TEST 3 complete - Physica Educator€¦ · 4 #5 7. Two identical charged particles each carrying...

This section contain 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of

which ONLY ONE is correct.

1. The space has electromagnetic field which is given as

particle having mass m and positive charge q is given velocity

coordinate of the particle when it passes through the z

(A) ��

��

(B) ��

��

(C) ��

(D) ��

��

2. An ideal monatomic gas undergoes a cyclic process ABCA as shown in

the figure. Graph of pressure versus volume of the cyclic process ABCA

is

3. An infinite uniform current carrying wire is kept along z

carrying current �� in the directi

OABCDEFG represents a circle (where all the points are equally

Physics

Single Correct Answer Type


The space has electromagnetic field which is given as �� and�� particle having mass m and positive charge q is given velocity �� ̂at origin at t=0 sec. The z

coordinate of the particle when it passes through the z-axis is (neglect gravity through motion)

An ideal monatomic gas undergoes a cyclic process ABCA as shown in

the figure. Graph of pressure versus volume of the cyclic process ABCA

An infinite uniform current carrying wire is kept along z-axis,

in the direction of the positive z-axis.

OABCDEFG represents a circle (where all the points are equally


��. A changed

at origin at t=0 sec. The z-

axis is (neglect gravity through motion)

spaced), whose centre at point (4m, 0m) and radius 4m as shown in the figure. If

�� in S.I unit, then the value of k is

(A) 4

(B) 8

(C) 3

(D) 6

4. An unchanged capacitor C and a value

variable resistance R are connected to an

ideal source and two resistors with the help

of a switch at t =0 as shown in the figure.

Initially capacitor is uncharged and switch S

is closed at t=0 sec. The graph between

�� for variable. Resistor R for its three

different values ��, �� !"#statement

(A) �� $ �� $ �%

(B) �� & �� & �%

(C) |!| $ |(| (D) |!| & |(|

5. Three blocks A,B and C whose masses are

9kg,9kg and 18kg respectively as shown in the

figure, are released from rest. The coefficient of

friction between block A and horizontal surface is

0.5 & the coefficient of friction between block B

and the horizontal surface is 0.5.

acceleration of block C just after release [take g =10 m/

(A) %�) */,�

(B) -�) */,�

(C) .�) */,�

(D) /�) */,�

6. A plane wave front (wavelength =

apparatus as shown in the figure. The lower half of

with water (refractive index =1.5)

How many maximas can be theoretically obtained on the

screen if d= 980 and D=20000

infinity)

(A) 245

(B) 246

(C) 122

(D) 123

spaced), whose centre at point (4m, 0m) and radius 4m as shown in the figure. If

in S.I unit, then the value of k is

An unchanged capacitor C and a value

variable resistance R are connected to an

ideal source and two resistors with the help

of a switch at t =0 as shown in the figure.

Initially capacitor is uncharged and switch S

graph between

for variable. Resistor R for its three

!"# �% versus time is shown in the figure II. Choose the correct

and C whose masses are

9kg,9kg and 18kg respectively as shown in the

figure, are released from rest. The coefficient of

friction between block A and horizontal surface is

0.5 & the coefficient of friction between block B

and the horizontal surface is 0.5. Find the

acceleration of block C just after release [take g =10 m/,�]. All strings and pulleys are ideal.

(wavelength =0) is falling on YDSE

apparatus as shown in the figure. The lower half of it is filled

with water (refractive index =1.5)

How many maximas can be theoretically obtained on the

and D=200000 (including the maxima at

spaced), whose centre at point (4m, 0m) and radius 4m as shown in the figure. If 1 ��2�3 . #5� �

versus time is shown in the figure II. Choose the correct

]. All strings and pulleys are ideal.

