Sec: XI_IIT_STU_IC & IR Date: 09-12-2024

Time: 1.5 Hrs. WARM-UP - CFTM – 06 Max. Marks: 180

IMPORTANT INSTRUCTIONS
JEE MAIN 2022 Model
PHYSICS
+Ve –Ve No. of Total
Section Question Type
Marks Marks Qs. marks
Sec – I (Q.N : 1 – 10) Questions with Single Correct Choice 4 –1 10 40
Questions with Integer
Sec–II (Q.N : 11 – 15) 4 –1 5 20
Answer Type (+ / –Number)
Total 15 60

CHEMISTRY
+Ve –Ve No. of Total
Section Question Type
Marks Marks Qs. marks
Sec – I (Q.N : 16 – 25) Questions with Single Correct Choice 4 –1 10 40
Questions with Integer
Sec–II (Q.N : 26 – 30) 4 –1 5 20
Answer Type (+ / – Number)
Total 15 60

MATHEMATICS
+Ve –Ve No. of Total
Section Question Type
Marks Marks Qs. marks
Sec–I (Q.N : 31 – 40) Questions with Single Correct Choice 4 –1 10 40
Questions with Integer
Sec–II (Q.N : 41 – 45) 4 –1 5 20
Answer Type (+ / – Number)
Total 15 60

Exam Syllabus

40% Excess of pressure, capillary rise ,Viscosity

40% Question on Application of Bernoulli's theorem, Surface Tension
20% MATHEMATICAL PHYSICS : Application of differentiation in physics, Maxima & Minima, Integration and its application in physics
Unit and Dimension : Introduction of physics, physical quantities and physical laws,Fundamental and derived quantities and ways to
write dimension, Unit and Dimension Uses of dimensional analysis (Principle of homogeneity) Unit and Dimension : Significant figures,
Errors in measurements Problems discussion from material KINEMATICS : Frame of Reference , Mathematical Expression and definition of
position, distance and displacement Avg velocity& instantaneous velocity, Avg speed & instantaneous speed, acceleration KINEMATICS :
Uniformly accelerated motion (1D) Motion under gravity Graphs, Motion under variable acceleration, Motion in a plane, Oblique projectile
motion Horizontal Projectile Motion Projectile motion from tower Practice on oblique and horizontal projectile motion Projectile motion in
PHYSICS inclined plane Relative Velocity, Kinematics of Circular Motion in a plane, Newton's Laws of Motion Equilibrium of Particles Pulley mass
system, Pseudo force, Constraint relations Introduction to Friction, Friction force in simple cases, angle of repose, angle of friction Multiple
block system with friction Dynamics of circular motion Work done by constant and variable force Work energy theorem, Conservation of
mechanical energy Motion in a vertical circle Location of centre of mass Motion of centre of mass Linear momentum, Impulse, Conservation
of linear momentum Collision in one Dimension, Collision in two Dimension Rotational kinematics Moment of Inertia of different Bodies
Parallel and perpendicular axis theorem and their applications Torque, Dynamics of rigid body Question on rotational dynamics Angular
momentum Angular Momentum conservation Rolling motion(Velocity, acceleration in case of rolling motion) Dynamics of Rolling Motion,
Collision of particles with rigid body Discussion on Instantaneous axis of rotation and related problems. Material problems discussion Law of
gravitation, Gravitational field Acceleration due to gravity and its variation with height, depth and rotation of earth Gravitational Potential
and Potential energy Escape velocity, Kepler laws, Geostationary satellites Hydrostatic pressure, Pascal’s law Archimedes’ principle
Equation of continuity, Bernoulli’s principle, Velocity of Efflux
40% acidic and basic order of organic compound , Aromaticity, reaction intermediates: stability of carbocations, free radicals,
40% Resonance, Electronic effects: Inductive effect, Electromeric effect, Mesomeric effect, Hypercongugation
20% Nature of Matter, Properties of matter & their measurement SI unit, Mass weight, Volume temperature, Need for standard
reference, Scientific notation, Precision & accuracy, Significant figure and calculation involving significant figure. Law of chemical
CHEMISTRY combination : (i) Law of conservation of mass, (ii) Law of constant combination, (iii) Law of multiple proportion, (v) Gay Lussac's law, (vi)
Avagdro law, (vii) Dalton's atomic theory Atomic mass Mole concept: Calculation based on mole concept, concept of gram atom, gram
molecule Percentage by mass (w/w), percentage by volume (v/v) ,Concentration terms: Molarity, molality, mole fraction and their
interconversions, relation between density & molarity , Concentration terms & their interconversions, relation between density & molarity
Question practice on concentration Concept of limiting reagent : Use of stoichiometry in balanced equation & limiting reagent concept

