compounds.Electronic displacements in a covalent bond : free radicals,carbocations, carbanions ; electrophiles and nucleophiles, types of organic reactions

Classif icat ion of Hydrocarbons : Alkanes : Nomenc lature,isomerism, conformations (ethane only), physical propeties,chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis.

Al kenes : Nomenclatures, structure of double bond (ethene),geometrical isomerism, physical properties, methods of preparation; chemical reactions : addition of hydrogen, halogen, water, hydro-gen halides (Markovnikov’s addition and peroxide effect),ozonolysis, oxidation, mechanism of electrophilic addition.

Alk ynes : Nomenclature, structure of triple bond (ethyne), physicalproperties, methods of preparation, chemical reactions : acidiccharacter of alkynes, addition reaction of - hydrogen, halogens,hydrogen halides and water.

Ar omat ic hy dro carbo ns : Introduction, IUPAC nomenclature ;Benzene : resonance, aromaticity ; chemical properties : mechanismof electrophilic substitution - nitration sulphonation, halogenation,Friedel Craft’s alkylation and acylation ; directive influence of func-tional group in mono-substituted benzene ; carcinogenicity and tox-

icity.

CLASS - XI (MATHEMATICS)Functions :Sets and their representations. Empty, finite and infinite sets, Subsets,Union and intersection of sets, Venn diagrams.Pictorial representation of a function domain, co-domain and rangeof a function domain and range of constant, identity, polynomial,rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.Trigonometric Functions :Measuring angles in radians and in degrees and conversion fromone measure to another. Signs of trigonometric functions and sketchof their graphs. Addition and subtraction formulae, formulae involvingmultiple and sub-multiple angles. General solut ion of trigonometric equations.


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Complex Number Algebra of complex numbers, addition, multiplication, conjugation,polar representation, properties of modulus and principal argument,triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations :Quadratic equations with real coefficients, formation of quadraticequations with given roots, symmetric functions of roots.Sequence & Series :

Ar ithmet ic , geomet ric and harmonic progress ions , ari thmetic,

geometric and harmonic means, sums of finite arithmetic andgeometric progressions, infinite geometric series, sums of squaresand cubes of the first n natural numbers.

Logarithm & exponents :

Logarithms and exponents and their properties. Exponential andlogarithmic series.

Binomial Theorem :Binomial theorem for a positive integral index, properties of binomialcoefficients. Binomial theorem for any index.

Permutations and combinations :Problem based on fundamental counting principle, Arrangement of alike and different objects, Circular permutation, Combination,formation of groups.

Straight Line :

Cartesian coordinates, distance between two points, sectionformulae, shift of origin. Equation of a straight line in various forms,angle between two lines, distance of a point from a line; Lines throughthe point of intersection of two given lines equation of the bisector of the angle between two lines, concurrency of lines; Centroid,orthocentre, incentre and circumcentre of a triangle.

Conic Sections :Equation of a circle in various forms, equations of tangent, normaland chord. Parametric equations of a circle, intersection of a circlewith a straight line or a circle, equation of a through the points of intersection of two circles and those of a circle and a straight line.Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal locus problems.Mental Ability :

Problem based on data interpretation, family relations & Logicalreasoning.

CLASS - XI (PHYSICS)General : Units and dimensions, dimensional analysis; least count,significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments:Experiments based on using Vernier calipers and screw gauge(micrometer), Determination of g using simple pendulum, Young’smodulus by Searle’s method.Mechanics : Kinematics in one and two dimensions (Cartesiancoordinates only), projectiles; Uniform Circular motion; Relativevelocity.Newton’s laws of motion; Inertial and uniformly accelerated framesof reference; Static and dynamic friction; Kinetic and potential en-ergy; Work and power; Conservation of linear momentum and me-

chanical energy.Systems of particles; Centre of mass and its motion; Impulse; Elasticand inelastic collisions.Law of gravitation; Gravitational potential and field; Acceleration dueto gravity; Motion of planets and satellites in circular orbits; Escapevelocity.Rigid body, moment of inertia, parallel and perpendicular axestheorems, moment of inertia of uniform bodies with simplegeometrical shapes; Angular momentum; Torque; Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation; Rolling without slipping of rings, cylinders and spheres;Equilibrium of rigid bodies; Collision of point masses with rigid bodies.

Linear and angular simple harmonic motions.

Hooke’s law, Young’s modulus.

Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy and

surface tension, capillary rise; Viscosity (Poiseuille’s equationexcluded), Stoke’s law; Terminal velocity, Streamline flow, equationof continuity, Bernoulli’s theorem and its applications.

Waves : Wave motion (plane waves only), longit udinal andtransverse waves, superposition of waves; Progressive andstationary waves; Vibration of strings and air columns;Resonance;Beats; Speed of sound in gases; Doppler effect (in sound).

Thermal physics : Thermal expansion of solids, liquids and gases;Calorimetry, latent heat; Heat conduction in one dimension; Elemen-tary concepts of convection and radiation; Newton’s law of cooling;Ideal gas laws; Specific heats (Cv and Cp for monoatomic and di-

atomic gases); Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and work; First law of thermodynamicsand its applications (only for ideal gases); Blackbody radiation:absorptive and emissive powers; Kirchhoff’s law; Wien’s displace-ment law, Stefan’s law.

CLASS - XII (CHEMISTRY)Physical ChemistryGeneral topics : Concept of atoms and molecules; Dalton’s atomictheory; Mole concept; Chemical formulae; Balanced chemicalequations; Calculations (based on mole concept) involving commonoxidation-reduction, neutralisation, and displacement reactions;Concentration in terms of mole fraction, molarity, molality and normality.Gaseous and liquid states : Absolute scale of temperature, idealgas equation; Deviation from ideality, van der Waals equation; Kinetictheory of gases, average, root mean square and most probable

velocities and their relation with temperature; Law of partialpressures; Vapour pressure; Diffusion of gases. Atomic str ucture and chemical bonding : Bohr model, spectrumof hydrogen atom, quantum numbers; Wave-particle duality, de Brogliehypothesis; Uncertainty principle; Qualitative quantum mechanicalpicture of hydrogen atom, shapes of s, p and d orbitals; Electronicconfigurations of elements (up to atomic number 36); Aufbau principle;Pauli’s exclusion principle and Hund’s rule; Orbital overlap and covalentbond; Hybridisation involving s, p and d orbitals only; Orbital energydiagrams for homonuclear diatomic species; Hydrogen bond; Polarityin molecules, dipole moment (qualitative aspects only); VSEPR modeland shapes of molecules (linear, angular, triangular, square planar,pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral andoctahedral).

Energetics : First law of thermodynamics; Internal energy, workand heat, pressure-volume work; Enthalpy, Hess’s law; Heat of

reaction, fusion and vapourization; Second law of thermodynamics;Entropy; Free energy; Criterion of spontaneity.

Chemical equilibrium : Law of mass action; Equilibrium constant,Le Chatelier’s principle(effect of concentration, temperature and pressure); Significanceof G and Go in chemical equilibrium; Solubility product, commonion effect, pH and buffer solutions; Acids and bases (Bronsted andLewis concepts); Hydrolysis of salts.

Electrochemistry : Electrochemical cells and cell reactions;Standard electrode potentials; Nernst equation and its relation to DG;Electrochemical series, emf of galvanic cells; Faraday’s laws of electrolysis; Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law; Concentration cells.

Chemical kinet ics : Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperaturedependence of rate constant (Arrhenius equation).