7. Two identical charged particles each carrying charge q=0.1 mC and of mass m = 10 mg are

projected along two parallel lines separated by a distance ‘l’ with equal speed �� 10 m/s in

opposite directions. In the beginning electrostatic interaction between the charges can be

ignored due to a large distance between them. The minimum distance between the particles is

found to be 12 cm. The value of l is equal to

(A) 6 cm

(B) 8 cm

(C) 12 cm

(D) 4 cm

8. A plane sound wave is generated in a medium along positive x-axis, whose equation is given as

y= A cos (ωt-kx). If c is the speed of wave in the medium. There is reference frame ‘k’ which is

moving with uniform acceleration ‘a’ in the negative direction of x-axis and at t=0 both wave in

reference frame ‘k’ is

(A) Y= A cos[ωt81 + :;�<= � �>′]

(B) Y= A sin[ωt81 � :;�<= � �>′]

(C) Y= A cos[ωt81 � :;< = � �>′]

(D) Y= A sin[ωt81 � :;< = � �>′]

Comprehension Type

This section contains 3 groups of questions. Each group has 2 multiple choice question based on a

paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is

correct.

Paragraph for questions 9 and 10

A water tank of height 7.5 m is half full of water. The upper

half contains air at atmosphere pressure (A� � 10- A!). The

tank is sealed at the top so that the air within is isolated from

the atmosphere. There is a tap (A) at the bottom of the tank

through which the water can flow out. The cross-section of the

outlet at A is much smaller than the horizontal cross-section of

the tank. Ignore any evaporation of water. Take g=10 m/,�

9. The speed of efflux of the water through the tap A, when it is initially opened, is approximately

(A) 2.5 m/s

(B) 8.5 m/s

(C) 10.0 m/s

(D) 12.5 m/s

10. Assuming that air behaves like an ideal gas and that the temperature of air is constant. Find the

maximum height of water remaining in the tank.

(A) 4.5 m

(B) 3.5 m

(C) 2.5 m

(D) 1.5 m


In the adjacent figure ‘OX’ is the principal axis of a

stationary spherical mirror (either concave mirror or

convex mirror). NM is an incident ray, after reflection it

passes through the origin O, such that∠DEF � 106�.

LM is another incident ray, which after reflection passes

through point k having coordinates (>�, 0), such

that∠DEF = 76�.

The point P (>�, 0) is the pole of the spherical mirror and

point C (>%, 0) is the centre of the curvature of spherical

mirror.

In the figure side of each square is equal to 1cm

Answer the following questions, best on the above paragraph.

11. Find the value of >� (in cm)

(A) √2

(B) √3

(C) 2

(D) √5

12. A point object is moving with velocity �̂ + 4N ̂cm/sec with respect to ground. Find the speed of

image with respect to ground, when it reaches 8.% O*, 0O*=

(A) 10 cm/s

(B) 15 cm/s

(C) 20 cm/s

(D) 25 cm/s


According to the principle of conservation

of linear momentum, if the external force

acting on the system is zero, the linear

momentum of the system will remain

conserve. It means if the centre of mass of

a system is initially at rest, it will remain at

rest in the absence of external force, i.e.

the displacement of centre of mass will be zero.

A plank of mass M is placed on a smooth horizontal surface. Two light identical springs each of stiffness

k are rigidly connected to struts at the end of the plank as shown in the figure. When springs are in its

natural length, their free ends are at a distance of 3l from y axis. A block of mass mis placed on the

plank and pressed against right spring so that it is compressed by 2

connected to the strut by means of a light string. Initially the system is at rest. The right spring is in its

natural length. Now the string is burnt.

13. The maximum displacement of plank is

(A) ��

P

(B) ��PQ�

(C) ��

PQ�

(D) /��

PQ�

14. Maximum kinetic energy of

(A) ��

�PRPQ�B

(B) ��

PRPQ�B

(C) �P��

�RPQ�B

(D) ��P��

RPQ�B

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) ot

of which ONE or MORE are correct

15. A system is shown in the figure, which is released

from rest. There is no friction between ground

and mass 5m. The coefficient of friction between

mass 5m and mass 2m is µ. The coefficient of

friction between mass 5m and mass m is also

Choose the correct statement(s)

(A) The acceleration of centre of mass of system

is zero.

(B) The magnitude of acceleration of mass

(C) The tension in the string is

(D) The magnitude of acceleration of mass 5m is zero if

16. Choose correct statement(s) the regarding photoelectric effect.

(A) No matter how small the intensity, if photoelectric emission takes place, the emission is

instantaneous.

(B) The maximum kinetic energy of a photoelectron does not depend upon the intensity of

incident light, if frequency of incident light is kept constant.

(C) Threshold frequency depends upon the intensity of incident light.

