Aakash Model Test Papers (AMTP)
Term-II Examination
Class
11
Physics
Chemistry
Biology
Mathematics
Process:
1. A student must go through the instructions carefully and adhere
strictly to them.
2. A student must finish answering the question paper of each subject
in stipulated time.
Benefits:
1. This booklet will help students to prepare for school examinations
as it comprises of most relevant questions as per guidelines and
paper pattern provided by CBSE for Term-II Exam.
2. These model test papers will help students to analyze where they
stand and what additional efforts are required for further
improvement in Term-II Exam.
Solutions:
After attempting the papers, a student must refer to the answers and
solutions available on our website www.aakash.ac.in. To get the text
solution, students are required to sign in their account with their log in
credentials.
Contents
S.No.
Subject
Page No.
1.
Physics ...........................................................01 – 14
2.
Chemistry ........................................................15 – 26
3.
Biology ............................................................27 – 40
4.
Mathematics ....................................................41 – 4
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Edition: 2021-22
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Model Test Paper-1
Physics (Class XI)
Model Test Paper-1
Time : 2 Hours
M.M. : 35
for
School/Board Exams (Term-II)
PHYSICS
Topics: Mechanical Properties of Solids, Mechanical Properties of Fluid, Thermal
Properties of Matter, Thermodynamics, Kinetic Theory, Oscillations and Waves.
General Instructions:
1. There are 12 questions in all. All questions are compulsory.
2. This question paper has three sections: Section A, Section B and Section C.
3. Section A contains three questions of two marks each, Section B contains eight
questions of three marks each, Section C contains one case study
study-based question of
five marks.
4. There is no overall choice. However, an internal choice has been provided in one
question of two marks and two questions of three marks. You have to attem
attempt only
one of the choices in such questions.
5. You may use log tables if necessary but use of calculator is not allowed.
SECTION-A
1. State Hooke’s law. Also, find Young’s modulus of elasticity for steel if a stress
of 50 MPa
a produces a strain of 2.5 × 10–4.
[2]
OR
With respect to stress-strain curve explain
(i) Proportional limit
[1]
(ii) Ultimate tensile strength
[1]
2. Define mean free path. Also, find its value for CO2 at 27°C, at pressure of
10–9 bar. Take molecular diameter of CO2 to be 500 pm.
[2]
25
22

−1 −1
23 
Given R = 3 J. mol K , 2 = 1.4, π = 7 , N A = 6 × 10 
3. Explain phenomenon of capillarity with two examples.
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[2]
Physics (Class XI)
Model Test Paper-1
SECTION-B
4. Derive an expression for elastic potential energy stored in a stretched
wire.
[3]
5. With help of suitable diagram show that energy of a spring block system during
SHM remains conserved. Also plot graph showing variation of kinetic energy,
potential energy and total energy with time.
[3]
6. If a big water drop of radius 10 cm splits into 1000 small droplets of water
(S = 0.07 N/m), then find the (S → Surface tension)
[3]
(i) Radius of small droplets.
(ii) Approximate work done in the process.
7. State principle of superposition of waves with a suitable diagram and show
that amplitude of resultant wave due to superposition of two waves
Y
=
a sin(Kx − ωt ) and Y=
a sin(Kx − ωt + φ) is function of φ.
1( x, t )
2 ( x, t )
[3]
8. A spring having with a spring constant 1000 N m–1 is mounted on a fixed
horizontal table as shown in figure. A mass of 2.5 kg is attached to the free
end of the spring. The mass is then pulled sideways to a distance of 2.0 cm
and released.
(i) Determine time period of oscillations of spring block system
[1]
(ii) Maximum acceleration of mass.
[1]
(iii) Speed when mass is at a distance equal to half of its amplitude from mean
position
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[1]
Model Test Paper-1
Physics (Class XI)
OR
Explain the following phenomenon in brief.
(i) Atmospheric pressure at a height of about 6 km decreases to nearly half
of its value at the sea level, though the height of the atmosphere is more
than 100 km.
[1]
(ii) A metallic key ring feels much colder than wooden key ring, both kept in
air conditioned room at same temperature.
[1]
(iii) Solids can support both longitudinal and transverse waves, but only
longitudinal waves can propagate in gases.
[1]
9. (i) Define extensive and intensive variables with examples
examples.
[1]
k statement and Clausius statement and also state their
(ii) State Kelvin-Planck
interpretation w.r.t. heat engine and refrigerator.
[2]
ound travels faster on cloudy days as compared to dry day. Justify (with
10. (i) Sound
proper formula)
[1]
(ii) Draw a neat diagram showing fifth harmonic of vibration of an air column
in a closed organ pipe. Also give an expression for frequency of the same.
[2]
how that for an ideal gas going under adiabatic expansion work done is given
11. Show
by expression
[3]
W =
µR(T1 − T2 )
(Symbols have usual meaning)
γ −1
OR
A Carnot engine is working between 500°C and a lower temperature Tlow. If
4000 J heat enters the engine on high temperature side and the work done is
2500 J, then
(i) Calculate efficiency of cycle.
[1]
(ii) Find the approximate value of Tlow
[1]
(iii) Draw a P-V diagram for cycle with proper direction.
[1]
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Physics (Class XI)
Model Test Paper-1
SECTION-C
12. In our everyday life, it has been observed that when a pan full of water is boiled
on a flame, its temperature increases, but when the flame is turned off, it slowly
cools down.
This is because of the phenomenon of heat transfer taking place between the
pan full of water and the flame. It has been established that heat transfer takes
place from hotter objects to colder object.
When there are objects which are at different temperatures or there is an
object at a different temperature from the surroundings, then the transfer of
heat takes place so that the object and the surrounding, both reach an
equilibrium temperature.
There can be 3 modes of heat transfer
(I) Conduction
(II) Convection
(III) Radiation
Based on above facts answer the following questions.
(a) A metallic rod is heated at two ends. The heat flow rate does not depends
on
[1]
(i) Area of cross-section of rod
(ii) Mass of rod
(iii) Time
(iv) Temperature gradient across the ends of rod
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Model Test Paper-1
Physics (Class XI)
(b) A body cools from 60°C to 50°C in 6 minutes. The time it takes to cool
from 40°C to 30°C, if the surrounding temperature is 10°C, is
[1]
(i) 6 min
(ii) 8 min
(iii) 8.7 min
(iv) 10.8 min
(c) The intensity of radiation emitted by a body at 200 K is I0. If the temperature
of body is raised to 400 K, the new intensity of radiation is
[1]
(i) 16I0
(ii) 12I0
(iii) 8I0
(iv) 4I0
(d) Which of the following is incorrect regarding convection?
con
[1]
(i) Convection
parts of fluid
ection involves bulk transport of different part
(ii) Convection is possible only in fluids
(iii) Blood pumping by heart is an example of forced convection
(iv) Natural convection requires some external agent like pump for
material movement
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Physics (Class XI)
Model Test Paper-1
(e) Two geometrically identical rods A and B of different material having ratio
of thermal conductivity 1 : 2 are kept in contact at junction C as shown.
The temperature of two ends is 70°C and 25°C. The junction temperature
is
[1]
(i) 50°C
(ii)
(iii) 40°C
(iv) 35°C