Solid state : Classification of solids, crystalline state, seven crystalsystems (cell parameters a, b, c, ), close packed structure of solids(cubic), packing in fcc, bcc and hcp lattices; Nearest neighbours,ionic radii, simple ionic compounds, point defects.

Solutions : Raoult’s law; Molecular weight determination fromlowering of vapour pressure, elevation of boiling point and depressionof freezing point.

Surface chemistry : Elementary concepts of adsorption (excludingadsorption isotherms); Colloids: types, methods of preparation andgeneral properties; Elementary ideas of emulsions, surfactants andmicelles (only definitions and examples).

Nuclear chemistry : Radioactivity: isotopes and isobars; Propertiesof rays; Kinetics of radioactive decay (decay series excluded),carbon dating; Stability of nuclei with respect to proton-neutron ratio;Brief discussion on fission and fusion reactions.


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Inorganic Chemistry

Isolation/preparation and properties of the following non-metals : Boron, silicon, nitrogen, phosphorus, oxygen, sulphur andhalogens; Properties of allotropes of carbon(only diamond and graphite), phosphorus and sulphur.Preparation and properties of the following compounds :Oxides, peroxides, hydroxides, carbonates, bicarbonates, chloridesand sulphates of sodium, potassium, magnesium and calcium; Boron:diborane, boric acid and borax; Aluminium: alumina, aluminium chloride

and alums; Carbon: oxides and oxyacid (carbonic acid); Silicon:silicones, silicates and silicon carbide; Nitrogen: oxides, oxyacidsand ammonia; Phosphorus: oxides, oxyacids (phosphorus acid,phosphoric acid) and phosphine; Oxygen: ozone and hydrogenperoxide; Sulphur: hydrogen sulphide, oxides, sulphurous acid,sulphuric acid and sodium thiosulphate; Halogens: hydrohalic acids,oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.

Transit ion elements (3d series) : Definition, generalcharacteristics, oxidation states and their stabilities, colour (excludingthe details of electronic transitions) and calculation of spin (onlymagnetic moment), Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisationisomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar andoctahedral).

Preparation and properties of the following compounds :Oxides and chlorides of tin and lead; Oxides, chlorides and sulphatesof Fe2+, Cu2+ and Zn2+; Potassium permanganate, potassiumdichromate, silver oxide, silver nitrate, silver thiosulphate.

Ores and minerals : Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminium, zinc and silver.

Extractive metallurgy : Chemical principles and reactions only(industrial details excluded); Carbon reduction method (iron and tin);Self reduction method (copper and lead); Electrolytic reduction method(magnesium and aluminium); Cyanide process (silver and gold).

Principles of qualitative analysis : Groups I to V (only Ag+, Hg2+,Cu2+, Pb2+, Bi3+, Fe3+, Cr 3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+);Nitrate, halides (excluding fluoride), sulphate and sulphide.

Organic Chemistry

Concepts : Hybridisation of carbon; Sigma and pi-bonds; Shapesof simple organic molecules; Structural and geometrical isomerism;Optical isomerism of compounds containing up to two asymmetriccentres, (R,S and E,Z nomenclature excluded); IUPAC nomenclatureof simple organic compounds (only hydrocarbons, mono-functionaland bi-functional compounds); Conformations of ethane and butane(Newman projections); Resonance and hyperconjugation; Keto-enoltautomerism; Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds:definition and their effects on physical properties of alcohols andcarboxylic acids; Inductive and resonance effects on acidity andbasicity of organic acids and bases; Polarity and inductive effects inalkyl halides; Reactive intermediates produced during homolytic andheterolytic bond cleavage; Formation, structure and stability of carbocations, carbanions and free radicals.

Preparation, properties and reactions of alkanes : Homologousseries, physical properties of alkanes (melting points, boiling pointsand density); Combustion and halogenation of alkanes; Preparationof alkanes by Wurtz reaction and decarboxylation reactions.

Preparation, properties and reactions of alkenes and alkynes: Physical properties of alkenes and alkynes (boiling points, densityand dipole moments); Acidity of alkynes; Acid catalysed hydration of alkenes and alkynes (excluding the stereochemistry of addition andelimination); Reactions of alkenes with KMnO

4 and ozone; Reduction

of alkenes and alkynes; Preparation of alkenes and alkynes byelimination reactions; Electrophilic addition reactions of alkenes withX

2, HX, HOX and H

2O (X=halogen); Addition reactions of alkynes;

Metal acetylides.Reactions of Benzene : Structure and aromaticity; Electrophilicsubstitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation; Effect of ortho, meta and para directinggroups in monosubstituted benzenes.

Phenols : Acidity, electrophilic substitution reactions (halogenation,nitration and sulphonation); Reimer-Tieman reaction, Kolbe reaction.

Characterist ic reactions of the following (including thosementioned above): Alkyl halides: rearrangement reactions of alkyl carbocation, Grignardreactions, nucleophilic substitution reactions; Alcohols :esterification, dehydration and oxidation, reaction with sodium,phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols

into aldehydes and ketones; Ethers:Preparation by Williamson’sSynthesis; Aldehydes and Keto nes: oxidation, reduction, oximeand hydrazone formation; aldol condensation, Perkin reaction;Cannizzaro reaction; haloform reaction and nucleophilic additionreactions (Grignard addition); Carboxylic acids: formation of esters,acid chlorides and amides, ester hydrolysis; Am ines: basicity of substituted anilines and aliphatic amines, preparation from nitrocompounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactionsof diazonium salts; carbylamine reaction; Haloarenes: nucleophilicaromatic substitution in haloarenes and substituted haloarenes(excluding Benzyne mechanism and Cine substitution).

Carbohydrates: Classification; mono- and di-saccharides (glucoseand sucrose); Oxidation, reduction, glycoside formation andhydrolysis of sucrose.

Am ino ac ids and pept ides : General structure (only primarystructure for peptides) and physical properties.

Properties and uses of some important polymers : Naturalrubber, cellulose, nylon, teflon and PVC.

Pract ical organic chemistry : Detection of elements (N, S,halogens); Detection and identification of the following functionalgroups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde andketone), carboxyl, amino and nitro; Chemical methods of separationof mono-functional organic compounds from binary mixtures.

CLASS - XII (MATHEMATICS)Complex Number and Quadratic equations :

Algebra of complex numbers, addition, multiplication, conjugation,polar representation, properties of modulus and principal argument,triangle inequality, cube roots of unity, geometric interpretations.Quadratic equations with real coefficients, formation of quadraticequations with given roots, symmetric functions of roots.

Sequence & Series : Ar ithmetic, geometric and harmonic progress ions , ari thmetic,geometric and harmonic means, sums of finite arithmetic andgeometric progressions, infinite geometric series, sums of squaresand cubes of the first n natural numbers.

Logarithms and their properties. Permutations and combinations,Binomial theorem for a positive integral index, properties of binomialcoefficients.Binomial theorem for any index, exponential and logarithmic series.

Matrices & Determinants :

Matrices as a rectangular array of real numbers, equality of matrices,addition, multiplication by a scalar and product of matrices, transposeof a matrix, determinant of a square matrix of order up to three,inverse of a square matrix of order up to three, properties of thesematrix operations, diagonal, symmetric and skew- symmetric matricesand their properties, solutions of simultaneous linear equation in twoor three variables.

Probability : Addition and multiplication rules of probability, conditional probability,baye’s theorem, independence of events, computation of probabilityof events using permutations and combinations.

