11th pcm paper for schools final exam 2015
TRANSCRIPT
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8/9/2019 11th Pcm Paper for Schools Final Exam 2015
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Mock Test Papersth
(For Class 11 CBSE Annual Exam)
Apex Institute for IIT-JEE / PMT
Head Office : 62 Nitikhand -3 Indirapuram Cont. +91-9990495952, +91-9910817866, www.apexiit.co.in
Mathematics Physics & Chemistry
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Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad : 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180 , 9990495952
Apex Institute Sample Paper: Class-XI(P.C.M.)
MATHEMATICS
Time Allowed : 3 Hrs Maximum Marks: 100
1. All questions are compulsory.
2. The question paper consist of 29 questions divided
into three sections A, B and C. Section A comprises
of 10 questions of one mark each, section Bcomprises of 12 questions of four marks each and
section C comprises of 07 questions of six marks
each.
3. All questions in Section A are to be answered in
one word, one sentence or as per the exact
requirement of the question.
4. Use of calculators is not permitted. You may ask
for logarithmic tables, if required.
Section-A
1. Evaluate2
3lim4x
x
x
2. Find the derivative of sin(x+1)
3. Find the truth value of p : Every real number is
either prime or composite.
4. Simplify1 3
1 2
i
i
5. A coin is tossed twice, find the probability of
getting atleast one head.
6. Write the equation of the parabola whose focus is
at (0, -4) and vertex is at (0, 0).7. Identify the conic section represented by the
equation 4x2+ y
2= 100 and draw its rough graph.
8. Write the equation of a circle whose centre is at
(2,-3) and radius is at 8.
9. Write the component statements of the given
statement
P:Number 7 is prime or it is odd.
10. Identify the OR used in the statement:
An ice-cream or a coke free with a large pizza.
Section-B
11.
A and B are two sets such that n(A-B) = 14+x , n(B-
A) = 3x and n(AB) = x , draw a Venn diagram to
illustrate the information. If n(A) = n(B) , then find
the value of x .
12. If the power sets of two sets are equal then show
that the sets are also equal.
13. If f and g are two functions :
; 2 1, 2 3,R R f x x g x x Then
evaluate (i) f g x (ii) f g x (iii)
f g x (iv) /f g x
14. Let R be a relation from N to N defined by R = { ( a,
b) N and a = b4} Is the relation(i) Reflexive (ii)
Symmetric (iii) Transitive (iv) Equivalence
15. Express 2 2(cos cos ) ( sin sin ) in
terms cosine.
16.
Comment on the nature of roots of the equation
also find the roots227 10 1 0x x
17. Find the probability that when 7 cards are drawn
from a well shuffled deck of 52 cards, all the aces
are obtained.
18.
From a group of 8 male teachers and 6 female
teachers a committee of 8 is to be selected. In how
many ways can this be done if it must consists of 3
men and 3 women?
19. In how many ways letters of the word
Mathematics be arranged so that the (i) vowelsare together (ii) vowels are not together
OR
In how many ways can 5 girls and 3 boys be seated
in a row with 11 chairs so that no two boys are
together?
20. A point M with x-coordinate 4 lies on the line
segment joining the points P(2,3, 4) and Q (8, 0,
10). Find the coordinates of the point M.
OR
Find the equation of the set of points such that the
sum of the square of its distance from the points
(3, 4, 5) and (-1, 3,-7) is a constant.
21. Find the general solution of the given
trigonometric equation: 2tan 2 sec 2 1 0x x
OR
Solve for x: sin sin 2 sin 3 0x x x 22. Find the derivative of the given function :
4 5sin
3 7 cos
x x
x x
OR
Find the derivative of the given functionsinn
x
x
Section-C
23. If / 2 x and tan 4 / 3x ,find
sin ,cos ,tan2 2 2
x x x
24. Find the mean deviation about the median for the
following data:
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Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad : 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180 , 9990495952
Apex Institute Sample Paper: Class-XI(P.C.M.)
Marks No. of students
0-10 5
10-20 10
20-30 20
30-40 5
40-50 10
25. Using mathematical induction prove the following :
31 1 1 1.....
1.2.3 2.3.4 3.4.5 1 2 4 1 2
n n
n n n n n
26.
(a)A box contains 10 red marbles, 20 blue marbles
and 30 green marbles. 5 marbles are drawn from
the box, what is the probability that (i)all will be
blue? (ii) at least one will be green?
(b)A die has two faces each with number 1, three
faces each with number 2 and one face with
number 3. If die is rolled once, determine
(i) P(2) (ii) P(1 or 3) (iii) P(not 3)
27. Find the length of the perpendicular drawn from
the points 2 2 , 0a b and 2 2 ,0a b
to the line cos sin 1x y
a b Show that their
product is2
b .