45°C

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Model Test Paper-2
Time : 2 Hours
Physics (Class XI)
Model Test Paper-2
M.M. : 35
for
School/Board Exams (Term-II)
PHYSICS
Topics: Mechanical Properties of Solids, Mechanical Properties of Fluids, Thermal
Properties of Matter, Thermodynamics, Kinetic Theory, Oscillations, Waves
General Instructions:
1. There are 12 questions in all. All questions are compulsory.
2. This question paper has three sections: Section A, Section B and Section C.
3. Section A contains three questions of two marks each, Section B contains eight
study-based question of
questions of three marks each, Section C contains one case study
five marks.
4. There is no overall choice. However, an internal choice has been provided in one
question of two marks and two questions of three marks. You have to attempt only
hoices in such questions.
one of the choices
5. You may use log tables if necessary but use of calculator is not allowed.
SECTION-A
1. (a) What do you mean by law of Equipartition of Energy?
(b) What percentage of total energy of an ideal diatomic gas at room
temperature is translational?
[2]
2. Oil and grease stains cannot be washed with plain water but are easily
removed by adding detergent to it. Explain why?
[2]
3. Drive the expression for elongation in a hanging rod due to its own weight. [2]
OR
A steel wire of length 1 m and cross-sectional area 1 cm2 is hanging from the
ceiling. Calculate the extension produced in steel wire.
Young’s modulus of steel = 200 GPa
Density of steel = 8000 kg/m3
Acceleration due to gravity = 10 m/s2
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[2]
Physics (Class XI)
Model Test Paper-2
SECTION-B
4. (a) Draw a graph showing stress versus strain relationship for a metal.
(b) Define yield point, proportional point and fracture point. Also show these
points on graph.
[3]
5. (a) What do you mean by terminal velocity for a body moving in viscous
medium?
(b) Terminal velocity of copper ball of radius 4.0 mm falling through a tank
of oil is 26 cm/s. Compute the viscosity of the oil. Density of oil is 1.5 ×
103 kg/m3 and density of copper is 8.9 × 103 kg/m3.
[3]
6. (a) What do you mean by anomalous behaviour of water?
wate How does it helps
in sustaining the marine life?
(b) Coefficient of thermal expansion of water is 210 × 10–6/°C at 20°C.
Temperature of 1000 L water is increased from 20°C to 21°C. What will
be increase in its volume?
[3]
7. (a) Define adiabatic
diabatic process.
(b) A monoatomic ideal gas undergoes adiabatic compression to get its
volume halved. What will be its final temperature if initial temperature of
gas was T kelvin?
[3]
OR
(a) What do you mean by isobaric process?
(b) A diatomic ideal gas is being heated in a container with movable piston
having 4 kg load
ad on it. What fraction of this supplied heat will increase the
internal energy?
[3]
8. One mole of a diatomic gas undergoes a cyclic process as shown. Calculate
the
(a) Change in internal energy of gas
(b) Work done by the gas
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Model Test Paper-2
Physics (Class XI)
9. Derive the expression of mean free path for a gas molecule.
[3]
OR
1
n m v 2 , where n is
3
is mass of a gas molecule and v is rms speed of
[3]
Prove that the pressure of an ideal gas is given as P =
number of molecules, m
molecules.
10. Position of a particle executing SHM is given as
=
x 10 sin 10πt +
π
2
(a) From which position does the particle start?
(b) Find speed of particle at t = 1 s.
(c) What is the maximum acceleration of particle?
[3]
11. (a) Derive an expression for speed of sound in air.
(b) What do you mean by L aplace correction?
[3]
SECTION-C
12. When two or more waves cross at a point, the displacement at that point is
equal to the sum of the displacement of the individual wave. This is known as
the principle of superposition of waves.
Answer the following questions on basis of above information.
(a)
Two wave pulses travelling in opposite direction (on a string) cross each
other. The amplitude of each pulse is 10 cm. The maximum possible
amplitude on superposition is
[1]
(i)
20 cm
(iii) 10 cm
(b)
(ii) 40 cm
(iv) 5 cm
In previous question, minimum possible amplitude is
(i)
20 cm
(iii) 0 cm
(ii) 10 cm
(iv) 5 cm
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[1]
Physics (Class XI)
(c)
Model Test Paper-2
Principle of superposition of waves applies to
(i)
Transverse waves only
(ii)
L ongitudinal waves only
(iii)
Both transverse and longitudinal waves
[1]
(iv) Neither transverse nor longitudinal waves
(d) Standing waves are formed by superposition of two waves
(i)
Travelling in same direction
(ii)
Travelling in opposite directions
(iii)
Travelling in different mediums
[1]
(iv) Travelling perpendicular to each other
(e) When two waves having opposite phase superimpose, the amplitude of
resulting wave
[1]
(i)
Is sum of individual amplitudes
(ii)
Is difference of individual amplitudes
(iii)
Greater than sum of individual amplitudes
(iv) L ess than difference of individual amplitudes



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Model Test Paper-3
Time : 2 Hours
Physics (Class XI)
Model Test Paper-3
M.M. : 35
for
School/Board Exams (Term-II)
PHYSICS
Topics: Mechanical Properties of Solids, Mechanical Properties of Fluid, Thermal
Properties of Matter, Thermodynamics, Kinetic Theory, Oscillations and Waves.
General Instructions:
1. There are 12 questions in all. All questions are compulsory.
2. This question paper has three sections: Section A, Section B and Section C.
3. Section A contains three questions of two marks each, Section B contains eight
questions of three marks each, Section C contains one case study
study-based question of
five marks.
4. There is no overall choice. However, an internal choice has been provided in one
question of two marks and two questions of three marks. You have to attempt only
one of the choices
hoices in such questions.
5. You may use log tables if necessary but use of calculator is not allowed.
SECTION-A
1. Why sound waves travel faster in solids and liquids as compared to gases?
[2]
2. At what distance from mean position, is the kinetic energy in a simple hormonic
motion equal to potential energy?
[2]
OR
W If the system
An electric heater supplies heat to a system at a rate of 200 W.
performs work at a rate of 85 joules per second. Find the rate of in
increase of
internal energy.
3. Explain why water on a clean glass surface tends to spread out while mercury
on the same surface tends to form drops.
[2]
SECTION-B
4. (a) What are ductile and brittle materials?
(b) State Hooke’s law?
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[1]
[1]
Physics (Class XI)
Model Test Paper-3
(c) A steel cable with a radius 1.5 cm supports a hanging trolley box. If the
maximum stress is not to exceed 108 N m–2, what is the maximum load
cable can support?
[1]
5. Explain in brief and derive an expression for Newton’s law of cooling.
[3]
6. A brass wire 2 m long at 30°C is held taut with little tension between two rigid
supports. If the wire is cooled to a temperature of 20°C, what is the tension
developed in the wire, if diameter is 2 mm? Coefficient of linear expansion of
[3]
brass = 2 × 10–5 K–1 and Young’s Modulus of brass = 0.91 × 1011 Pa.
7. Mention the principle behind working of venturimeter and derive an expression
venturimet
for the velocity of a fluid at the wide neck in a venturimeter.
[3]
8. (a) Draw the carnot cycle for a heat engine with an ideal gas as working
substance and explain all the processes involved.
[1]
(b) What is the ratio of slopes of P-V
processes?
graphs for adiabatic and isothermal
[1]
(c) Explain the steps which the working substance in a refrigerator goes
through.
[1]
OR
(a) State the law of equipartition of energy?
(b) Mention the factors on which average kinetic energy of an ideal gas
molecule depends.
(c) Explain the conditions under which a real gas behaves like an ideal gas.
9. Estimate the total number of air molecules in a room of capacity 25 m3 at a
temperature of 27°C, (Assume the pressure in the room to be atmospheric
pressure).
[3]
10. Obtain the expression for time period of a simple pendulum and calculate the
length of seconds pendulum?
[3]
(Take g = 9.8 m s–2)
11. A spring with a spring constant of 1400 N m–1 is mounted on a horizontal table.
A mass of 7 kg is attached to the free end of spring. The mass is pulled
sideways to a distance of 3 cm and released. Determine
[3]
(a) The frequency of the oscillations.
(b) Maximum acceleration of mass.
(c) Maximum speed of mass.
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Model Test Paper-3
Physics (Class XI)
OR
(a) Explain wave propagation constant.
(b) Explain the principle of superposition and obtain the conditions for
maximum amplitude for interference of two waves of same amplitude.
SECTION-C
12. The proportional region within the elastic limit of the stress strain curve is of
great importance for structural and manufacturing engineering designs. The
ratio of stress and strain is called modulus of elasticity.
[5]
pt the following questions.
Based on the above paragraph attempt
(a) The Young’s modulus of elasticity can be defined as ratio of
(i)
Normal stress
L ateral strain
(ii)
Normal stress
L ongitudinal strain
(iii)
Tensile stress
L ateral strain
(iv)
L ateral strain
L ongitudinal strain
(b) The ratio of modulus of rigidity to the Young’s modulus of elasticity for most
of the materials is
(i)
1
2
(ii)
3
4
(iii)
1
3
(iv)
4
3
(c) The ratio of hydraulic stress to the corresponding V olumetric strain is
called
(i) Modulus of Rigidity
(ii)
Poisson Ratio
(iii) Shear Modulus
(iv) Bulk Modulus
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Physics (Class XI)
Model Test Paper-3
(d) A steel rod has a radius of ‘ r’ and length ‘ l ’. When stretched by a load equal
to Mg then the elongation produced is l . Calculate the Young’s modulus
of elasticity for steel rod.
(i)
(iii)
2m g
πr
2
m g
(ii)
l
l
(iv)
πr l
2
m g l
πr 2 l
2m g
l
πr l
2
(e) The Young’s modulus and shear modulus hold relevance for
(i) Solids
(iii) Gases
(ii) L iquids
(iv) All of these