(D) The photoelectric current is inversely proportional to the intensity of incident light and is

independent of its frequency.

17. Choose correct statement regarding X

plank and pressed against right spring so that it is compressed by 2l. To keep the block at rest it is

onnected to the strut by means of a light string. Initially the system is at rest. The right spring is in its

natural length. Now the string is burnt.

The maximum displacement of plank is

Maximum kinetic energy of block m is

Multiple Correct Answer(s) Type


A system is shown in the figure, which is released

from rest. There is no friction between ground

and mass 5m. The coefficient of friction between

. The coefficient of

friction between mass 5m and mass m is also µ.

t statement(s)

The acceleration of centre of mass of system

The magnitude of acceleration of mass 5m is zero if µ = 0

The tension in the string is �S%√% if µ =

�√%

The magnitude of acceleration of mass 5m is zero if µ = �

√%

statement(s) the regarding photoelectric effect.

No matter how small the intensity, if photoelectric emission takes place, the emission is

The maximum kinetic energy of a photoelectron does not depend upon the intensity of

frequency of incident light is kept constant.

Threshold frequency depends upon the intensity of incident light.

The photoelectric current is inversely proportional to the intensity of incident light and is

independent of its frequency.

ement regarding X-ray

. To keep the block at rest it is

onnected to the strut by means of a light string. Initially the system is at rest. The right spring is in its


No matter how small the intensity, if photoelectric emission takes place, the emission is

The maximum kinetic energy of a photoelectron does not depend upon the intensity of

The photoelectric current is inversely proportional to the intensity of incident light and is

(A) If the target material in a Coolidge tube is changed keeping the acceleration voltage

constant, the minimum wavelength of the X

(B) X-ray do not get deflected on application of electric or magnetic fields.

(C) X-ray can ionize a gas.

(D) X-ray can be reflected, refracted, diffracted and polarized under suitable condition.

18. Two identical discs, each of negligible mass and radius

r(<<<l) are connected by a uniform rod of mass m and

length l as shown in the figure. The disc

with an ideal spring of spring constant k at its centre.

The spring is un-stretched when

slipping at any contact at any

motion. Choose the correct statement [spring always

obeys Hook’s Law and mg = k

each disc remains in contact with the contact surface.

(A) The value of θ ,when the system is in stable

equilibrium is 60�

(B) The value of θ ,when the system is in stable equilibrium is

(C) Spring potential energy of the system in the state of stable equilibrium is

(D) The angular speed of the rod when it passes through the position of the stable equilibrium is T%S�

19. A string OP of length L is fixed at

both ends and vibrates in its first

overtone with time period T and

maximum amplitude ‘A’. At any

time, the shape of string is shown in

the figure. Points O, C and P

represent nodes. OB=BC=CD=DP,

(BQ=DR=A) Choose the correct statement(s)

(A) The net flow of energy through section OS is depende

(B) The net flow of energy through section OQ is dependent on time.

(C) The net flow of energy through se

(D) The net flow of energy through section OT is dependent on time.

20. A projectile launched from the ground (from origin O

mass at the highest point A of the trajectory. One of the fragments lands

explosion; two other fragments land simultaneously 2

projectile does not explode, th

maximum height (H) of projectile. Choose the incorrect statement(s)

(A) The speed of projection of projectile is 50 m/sec

(B) The angle of projection of projectile with ground is

(C) The value of R is 240 m

(D) If projectile does not explode, the time of flight of projectile is 6 sec.

If the target material in a Coolidge tube is changed keeping the acceleration voltage

constant, the minimum wavelength of the X-rays produced will change.

ray do not get deflected on application of electric or magnetic fields.

ray can be reflected, refracted, diffracted and polarized under suitable condition.

Two identical discs, each of negligible mass and radius

) are connected by a uniform rod of mass m and

as shown in the figure. The disc A is connected

with an ideal spring of spring constant k at its centre.

stretched when θ = 0� . There is no

slipping at any contact at any point of time during the

motion. Choose the correct statement [spring always

g = kl]. During the motion,

each disc remains in contact with the contact surface.