28. Prove that
2 2 2cos
3cos cos
3 3 2x x x
29. Solve the inequalities and represent the solution
graphically
5 2 7 3 2 3 0; 2 19 6 47x x x x and
3 117 11
2
x
PHYSICS
1 All questions are compulsory.
2 There are 30 questions in total. Questions 1 to 8
carry one mark each, questions 9 to 18 carry two
marks each, questions 19 to 27 carry three marks
each and questions 28 to 30 carry five marks each.
3 There is no overall choice. However, an internal
choice has been provided in one question of two
marks, one question of three marks and all three
questions of five marks each. You have to attempt
only one of the given choices in such questions.
4 Use of calculator is not permitted.
5
You may use the following physical constantswherever necessary.
e 1.61019
C, c 3108ms
1, h 6.610
34JS,
o 4107NA
2k B 1.3810
23JK
1
N 6.0231023
/mole, m 1.61027
kg
Section-A
1. Can a physical quantity have units but still be
dimensionless?2. Give an example to show that the direction of
velocity of a body can change even when its acceleration
is constant.
3. Two vectors A and B are directed along y-axis and z-
axis respectively. What is the direction of the
vector(BA) ?
4.
What does the area of the shaded portion of the
graph represent?
.
5. Why do we prefer to use a wrench (spanner) of
longer arm?
6. What is the degree of freedom of a mono atomic
gas?
7. For an ideal gas, show the nature ofPV
nTversus P
graph, where the symbols have their usual meaning.8. State the Kelvin-Planck statement of the second law
of thermodynamics.
Section-B
9. Differentiate between systematic errors and random
errors.
10.Two blocks of mass 3 kg and 2 kg are in contact with
each other on a frictionless table. Find the force
exerted by the smaller block on bigger block if a
force of 5 N is applied on the bigger block.
OR
Mention two ways in which static friction is a self
adjusting force. How much force of static friction is
acting on the block of mass 2 kg shown in figure below if
the coefficient of static friction between the block and
the surface is 0.2?
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Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad : 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180 , 9990495952
Apex Institute Sample Paper: Class-XI(P.C.M.)
11.The kinetic energy of a body is increased by 21%.
What is the percentage increase in the linear
momentum of the body?
12.Find the magnitude and direction of angular
momentum of the body of mass m (about point O)which is moving with velocity as shown.
13.Name the satellites which have Sun synchronous
orbit. How is their orbit different from that of the
satellites used for communicationpurpose? What is
the significance of negative total energy of a
satellite?
14.Define breaking stress. A heavy wire is suspended
from a roof and no weight is attached to its lower
end. Is it under stress?
15.Calculate the fall in pressure of helium initially at
1600 Pa, when it is suddenly expended to 8 times its
original volume. Given5
3
16.What is the change in internal energy of a gas during
(i) isothermal expansion and (ii) adiabatic expansion?
17.What do you understand by stationary wave? Draw
the fourth harmonic produced in a stretched sting
tied at two ends and mark the position of the node
and one antinode on it.
18.Distinguish between damped and forced oscillations.
What do you mean by resonant oscillations?
Section-C19.On a two lane road, car A is travelling with a speed
of 36 km/h Two cars B and C approach car A from
opposite directions with speeds of 54 km/h each. At
a certain instant, when both car B and C are at a
distance of 1 km from A, B decides to overtake car A
before C does. What minimum acceleration of B is
required to avert an accident?
20.A particle of mass m moves in a straight line with
retardation proportional to its displacement. Find
the expression for loss of kinetic energy for any
displacement x?
21.Give reasons for the following:
a. A load on a thiefs back does not apply any
force on him when he jumps from the upper story
of a house.
b. A gun recoils on being fired.
c. A man falling from a height receives more injury
when he falls on cemented floor rather than when
he falls on a heap of sand.
22.Mention two factors on which the moment of inertia
of a body depends. A particle performing uniform
circular motion has angular momentum L. What will
be the new angular momentum if its angular
frequency is doubled and its kinetic energy halved?
23.A cubical ice box of thermocole has each side 30 cm
long and a thickness of 5 cm. 4 kg of ice is put in the
box. If outside temperature is 45C and the
coefficient of thermal conductivity is0.01 J/S/m/C,
calculate the mass of ice left after 6 hours. Latentheat of fusion of ice = 335 10
3J/kg.
24.Three equal masses of m kg each are fixed at the
vertices of an equilateral triangle ABC. What is the
force acting on mass 2 m placed at the centroid P of
the triangle? Take AP =BP = CP = 1 m
25.A tank of volume 0.3 m3contains 2 moles of helium
gas at 20C. Assuming that helium behaves like an
ideal gas.
a. Find the total thermal energy of the system
b. What is the average kinetic energy per molecule?