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Model Test Papers
CHEMISTRY
Model Test Paper-1
Time : 2 Hours
Chemistry (Class XI)
Model Test Paper-1
for
School/Board Exams (Term-II)
M.M. : 35
CHEMISTRY
Topics: States of matter: Gases and L iquids, Chemical Thermodynamics, Equilibrium,
s -Block Elements, Some p-Block Elements, Hydrocarbons
General Instructions:
Read the following instructions carefully.
1. There are 12 questions in this question paper with internal choice.
2. Section A - Q. No. 1 to 3 are very short answer questions carrying 2 marks each.
3. Section B - Q. No. 4 to 11 are short answer questions carrying 3 marks each.
4. Section C - Q. No. 12 is case based question carrying 5 marks.
5. All questions are compulsory.
6. Use of log tables and calculators is not allowed.
SECTION-A
1. Answer the following questions (Any 2)
(a) Calculate pH of 2 × 10–2 M NaOH solution
solution.
(b) What is a L ewis acid? Give one example.
example
(c) Write conjugate acid base pair of HCO3−
[1 × 2 = 2]
2. Calculate density of O2 gas at 27°C and 0.82 atm pressure (R = 0.082 L atm
K–1 mol–1)
[2]
3. Write balanced equations for
(a) Sn + H2 O
(b) Al + O2
→
→
[1 × 2 = 2]
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Chemistry (Class XI)
Model Test Paper-1
SECTION-B
4. Answer the following questions.
(a) Which alkali metal chloride crystallises as a hydrate?
(b) What happens when sodium metal is dropped in water?
(c) Draw the structure of BeCl2 in solid state.
[1 × 3 = 3]
OR
Convert the following
(a) Acetylene to Acetophenone
(b) 2-Bromopropane to 1, 2-Dibromopropane
Dibromopropane
[1 × 3 = 3]
(c) Propyne to Acetone
5. Answer the following questions.
(a) In a process, 550 J of heat is absorbed by a system and 285 J of work is
done by the system. What is the change in internal energy for the
process?
(b) Define extensive property. Give one example.
[2 + 1 = 3]
OR
Answer the following questions
(a) A closed container contains 28 g of N2 and 8 g of He gas. The total
pressure exerted by the gas mixture is 12 atm. Calculate the partial
pressure of He gas.
(b) State Boyle’s law.
[2 + 1 = 3]
6. Account for the following.
(a) Alkene decolourises bromine present in CCl4
(b) Propyne liberates hydrogen gas on reaction with sodium
(c) Cyclopentadienyl anion is an aromatic species
[1 × 3 = 3]
7. 2 moles of an ideal gas undergoes expansion in volume isothermally and
reversibly from 1 L to 20 L at 27°C. Calculate work done by the gas.
[3]
8. A secondary alcohol A having molecular formula C3H8O on dehydration gives
an alkene B. B on reaction with Baeyer’s reagent gives a compound C.
Reductive ozonolysis of B gives compounds D and E. D shows keto-enol
tautomerism. Identify B, C, D and E and write the reactions involved.
[3]
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Model Test Paper-1
Chemistry (Class XI)
9. (a) Why PbI4 does not exist?
(b) [ SiF6] 2– is known whereas [ SiCl6] 2– not. Give possible reasons.
(c)
Explain why catenation property of carbon family decreases down the
group?
[1 × 3 = 3]
OR
(a)
How would you explain the lower atomic radius of Ga as compared to Al?
(b)
What is the state of hybridisation of carbon in graphite?
(c)
How can you explain higher stability of BCl3 as compared to TlCl3?
[1 × 3 = 3]
10. Consider the following reaction at equilibrium


A(aq) + 2B(aq) 
 3C(aq)
If equilibrium concentration of A, B and C are 0.25 M, 0.5 M and 0.5 M
respectively, then calculate standard Gibbs free energy ( G°) at 27°C of the
reaction.
[3]
11. (a)
(b)
Calculate the solubility of AgCl in 0.1 M CaCl2 solution (Solubility product
of AgCl = 1.8 × 10–10)
If solubility of a sparingly soluble salt A2B3 is s mol L
solubility
lubility product.
–1
then calculate its
[2 + 1 = 3]
OR
(a)
A closed cylinder having 10 L volume contains 128 g of SO2 at 127°C.
Calculate the pressure exerted by the gas in the cylinder.
(b)
gas. [2 + 1 = 3]
Write van der Waals gas equation for one mole of a real gas
SECTION-C
12. Read the passage given below and answer the questions that follow.
All the alkali metals are silvery white, soft and light metals. Because of the
large size, these elements have low density which increases down the group
from L i to Cs. However, potassium is lighter than sodium. The melting and
boiling points of the alkali metals are low. The alkali metals and their salts
impart characteristic colour to an oxidizing flame.
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Chemistry (Class XI)
Model Test Paper-1
The alkali metals tarnish in dry air due to the formation of their oxides which in
turn react with moisture to form hydroxides. They burn vigorously in oxygen
forming oxides.
The alkali metal halides are all high melting, colourless crystalline solids. They
can be prepared by the reaction of the appropriate oxide, hydroxide or
carbonate with aqueous hydrohalic acid (HX ). All of these halides have high
negative enthalpies of formation.
(a) Why alkali metals have low melting point?
[1]
(b) Which alkali metal show blue colour to the flame test?
[1]
(c) Why L iF and CsI are less soluble in water?
[2]
(d) What is the oxidation state of oxygen in potassium superoxide?
[1]
OR
Why alkali metals and their salts impart characteristic colour to the
oxidising flame?



