11th Pcm Paper for Schools Final Exam 2015

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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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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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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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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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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(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

For Detail Solution

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Admission cum Scholarship Test

15th & 22nd March 2015

60%

ScholarshipUpto

100%

Dhwani Jain is pursuing Chemical Engineering from

N.U.S. (National university of Singapore)Ranked 2ndUniversity in Asia. she was our two years classroom

program Student.

Prakhar Goel is studying in Maulana Azad

Medical College Delhi. He was our One year

Dropper Batch Student

Prerna Kashyap is pursuing B.Tech (EC) fromNIT Kurukshetra. She was our Two yearsclassroom program Student

Shubham Mukherjee is studying in IIT-Guwahati.He was our One year Dropper Batch Student

Shiddhant Rathore is pursuing B.Tech (Mechanical)

from BITS Goa.He was our Three years Classroom

Program Student.

AIR 427(GE)

Arindham Roy is pursuing B.Tech from NITPatna. She was our Two years classroomprogram Student

AIR 1823(GE)

AIR 5982 (IITAdvanced)

Arindham Roy

AIR 521(GE)

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11th Pcm Paper for Schools Final Exam 2015