OR
Nine particles of a gas have speeds of 5.00,
8.00, 12.00, 12.00, 12.00, 14.00, 14.00, 17.00
and 20.00 m/s.
(a) Find the average speed
(b) What is the rms speed?
(c) What is the most probable speed of the
particles?
26.(a) Which characteristic of a wave remains constant
as it moves from one medium to another and why?
(b) The phase difference between two points on a
progressive wave is
What will be the
corresponding path difference(c) Mention one
condition for production of beats
27.Two identical springs of spring constant k are
attached to a block of mass m and to fixed
supports as shown below Show that the mass
executes simple harmonic motion when displacedfrom its rest position on either side.
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Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad : 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180 , 9990495952
Apex Institute Sample Paper: Class-XI(P.C.M.)
Also, find the period
Section-D
28.The displacement of a body is given to be
proportional to the cube of time elapsed. What is
the nature of the acceleration of the body? Justify
your answer. A car accelerates from rest at a
constant rate of a for some time; after which it
decelerates at constant rate of b to come to rest. If
the total time elapsed is T second.
a. Draw a velocity time graph for the motion.
b. Calculate maximum velocity attained in terms of a,
b and T.
OR
a. From the top of a building a ball is dropped
while another is projected horizontally at the
same time.
(i).Which ball will strike the ground first?
(ii). Which will strike the ground with more
speed? Justify your answer in each case.
b. A body is projected with speed u at an angle q to
the horizontal to have maximum range. What is the
velocity at the highest point?
c. What is the angle of projection of a projectile
motion whose range R is n times the maximum
height
29.
(a) Is the centrifugal force a reaction of thecentripetal force? Give reason for your answer
(b) What is the effect of reversing the sense of
revolution on the centripetal force?
(c) What provides the centripetal force to a car
taking a turn on level road?
(d) What is angle of banking?
(e) What is the advantage of banking?
OR
(a) A lawn mower is pulled with some external force.
Draw a free body diagram of the system to show all
the forces acting on it. Why is it easier to pull itrather than push it?
(b) Why vehicles are provided with round tyres
only and not any other shape?
Mention two instances when friction between two
surfaces is deliberately increased. Justify the action
in each case
30.Explain the Magnus effect with respect to
the motion of a moving ball. What do you
understand by viscosity? Give its dimensions
and SI unit. On what factors does the coefficient
of viscosity of a liquid depend?OR
State Stokes law for the viscous drag
experienced by the spherical body falling through
a viscous liquid. Why does a spherical body
achieve terminal speed? On what factors does
the terminal speed depend? Give one example
each of motion around us with (i) Positive (ii)
Negative terminal velocity.
CHEMISTRYTime: Three Hours
General Instructions
1. All questions are compulsory.
2. Question nos. 1 to 8 are very short answer questions
and carry 1 mark each.
3. Question nos. 9 to 18 are short answer questions
and carry 2 marks each.
4. Question nos. 19 to 27 are also short answer
questions and carry 3 marks each
5. Question nos. 28 to 30 are long answer questions
and carry 5 marks each
Use log tables if necessary, use of calculators is
not allowed
Section-A
1. Which of these contain the largest number of atoms
1.0 g Li(s) and 1g Na(s)?
2. HI is put in a sealed glass bulb and is then heated to
decompose HI into H2and I2? What type of system
does the reaction mixture represent?
3. What is the difference between a vapour and a gas?
4. Calculate the maximum number of electrons in f
sub shell with same spin.
5. What is the direction of flow of electrons and of
conventional current in the following cell?
Zn(s)|Zn2+
(aq)||Ag+(aq)|Ag(s)
6. Give IUPAC name of allyl alcohol.
7. Calculate the pH of 0.001M NaOH.
8. Why is Ga smaller in size than Al?
Section-B
9. Convert
(a)C and H2to benzene
(b) Calcium carbide to oxalic acid
10.Q10: Give reason for the following
F has lower electron gain enthalpy than Cl.
Ionization enthalpy of N is higher than O
11.Arrange the following in increasing order of size.
Give reason for your answer.
Mg2+ O2- Na+ F- Al3+
12.
The density of 3M solution of NaCl is 1.25g/mL.
Calculate the molality of the solution.
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Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad : 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180 , 9990495952
Apex Institute Sample Paper: Class-XI(P.C.M.)
13.Which of the two is steam volatile and why? o-
nitrophenol or p-nitrophenol
OR
Which of the two as higher dipole moment and why?
NF3or NH3
14.
Calculate the enthalpy change when 2.38g ofCO vaporizes at its normal boiling point?
Enthalpy of vaporization of CO is 6.04 kJ/mol.
15. Balance the following equation in acidic
medium by half reaction method.