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Model Test Paper-2
Chemistry (Class XI)
Model Test Paper-2
Time : 2 Hours
M.M. : 35
for
School/Board Exams (Term-II)
CHEMISTRY
Topics: States of Matter: Gases and L iquids, Chemical Thermodynamics, Equilibrium,
s -Block Elements, Some p-Block Elements, Hydrocarbons
General Instructions:
Read the follow ing instructions carefully.
1. There are 12 questions in this question paper with internal choice.
2. Section A - Q . No. 1 to 3 are very short answer questions carrying 2 marks each.
3. Section B - Q . No. 4 to 11 are short answer questions carrying 3 marks each.
4. Section C - Q . No. 12 is case based question carrying 5 marks.
5. All q uestions are compulsory.
6. U se of log tab les and calculators is not allow ed.
SECTION-A
1. Answer the following questions.
[2]
(a) Define extensive properties [ give one example] .
(b) Change in enthalpy is a state function while work is not
not. Give reason in
support of your answer.
2. Arrange the following in the decreasing order of their property indicated.
[ Any 2]
[2]
(a) Si, C, Sn, Ge (Melting point)
(b) B, Ga, Al, In (Density)
(c) Na+ , Cs+ , K+ , L i+ , (Hydration enthalpy)
3. Answer the following questions.
(a) Draw the geometrical isomers of but-2-ene.
(b) Which geometrical isomer of but-2-ene is more polar and why?
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[2]
Chemistry (Class XI)
Model Test Paper-2
SECTION-B
4. Answer the following questions.
[3]
(a) Write the relation between G and Q
(b) Define the term Q
c
c.
and Kc.
(c) In which direction the reaction proceeds when Q
c
> Kc?
OR
Ammonia gas is industrially manufactured by Haber’s process as per the
following reaction.


N2 (g) + 3H2 (g) 
 2NH3 (g)
f H°
= – 46.1 kJ mol–1
(a) Write an expression for Kp for the above reaction.
(b) How will the value of Kp and composition of equilibrium mixture be affected
by
(i) Increase in pressure.
(ii) Addition of neon at constant volume.
5. Answer the following questions.
[1 + 2]
(a) Define Markovnikov rule with an example.
(b) Write the structures and IUPAC names of the products obtained by
ozonolysis of 1-Phenylprop-1-ene.
OR
Convert the following.
[3]
(a) Benzene into p-nitrotoluene.
nitrotoluene
(b) Ethene into benzene.
(c) Propyne into propanone
6. At 27°C and 760 mm Hg of pressure, a gas occupies 400 mL volume. What
will be its pressure at a height where temperature is 17°C and volume of the
gas becomes 440 mL ?
[3]
7. Calculate the volume of water required to dissolve 0.2 g barium (II) chloride to
get a saturated solution (Ksp of BaCl2 = 4 × 10–9, atomic mass of
Ba = 137 u).
[3]
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Model Test Paper-2
Chemistry (Class XI)
8. (a) Write the IUPAC name of the following compound:
CH3 – CH = CH – CH2 – C
[3]
C – CH3
(b) What happens when
(i) Benzene is heated with acetic anhydride in presence of anhydrous
AlCl3.
(ii) Methane is heated with regulated supply of air in presence of catalyst
Mo2O3.
9. Give reason to support the answer.
[3]
(a) BCl3 behaves as a L ewis acid.
(b) Gallium is smaller in size than aluminium.
(c) Graphite is used as a dry lubricant in machines running at high
temperature.
OR
(a) Carbon exhibits many allotropic forms.
(b) PbCl2 is thermally more stable than PbCl4.
(c) [ SiF6] 2– is known whereas [ CF6] 2– not.
10. Arrange the following in the increasing order of their property indicated.
[3]
(a) Pentane,, 2-methylbutane, 2, 2-dimethylpropane (Boiling point).
(b) Propane, Propyne, Propene (Acidic character)
character).
(c) Bromobenzene, 2, 4-dinitrobromobenzene, p
p-nitrobromobenzene
(Electrophilic substitution reaction).
11. In a process, 620 J of heat is absorbed by a system and 294 J of work is done
by the system. What is the change in internal energy for the process?
[3]
OR
Calculate
rG°
(in kJ) for a reaction at 300 K whose equilibrium constant is 20.
SECTION-C
12. Read the passage given below and answer the questions that follow.
The first element in each group, lithium in the first group and beryllium in the
second group differs from the rest of the elements but have similar properties
to diagonally situated elements. L ithium resembles magnesium, beryllium
resembles aluminium. The compounds of alkali metals are predominantly
ionic. The oxides and hydroxides are soluble in water forming strong alkalies.
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Chemistry (Class XI)
Model Test Paper-2
The oxides and hydroxides of group 2 elements are less basic than that of
group 1 elements. All the alkali metals are silvery white, soft and light metals.
Because of the large size, these elements have low density which increases
down the group from L i to Cs. However, potassium is lighter than sodium. The
melting and boiling points of the alkali metals are low. All group 1 elements
and many group 2 elements impart characteristic colour to an oxidizing flame.
Therefore, they can be detected by the respective flame tests and can be
determined by flame photometry or atomic absorption spectroscopy. However
these tests are fruitless for the detection of beryllium and magnesium
(a) Why does the first element of each group differs from rest of the elements?
[1]
(b) Why potassium is lighter than sodium?
[1]
(c) Alkali metals have low boiling point. Give reason.
[1]
(d) Why do group 1 elements give flame test and also write the colour of flame
?
produced by sodium?
[2]
OR
What is the cause of diagonal relationship and also write the name of
element having diagonal relationship with boron?