,when the system is in stable

,when the system is in stable equilibrium is 30�

Spring potential energy of the system in the state of stable equilibrium is ��/

The angular speed of the rod when it passes through the position of the stable equilibrium is

A string OP of length L is fixed at

both ends and vibrates in its first

overtone with time period T and

maximum amplitude ‘A’. At any

time, the shape of string is shown in

the figure. Points O, C and P

represent nodes. OB=BC=CD=DP,

(BQ=DR=A) Choose the correct statement(s)

The net flow of energy through section OS is dependent on time.

The net flow of energy through section OQ is dependent on time.

The net flow of energy through section OC is dependent on time.

The net flow of energy through section OT is dependent on time.

A projectile launched from the ground (from origin O) explodes into three fragments of equal

mass at the highest point A of the trajectory. One of the fragments lands T%�- seconds after the

explosion; two other fragments land simultaneously 2T%�- seconds after the explosion. If

projectile does not explode, the range(R) of projectile would have been three times the

maximum height (H) of projectile. Choose the incorrect statement(s)

The speed of projection of projectile is 50 m/sec

The angle of projection of projectile with ground is 30�

The value of R is 240 m

If projectile does not explode, the time of flight of projectile is 6 sec.

If the target material in a Coolidge tube is changed keeping the acceleration voltage

ray can be reflected, refracted, diffracted and polarized under suitable condition.

��/

The angular speed of the rod when it passes through the position of the stable equilibrium is

) explodes into three fragments of equal T seconds after the

seconds after the explosion. If

e range(R) of projectile would have been three times the

Chemistry

Straight Objective Type

This section contains 8 multiple choice questions numbered 1 to 8. Each has 4 choices (A), (B), (C) and

(D), out of which ONLY ONE is correct.

1. In which of the following reactions, retention product is more than inverted product?

2. Which of the following compound is most covalent? (Atomic number : Ti=22, V=23, Zr=40,

Hf=74)

(A) TiC�

(B) VC�

(C) ZrC�

(D) HfC�

3. Consider the following two solutions

“0.01 m aqueous solution of hexaqua iron (III) chloride (M)” and, “0.02 m aqueous solution of

diammine silver (I) chloride (N)”

Now, identify the correct statement regarding the solution (M) & (N). (Assume molality equals

to molarity and solution to be dilute)

(A) Solution (M) freezes at lower temperature than solution (N)

(B) Solution (M) boils at higher temperature than solution (N)

(C) Osmotic pressure of ‘M’ is more than ‘N’ at the same temperature.

(D) At 373K, the vapour pressure of ‘M’ and ‘N’ are same

4. Oxygen gas is obtained on the surface of activated charcoal and the numbers of surface sites

occupied per oxygen gas molecule are 2. On heating oxygen gas is evolved from sites and were

collected at 0.001 atm and 298 K in a container of volume 2.46 c*%. If density of surface sites is

6.023 x 10� per O*� and surface area is 1000 O*�, then % of surface sites occupied by D�(g),

is:

(A) 10%

(B) 15%

(C) 20%

(D) 25%

5. The first unsymmetrical ketone of ketone homologous series is treated with methyl magnesium

bromide followed by hydrolysis acidic, conditions gives a compound (P). The compound (P) is

reduced by red P/HI to produce a new product (Q).

Now,

(Q) Number of isomeric monochloro products Number of fractions of

monochloro products (M) Number of fractions of monochloro products(M)

Hence, M & N respectively, are:

(A) 5,5

(B) 5,4

(C) 6,4

(D) 6,5

6. If the pressure of a given amount of gas is increased by 5.26% at constant temperature then the

% decrease in volume will be:

(A) 3%

(B) 5%

(C) 6%

(D) 4%

7. 50 ml, 0.6 aq. Solution of BaC�� is mixed with 50 ml, 0.6 M F!%AD solution at 25�U, the

concentration of !�Q ions in the solution at 25�U is:

(A) 1 V 10� E

(B) 2 V 10% E

(C) 3 V 10% E

(D) 3 V 10� E

8. Molar heat capacity of an ideal gas at constant volume is given by UW = 16.5 + 10� T(in

joules). If 3.5 moles of this ideal gas are heated at constant volume from 300 K to 400 K, then

the change in internal energy (in kJ) will be approximately:

(A) 3

(B) 5

(C) 7

(D) 9

Comprehension Type

This section contains 3 groups of questions. Each group has 2 multiple choice question based on

paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is

correct.