Straight Line :Cartesian coordinates, distance between two points, sectionformulae, shift of origin. Equation of a straight line in various forms,angle between two lines, distance of a point from a line; Lines through

the point of intersection of two given lines equation of the bisector of the angle between two lines, concurrency of lines; Centroid,orthocentre, incentre and circumcentre of a triangle.


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Conic Section :Equation of a circle in various forms, equations of tangent, normaland chord. Parametric equations of a circle, intersection of a circlewith a straight line or a circle, equation of a through the points of intersection of two circles and those of a circle and a straight line.Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal locus problems.

Three dimensions :

Direction cosines and direction ratios, equation of a straight line inspace, equation of a plane, distance of a point from a plane

Vectors : Addition of vectors, scalar multiplication, dot and cross products,scalar triple products and their geometrical interpretations. Positionvector of a point dividing a line segment in a given ratio. Projection of a vector on a line.

Function :Real valued functions of a real variable, into, onto and one-to-onefunctions, sum, difference, product and quotient of two functions,composite functions, absolute value, polynomial, rational,trigonometric, exponential and logarithmic functions. Even and oddfunctions, inverse of a function, composite function.

Limit, Continuity & Derivability :Limit and continuity of a function, limit and continuity of the sum,difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions even and odd functions, inverse of afunction, continuity of composite function. intermediate value propertyof continuous functions.

Differentiation :

Derivative of a function, derivative of the sum, difference, productand quotient of two functions, chain rule, derivatives of polynomial,rational, trigonometric, inverse trigonometric, exponential andlogarithmic functions. Derivatives of implicit functions, derivatives upto order two.

Tangent & Normal :

Geometrical interpretation of the derivative, tangents and normal.

Maxima & Minim a :Increasing and decreasing functions, maximum and minimum values

of a function, rolle’s theorem and Lagrange’s Mean value theorem.Integral calculus :

Integration as the inverse process of differentiation, indefinite integralsof standard functions, integration by parts, integration by the methodsof substitution and partial fractions.Definite integrals and their properties, fundamental theorem of integralcalculus. Application of definite integrals to the determination of areasinvolving simple curves.Formation of ordinary differential equations, solution of homogeneousdifferential equations, separation of variables method, linear firstorder differential equations.

Trigonometry :Trigonometric functions, their periodicity and graphs addition andsubtraction formulae, formulae involving multiple and sub-multipleangles, general solution of trigonometric equations.

Relations between sides and angles of a triangle, sine rule, cosinerule, half-angle formula and the area of a triangle, inverse trigonometricfunctions (principal value only).

CLASS - XII (PHYSICS)General : Units and dimensions, dimensional analysis; least count,significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments:Experiments based on using Vernier calipers and screw gauge(micrometer), Determination of g using simple pendulum, Young’smodulus by Searle’s method, Specific heat of a liquid using calorimeter,focal length of a concave mirror and a convex lens using u-v method,Speed of sound using resonance column, Verification of Ohm’s lawusing voltmeter and ammeter, and specific resistance of the materialof a wire using meter bridge and post office box.

Mechanics : Kinematics in one and two dimensions (Cartesian co-

ordinates only), Projectile Motion; Uniform Circular Motion; RelativeVelocity.

Newton’s laws of motion; Inertial and uniformly accelerated framesof reference; Static and dynamic friction; Kinetic and potential en-ergy; Work and power; Conservation of linear momentum and me-chanical energy.

Systems of particles; Centre of mass and its motion; Impulse; Elasticand inelastic collisions.Law of gravitation; Gravitational potential and field; Acceleration dueto gravity; Motion of planets and satellites in circular orbits; Escapevelocity.

Rigid body, moment of inertia, parallel and perpendicular axestheorems, moment of inertia of uniform bodies with simple geometricalshapes; Angular momentum; Torque; Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation;Rolling without slipping of rings, cylinders and spheres; Equilibriumof rigid bodies; Collision of point masses with rigid bodies.

Linear and angular simple harmonic motions.

Hooke’s law, Young’s modulus.

Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy andsurface tension, capillary rise; Viscosity (Poiseuille’s equationexcluded), Stoke’s law; Terminal velocity, Streamline flow, equationof continuity, Bernoulli’s theorem and its applications.

Waves : Wave motion (plane waves only), longitudinal and trans-verse waves, superposition of waves; Progressive and stationarywaves; Vibration of strings and air columns;Resonance; Beats;Speed of sound in gases; Doppler effect (in sound).

Thermal physics : Thermal expansion of solids, liquids and gases;Calorimetry, latent heat; Heat conduction in one dimension; Elemen-tary concepts of convection and radiation; Newton’s law of cooling;Ideal gas laws; Specific heats (Cv and Cp for monoatomic and di-atomic gases); Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and work; First law of thermodynamicsand its applications (only for ideal gases); Blackbody radiation:absorptive and emissive powers; Kirchhoff’s law; Wien’s displace-ment law, Stefan’s law.

Electricity and magnetism : Coulomb’s law; Electric field andpotential; Electrical potential energy of a system of point chargesand of electrical dipoles in a uniform electrostatic field; Electric fieldlines; Flux of electric field; Gauss’s law and its application in simple

cases, such as, to find field due to infinitely long straight wire, uni-formly charged infinite plane sheet and uniformly charged thin spheri-cal shell.

Capacitance; Parallel plate capacitor with and without dielectrics;Capacitors in series and parallel; Energy stored in a capacitor.

Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells; Kirchhoff’s laws and simple applications;Heating effect of current.

Biot–Savart’s law and Ampere’s law; Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside along straight solenoid; Force on a moving charge and on a current-carrying wire in a uniform magnetic field.Magnetic moment of a current loop; Effect of a uniform magnetic fieldon a current loop; Moving coil galvano- meter, voltmeter, ammeter

and their conversions.Electromagnetic induction: Faraday’s law, Lenz’s law; Self and mu-tual inductance; RC, LR and LC circuits with d.c. and a.c. sources.

Optics: Rectilinear propagation of light; Reflection and refraction atplane and spherical surfaces; Total internal reflection; Deviation anddispersion of light by a prism; Thin lenses; Combinations of mirrorsand thin lenses; Magnification.

Wave nature of light: Huygen’s principle, interference limited to Young’sdouble-slit experiment.

Modern physics : Atomic nucleus; Alpha, beta and gammaradiations; Law of radioactive decay; Decay constant; Half-life andmean life; Binding energy and its calculation; Fission and fusionprocesses; Energy calculation in these processes.

Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Charac-teristic and continuous X-rays, Moseley’s law; de Broglie wave-length of matter waves.