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Model Test Paper-3
Time : 2 Hours
Chemistry (Class XI)
Model Test Paper-3
for
School/Board Exams (Term-II)
M.M. : 35
CHEMISTRY
Topics: States of Matter: Gases and L iquids, Chemical Thermodynamics, Equilibrium,
s -Block Elements, Some p-Block Elements, Hydrocarbons
General Instructions:
Read the following instructions carefully.
1. There are 12 questions in this question paper with internal choice.
2. Section A - Q. No. 1 to 3 are very short answer questions carrying 2 marks each.
3. Section B - Q. No. 4 to 11 are short answer questions carrying 3 marks each.
4. Section C - Q. No. 12 is case based question carrying 5 marks.
5. All questions are compulsory.
6. Use of log tables and calculators is not allowed.
SECTION-A
1. Attempt (any two)
(a) Name any two intensive properties.
(b) State first law of thermodynamics.
(c) When 210 J of work was done on a system, it lost 100 J of energy as heat.
Calculate the value of internal energy change ( U) for this process.
[1 × 2 = 2]
2. Account for the following
(a) Alkali metals give characteristics flame tests.
(b) The mobilities of the alkali metal ions in aqueous solution are
L i+ < Na+ < K+ < Rb+ < Cs+
[1 × 2 = 2]
3. The solubility product of AgCl in water is 1.8 × 10–10. Calculate its solubility in
0.01 M NaCl solution.
[2]
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Chemistry (Class XI)
Model Test Paper-3
SECTION-B
4. (a) Arrange the following compounds in the increasing order of their thermal
stability
Mg(OH)2, Ca(OH)2, Sr(OH)2, Ba(OH)2
(b) Complete the following reaction,
(i)
4L iNO3
(ii) 2NaNO3
→
→
[1 × 3 = 3]
5. Identify A, B and C in the following sequence of reactions
reactions,
CaC2
H2O
→A
Re d hot Fe Tube
→B
873 K
Cl2 / Anhyd AlCl3
[3]
→C
6. Account for the following
(a) [ SiF6] 2– is known whereas [ SiCl6] 2– is not,
(b) Carbon shows catenation property remarkably.
(c) PbCl4 is a good oxidising agent
[1 × 3 = 3]
OR
(a) Give reason: SiCl4 is readily hydrolysed whereas CCl4 is not.
(b) Explain the difference in properties of diamond and graphite
[1 + 2]
7. Why is Wurtz reaction not preferred for preparation of alkanes containing odd
number of carbon atoms? Illustrate your answer by taking one example. [3]
8. Consider the following graph
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Model Test Paper-3
Chemistry (Class XI)
(a) Which law is represented in the above graph?
(b) Arrange the temperatures T1, T2, T3 in the increasing order.
(c) A balloon is filled with hydrogen at room temperature. It will burst if
pressure exceeds 0.2 bar. If at 1 bar pressure the gas occupies 2.27 L
volume, upto what volume can the balloon be expanded?
[1 × 3 = 3]
9. Standard heat of formation of hydrazine [ N2H4(l)] , hydrogen peroxide [ H2O2(l)] ,
and water [ H2O(l)] are –50.4, –193.2 and –242.7 kJ/mol respectively. Calculate
the standard heat of formation for the following reaction,
[3]
N2H4(l) + 2H2O2(l) → N2(g) + 4H2O(l)
OR
Give a brief note on the following thermodynamic terms.
(a) State Hess’s law.
(b) Standard enthalpy of combustion
[1 × 3 = 3]
(c) Standard enthalpy of formation
10. Describe the general trends in the following properties of the elements of
group 13.
(a) Atomic size
(b) Ionisation enthalpy
[1 × 3 = 3]
(c) Oxidation state
11. Complete the following reaction,
(a) CH3 CH2Br
(b) CH
CH
alc KOH
dil H2SO4
HgSO4
→
→
=
CH2 + H2O + [ O]
(c) CH
2
dil KMnO4
→
[1 × 3 = 3]
OR
(a) Write the structure of 3, 4-dimethylhept-3-ene
(b) Name the compounds obtained by reductive ozonolysis of 3-methylpent2-ene
(c) Write the chemical reaction for the Friedel Crafts alkylation reaction.
[1 × 3 = 3]
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Chemistry (Class XI)
Model Test Paper-3
SECTION-C
12. Read the passage given below and answer the questions that follow.
Equilibrium constant, KC is expressed as the concentration of products divided
by reactants, each term raised to the stoichiometric constant. Equilibrium
constant has constant value at a fixed temperature and at this stage all the
macroscopic properties such as concentration, pressure etc. become
constant. For a gaseous reaction equilibrium constant is expressed as KP and
written by replacing concentration terms by partial pressures in KC expression.
The direction of reaction can be predicted by reaction quotient Q C which is
equal to KC at equilibrium.
L e-Chatelier’s Principle states that the change in any factor such as
temperature, pressure, concentration etc will cause the equilibrium to shift in
such a direction so as to reduce or counter act the effect of the change.
(a) Write the expression for the equilibrium constant KC for the following
equilibrium:
3Fe(s) + 4H2O(g)  Fe3 O4 (s) + 4H2 (g)
[1]
(b) Equilibrium constant for a reaction is 10. What will be the equilibrium
[1]
constant for the reverse reaction?
(c) For the reaction.
A 2 (g) + 3B2 (g)  2AB3 (g) + heat
on the basis of L e-Chatelier’s principle explain the effect of temperature
[1]
and pressure to yield maximum amount of AB3.
(d) At equilibrium, the concentration of N2, O2 and NO in a sealed tube at
800 K are N2 = 3.0 × 10–4 M, O2 = 4.2 × 10–4 M and NO = 2.8 × 10–4 M
Calculate the equilibrium constant KC for the reaction
N2 (g) + O2 (g)  2NO(g)
OR
Derive the relationship between KP and KC.
.


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[2]
Model Test Papers
BIOLOGY
Model Test Paper-1
Time : 2 Hours
Biology (Class XI)
Model Test Paper-1
for
School/Board Exams (Term-II)
M.M. : 35
BIOL OGY
Topics: Cell Cycle and Cell Division, Photosynthesis in Higher Plants, Respiration in Plants,
Plant Growth and Development; Breathing and Exchange of Gases, Body Fluids and
Circulation, Excretory Products and their Elimination, L ocomotion and Movement, Neural
Control and Coordination, Chemical Coordination and Integration
General Instructions:
1. All questions are compulsory.
2. The question paper has three sections (A, B & C) and 13 qu
questions. All questions are
compulsory.
3. Section-A has 6 questions of 2 marks each; Section-B has 6 questions of 3 marks
each and Section-C has a case-based question of 5 marks.
4. There is no overall choice. However, internal choices have been provided in some
questions. A student has to attempt only one of the alternatives in such questions.
5. Wherever necessary, neat and properly labeled diagrams should be drawn.
SECTION-A
1. Mechanism of respiration or breathing vary among different groups of animals,
depending on their habitat and level of organisation. Justify this statement by
giving four examples.
[2]
2. A diagrammatic view of cell cycle is given below:
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Biology (Class XI)
Model Test Paper-1
Write one characteristic feature of G0 stage and give an example of the type
of cell entering this stage. Are these cells metabolically active in this stage?
[1 + ½ + ½ ]
OR
If a diploid cell having 10 chromosomes and 30 pg DNA content enters cell
cycle, what number of chromosomes and amount of DNA content will cell have
at the end of S-phase? Explain.
[½ + ½ + 1]
3. Beside kidneys, there are certain organs in animal kingdom which help in the
elimination of excretory wastes. Name
ame three such organs as well as the
excretory wastes removed by them.
[2]
[1 + 1]
4. What is light harvesting complex?
? What is its role?
5. Mention the events takes place during pachytene stage of meiosis I and name
the enzyme involved in crossing over in this stage.
[1½ + ½ ]
6. (a) Name the tissues which undergo mitotic division in plants and give one
importance of meiosis?
[½ + ½ ]
(b) Pyruvate undergoes oxidative decarboxylation. Write the reaction for this
[½ + ½ ]
process and also give the site where it occurs.
OR
(a) Define respiratory quotient and write its value for tripalmitin.
[½
+½ ]
(b) Define plasticity and given an example of plant which shows heterophylly?
[½
+½ ]
SECTION-B
SECTION
7. Define the reflex action with two examples as well as elaborate the process
involved in the reflex action.
[3]
OR
Name the structure ‘ A’ that lies at the base of the thalamus and if any injury is
localized to ‘ A’, then which functions are most likely to be disrupted?
8. Methods of locomotion performed by animals vary with their habitats and the
demand of the situation. Describe the various types of movements observed
in different cells.
[3]
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Model Test Paper-1
Biology (Class XI)
9. Observe the given oxygen dissociation curve and answer accordingly.
[3]
What are the factors responsible for shifting the curve to right and what does
this shifting indicates?
10. Complex V in electron transport system of mitochondria is responsible
synthesis of ATP molecules.
(a) Draw a well labeled diagram of complex V .
(b) Explain structure of ATP synthase.
(c) How many ATPs are formed when 4H+ passes through it?
11. A and B are two electron transport systems operating in the chloroplast.
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for
[1]
[1]
[1]
Biology (Class XI)
Model Test Paper-1
(a) Where are PS I and PS II located in the chloroplast?
[1+ ½ ]
(b) Where is water splitting complex located and what is its significance?
[½
+ 1]
12. The image below depicts the gland present above kidney.
(a) Which of the labeled part of gland is responsible for secretion of hormones
produced when a person is having stage fear? Name the hormones as
well as its response.
[1+ ½ ]
(b) Name the hormone which is administered during kidney transplant to
prevent graft rejection and identify the labeled part from where this
hormone is produced.
[1+ ½ ]
SECTION-C
SECTION
13. A farmer is planning to create hedge plants in his farm and also wants a weed
free lawn. To achieve, the same he starts cutting of plants and sprays a
phytohormone in the field.
(a) How will cutting of plant tips help in hedge formation?
[1½ ]
(b) Which hormone would be helpful to eliminate dicot weeds?
[1]
(c) Name any two synthetic auxins.
[1]
(d) Where is this hormone produced naturally in the plants and from what
source it was isolated first?
[1½ ]
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Model Test Paper-1
Biology (Class XI)
OR
In a certain road accident a person suffers from a blood loss due to an accident
and needs immediate blood transfusion. His one friend who has a valid
certificate of his own blood type, offers for blood donation without delay.
(a) What was the blood group of the donor and why he was allowed to donate
his blood?
[2]
(b) Usually after sometime the wound does not continue to bleed for a longer
period.. It usually stops after bleeding sometime. Which property of blo
blood
assists in this and explain the mechanism behind this
this?
[3]