Paragraph for question nos. 9 to 10

For any reversible reaction, A+B⇌ C+D; the free energy change R∆ZB and standard free energy change

R∆Z�B are related with each other by following relation:

∆Z � ∆Z� + �[5"\<, where ‘R’ = universal gas constant, T=temperature in Kelvin.

\< = Reaction quotient =[^][�]

[2][�] and at equilibrium, \< � _`� (Equilibrium constant)

The value of _`� can give an idea about the extent of completion of a chemical reaction before the

equilibrium is attained.

Now, answer the following questions

9. Which of the following graph represents that reacting species of a chemical reaction are almost

completely consumed?

10. Acetic acid can form a dimer in the gas phase. The dimer is held together by two H-bonds with a

total strength of 66.5 kJ *a5� of dimer. If at 25�U, the equilibrium constant for the

dimerisation is 1.3 V 10% then, standard energy entropy change R∆b�B for the reaction.

2Uc%UDDc ⇌ RUc%UDDcB� ; is (R=8.134 Jmo5�_�)

(A) -0.764 kJ

(B) -0.163 kJ

(C) -0.980 kJ

(D) -0.264 kJ

Paragraph for Question Nos. 11 to 12

Two beakers (A) and (B) are shown below:

Beaker (A) contains 250 ml, 0.1 M ZnSDR!d. ) solution while Beaker (B) contains 250 ml, 0.1 M UebD(aq.) solution. The solution in Beaker (B) is electrolyzed by passing a current of 3.512 ampere for

1368 seconds. Assume that ]Ue(Fc%)@�Q is detectable upto its concentration level as low as 1 V10%E and formation constant of [UeRFc%B]�Q is1.1 V10�%. Also given that �^f�g|^f� =0.34 V and �hi |hi�� =0.76 V log�� 4.4 =0.65 and �.%�%mn3 =0.06

Now, answer the following question:

11. After electrolysis, if Beaker (B) is connected with Beaker (A) through a voltmeter, and a salt

bridge the reading of voltmeter at t=0, will be:

(A) 1.10 V

(B) 1.03 V

(C) 1.20 V

(D) -1.03 V

12. After electrolysis of the solution in Beaker (B), if sufficient quantity of Fc%(!d) is added to

electrolysed solution maintaining ]Fc%@=0.10 M, then colour of the solution in Beaker(B)

becomes:

(A) Red

(B) Purple

(C) Blue

(D) Colourless


∝-phenyl ethyl acetate is treated with diethyl carbonate in the presence of sodium ethoxide to produce

the compound (X). Compound (X) on further treatment with sodium ethoxide and methyl iodide gives

(Y). Compound (Y) on hydrolysis followed by heating gives compound (Z). compound (Z) on treatment

with red P/HI gives (P).

Now, answer the following question:

13. Compound (P) Product (Q)

Hence, the product (Q) is:

14. The compound (P) on acetylation with acetic anhydride and anhydrous p5U5%,gives major

product (M) and minor product (N). The product (N) is subjected to the same treatment as in

question no. (13), and the new product so obtained is heated with dilute alkali to produce (K).

Product (K) on acidification produces (L) as the main product. Hence, (L) is:

Multiple Correct Choice Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its

answer, out which ONE OR MORE is/are correct.

15. Which of the following reaction(s) takes place with the evolution of nitrogen gas:

16. In which of the following reactions, the oxidation state of chromium metal in the product is at

least five?

(A) Chromyl chloride

(B) _�Uq�D.

(C) _�Uq�D. rst(:�)uvvvvw

(D) F!�Uq�D. <xi<.s�yz{uvvvvvvvw

17. If green Vitriol is heated strongly, then identify the correct statement(s) about the products of

this reaction:

(A) A violet coloured solid is formed which dissolves in conc. HCL.

(B) Three of the products are gases at room temperature.

(C) One of the gaseous products when passed into c�b gas produces colloidal sulphur.

(D) Crystalline form of one of the gaseous product is cyclic and contains three S-O-S bonds per

molecule.

18. Consider the following compound:

If all stereo-isomeric forms of the above compound are saponified then which of the following

statement(s) is/are correct?

(A) Total number of different organic products obtained in this reaction are 4

(B) Only one product gives bromine water test.