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Toll Free : 1800 200 2244 | 1800 258 5555| CIN: U80302RJ2007PLC024029 JA/JB-PAGE # 9

SAMPLE TEST PAPER -I

(For Class-X Appearing / Passed Students)

Course : VIKAAS (JA) & VIPUL (JB)

S.No. Subject Sections No. of questions Marks Negative marks Total

1 to 24 Sections-I 24 3 -1 72

25 to 28 Sections-II 4 4 0 16

29 to 36 Sections-IIIComprehension (vuq PNs n)

(SCQ)2 x 4 = 8 8 4 -1 32

37 to 44 Sections-I 8 3 -1 24


49 to 56 Sections-I 8 3 -1 24


60 200

Multiple choice questions (MCQ)

( ds oy ,d ;k ,d ls vf/kd fodYi lgh)





PART-II

(PHYSICS)

PART-III(CHEMISTRY)

Single choice questions (SCQ)

( ds oy ,d fodYi lgh)

Single choice questions (SCQ)

( ds oy ,d fodYi lgh)

Nature of Questions

Single choice questions (SCQ)( ds oy ,d fodYi lgh)

PART-I

(MATHS)

Total

PART - I (Hkkx - I)

SECTION - I ([k.M- I)

Straight Objective Type (lh/k s oLrqfu B izdkj )

This section contains 24 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of

which ONLY ONE is correct.

bl [k.M esa 24 iz'u gSaA izR;sd iz'u ds 4 fodYi (A), (B), (C) rFkk (D) gSa] ftuesa ls flQ Z ,d lgh gSA

1. The median AD of ABC meets BC at D. The internal bisectors of ADB and ADC meet AB and AC at Eand F respectively. Then EF(A) is perpendicular to AD (B) is parallel to BC(C) divides AD in the ratio of AB : AC (D) none of these

ABC dh ekf/;dk,a AD Hkqtk BC dks D ij feyrh gSA ADB vkSj ADC ds vkUrfjd dks.k v/kZd AB vkSj AC dks Øe'k% E vkSj F ij feyrs gS] rc EF(A) AD ds yEcor~ gS (B) BC ds lekUrj gS

(C) AD dks vuqikr AB : AC esa foHkkftr djrk gS (D) buesa ls dksbZ ugha

2. If A is an acute angle such that sin A =5

3, then the value of

Acos Asin

Acos Asin133

is

;fn U;wudks.k A bl çdkj gS] fd sin A =5

3 gS] rks

Acos Asin

Acos Asin133

dk eku gS&

(A)5

7(B) –

5

1(C)

12

35 (D) None of these ( buesaa ls dksbZ ugha)


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3. If the diagonal and the area of a rectange are 25 m and 168 m2 respectively, what is the length of therectangle ?

fdlh vk;r ds fod.kZ vkSj {ks=kQy Øe'k% 25 m rFkk 168 m2 gS] rks vk;r dh yEckbZ gksxh ?(A) 17 m (B) 31 m (C) 12 m (D) 24 m

4. If x = 7 + 4 3 then the value of

x

1x is

;fn x = 7 + 4 3 gks] rcx

1x dk eku gS&

(A) 8 (B) 6 (C) 5 (D) 4

5. In an A.P., the sum of first n term is2

n5

2

n3 2 . Its 25th term is

fdlh lekUrj Js


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11. The value of (a1/8 + a –1/8) (a1/8 – a –1/8) (a1/4 + a –1/4)(a1/2 + a –1/2) is

(a1/8 + a –1/8) (a1/8 – a –1/8) (a1/4 + a –1/4)(a1/2 + a –1/2) dk eku gS&(A) (a + a –1) (B) (a – a –1) (C) (a2 – a –2) (D) (a1/2 – a –1/2)

12. If a, b, c are real and distinct numbers, then the value of)ac(.)cb(.)ba(

)ac()cb()ba( 333

is

(A) 1 (B) a b

c (C) 2 (D) none of these

;fn a, b, c okLrfod vkSj fofHkUu la[;k,a gS] rks)ac(.)cb(.)ba(

)ac()cb()ba( 333

dk eku gS&

(A) 1 (B) a b

c (C) 2 (D) buesa ls dksbZ ugha

13. In figure, CDEF is a cyclic quadrilateral, DE and CF are produced to A

and B respectively such that AB || CD. If FED = 80°, find FBA. fn;s x;s fp=k esa CDEF ,d pØh; prqHkZqt gS ftlesa DE vkSj CF dks Øe'k% AvkSj B rd bl izdkj c


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18. Recurring decimal 352.0 , when expressed in the formq

p, is (where p and q are integers and q 0).

vkorhZ n'keyo 352.0 dksq

p ds :i esa O;Dr djus ij cjkcj gS ( tgk¡ p rFkk q iw.kkZad gSa rFkk q 0)

(A) 1000

235

(B) 990

243

(C) 990

233

(D) 990

223

.

19. The sum of all natural numbers less than 400 which are not divisible by 6, is :

400 ls de lHkh izkÑr la[;kvksa dk ;ksx tks fd 6 ls foHkkftr ugh gS] gksxk :(A) 13266 (B) 66534 (C) 79800 (D) 93066

20. Ram sets his watch at 6 : 10 am on Sunday, which gains 12 minutes in a day. On Wednesday if this watchis showing 2 : 50 pm. What is the correct time ?

jke viuh ?kMh jfookj dks 6 : 10 am ij feykrk gS] tks fd ,d fnu esa 12 feuV vkxs gks tkrh gSA cq/kokj dks ;fn ;g ?kMh 2 : 50 pm fn[kk jgh gS] rks lgh le; D;k gksxk ?(A) 1 : 50 pm (B) 2 : 10 pm (C) 2 : 30 pm (D) 3 : 30 pm

21. If , be the roots of x2

– a(x –1) + b = 0, then value of a –

12 + a –

1

2 + ba

2

is

;fn x2 – a(x –1) + b = 0 ds ewy , gks] rks a –

12 + a –

12 + ba

2

dk eku gS &

(A) 1 (B) 0 (C) 2 (D) 3

22. A square sheet of paper is converted into a cylinder by rolling it along its length. What is the ratio of thebase radius to the side of the square ?

,d oxkZdkj dkxt dks mldh yEckbZ ds vuqfn'k ?kqekdj ,d flysUMj esa :ikUrfjr fd;k tk;sA rks mldh vk/kkj f=kT;k dk oxZ dh Hkqtk ls vuqikr D;k gksxk ?

(A)1

2(B)

2

(C)

1

2(D)

1

23. In which of the following case(s) , the equation , a x2 + b x + c = 0 always has imaginary roots

fuEu esa ls dkSuls fodYi lehdj.k a x2 + b x + c = 0 ds lnSo dkYifud ewy gS&

(A) a > 0 , b > 0 , c > 0 (B) a > 0 , b < 0 , c = 0(C) a > 0 , b = 0 , c > 0 (D) a < 0 , b = 0 , c > 0

24. The value of x satisfying the equation (considering only positive root)

625625/625625 = 2/x is

x ds eku tcfd lehdj.k

625625/625625 = 2/x dks larq"V djrs gS&

( dsoy /kukRed ewy ysrs gq,)

(A) 6 (B) 3 (C) 3 (D) 2/9

SECTION - II ([k.M- II)

Multiple Correct Answer Type (cg qy lgh fodYi i zdkj)This section contains 4 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct.

bl [k.M esa 4 iz'u gSaA izR;sd iz'u ds mÙkj ds fy, 4 fodYi (A), (B), (C) rFkk (D) gSa] ftues a ls ,d ;k ,d l svf/ kd lgh gSA

25. The expression (5a – 3b)3 + (3b – 7c)3 – (5a – 7c)3 is divisible by :

O;atd (5a – 3b)3 + (3b – 7c)3 – (5a – 7c)3 foHkkftr gksxk(A) (5a + 3b + 7c) (B) (5a – 3b – 7c) (C) (3b – 7c) (D) (7c – 5a)


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26. (2x2 + 3x + 5)1/2 + (2x2 + 3x + 20)1/2 = 15, therefore x is :

(2x2 + 3x + 5)1/2 + (2x2 + 3x + 20)1/2 = 15, rc x gS :(A) (–8/3) (B) (14/5) (C) (–11/2) (D) 4

27. The difference between areas of outside and inside surfaces of a cylindrical metallic pipe 14 cm long is44 cm2. If the pipe is made of 99 cubic centrimeters of metal and outer radii and inner radii are R and r respectively, then