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Percentage calculation of elements, Formula representation of molecule : (i) Empirical formula, (ii) Molecular formula, (iii) Formula unit n-
factor of acid, base and salts equivalent weight & related numericals (excluding redox), Normality and equivalent concept, calculation based
on weight-weight relation, weight-volume relation, volume-volume relation (Excluding redox and double titration), Relation between
normality and molarity, percentage of free SO3 in oleum, Volume strength of H2O2, hardness of water (ppm), Practice questions and
Package Discussion (i)Basic discovery of subatomic particles (Cathode rays, anode rays, Chadwick experiment), (ii) Rutherford experiment
i) Introduction to electromagnetic wave, (ii) Principle of quantization (Planck theory), (iii) Black body radiation, (iv) Photoelectric effect
Bohr's Atomic Model with mathematical derivations Emission and Absorption Spectrum, Hydrogen spectrum (i)Dual Behaviour of matter, (ii)
de-broglie equation, Heisenberg's principle of Uncertainity Quantum numbers, Introduction of wave mechanical model of atom (ψ,ψ2),
Shape of orbitals Radial probability graphs for various orbitals Aufbau principle, Pauli's exclusion principle, Hund's rule of maximum
multiplicity Electronic configuration, Electronic configuration of Half-filled and full-filled orbitals Modern periodic law and prediction of
periodic table, IUPAC naming of element (Z > 100), Location of element by using atomic number and vice versa Periodic properties: atomic
and ionic size including screening effect, ionization enthalpy, electron affinity & electon gain enthalpy. Anomalous behaviour of 2nd period
elements Types of bond ionic, covalent and coordinate covalent, properties of ionic compounds, VBT (including types of overlaping sigma
and pie bonds), Fajans Rule Hybridisation, VSEPR Theory, Dipole moment Molecular orbital theory, shape of molecular orbitals, bond order
of diatomic molecules, calculation of bond order from resonance, hydrogen bonding Intermolecular force and thermal energy,Gaseous state:
Introduce volume, pressure and temperature their various units and relation among them, Gas laws: Boyle's law,Charle's law, Gay Lusac's
law, Avogardo's law, ideal gas equation, Dalton's law of partial pressure diffusion of gases, Kinetic theory of gases, distribution of
moleculaar speeds, ideal and non-ideal gases Compressibility factor and van der Waal equation, liquification of gases Introduction to Basic
Terms : (i) Types of system, (ii) State of a System, (iii) State function, (iv) State variable, (v) path function, (vi) Extensive intensive
property, (vii) Thermodynamic process, Internal Energy as a state function, Pressure volume work, First law of thermodynamics with
Enthalpy. (i) Heat capacity, (iii) Relation between Cp and Cv for an ideal gas, (iii) Isothermal reversible process, (iv) Reversible adiabatic
process. Enthalpy: (i) Measurement of DU and DH, (ii) Enthalpy change of a reaction, (iii) Standard enthalpy of formation (DH°f), (iv)
Enthalpy change for different type of reaction. Hess's law (i) Second law of thermodynamics, (ii) Spontaniety and Enthalpy change, (iii)
Introduction to Entropy, (iv) Entropy change in various process.(i) Numericals based on entropy (ii) Gibbs free energy change and
spontaneity: (i) Calculation of Gibbs energy for a reaction. (ii) Thermodynamics of equilibrium state, (ii) Third law of thermodynamics
Chemical equilibrium: Reversible reactions, equilibrium constant, properties of equilibrium constant, relation between Kp and Kc Chemical
equilibrium: Simultaneous Equilibrium, Reaction Quotient, Le Chatelier's Principle Ionic equilibrium in solution : (i) Acids, bases and salts,
(ii) Acids and bases- Arrhenius concept, Bronsted and Lowry concept and Lewis concept. Ionization of water (Kw) and pH-scale, pH of
strong acid and base. pH of weak acid and base, dissociation of weak poly-protic acid, Salt hydrolysis and pH os a salt solution buffer
solution, buffer capacity solubility and solubility product, Indicators and pH-metric titration, double titration, Redox reaction, redox
titration, Classification of organic compounds; Rules of IUPAC nomenclature for aliphatic & aromatic compound and functional group
40% Equation of tangent in different form, condition of tangency, point of intersection of tangent Equation of pair of tangents chord of
contact locus problem, properties of parabola
40% PARABOLA Standard equation of parabola, parametric equation, position of a point w.r.t parabola. PARABOLA focal distance,
focal chord, important points related of focal chord