(C) Two enantiomeric pairs are produced as products.

(D) Only two of the products can react with N-bromo succinimide in the presence of light.

19. A colourless solid (A) is formed by heating a mixture of xenon and fluorine in the molar ratio of

1:5 at 400�U in a nickel tube. Which of the following product(s) may be formed by hydrolysis of

compound (A):

(A) V|D%

(B) c}

(C) XE

(D) D�

20. Which of the following sugars gives silver mirror test positively?

Mathematics

Straight Objective Type

This section contains 8 multiple choice questions numbered 1 to 8. Each question has 4 choices (A), (B),

(C) and (D) out of which ONLY ONE is correct.

1. Let f(x)=~ ��`�R��B, ��:�Si(�Q�) ��(��)Q��, �� If f(x) is differentiable at x=1, then (where sgn x denotes signum function of (x)

(A) a=-1 , b=2

(B) a=-3 , b=-2

(C) a=-2 , b=4

(D) a=-5 , b=-4

2. let x ∈ 80, ��= and log��i�(24Oa,>) = %�, then the value of Oa,|O�> − 8�!"�>, is equal to

(A) 3

(B) 6

(C) 8

(D) 9

3. The roots α and β of a quadratic equation are the square of two consecutive natural numbers.

The geometric mean of the two roots is 1 greater than the positive difference of the roots. If

exactly one root of >� − O> + 32 � 0 lies between α and β, then find the minimum integral

value of c

(A) 4

(B) 12

(C) 13

(D) None of these

4. Let Ei � �*�� denotes a square matrix of order n with entries as follows for 1≤ � ≤ ", *�� =10; for 1≤ � ≤ " � 1, *�Q�, � = *�,�Q� = 3 and all other entries in Ei are zero. Let �i be the

determinant of

(A) 0

(B) 1

(C) 2

(D) None of these

5. Let triangle ABC have altitudesℎ:, ℎ�, ℎ< from points A, B, C respectively. If ℎ:=8, ℎ�=8, ℎ<=10.

The perimeter of the triangle formed by joining feet of altitudes of ∆p U is

(A) %�√��-

(B) ��√��-

(C) ��√��-

(D) None of these

6. The number of permutations of �>�,>�,>%, … … . . >i,� of �1,2,3 … . .100� such that the cyclic sum

of ∑ |>� � >�Q�|i�� (with >iQ� � >�) is minimum, is

(A) 100.2)/

(B) 99. 2))

(C) 2. 3)/

(D) None of these

7. If � :→ +��uw +%<→ , �→ +�<→ + %:uw , <→ +�:uw +%�uw =36, where :→, �→ !"# <→ are three vectors then the

value of ¡ :.→ :→ :.→ �→ :.→ <→:.→ �→ �.→ �→ �.→ <→:.→ <→ <.→ �→ <.→ <→¡ is

(A) 4

(B) 6

(C) 3

(D) None of these

8. Let the curve, C:y = >� + !>- + (> + O>% + #>� + |> + ¢ touches the line L:y mx+n at x=1,2,3.

Find the area bounded by these graph?

(A) %%

(B) ��-

(C) -%

(D) None of these

Comprehension Type

This section contains 3 paragraphs. Based upon paragraph 2 multiple choice questions have to be

answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is

correct.


Read the following write up carefully and answer the following questions:

There are ‘n’ black identical balls and two identical red balls in a bag. One by one, balls are drawn at

random out of the bag. Kartikey wins as soon as two black balls are drawn and Farhan wins as soon as

two red balls are drawn. The game continues until one of the two wins. Let J(n) and F(n) be the two

probabilities that Kartikey and Farhan win, respectively.

9. The value of F(1) + F(2)+……..F(2013) is

(A) �%

(B) ��%)��-

(C) ��-

(D) None of these

10. The value of limi→¥ ∏ §(q)�̈�� is

(A) �%

(B) �-

(C) �

��

(D) None of these


Read the following write up carefully and answer the following questions:

Let P(x) be a polynomial with real coefficient such that R>� + > + 1B PR> � 1B=R>� � > + 1B P(x) ∀ > ∈ R

and P (1) =3

11. If 1 �!"�� 8 ��Qª(��)=dx + 1 �!"�� (> + 1) dx = �� (« − 5"4) then value of k is

(A) 10

(B) 8

(C) 12

(D) None of these

12. Let 5i=1 �A(>�) + A(>� − 1)�� idx. If (k+1) 5i = 2�(1 + 5i�), then the value of n is (k, n∈ F)

(A) 1

(B) 2

(C) 4

(D) None of these


A variable circle touches straight line x=y and cut off a constant length of 2√2 units from x+y=0. The

locus of centre of circles is curve C.