14 cm yEcs ,d /kkrq ls cus csyukdkj ikbZi dh ckÐ; rFkk vkUrfjd lrgksa ds {ks=kQyksa ds e/; varj 44 cm2

gSA ;fn ikbZi 99 /ku lsVhehVj /kkrq ls cuk;k tkrk gS rFkk ikbZi dh ckÐ; f=kT;k o vkUrfjd f=kT;k Øe'k% R rFkk r gS] rks &(A) R = 2.5 (B) R = 2 (C) r = 1.5 (D) r = 2

28. For any real number a, b, c & d which of the following statement(s) is/are true ?(A) If a > b then ac > bc (B) If a > b then a – c > b – c

(C) If a > b > 0 and c > d > 0, thend

a >

c

b(D) If a > b and c > d then a – c > b – d.

fdUgha okLrfod la[;kvksa a, b, c ,oa d ds fy, fuEufyf[kr esa ls dkSu ls dFku lR; gS \(A) ;fn a > b gks] rks ac > bc (B) ;fn a > b gks] rks a – c > b – c

(C) ;fn a > b > 0 ,oa c > d > 0 gks] rks d

a >

c

b(D) ;fn a > b ,oa c > d gks] rks a – c > b – d

SECTION - III ([k.M - III)

Comprehension Type (ck s/ku çd kj)This section contains 2 paragraphs. Based upon each paragraph, there are 4 questions. Each questionhas 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

bl [k.M esa 2 vuqPNsn (paragraphs) gSA çR;sd vuqPNsn ij vk/kkfjr 4 ç'u gSA çR;sd ç'u ds 4 fodYi(A), (B), (C) rFkk (D) gS , ftuesa ls flQZ ,d lgh gSA

Paragraph for Question Nos. 29 to 32

In the following figure, the smaller triangle represents the teachers;

the big triangle, the politicians; the circle, the graduates and therectangle, the members of parliament. Different regions are beingrepresented by the letters of english alphabet

On the basis of the about diagram, answer the following questions :29. Who among the following are graduates or teachers but not politicians ?

(A) B, G (B) G, H (C) A, E (D) E, F

30. Who among the following politicians are graduates but not the members of parliament ?(A) B, C (B) L, B (C) D, L (D) A, H, L

31. Who among the following politicians are neither teachers nor graduates ?(A) E, F (B) D, E (C) C, D (D) L, H

32. Who among the following members of parliament is a graduate as well as a teacher?(A) G (B) F (C) C (D) H

iz'u 29 l s 32 ds fy, vuqPN sn

fuEu vkys[k esa] NksVk f=kHkqt] v/;kidksa dks çnf'kZr djrk gS rFkk cM+k f=kHkqt] usrkvksa dks çnf'kZr djrk gSA o`Ùk] LukÙkd dks çnf'kZr djrk gS rFkk vk;r] laln ds lnL;ksa dks çnf'kZr djrk gSA çR;sd fofHké {ks=kksa dks vaxzsth o.kZekyk ds v{kjksa }kjk vyx&vyx çnf'kZr fd;k x;k gS&

Åij fn;s x;s fp=k ds vk/kkj ij fuEu ç'uksa dk mÙkj nhft;s&29. fuEufyf[kr esa ls dkSuls @lk Lukrd ;k v?;kid gS ijUrq usrk ugha gks ?

(A) B, G (B) G, H (C) A, E (D) E, F


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30. fuEufyf[kr esa ls dkSuls @lk usrk Lukrd gS ijUrq laln dk lnL; ugha gS ?(A) B, C (B) L, B (C) D, L (D) A, H, L

31. fuEufyf[kr esa ls dkSuls @lk usrk] u rks v/;kid gS vkSj u gh Lukrd gS ?(A) E, F (B) D, E (C) C, D (D) L, H

32. fuEufyf[kr esa ls dkSuls @lk laln dk lnL;] Lukrd gS rFkk v/;kid gS ?(A) G (B) F (C) C (D) H

Paragraph for Question Nos. 33 to 36

Four different integers a, b, c and d form an increasing A.P. One of these numbers is equal to thesum of the squares of the other three numbers. Then

33. The smallest number is :(A) – 2 (B) 0 (C) – 1 (D) 2

34. The common difference of A.P. is(A) 2 (B) 1 (C) 3 (D) 4

35. c, d and d2 are in(A) A.P. (B) G.P. (C) H.P. (D) None of these

36. The value of (a + c)2 + (d – 2c)2 is equal to(A) 0 (B) 1 (C) 2 (D) 4

i z'u 33 l s 36 ds fy, vu qPN sn

pkj fHkUu iw. kkZ ad a, b, c rFkk d ,d c


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38. An electron enters a magnetic field at right angles to it, as shown in figure.The direction of force acting on the electron will be :(A) to the right (B) to the left(C) out of the page (D) into the page

,d bys DVªkWu fp=kkuqlkj pq Ecdh; {ks=k eas yEcor~ :i ls iz os'k djrk gS rks bys DVªkWu ij vkjksfir cy dh fn'kk gksxh A(A) nka;h rjQ (B) cka;h rjQ

(C) dkxt ds ry ls ckgj dh rjQ (D) dkxt ds ry esa vUnj dh rjQ39. If the distance between two masses is doubled, the gravitational attraction between them.

(A) Is doubled (B) Becomes four times (B) Is reduced to half (D) Is reduced to a quarter nks nzO;ekuks ds e/; nwjh nqxquh dj nh xbZ gS rks buds e/; xq:Rokd"kZ.k cy gksxkA(A) nqxquk (B) pkj xquk (B) vk/kk jg tk;sxk (D) ,d pkSFkkbZ jg tk;sxk

40. A force vector applied on a mass is represented as F i j k 6 8 10 and accelerates with 1 m/s2. What

will be the mass of the body-

fdlh fi.M ij yxk;k x;k cy F i j k 6 8 10 gS] rFkk ;g 1 eh@ls-2 ls Rofjr gks rk gS rks fi.M dk nz O;eku D;k gks xk&

(A) 210 kg (B) 102 kg (C) 10 kg (D) 20 kg

41. A particle of mass m at rest is acted upon by a force F for a time t. Its kinetic energy after an

interval t is :m nzO;eku dk ,d d.k fojke ij gS bl ij t le; ds fy, F cy vkjksfir jgrk gSA t le;kUrjky ds ckn bldh xfrt

ÅtkZ gS %

(A)m

tF 22(B)

m2

tF 22(C)

m3

tF 22(D)

m2

tF

42. The displacement-time relationship for a particle is given by 20 1 2x a a t a t . The acceleration of the

particle is

;fn ,d d.k ds foLFkkiu≤ dk lEcU/k 20 1 2x a a t a t gks rks mldk Roj.k gksxk&

(A) 0a (B) 1a (C) 2a (D) 22a

43. Light ray AB incidents on a plane mirror XY at an angle of 50º from normal. The second plane mirror isplaced is such a way that the reflected ray BC from the mirror XY retraces its path. Angle of inclination of two mirrors will be:

izdk'k dh fdj.k AB lery niZ.k XY ij vfHkyEc ls 50º ds dks.k ij vkifrr gksrh gSA nwljk lery niZ.k bl izdkj j[kk tkrk gS fd lery niZ.k XY ls ijkofrZr fdj.k BC nwljs niZ.k ls ijkofrZr gksdj vius iFk ij okil tkrh gSaA nksuksa niZ.kksa ds e/; ikjLifjd >qdko gSa :(A) 25º (B) 50º (C) 75º (D) 90º