20% SEQUENCE AND SERIES Introduction of Sequence and Series,nth term of AP. Properties of A.P. ,Sum of n term of an
AP,Arithmetic Mean, nth term of G.P.,sum of n term of GP. Properties of G.P.,Geometric mean, A.G.P. Introduction to HP, HM, Relation
between AM, GM and HM, Difference method, Vn method, special series TRIGONOMETRIC FUNCTIONS Angle, system of measurement
of angles, trigonometric function, Values of trigonometric function for some specific angles , Trigonometric ratios of allied
angles,Transforming product into sum or difference, Transforming the sum or difference into product. Domain and ranges of trigonometric
function, Graph of trigonometric functions Trigonometric ratio of multiple angles, sub-multiple angles. maximum and minimum value of
trignometric expressions, anaylsis of the form y=asinx+bcosx., conditional identities, sum of Trigonometric series.
TRIGONOMETRIC EQUATIONS: Types of trigonometric equation, Principal value, General solution of basic trigonometric
equation. Solution by reducing trigonometric equations to algebraic one's, solution of the form acos x + bsin x = c Problems involving more
than one equation, equation containing more than one variable. Equation containing different functions and variables , Trigonometric
Inequalities. Quadratic Equations Introduction, nature of roots of quadratic equations ax2 + bx+ c= 0, Relation between roots of an
equation., Transformation of equation, Condition for common roots of quadratic equations. Quadratic expression y = ax2 + bx + c, sign of
quadratic expression., maximum and minimum value of quadratic equations Location of roots, Descartes rule of signs, Quadratic expression
in two variables Theory of Equations Binomial theorem Introduction: Notation of factorial and definition of C(n, r) and P(n, r) Pascal
triangle, Binomial theorem for a positive integer index, Some special forms of binomial theorem.
MATHEMATICS Problem based on direct expansion, General term in the expansion of (a + x)n, middle term in the expansion of (a + x)n Greatest
binomial coefficient, numerically greatest term in the binomial expansion. properties of Binomial coefficients, Binomial series. Straight Line
Introduction, distance formula, section formula, area of triangle. Definitions of centroid, circumcentre and orthocentre of triangle Collinearly
of three points, slope of line, various forms of line, locus of a point., Position of two points relative to a line, Angle between two lines,
condition for two lines to be parallel and perpendicular Perpendicular distance of a point from a line, distance between two parallel lines,
foot of perpendicular, Image of point w.r.t a line. Condition of concurrency for three lines, Family of lines. Equation of bisectors
Transformation of axes, General equation second degree, homogenaous equation of second degree Angle between lines , nature of pair
of lines, homogenious concept. , Circles Definition of circle, different form of a circle, general equation, Diameter for, parametric form,
equation of circle passing through non-collinear points. Position of a point w.r.t circle, length of intercept on coordinate axes condition for
circle touching cordinate axes. Line and circle, length of intercept on a line condition for tangency to circle, Equation of tangent to a circle.
Length of tangent from an external point, director circle. Equation of chord with a given mid-point, Equation of chord of contact,
equation of pair of tangents. Family of circles, Radical axis, common tangents, angle between two circles, Locus Problems. Complex
numbers Definition of a complex number, Argand plane, Algebra of complex number, Modulus of a complex number, properties of modulus,
triangle inequality Properties of arguments, Conjugate of a complex number, different forms of a complex number,De moivre's theorem.
Logarithm of a complex number, Square root of a complex number, cube roots of unity. nth roots of unity and their properties.
Geometry of complex numbers, section formulae, condition, for quadrilateral,Rotation of complex number. Straight line in Argand plane,
circle, Important loci in Argand plane. Permutation and Combination Fundamental principle of counting, multiplication principle, addition
rule, Permutation of different and identical things Rank of a word, circular permutation and their applications Combinations, Difference
between a permutation, Combination of different type of objects, Divisors Sum of the numbers formed by n digits. Exponent of a prime
number in a factorial. Division and distribustion into groups, Number of integral solution of an equation Application of multinomial
expansion. Principle of inclusion & exclusion, derangement.