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Biolog y (Class XI)
Model Test Paper-2
Model Test Paper-2
Time : 2 Hours
M.M. : 35
for
School/Board Exams (Term-II)
BIOL OGY
Topics: Cell Cycle and Cell Division, Photosynthesis in Higher Plants, Respiration in Plants,
Plant Growth and Development; Breathing and Exchange of Gases, Body Fluids and
Circulation, Excretory Products and their Elimination, L ocomotion and Movement, Neural
Control and Coordination, Chemical Coordination and Integration
General Instructions:
1. All questions are compulsory.
2. The question paper has three sections (A, B & C) and 13 questions. All questions are
compulsory.
3. Section-A has 6 questions of 2 marks each; Section-B has 6 questions of 3 marks
each and Section-C has a case-based question of 5 marks.
4. There is no overall choice. However, internal choices have been provided in some
questions.
ns. A student has to attempt only one of the alternatives in such questions.
5. Wherever necessary, neat and properly labeled diagrams should be drawn.
SECTION-A
1. Arrange the following terms based on their volumes in an ascending order and
relationship among them.
write the inter-relationship
(a) Tidal V olume (TV )
(b) Inspiratory Reserve V olume (IRV )
(c) Inspiratory Capacity (IC)
(d) Expiratory Reserve V olume (ERV )
(e) V ital Capacity (V C)
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[2]
Model Test Paper-2
Biolog y (Class XI)
2. The diagram given below represents a stage of mitosis. What are the key
events related to this stage?
[2]
3.
4.
5.
6.
OR
Mitosis is also known as equational division. Write down the significance of
this type of cell division.
‘ The JGA plays a complex regulatory role.’ Explain.
[2]
What is glycolysis. Mention the site where glycolysis takes place in living
organisms?
[2]
Abscisic acid is also known as ‘ stress hormone’. Mention the reasons that
justify this statement.
[2]
Calvin cycle occurs in all photosynthetic plants. There are few stages to
complete this cycle. Briefly write about the reduction stage in C3 cycle. How
many turns of C3 cycle are required for production of two molecules of
glucose?
[2]
OR
Why is photorespiration called wasteful process?
SECTION-B
SECTION
7. Is knee jerk a monosynaptic reflex or polysynaptic reflex?
Explain with the help of a diagram.
OR
Where is the master of the master endocrine gland located?
Write its 4 functions.
8. Write the difference between red and white muscle fibres.
9. Which disease occurs if following conditions take place in the body?
Write two symptoms each.
(a) Hypersecretion of growth hormone in adults
(b) Hypothyroidism during pregnancy
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[3]
[3]
[3]
Biolog y (Class XI)
Model Test Paper-2
10. (a) Give a brief account about the quiescent stage of the cell cycle?
(b) During mitosis, which stage is the best to study the morphology of
chromosomes?
(c) What is interkinesis?
[3]
11. The diagram given below represents a phenomenon which is widely used in
hedge-making.
(a) Which plant growth hormones are concerned with this phenomenon?
(b) What does the phenomenon in the figure show? Briefly mention the same.
[3]
12. Given below is the diagrammatic representation of a section of an endocrine
gland.
[3]
(a) Identify the gland and its location.
(b) Name the different layers of ‘ A’.
(c) Name and write one function of the main mineralocorticoid in our body.
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Model Test Paper-2
Biolog y (Class XI)
SECTION-C
13. A farmer is associated with mango farming in his farm land. He brought some
chemicals from the shop to control the weeds growing nearby the farm and for
other purposes. On applying the aqueous solution of one of them he observed
that it induced flowering in mango trees.
(a) What is the name of the chemical sprayed by the farmer on the tree that
induced flowering?
(b) Which phytohormone is used as weedicide?
(c) Write down any two other functions of the chemical sprayed on the tree.
(d) The plant growth hormone applied by the farmer is a ‘ plant growth
promoter’ or ‘ plant growth inhibitor’ in nature?
[5]
OR
A family of five went to a pet shop and they bought Ps ittacu l a for the eldest
child and an aquarium for the youngest. The eldest child was very curious and
he observed that in the cage of Ps ittacu l a there were pellet droppings. Then
he went to observe the fishes in aquarium but didn’t find any pellets.
He then asked his parents about the same and they told him that the pellet
droppings are the excretory product of Ps ittacu l a. But they had no idea about
the excretory product of an aquarium fish. So, he went to a library and read
about it.
Answer the following questions:
(a) What is the excretory product of Ps ittacu l a and an aquarium fish?
(b) Why is the excretory product of a fish not seen? Why do they differ in their
excretory product?
(c) Name the third type of main nitrogenous waste and two examples of
animals who excrete it.