2 3
2 7 2 4 2 4 2Cr O C H O C H O Cr
16.Explain
a. LiCl is more covalent than KCl
b. In aqueous solution Li+has lowest mobility.
17. In the estimation of sulphur by Carius method, 0.468
g of an organic sulphur compound afforded 0.668 gof barium sulphate. Find out the percentage of
sulphur in the given compound.
18. How many neutrons and protons are there in
following nuclei?
(a)56
26Fe (b) 3888
Sr
Section-C
19. (i)Which of the two is more stable and why? H2+or
H2-
(ii) All bonds in PCl5are not equal. Explain.
(iii) Which of the two is more ionic and why?NaCl or NaI
20. Give reasons:
(i) Evaporation causes cooling
(ii) Falling liquids drops are spherical
(iii) Vapour pressure of acetone is less than that
of ether at same temperature
21.The combustion of one mole of methanol takes
place at 298 K and 1 atm. After combustion CO2(g)
and H2O(l) are produced and 726 kJ of heat is
liberated. Calculate the standard enthalpy of
formation of one mole of CH3OH(l). Standard
enthalpies of formation of CO2(g) and H2O(l) are -
393 kJ mol-1
and -286 kJ mol-1
respectively.
22.(i) Name the class of hydrides to which H2O and NaH
belong.
(ii) What is understood by hydride gap ?
(iii) What do you mean by 15 volume H2O2solution ?
23.Comment on each of the following observations:
(a) Lithium forms a nitride directly like
magnesium. Give equation involved.
(b) BaO is soluble but BaSO4is insoluble in water.
24.Explain:
(i) Boron is unable to form BF63-
ion.
(ii) [SiF6]2-
is known whereas [SiCl6]2-
not known.
(iii)Conc. HNO3 can be stored in aluminium
container
25.How much energy is required to ionize a Hatom if
the electron occupies n = 5 orbit? Compare youranswer with the ionization enthalpy of Hatom
(energy required to remove the electron from n = 1
orbit).
OR
(a) Lifetimes of the molecules in the excited states are
often measured by using pulsed radiation source of
duration nearly in the nano second range. If the
radiation source has the duration of 2 ns and the
number of photons emitted during the pulse source is
2.5 x 1015
, calculate the energy of the source.
(b) Calculate the wave number for the longest
wavelength transition in the Balmer series of atomic
hydrogen
26.Write balance equation for:
(i) BF3is reacted with ammonia.
(ii) Al is treated with dilute NaOH
(iii) Sodium hydride is reacted with diborane
27.(i) What is photochemical smog and what are its
harmful effects?
(ii) What are the reactions involved for ozone
layer depletion in the stratosphere?
Section-D
28.(a) The species H2O, HCO3, HSO4-and NH3can act
both as Bronsted acids and bases. For each
case give the corresponding conjugate acid
and base. Consider the following ndothermic
reaction
4 2 2 3 )(CH g H O g CO g H g
(i) Write expression for Kpfor the above reaction.
(ii) How will the equilibrium be affected by 1.
Increasing the pressure 2. Using a catalyst
OR
(a)Predict the acidic, basic or neutral nature of
the following salt : NaCN, KBr, NaNO2, NH4NO3
(b)How many grams of KBr be added to 1 L of 0.05 M
solution of silver nitrate just to start the
precipitation of AgBr? Kspof AgBr = 5.0 x 10-13
29.(a) In which C-C bond of CH3CH2CH2Br, the inductive
effect is expected to be least?
(b)Which of the following compound shows
geometrical isomerism?(i)
Pent-1-ene
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Apex Institute IIT-JEE, AIPMT, NTSE and Olympiad : 62, Nitikhand-3 Indirapuram (Gzb.): 0120-4331180 , 9990495952
Apex Institute Sample Paper: Class-XI(P.C.M.)
(ii) Pent-2-ene
(iii)
2-Methylbut-2-ene
(c) What type of isomerism is present in the
following pairs?
(i)
(ii) CH3CH2COCH2CH3 and CH3COCH2CH2CH3
(iii) CH3CH2OH and CH3OCH3
OR
(a)Identify the functional groups in the following
(b)Draw the bondline formula of heptan-4-one
How many isomers are possible for mono
substituted and di substituted benzene?
30.
(a) Do the following conversions:
(i) Benzene to p-nitrobromobenzene
(ii) Ethyl chloride to ethene
(iii) Give mechanism of addition of HBr to propene.
(iv) Write a note on Friedel-Crafts alkylation.
OR
(a)Out of n-hexane and ethyne which will be more
acidic. Also give reason for this behaviour.
(b)Explain with example
(i)Wurtz reaction
(ii)Acidic dehydration
(c) Convert propyne to propanone
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