44. A body moves on three quarters of a circle of radius r. The displacement and distance travelled by it are : ,d oLrq r f=kT;k ds o`Ùk ij rhu pkSFkkbZ Hkkx pyrh gS] blds }kjk r; fd;k x;k foLFkkiu o nwjh gS :

(A) r, 3r (B) 2r , 2

r 3(C) 2r,

2

r 3(D) 0,

2

r 3

SECTION - II ([k.M

- II)

Multiple Correct Answers Type (cgqy lgh mÙkj i zdkj )This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B),(C) and (D), out of which ONE OR MORE THAN ONE is/are correct.

bl [k.M esa 4 cgq lgh mÙkj izdkj ds iz'u gSaA izR;sd iz'u ds 4 fodYi (A), (B), (C) rFkk (D) gSa, ftuesa ls ,d ;k ,d ls vf/kd fodYi lgh gS ¼gSa½A

45. A beam of green light is incident from air and after refraction enters water. In comparison to that in air :(A) Speed of light is less in water (B) Frequency of light is less in water (C) Wavelength of light is less in water (D) Speed of light is more in water

ok; q ls vkifrr gjs i zdk'k dh fdj.k] viorZu ds ckn ty esa i zos 'k djrh gSA ok; q dh rqyuk es a &(A)

ty es a izdk'k dh pky de gksxh(B)

ty es a izdk'k dh vko` fÙk de gk sxh(C) ty es a izdk'k dh rjaxnS/;Z de gk sxh (D) ty es a izdk'k dh pky T;knk gk sxh


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46. A household electric power outlet (assume 220 V constant voltage) is fused to cut at if the current equals or exceeds 20 Ampere. A 2 kW heater, 1kW Air conditioner and three 100 W bulbs are already running atrated power. If now somebody wants to run a computer then computer can run without causing fuse to burnif power requirement of computer is (neglect losses in current carrying wire)

,d ?kjsyw fo|qr 'kfDr ifjiFk (220 V vpj ekusa) esa ;fn /kkjk 20 A ;k mlls vf/kd gks tk;s rks ¶;wt VwV tkrk gSA ,d2 kW dk ghVj, 1kW dk ,;j df.M'kuj rFkk rhu 100 W ds cYc mudh vafdr 'kfDr ij dk;Zjr gSA vc ;fn dksbZ

,d dEI;wVj pykuk pkgrk gS rFkk dEI;wVj ¶;wt tyk;s fcuk gh dk;Z dj ldrk gS ;fn dEI;wVj dh vko';d 'kfDr gksxh& (/kkjkokgh rkj esa gkfu ux.; ysaos)(A) 1000 W (B) 1100 W (C) 100 W (D) 1200 W

47. Which of the following statements is/are true :(A) An electric motor converts mechanical energy into electrical energy.(B) An electric generator works on the principle of electromagnetic induction.

(C) This symbol is used for variable register..

(D) A wire with a green insulation is usually the live wire of an electric supply.

fuEu eas ls dkSulk@ls dFku lR; gSA(A) fo|qr eksVj ;kaf=kd ÅtkZ dks fo|qr ÅtkZ esa ifjofrZr djrh gSA

(B) fo|r tfu=k fo|qr pqEcdh; izsj.k fl)kUr ij dk;Z djrk gSA

(C) bl ladsr dk iz;ksx ifjofrZ izfrjks/k ds fy;s fd;k tkrk gSA

(D) ?kjks esa fo|qr vkiwfrZ ds fy, gjk fo|qr jks/kh rkj ,d /kkjkokgh rkj ds :i esa iz;qDr fd;k tkrk gSA

48. A cuboid block of mass 12 kg is lying on the ground (Assume air is absent). Take g = 10 m/sec.2 :(A) Pressing force applied by the block on the ground is 120 N.(B) If the surface ABCD is lying on the ground, then pressure(stress) exerted by the block on the ground will be 20 Pa.(C) If surface ABEF is lying on the ground, then the pressure(stress) exerted by the block on the ground will be 60 Pa.

(D) If we place the block on the ground such that different planesurfaces lie on the ground, pressure (stress) on the ground willbe maximum when surface BCFG lies on the ground.

12 kg nzO;eku dk ?kukHk ds vkdkj dk ,d Bksl CykWd tehu ij j[kk gqvk gSA g dk eku = 10 m/sec.2 ysaA(A) CykWd }kjk tehu ij yxk;k x;k ncko cy 120 N gSA(B) ;fn CykWd dks lrg ABCD ds lgkjs tehu ij j[kk gS] rks CykWd }kjk tehu ij yxk;k x;k nkc ( izfrcy) 20 Pa gks xkA(C) ;fn CykWd dks lrg ABEF ds lgkjs tehu ij j[kk gS] rks CykWd }kjk tehu ij yxus okyk nkc ( izfrcy) 60 Pa gks xkA(D) ;fn ge CykWd dks tehu ij vyx-vyx lery lrgks ds lgkjs j[ks rks tehu ij nkc ( izfrcy) vf/kdre rc gksxk

tc CykWd dks lrg BCFG ds lgkjs tehu ij j[ksA

PART - III (Hkkx

- III)SECTION - I ([k.M- I)

Straight Objective Type (lh/k s oLrqfu B izdkj )

This section contains 8 multiple choice questions. Each question has choices (A), (B), (C) and (D),out of which ONLY ONE is correct.

bl [k.M esa 8 cgq&fodYih iz'u gSA izR;sd iz'u ds 4 fodYi (A), (B), (C) rFkk (D) gSa, ftuesa ls flQZ ,d lgh gSA

49. Which has highest e/m ratio ?

fuEu es a ls fdldk e/m vuqikr vf/kdre gS \(A) He2+ (B) H+ (C) He+ (D) H


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50. For a chemical reaction 3X(g) + Y(g) X3Y(g), the amount of X

3Y at equilibrium is affected by

(A) temperature and pressure (B) temperature only(C) pressure only (D) temperature, pressure and catalyst

fdlh jklk;fud vfHkfØ;k ds fy, 3X(g) + Y(g) X3Y(g), lkE; ij X

3Y dh ek=kk fuEu }kjk izHkkfor gksxh&

(A) rki vkSj nkc (B) dsoy rki (C) dsoy nkc (D) rki] nkc vkSj mRizsjd

51. The maximum & minimum oxidation state of Bromine is:

czksehu dh vf/kdre rFkk U;wure vkWDlhdj.k voLFkk dkSulh gS\(A) +6, –2 (B) +7, –1 (C) +1, –1 (D) +5, –1

52. The value of Planck’s constant is 6.63 × 10 –34 Js. The velocity of light is 3 × 108 m/sec. Which value isclosest to the wavelength of light with frequency of 8 × 1015 sec –1 ?