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Biology (Class XI)
Time : 2 Hours
Model Test Paper-3
Model Test Paper-3
for
School/Board Exams (Term-II)
M.M. : 35
BIOL OGY
Topics: Cell Cycle and Cell Division, Photosynthesis in Higher Plants, Respiration in Plants,
Plant Growth and Development; Breathing and Exchange of Gases, Body Fluids and
Circulation, Excretory Products and their Elimination, L ocomotion and Movement, Neural
Control and Coordination, Chemical Coordination and Integration
General Instructions:
1. All questions are compulsory.
2. The question paper has three sections (A, B & C) and 13 questions. All qu
questions are
compulsory.
3. Section-A has 6 questions of 2 marks each; Section-B has 6 questions of 3 marks
each and Section-C has a case-based question of 5 marks.
4. There is no overall choice. However, internal choices have been provided in some
questions. A student has to attempt only one of the alternatives in such questions.
5. Wherever necessary, neat and properly labeled diagrams should be d
drawn.
SECTION-A
1. Give the general steps involved during respiration in the human body.
[2]
2. What type of growth curve is given below and write the equation for expression
of this type of growth curve.
[2]
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Model Test Paper-3
Biology (Class XI)
OR
Name the pigments involved in photosynthesis and the region of spectrum
where maximum photosynthesis occurs in plants.
3. Describe the role of lungs, liver and skin in the elimination of excretory wastes
in the human body.
[2]
4. What is interphase and write name of any of its two phases?
[2]
5. How many NADH + H+ , FADH2 and ATP molecules are formed in Krebs cycle
from two molecules of acetyl CoA?
[2]
6. A woman
n was doing exercise in the park, after some time she started feeling
pain in the muscles of her legs. Explain why?
[2]
OR
Enlist the assumptions considered for theoretical calculation of net gain of ATP
for every glucose molecule.
SECTION-B
7. What are the functions of the following structures?
[3]
(i) Medulla oblongata
(ii) L imbic lobe
(iii) Thalamus
OR
Describe the three types of neurons based on the number of axon
axons and
dendrites.
8. Give an example each of–
(i) Ball and socket joint
(ii) Hinge joint
(iii) Gliding joint
(iv) Saddle joint
What is myasthenia gravis?
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[3]
Biology (Class XI)
Model Test Paper-3
9. Using a flowchart, write the step-by-step process of coagulation of blood. [3]
10.
[3]
(a) Why mitosis is also called as equational division? Explain.
(b) In which phase of Prophase I, synaptonemal complex is formed and
terminalisation of chiasmata occurs respectively?
(c) Name the stage between two meiotic divisions and write its one
characteristic feature.
11.
[3]
(a) Identify the given metabolic pathway/cycle of plants and describe the
stages involved in it
(b) For every CO2 molecule entering in Calvin cycle, how many ATP and
NADPH molecules are required?
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Model Test Paper-3
Biology (Class XI)
12.
[3]
(a) Which hormones are secreted by the part labelled B
B? In which situation
are they released and write any two of their effects on the body
body?
(b) Write any two functions of the group of hormones produced by A in the
above figure which are involved in carbohydrate metabolism.
metabolism
SECTION-C
13. A lady have her own farm land in which she grows lots of vegetable e.g.
tomato, grapes, cabbage, etc.
[5]
One day a farmer gave her some bottles filled with chemicals for good crop
health and growth.
(a) After application of chemical of bottle A, tomato obtained become seedless
seed
and growth of unwanted weeds are also reduced. Explain the reason of
these phenomena.
What is the chemical nature of A?
(b) Application of another chemical of bottle B leads to internode elongation
in rosette habit plants. Name the plant growth regulator involved.
(c) What chemical can be present in bottle C, which hasten fruit ripening in
tomato?
(d) After harvesting of crop, lady wants to store seeds for longer period of
time. Suggest any two chemicals for storage of seeds.
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Biology (Class XI)
Model Test Paper-3
OR
A group of medical students were studying a fresh human cadaver. One of the
organs the professor started teaching about created a lot of interest among
the students. These are in a pair, placed in the hollows of the skull, with
lacrimal bones in the inner corners.
(a) Which organ has been described in the above case study?
[½ ]
(b) Different people have differently coloured portions w.r.t. the organs
described in the case study.
[½ ]
Which part is this coloured portion?
(c) Explain the following terms w.r.t. organ given.
(1)
Fovea
(2)
Blind spot
(3)
Ciliary body
(4)
Orbits
(d) Explain the mechanism of the function of this organ.



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[2]
[2]
Model Test Papers
MATHEMATICS
Model Test Paper-1
Mathematics (Class XI)
Model Test Paper-1
Time : 2 hrs.
M.M. : 4 0
for
School/Board Exams (Term-II)
MATHEMATICS
Topics: Trigonometric Functions, L inear Inequality, Permutations and Combinations,
Conic Sections, Introduction to 3-D Geometry, Derivatives and Probability
General Instructions:
1. This question paper contains three sections - A, B and C. Each part is compulsory.
2. Section - A has 6 short answ er type (SA1) q uestions of 2 marks each.
3. Section - B has 4 short answ er type (SA2) q uestions of 3 marks each.
4. Section - C has 4 long answw er type q uestions (L A) of 4 marks each.
5. There is an internal choice in some of the questions.
6. Q 14 is a case-bb ased prob lem having 2 sub parts of 2 marks each.
SECTION-A
1.
Find the value of
1 − tan2 15
.
1 + tan2 15
[2]
OR
If tan + sec =
5
&
3
is acute angle then find the value of sin .
x
4
5x − 2 7x − 3
−
3
5
2.
Solve the inequality
3.
In a class of a school, 40%
biology, 10%
of students study mathematics and 30%
[2]
study
of the class study both mathematics and biology. If a student
is selected at random from the class, find the probability that he will be
studying mathematics or biology.
4.
[2]
Find the equation of a circle with centre (2, 2) and passes through the point
(4, 5)
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[2]
Mathematics (Class XI)
Model Test Paper-1
sec x − 1
sec x + 1
5.
Differentiate
[2]
6.
In how many ways can one select a cricket team of 11 from 17 players in
which only 5 players can bowl if each cricket team of 11 must include
exactly, 4 bowlers?
[2]
SECTION-B
4 x + 5 sin x
3 x + 7cos x 7
7.
Find derivative of f ( x ) =
8.
Find the ratio in which the line segment joining the points (4, 8, 10) and (6,
c
o
s
8) is divided by the yz-plane.
10, –8)
9.
[3]
[3]
The longest side of a triangle is 3 times the shortest side and third side is 2
cm shorter than the longest side. If the perimeter of the
is at least 61 cm,
find the minimum length of the shortest side.
[3]
OR
Find all pairs of consecutive odd natural numbers, both of which are larger
than 10 such that their sum is less than 40.
ordinate of the foci, the vertices, the length of major axis, the
10. Find the co-ordinate
minor axis, the eccentricity and length of latus rectum of ellipse
x2 y 2
+
=
1 .[3]
36 16
OR
Find the equation of the hyperbola satisfying the given conditions, vertices
( 2, 0) and foci ( 3, 0).
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Model Test Paper-1
Mathematics (Class XI)
SECTION-C
11. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6,
7, if no digit is repeated?
12. Prove that
[4 ]
cos 4 x + cos3 x + cos 2 x
= cot3x.
sin 4 x + sin3 x + sin 2 x
[4 ]
OR
Prove that
sin A + sin3 A + sin5 A + sin7 A
= tan4
tan4A
cos A + cos3
c
o A + cos5
s
A + cos7cA
o
s
3
c
respectively Find the equation
13. If A and B be the points (3, 4, 5) and (–1, 3, –7) respectively.
of a set of point P such that PA2 + PB2 = K2 where K is a constant.
[4 ]
CASE-BASED /D ATA-BASED
14. For extra-curricular
curricular activity, 60 students of a class opted either for NCC or
NSS. 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and
NSS. If one of these student is selected at random, find the probability that
(i) The student opted for NCC or NSS.
[2]
(ii) The student has opted neither NCC nor NSS.
[2]