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PHYSICS Max Marks: 60

SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of
which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.
1. A sphere of radius r and density  is sinking in container filled with liquid of density  and viscosity
. Container is placed in a elevator moving upward with an acceleration of g/2. Then terminal
velocity of sphere relative to elevator is :
2 2 3  2 2 3 1
r g     r g     g(   ) g  (   )
2 2  2 
(A) 9  2  (B) 9 (C) r (D) 2 r 2  2 
  9  9 
2. A water drop of radius R is split into n drops each of radius r. If the surface tension of
water is T, the energy required to split the drop is given by:
(A) (4 r 2 n  4 R 2 )T (B) [(4 r 2 n1/3 )  (4 R 2 )]T
(C) (4 r 2  4 R 2 )nT (D) None
3. In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross section of
the tube at A and B is 6 mm2 and 10 mm2 respectively. The rate at which water flows through the

tube is g  10ms 2 

(A) 7.5 cc/s (B) 8.0 cc/s (C) 10.0 cc/s (D) 12.5 cc/s
4. Which of the following is the incorrect graph for a sphere falling in a viscous liquid? (Given at t = 0,
velocity v = 0 and displacement x = 0.)

(A) (B)

(C) (D)

R
5. The decrease in the value of g on going to a height above the earth's surface will be –
2
5g 4g g
(A) g/2 (B) (C) (D)
9 9 3

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6. A ball 'A' is projected from origin with an initial velocity v0 = 700 cm/sec in a
direction 37º above the horizontal as shown in fig .Another ball 'B' 300 cm from
origin on a line 37º above the horizontal is released from rest at the instant A
starts. How far will B have fallen when it is hit by A ?
Y
B


A
y-axis
37º
O X
(A) 9 cm (B) 90 cm (C) 0.9 cm (D) 900 cm
7. An air bubble of radius r in water is at a depth h below the water surface at some instant. If P is
atmospheric pressure, d and T are density and surface tension of water respectively, the pressure
inside the bubble will be :
4T 2T 2T 4T
(A) P  h dg  (B) P  h dg  (C) P  h dg  (D) P  h dg 
r r r r
8. An incompressible liquid flows through a horizontal tube LMN as shown in the figure. Then the
velocity ‘V’ of the liquid through the tube N is:

(A) 1 ms–1 (B) 2 ms–1 (C) 4.5 ms–1 (D) 6 ms–1

9. Viscosity is the property by virtue of which a liquid
(A) occupies minimum surface area
(B) offers resistance for the relative motion between its layers
(C) becomes spherical in shape
(D) tends to gain its deformed position
10. A tennis ball dropped from a height of 2 m rebounds only 1.5 metre after hitting
the ground. What fraction of energy is lost in the impact –
1 1 1 1
(A) (B) (C) (D)
2 4 8 16

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SECTION-II
(Numerical Value Answer Type)
This section contains 5 questions.The answer to each question is a Numerical value. If the Answer is in the decimals, Mark
the nearest Integer only. Question will be evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.
11. A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now
pulled with a horizontal force of 40 N and the cylinder is rolling without slipping on a horizontal
surface (see figure) then the angular acceleration of the cylinder will be 2  n then find the value of n
( Neglect the mass and thickness of the string)

12. A capillary tube of radius r is immersed in water and water rises in it to a height h. the mass of the
water in the capillary tube is m. Another capillary of radius 2r is immersed in water. The mass of
water that will rise is this tube is  n  m  . Find the value of ‘n’
13. The excess pressure inside the soap bubble is twice the excess pressure inside a second soap bubble.
The volume of the first bubble is 1/n times the volume of second. Find the value of ‘n’
14. A spherical liquid drop of radius R is divided into eight droplets. If surface tension is T, then work
done in the process is n R 2T . .find the value of ‘n’.
15. For an ideal fluid, viscosity is

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CHEMISTRY Max Marks: 60

SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of
which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.
16. The covalent and Vander Waals radii of chlorine repectively are
A) 1.80 A0 & 0.99 A0 B) 0.99 A0 & 1.80 A0
C) 1.80 A0 & 1.80 A0 D)0.99 A0 & 0.99 A0
17. When work done by a system was 10J, the increase in the internal energy of the
system was 30J. The heat ‘q’ supplied to the system was:
A) -40J B) +20J C) 40J D) -20J
18. The IUPAC name of the compound

A) 3, 3-dimethyl cyclohexane carbaldehyde

B) 1, 1- dimethyl -3-hydroxy cyclohexane
C) 3, 3-dimethyl-1-hydroxy cyclohexane
D) 1, 1-dimethyl-3-cyclohexanol
19. Which of the following is stabilized by hyperconjugation?
 