13. The eccentricity of curve C is

(A) √2

(B) √3

(C) 2

(D) 3

14. The line x+2y=1 intersects the curve C at P and Q (where P is above x-axis). The centre of circle

which touches the curve C at P and passes through Q is

(A) 8� , �=

(B) 8� , �=

(C) 8� , � =

(D) 8� , � =

Multiple Correct Answer(s) Type

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out

of which ONE OR MORE are correct.

15. Consider a function f(x) = 1 `¬;√�;�

��i�<x�� ; x∈ 8«, %�� =

(A) F(x) id decreasing in the interval

(B) If g is the inverse of then the value of g’(0) is − �� |√�

(C) F(x) is increasing in the interval

(D) If g is the inverse of f then the value of g’(0) is- �� | �√�

16. A line L with slope m>0 is drawn through P(0,0) to meet the lines ®�:2x+y-1=0 and ®�:2x+y-6=0

at A and B respectively. From A, a line perpendicular to L is drawn meeting the parallelogram pp� � is formed. The equation of line L is obtained so that the area of the parallelogram pp� � is least.

(A) The equation of line L is 3x-y=0

(B) The equation of line L is 3y-x=0

(C) The minimum area of parallelogram pp� � is 5

(D) The minimum area of parallelogram pp� � is 5

17. Let f(x)=¯ �t:��Q��%�Q� 0 $ > $ 1 (�>� + (> + 1, > = 1 (| Oa"��"ae, !� > = 1, �ℎ|" °ℎ�Oℎ a¢ �ℎ| (1 + ln O. �!"�(> − 1))�/(²³ �)� 1 < > < 2 � Following relation can hold good?

(A) b+c =4

(B) ac =9

(C) c-b =5

(D) a-b =2

18. Let M be a 3 X 3 orthogonal matrix. Let A be the 2 X 2 matrix in the upper-left corner of M and

let B be the 1 X 1 matrix in the lower-right corner of M. Let E� be the 3 X 3 matrix whose first 2

columns are first 2 columns of M and whose remaining 1 columns is the last column of 5%. Let E� of the following is(are) correct?

(A) EE� = E�

(B) EnE� = E�

(C) |#|�RE�B| � |#|�RE�B| (D) |#|�RpB| � |#|�R B|

19. During the weekends, A delivers milk in the complex plane. On Saturday, he beings at z and

delivers milk to houses located ´%, ´-, ´.…………..´��% in that order. On Sunday, he begins at 1

and delivers milk to houses located at ´�, ´, ´�,………… ´�� in that order. Mr. A travels in a

straight line between two houses. The distance he must travel from his starting point to the last

house is √2012 on both days.

(A) |´| � 1

(B) |´| � ��

(C) Re R´�B � ��-��

(D) Re R´�B � ��

20. Let ¢: R0,1) → (0,1) be the strictly monotonic polynomial function such that for every positive

integer ‘n’ and odd positive integer ! < 2i, there exists an odd positive integer ( < 2i such

that 8 :�¶= = �

�¶ , which of the following may be correct?

(A) ¢·(>) ≠ 0 ∀ > ∈ (0, 1)

(B) ¢·(>) = 0 ¢aq ,a*| > ∈ (0, 1)

(C) ¢· 8��= = 1

(D) ¢· 8��= = −1

ANSWERS

Q. No. Physics Chemistry Mathematics

1 A B A

2 C D C

3 B D B

4 B C B

5 C C B

6 A B A

7 A C A

8 A C B

9 B B B

10 C B C

11 B B C

12 B D B

13 B B A

14 D C C

15 A,B,C,D B,C,D A,D

16 A,B A,B,D A,D

17 B,C,D C,D A,B,C,D

18 A,C,D C,D A,C,D

19 A,D A,B,C,D A,C

20 B,D B,C A,C,D

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