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o
Mathematics (Class XI)
Time : 2 hours.
Model Test Paper-2
Model Test Paper-2
M.M. : 4 0
for
School/Board Exams (Term-II)
MATHEMATICS
Topics: Trigonometric Functions, L inear Inequality, Permutations and Combinations,
Conic Sections, Introduction to 3-D Geometry, Derivatives and Probability
General Instructions:
1. This question paper contains three sections - A, B and C. Each part is compulsory.
2. Section - A has 6 short answ er type (SA1) q uestions of 2 marks each.
3. Section - B has 4 short answ er type (SA2) q uestions of 3 marks each.
4. Section - C has 4 long answw er type q uestions (L A) of 4 marks each.
5. There is an internal choice in some of the questions.
6. Q 14 is a case-bb ased prob lem having 2 sub parts of 2 marks each.
SECTION-A
1.
Find the value of cos 210 + sin
5π
.
3
[2]
OR
Prove that
sin(90° – ) + cos(90° – ) + sin(90° +
) + cos(90° +
) = 2cos
2.
Find n , if (n + 1)! = 12.nn !
3.
Find the centroid of the triangle whose vertices are (0, 1, 2), (2, –1, 3) and
(4, –4, 1).
4.
[2]
Find the equation of the circle which touches y-axis and whose centre is
(1, 3).
5.
[2]
[2]
A box contains 1 red and 3 black balls. Two balls are drawn at random in
succession without replacement. Write the sample space for this
experiment.
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[2]
Model Test Paper-2
6.
Mathematics (Class XI)
A bag contains 4 white and 3 red balls. Two balls are selected at random.
What is probability that both the balls are red?
[2]
SECTION-B
7.
Prove that sin4A = 4sinA cos3A – 4cosA sin3A.
8.
How many words can be formed out of the letters of the word PECUL IAR
[3]
using all the letters, beginning with P and ending with R?
[3]
OR
In how many ways can the letters of the word FRACTION be arranged so
that no two vowels are together?
9.
Solve the inequality, –12 < 3xx – 5 ≤ –4
10. If the eccentricity of an ellipse is
[3]
13
and distance between its foci is
7
2 13 , then find the length of the latus rectum of the ellipse.
[3]
OR
x2 = 144.
Find the eccentricity of the hyperbola 144yy2 – 12x
SECTION-C
11. Prove that
sin(iAi +n Bn)( + cos(
s
( B)− A))c cos
o cA
s + o(sin As
.
=
sin(iBi −nAn)(+ cos(
s
( B+
) A)) c cos
ocAs− o
sin
( As
12. Find the derivative of the following function
)(
()
c o) s c so i sn
[4 ]
c ) o s c os is n
x 2 + 3x + 9
x 6 + cos x
[4 ]
OR
Find the derivative of the following function
x 2 log x
x sin x + tan x
13. Find the equation of the hyperbola with x-axis and y-axis as its transverse
axis and conjugate axis respectively, length of the conjugate axis as
2 5 units and the distance between the foci is 6 units.
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[4 ]
s
s
i
i
Mathematics (Class XI)
Model Test Paper-2
CASE-BASED /D ATA-BASED
14. A bag contains lottery tickets having numbers written on them from 1 to 20.
A person is asked to pick two tickets randomly from the bag.
(i) What is the probability that both the tickets chosen have prime numbers
on them?
[2]
(ii) What is the probability that on one ticket, there is a prime number and
on the other there is a multiple of 4?



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[2]
Model Test Paper-3
Time : 2 hrs.
Mathematics (Class XI)
Model Test Paper-3
M.M. : 4 0
for
School/Board Exams (Term-II)
MATHEMATICS
Topics: Trigonometric Functions, L inear Inequality, Permutations and Combinations,
Conic Sections, Introduction to 3-D Geometry, Derivatives and Probability
General Instructions:
1. This question paper contains three sections - A, B and C. Each part is compulsory.
2. Section - A has 6 short answ er type (SA1) q uestions of 2 marks each.
3. Section - B has 4 short answ er type (SA2) q uestions of 3 marks each.
4. Section - C has 4 long answw er type q uestions (L A) of 4 marks each.
5. There is an internal choice in some of the questions.
6. Q 14 is a case-bb ased prob lem having 2 sub parts of 2 marks each.
SECTION-A
1.
Find the value of sin 240º + tan
5π
6
[2]
OR
Prove that: cos(360º
360º – ) + sin(180º – ) + sin(270º
sin
+
) + cos(90º +
)=0
2.
In how many ways the letters of the word EAMCOT can be arranged?
3.
Find the coordinates of the point which divides the join of the points (5, 4, 2)
[2]
and (1, 2, 3) in the ratio 2 : 3 internally.
[2]
4.
Find the centre and radius of the circle (x + 1)2 + (y + 3)2 = 16.
[2]
5.
A bag contains 3 black and 4 red balls. Three balls are drawn at random.
What is the probability that all the drawn three balls are of same colour? [2]
6.
Five cards are drawn at random from a well shuffled pack of 52 cards, find
the probability that all the five cards are hearts.
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[2]
Mathematics (Class XI)
Model Test Paper-3
SECTION-B
7.
A circular wire of radius 3 cm is cut and bent so as to lie along the
circumference of a hoop whose radius is 48 cm. Find the angle, in degrees,
which is subtended at the centre of the hoop.
8.
[3]
Out of 11 tickets with numbers 1 to 11, three tickets are drawn at random,
find the probability that the numbers on them are in A.P.
[3]
OR
Two cards are drawn at random from a pack of 52 cards. Find the
probability that both the cards are of black colour or they are queens.
9.
Solve the inequality,
4 + 2x
3
x
–3.
2
[3]
[3]
10. Find the length of major and minor axis, co-ordinates of the vertices and the
foci, eccentricity and length of the latus rectum of the ellipse y2 + 36x2 = 36.
[3]
OR
Find the equation of the parabola which is symmetric about the y-axis, has
its vertex at (0, 0) and passes through the point (4, –2).
[3]
SECTION-C
SECTION
11. Prove that tan189 =
cos36 − sin36
cos36 + sin36
12. Find the derivative of f(x) = 5 x sin x (1 + e x ) .
[4 ]
[4 ]
OR
Find the derivative of f(x) =
x 2 + cos x
.
tan x
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[4 ]
Model Test Paper-3
Mathematics (Class XI)
13. If the lines 2x + y – 6 = 0 and 4x – 5y + 16 = 0 are the diameters of a circle
of area 154 sq. units, then find the equation of the circle. Use π =
22
7
[4 ]
CASE-BASED /D ATA-BASED
14. A manufacturing company makes marbles and provide marbles in
packaging of six white and five red marbles. A person is asked to select four
marbles from a packet. All marbles in a packet are considered
to be
conside
different from each other.
(i)
Find the number of ways of selecting four marbles if they can be of any
colour.
[2]
(ii) Find the number of ways of selecting four marbles if they must be of the
same colour.
[2]



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