A) CH2  CH2 B) C H3 C) CH3CH=CHCH3 D) CH3  CH 2
20. The correct stability order for the following species is

(I) (II)

(III) (IV)
A) II > IV > I > III B) I > II > III > IV
C) II > I > IV > III D) I > III > II > IV
21. The least stable carbocation is

A) B)

C) D)

22. Examine the two structures for anilinium ion and choose the correct statement
from the ones below

A) II is not acceptable resonating structure because carbocations is less stable

than ammonium ion.
B) II is not the acceptable structure because it is non aromatic.
C) II is not acceptable because ‘N’ has 10 valence electrons.
D) II is an acceptable resonating structure as both has same number of double Bonds

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23. The correct order of stability of carbocations is

+ +
O O
O
+
(I) (II) (III)
(A) (I) > (II) > (III) (B) (I) > (III) > (II)
(C) (III) > (I) > (II) (D) (II) > (III) > (I)

24. Which carbocation is most stable



C H2

C H2

C H2 C H2
(A) (B) (C) (D)
CH3 CH 3 NO2
25. Number of -electrons present in the species :
and would be
O
(A) 2, 4 (B) 1, 4 (C) 2, 6 (D) 1, 6

SECTION-II
(Numerical Value Answer Type)
This section contains 5 questions. The answer to each question is a Numerical value. If the Answer is in the decimals,
Mark the nearest Integer only. Question will be evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

26. The number of waves made by a Bohr electron in hydrogen atom in one complete revolution in the
3rd orbit is.

27. Find out number of aromatic compounds or ions in the following.

28. The purine hetrocycle occurs mainly in the structure of DNA. Identify number of ‘N’ atoms having
localized lone pair of electron.

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pq
29. Find the value of forgiven structure
2

P = degree of unsaturation
q= number of 20 carbon
30. Find out total number of compounds which are more stable in its ionic form

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 NARAYANA IIT ACADEMY XI_STU_IC & IR_IIT_CFTM-06_09-12-2024_WARM UP

MATHS Max Marks : 60

SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of
which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.

31. The equation of the tangent at the vertex of the parabola x2 +4x +2y = 0 is
(A) x = –2 (B) x = 2 (C) y =2 (D) y = –2.
32. Let (x,y) be any point on the parabola y 2  4 x . Let P be the point that divides the line segment
from (0,0) to (x,y) in the ratio 1:3 . Then the locus of P is
(A) x2 = y (B) y2 =2x (C) y2 = x (D) x2 =2y
33. The angle between tangents drawn form the point (3, 4) to the parabola y2 –2y + 4x = 0 is
8 5 12 5
(A) tan1 (B) tan1 (C) tan1 (D) none of these
7 5 7

34. If the line x + y – 1 = 0 touches the parabola y2 = kx, then the value of k is
(A) 4 (B) –4 (C) 2 (D) –2
35. The number of focal chord(s) of length 4/7 in the parabola 7y2 = 8x is
(A) 1 (B) zero (C) infinite (D) none of these
36. The ends of line segment are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PR:
RQ = 1:. If R is an interior point of parabola y2 = 4x, then
3 1 3
(A)   (0, 1) (B)    , 1 (C)    ,  (D) none of these
 5  2 5

37. The point (1, 2) is one extremity of focal chord of parabola y2 = 4x. The length of this focal chord is
(A) 2 (B) 4 (C) 6 (D) none of these
38. If AFB is a focal chord of the parabola y2 = 4ax and AF = 4, FB = 5, then the latus-rectum of the
parabola is equal to

(A) 80 (B) 9 (C) 9 (D) 80

9 80

39. The parabola y2 = 4x and the circle (x – 6)2 + y2 = r2 will have no common tangent if ‘r’ is equal to
(A) r > 20 (B) r < 20 (C) r > 18 (D) r  ( 20 , 28 ).
40. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola
y2 = 4ax is another parabola with directrix
(A) x = 0 (B) x =  a/2 (C) x = –a (D) x = a/2

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 NARAYANA IIT ACADEMY XI_STU_IC & IR_IIT_CFTM-06_09-12-2024_WARM UP

SECTION-II
(Numerical Value Answer Type)
This section contains 5 questions. The answer to each question is a Numerical value. If the Answer is in the decimals,
Mark the nearest Integer only. Question will be evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, 0 if not attempted and -1 in all other cases.
41. Number of integral values of a for which the equation cos2 x  sin x  a  0 has roots when
x   0,  / 2  is
42. Two sides of a rectangle are 3 x  4 y  5  0, 4 x  3 y  15  0 and one of its vertices is (0,0) . The area
of rectangle is____.
2
43. The sum of the slopes of the lines tangent to both the circles x 2  y 2  1 and  x  6   y 2  4 is
3
44. If the tangents drawn from the point (0, 2) to the parabola y 2  4ax are inclined at an angle , then
4
|a| equals......

45. If a chord of the parabola y2  8x passing through its focus F meets it in P and Q, then
1 1 1
  then  is.......
| FP | | FQ | 

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