Iykad fLFkjkad dk eku 6.63 × 10 –34 Js gSA izdk'k dk osx 3 × 108 [email protected] gSA dkSulk rjaxnS/;Z eku izdk'k dhvko`fr 8 × 1015 lSd.M –1 ds lehi gS ?(A) 5 × 10 –18 m (B) 4 × 10 –8 m (C) 3 × 107 m (D) 2 × 10 –25 m

53. Which of the following is the IUPAC nomenclature of ethyl methyl ketone?

(A) Propan-1-one (B) Butanone (C) Butan-1-one (D) Propan-2-one

fuEu esa ls dkSulk uke ,fFky esfFky dhVksu dk IUPAC ukedj.k gS\

(A) izksisu-1-vkWu (B) C;wVsukWu (C) C;wVsu-1-vkWu (D) izksisu-2-vkWu

54. Lucas reagent is used to convert alcohol into alkyl halide. In this rate of reaction with respect to 1º, 2º, 3º

alcohol will be–

(A) 1º > 2º > 3º (B) 3º > 2º > 1º (C) 3º = 2º = 1º (D) None of these

Y;wdkl vfHkdeZd dk mi;ksx ,Ydksgy dks ,fYdy gSykbM esa cnyus esa gksrk gSA 1º, 2º o 3º ,Ydksgy ds lUnHkZ esa

vfHkfØ;k dh nj gksxhA

(A) 1º > 2º > 3º (B) 3º > 2º > 1º (C) 3º = 2º = 1º (D) buesa ls dksbZ ugha

55. What is the formula of sodium periodate?

fuEu esa ls lksfM;e ijvk;ksMsV dk lw=k dkSulk gS\(A) NaIO

4(B) NaIO

3(C) NaIO

2(D) NaIO

56. IUPAC name of the compound

33

323

CHCH||

CHCHCHCHNHCH is

(A) 2-(N-methylamino)-4-methylpentane (B) N-Methyl-4-methylpentan-2-amine(C) 2-(N-methylamino)-3-isopropylpropane (D) 2-(N-methylamino)-1, 4, 4-trimethylbutane

;kSfxd

33

323

CHCH||

CHCHCHCHNHCH dk IUPAC uke gSA

(A) 2-(N- esfFky,feuks)-4- esfFkyisUVsu (B) N- esfFky-4- esfFkyisUVsu-2- ,s ehu(C) 2-(N- esfFky,feuks)-3-vkblksizks fiyizksisu (D) 2-(N- esfFky,ehuks)-1, 4, 4- VªkbZesfFkyC;wVsu

SECTION - II ([k.M - II)

Multiple Correct Answers Type (cgqy lgh mÙkj i zdkj )

This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A),(B), (C) and (D), out of which ONE OR MORE THAN ONE is/are correct.

bl [k.M esa 4 cgq lgh mÙkj izdkj ds iz'u gSaA izR;sd iz'u ds 4 fodYi (A), (B), (C) rFkk (D) gSa, ftuesa ls ,d ;k ,d ls vf/kd fodYi lgh gS ¼gSa½A

57. Which of the given particles are -vely charged?(A) proton (B) electron (C) antiproton (D) positron

fuEu esa ls dkSuls d.k _.kvkosf'kr gSa\(A) izksVksu (B) bysDVªkWu (C) ,UVhizksVksu (D) iksftVªkWu


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58. The pair of compounds having the same general formula.

fuEu esa ls dkSulk ;qXe leku lkekU; lw=k j[krk gSaA

(A) and ( rFkk) (B) and ( rFkk)

(C) and ( rFkk) (D) and ( rFkk) H—CC—CC—H

59. A hydrogen - like atom has ground state binding energy 122.4 eV. Then :(A) its atomic number is 3(B) a photon of 90 eV can excite it to a higher state(C) a 80 eV photon cannot excite it to a higher state(D) None

,d gkbMªkstu leku ijek.kq dh vk| voLFkk dh cU/ku ÅtkZ 122.4 eV gSa rks &(A) bldk ijek.kq Øekad 3 gSA(B) 90 eV okyk QksVkWu bls mPp voLFkk esa mÙksftr dj ldrk gSA(C) 80 eV okyk QksVkWu bls mPp voLFkk esa mÙksftr ugha dj ldrk gSA

(D) dksbZ ugah

60. Which compound is/are the isomer of 3-Ethyl-2-methylpentane ?

dkSulk@dkSuls ;kSfxd 3- ,fFky-2- esfFkyisUVsu ds leko;oh gSa \

(A) (B)

(C) (D)

ANSWER KEY TO SAMPLE TEST PAPER-I

1. (B) 2. (D) 3. (D) 4. (D) 5. (B) 6. (A) 7. (B)

8. (C) 9. (C) 10. (D) 11. (B) 12. (D) 13. (C) 14. (B)

15. (A) 16. (D) 17. (B) 18. (C) 19. (B) 20. (B) 21. (B)

22. (A) 23. (C) 24. (B) 25. (CD) 26. (CD) 27. (AD) 28. (BC)29. (C) 30. (A) 31. (D) 32. (B) 33. (C) 34. (B) 35. (B)36. (A) 37. (D) 38. (D) 39. (D) 40. (A) 41. (B) 42. (D)43. (B) 44. (B) 45. (AC) 46. (ABC) 47. (BC) 48. (ABD) 49. (B)

50. (A) 51. (B) 52. (B) 53. (B) 54. (B) 55. (A) 56. (B)

57. (BC) 58. (ABD) 59. (AC) 60. (ACD)

HINTS & SOLUTION TO SAMPLE TEST PAPER-I

1. Since DE is angle bisector AE : EB = DA : DB .... (i)Since DF is angle bisector AF : FC = DA : DC = DA : DB .... (ii)from (i) and (ii) we get AE : EB = AF : FC EF // BC

3. The diagonal d = 25m. and area A = 168m 2. Let ‘I’ be the length and ‘b’ be the width of the rectangle.Therefore, I2+b2 = d2. and Ib = A We can therefore write (I + b) 2 = d2 + 2A and (I b)2 = d2 2A.Substituting and solving we get, I + b = 31 and I b = 17. Hence I = 24 and

b = 7.


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4. x = 7 + 34

x = 32 x

1 = 32 So x +

x

1 = 2 + 3 + 32 = 4

5. Sn = 2

n5

2

n3 2

Sn–1

=2

3(n – 1)2 +

2

5(n – 1) a

n = s

n – s

n–1 =

2

3(2n – 1) +

2

5 a

25 = 76

6. In ABC, we have A+ B + C = 180°

60° + B + 50° = 180° 110° + B = 180°

B = 180° – 110° B = 70°

Since D and E are the mid-points of AB and AC respectively. Therefore,

DE || BC and DE =1

2BC

Now, DE || BC and the transversal AB cuts them at D and B respectively. EDB + B = 180°

Interior angles on thesameside of

the transversal aresup plementary

EDB + 70° = 180° EDB = 180° – 70° = 110°

7. AB is perp. bisector of PQ APQ = AQPand PBA = QBABut PQ is perpendicular bisector of AB is not always true(It is true only when the circles are of equal radius)

9. ACB = ABP = 60° ABC = ACQ = 70° BAC = 180° – (60° + 70°) = 50° BOC = 100° BTC = 180° – 100° = 80°

10. Selling price = Rs. 24 = 80% of marked price.Marked price = 30

Now selling price = 70% of marked price =100

70× 30 = 21

11. (a1/8 + a –1/8)(a1/8 – a –1/8)(a1/4 + a –1/4)(a1/2 + a –1/2)

= (a1/4 – a –1/4)(a1/4 + a –1/4)(a1/2 + a –1/2)= (a1/2 – a –1/2)(a1/2 + a –1/2)= (a – a –1).

13. FCD = 180° – 80° = 100°[Opposite angles of a cyclic quadrilateral are supplementary]Now AB || CD ABC + DCB = 180° [Co-interior angles]FBA + 100° = 180°So. FBA = 80°


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15. We have ( gesa fn;k gS )

31

3 – 1

sincos

sin – cos

)sin(cos – )sin – (cos

)sin(cos)sin – (cos

=)31( – )3 – 1(

)31()3 – 1(

[Applying componendo and dividendo] [ ;ks xkUrjkuq ikr

dk mi;ksx djus ij]

sin2 –

cos2 =

32 –

2 cot =

3

1

tan = 3 tan = tan60º = 60º

16. AOB = 2 ( APB)b = AOB = 2 (85°) = 170°In AOB, b + 2a = 180° (OA = OB)170° + 2a = 180° a = 5°

17.

QRC and PRA are similar

AR : RC =10/7

5/3 = 6 : 7

AR : AC = 6 : 13

18. Let x = 352.0

10x = 35.2

1000x = 235.35 +99

35

990x = 233

x =990

233 x = –

2

3, y =

2

3

19. Sum of all natural numbers less than 400

S1 = 1 + 2 + 3 + 4 +......399 =

399 40079800

2

Sum of all natural number divisible by six.S

2 = 6 + 12 + 18 +.......396

Number of terms 396 = 6 + (n–1)6n = 66

66sum [2 6 (66 1)6]

2

S2 = 13266

S1 – S

2 = 79800 – 13266 = 66534.


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20. Incorrect watch covers 1452 min in 1440 min. So, it will cover 1 min in1452

1440 min. Therefore it will cover

4840 min in1452

1440 × 4840 = 4800 min = 80 h. Therefore 80 h = 3 days and 8 h.

21. 2 – a = –a – b2 – a = –a – b

a –

12 + a –

1 +

ba

2

=

ba

2

ba

1 –

ba

1 –

= 0

22. Surface area of the cylinder = surface area of the square 2rh = a2

Here height ‘h’ of the cylinder = side of the square since it is rolled along its length. 2ra = a2.

base radiusa

r 2

Ratio of base radius to side of squarea 1

:a2 2

24. 2

x

625625

625625

625 = 23

625 = 23

So,2

x

2323

2323

2x

22

32 2

3

2

x x = 3

25. (5a – 3b)3 + (3b – 7c)3 – (5a – 7c)3

Let 5a – 3b = x, 3b – 7c = y and 7c – 5a = zx3 + y3 + z3 = 3xyz, if x + y + z = 0.x + y + z = 5a – 3b + 3b – 7c + 7c – 5a = 0(5a – 3b)3 + (3b – 7c)3 + (7c – 5a)3

= 3 (5a – 3b) (3b – 7c) (7c – 5a) It is div isible by 5a – 3b, 3b – 7c, 7c – 5a.

26. (2x2 + 3x + 5)1/2 + (2x2 + 3x + 20)1/2 = 15

Let 2x2 + 3x + 5 = y2 y + (y2 + 15)1/2 = 15

y2 + 15 = (15 – y)2

y2 + 15 = 225 + y2 – 30y

30y = 210210

y 7.30

2x2 + 3x + 5 = 492x2 + 3x – 44 = 02x2 – 8x + 11x – 44 = 02x(x – 4) + 11 (x – 4) = 0x = –11/2 & x = 4.

Hence, two solutions x = –11/2 & x = 4 are possible.


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28. a > b if ;fn c < 0 ac < bc so (A) is incorrect. xyr gSAa > b a – c > b – c so (B) is correct. lgh gS

If ;fn a > b > 0 , c > d > 0 d

a >

c

b so (C) is correct. lgh gSA

If ;fn a > b , c > d c = 50, d = 2, a = 10, b = 1 a – c = – 40, b – d = – 1

= – 1 1

29 to 32

Sol.

29. A,E

30. B,C

31. L,H

32. F

(33-36)

Sol. Let four integers be a–d, a , a + d and a + 2dwhere a and d are integers and d > 0. a + 2d = (a – d)2 + a2 + (a + d)2

2d2

– 2d + 3a2

– a = 0 ...............(i)

d =2

1

2a6a211 ...............(ii)

Since d is positive integer 1 + 2a – 6a2 > 0

6a2 – 2a – 1 < 0

6

71 < a <

6

71 a is an integer

a = 0 Put in (ii) d = 1 or 0 but d > 0 d = 1 The four numbers are : –1, 0, 1, 2

35. c, d, d2 1, 2, 4 they are in G.P.

36. (– 1 + 1)2 + (2 – 2)2 = 0

37. F 2r

1. If r becomes double then F reduces to

4

F

38. mass nzO;eku m =|a|

|F|

=

1

200 = 10 2


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39. a =m

F, S =

2

1

2tm

F

, W

F = FS = F

m2

Ft2

40. x = a0 + a1 t + a2 t2

dt

dx

= 0 + a1 + 2a2 t a = 2

2

dt

xd

= 0 + 2a2

41. 50º

N

X40

A

B

C

50º

Y

Ray BC retraces its path when A fall on second mirror perpendicularly, so as per figure L BYC will be euqal to50º.

42. S Q

P

R

r f=kT;k ds o`rh; iFk ij 3/4 Hkkx r; djus ij

(i) Displacement ( foLFkkiu) = 22 r r = r 2

(ii) Distance ( nwjh) = r 24

3 =

2

r 3

43. We know that v = f f = constant(i) speed of light

v 1

w >

air

so vw <

air

(ii) vso

w <

air

ge tkurs g S fd v = f f = fu;r(i) izdk'k dh pky

v 1 w > air

vr% vw <

air

(ii) vvr%

w <

air

44. Total power supplied dqy fn xbZ 'kfDr = 20 × 220 = 4400 Watt Already existing load tks yksM ij igys ls mifLFkr gS = 2000 + 1000 + 300 = 3300 WattWe can increase load upto 4400 Watt so A, B & C are correct options.

ge yksM 4400 Watt rd c


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45. Based on information

lwpuk ij vk/kkfjr

46. (A) Pressing force ncko cy = mg = 12 g = 120 N

(B) P = A

F =

23

120

= 20 Pa

(C) P = A

F =

13

120

= 40 Pa

(D) Area of surface BCFG is minimum So, pressure will be maximum.

lrg BCFG dk {kS=kQy U;qure gS vr% nkc vf/kdre gksxkA

49. For He2+ PM4

e2 ; For H+

PM

e ; For He+

PM4

e ; For H

0

M

e

gy % He2+ ds fy,PM4

e2 ; H+ ds fy,

PM

e ; He+ ds fy,

PM4

e ; H ds fy,

0

M

e

50. Equilibrium is affected by pressure and temperature but not by catalyst.

gy - lkE; ij nkc o rki dk izHkko iMrk gS ysfdu mRizsjd dk ughaA

51. Br show oxidation state varying from –1 to +7.

Br, –1 ls +7 rd ifjofrZr gksus okyh vkWDlhdj.k voLFkk n'kkZrk gSA

52. 15

8

108

103c

= 3.75 × 10 –8 m.

53.

CH3 –C–CH2 –CH3

O

– Ethyl methyl ketone

Butanone – IUPAC name.

CH3 –C–CH2 –CH3

O

– ,fFkyesfFkydhVksu

C;wVsukWu – IUPAC uke .

59. Ground state binding energy = 13.6 Z2 = 122.4 eV. Z = 3.1st excitation energy = 10.2 Z2 = 91.8 eV. an 80 eV electron cannot excite it to a higher state.

gy % vk| voLFkk esa cU/ku ÅtkZ = 13.6 Z2

= 122.4 eV. Z = 3.1st mÙkstu ÅtkZ = 10.2 Z2 = 91.8 eV. ,d 80 eV dk QksVkWu bls mPp voLFkk esa mÙksftr ugha dj ldrk gSA

60. ACD are 8 carbon alkanes but B has only 6 carbons atoms.

vU; lHkh esa 8 dkcZu gSa] tcfd B esa dsoy 6 dkcZu gSaA


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Jee Adv Sample TestPaper ResoNET-2016

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