(Academic Session : 2016 - 2017) LEADER & ENTHUSIAST COURSE · 2018-10-21 · ALL INDIA OPEN...

Paper Code : 0000CT103116004Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)E

NG

LIS

H

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Your Target is to secure Good Rank in JEE (Main) 2017

Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main

TEST DATE : 19 - 03 - 2017

TARGET : JEE (MAIN) 2017

LEADER & ENTHUSIAST COURSE

Important Instructions

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3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry andMathematics having 30 questions in each part of equal weightage. Each question is allotted 4(four) marks for correct response.

6. One Fourth mark will be deducted for indicated incorrect response of each question. No deduction

from the total score will be made if no response is indicated for an item in the Answer Sheet.

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ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017

E-1/180000CT103116004

SPACE FOR ROUGH WORK

PART A - PHYSICS

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

1. A charge particle q0 of mass m

0 is projected

along the y-axis at t = 0 from origin with a

velocity V0. If a uniform electron field E

0 also

exists along the x-axis, then the time at

which de-broglie wavelength of the particle

becomes half of the initial value is :-

(1) 0 0

0 0

m v

q E (2) 0 0

0 0

m v2

q E

(3) 0 0

0 0

m v3

q E (4) 0 0

0 0

m v3

q E

2. The charge flowing through a resistor R

varies with time t as Q = 3t – 6t2. The heat

produced in R till the current in it becomes

zero is :-

(1) 3R

4(2)

3R

2

(3) 4R

2(4)

9R

2

3. A particle moves along a circle with aconstant angular speed . Its displacement,with respect to this position of the particleat time t = 0 is plotted against time. Thegraph would look like :

(1)

t

S

circular

/

(2)

t

S

circular

2 /

(3)

t

S

sine curve

2 /

(4)

t

S

2 / /

4. A metallic rod is placed in a uniformelectric field. Select the correct option.

A B

E0

(1) Inside the rod there will be an inducedelectric field from B to A.

(2) Free electrons will accumulate at theend B of the rod.

(3) The potential of the end A will be morethan that at B.

(4) The electric field outside the rod willnot change due to the induced chargedin the rod.

0000CT103116004E-2/18



5. Calculate energy needed for moving a mass

of 4kg from the centre of the earth to its

surface (in joule), if radius of the earth is

6400 km and acceleration due to gravity at

the surface of the earth is g = 10 m/sec2.

(1) 1.28 × 108 J

(2) 1.28 × 106 J

(3) 2.56 × 108 J

(2) 2.56 × 1010 J

6. A ball of mass 'm' is released from the top

of a smooth movable wedge of mass 'm'.

When the ball collides with the floor,

velocity of the wedge is 'v'. Then the

maximum height attained by the ball after

an elastic collision with the floor is :

(Neglect any edge at the lower end of the

wedge).

45°

msmooth

m

(1)

22v

g(2)

2v

4g

(3)

24v

g(4)

2v

2g

7. A particle is acted upon by a force whose

component's variations with time are

shown in diagrams. Then the magnitude of

change in momentum of the particle in

0.1sec will be :-

Fx

0 t=0.1 sec

30N

Fy

0 t=0.1 sec

80N

Fz

0

t=0.1 sec

–50N

(1) m

2kgsec

(2) m

10kgsec

(3) m

12kgsec

(4) m

5 2 kgsec

8. A steel rod is projecting out

A B

E

F

CD

of rigid wall. The shearing

strength of steel is 345 MN/m2.

The dimensions AB = 5 cm,

BC = BE = 2 cm. The

maximum load that can be

put on the face ABCD is

(neglect bending of the rod)

(g = 10 m/s2)

(1) 3450 kg (2) 1380 kg

(3) 13800 kg (4) 345 kg


E-3/180000CT103116004


9. In a cylindrical container open to the

atmosphere from the top a liquid is filled

upto 10 m depth. Density of the liquid

varies with depth from the surface as

(h) = 100 + 6h2 where h is in meter and

is in kg/m3. The pressure at the bottom of

the container will be : (atmosphere pressure

= 105 Pa, g = 10 m/sec2)

(1) 1.7 × 105 Pa (2) 1.4 × 105 Pa

(3) 1.6 × 105 Pa (4) 1.3 × 105 Pa

10. A plane electromagnetic wave of angular

frequency propagates in a poorly

conducting medium of conductivity and

relative permittivity . Find the ratio of

conduction current density and

displacement current density in the

medium.

(1) 0

(2)

0

(3) 0

(4) 0

11. A screw gauge has some zero error but its

value is unknown. We have two identical

rods. When the first rod is inserted in the

screw, the state of the instrument is shown

by diagram (I). When both the rods are

inserted together in series then the state

is shown by the diagram (II). What is the

zero error of the instrument ?

1 msd = 100 csd = 1 mm :-

12

10

(1) –0.16 mm (2) +0.16 mm(3) +0.14 mm (4) –0.14 mm

12. A transistor is operating in the activemode. v

1 is potential barrier across base

emitter junction and v2 is potential barrier

across collector base junction. b1 is width

of depletion layer of base emitter junctionand b

2 is width of collector base junction.

(1) v1 > v

2, b

1 > b

2(2) v

1 < v

2, b

1 < b

2

(3) v1 > v

2, b

1 < b

2(4) v

1 < v

2, b

1 > b

2

13. Inside a closed furnace held at a temperatureof 400 K, we have a black body. A hole of

area 10 cm2 is opened in the furnace so thatsunlight starts falling on black body. The

intensity of sunlight is 2000 W/m2. In thesteady state

(1) The black body and furnace can't bedistinguished.

(2) The black body will appear darker thanthe furnace

(3) The black body will appear brighterthan the furnace

(4) Information insufficient

0000CT103116004E-4/18



14. A thin rectangular magnet suspended freely

has a period of oscillation equal to T. Now it

is broken into two equal halves (each having

half of the original length) and one piece is

made to oscillate freely in the same field.

If its period of oscillation is T', the ratio

T'/T is :-

(1) 1

2 2(2)

1

2

(3) 2 (4) 1

4

15. For a GPS navigation to track a mobile

device, we use :-

(1) 3-satellites one for latitude, another for

longitude and third for altitude

(2) 4-satellites one for altitude and 3 for

position on ground.

(3) 2-satellites one for position on ground

on for altitude

(4) 1 satellite only.

16. Identify the terminals on this BJT, and also the

type of BJT it is (NPN or PNP): (Starting from

left). The multimeter reads resistance and the

black terminal is connected to the negative

terminal of the battery :-

AV

AV

OFF

com

AV

AV

OFF

com

0.623 0.625

RedRed

BlackBlack

(1) Emitter base collector NPN

(2) Emitter base collector PNP

(3) Collector base emitter NPN

(4) Collector base emitter PNP

17. A physical quantity A is dependent on

other four physical quantities p, q, r and s

as given below 2 3

pqA

r s . The percentage

error of measurement in p, q, r and s 1%,

3%, 0.5% and 0.33% respectively, then the

maximum percentage error in A is :

(1) 2% (2) 0% (3) 4% (4) 3%


E-5/180000CT103116004


18. Three rods AB, BC and AC having thermal

resistances of 10 units, 10 units and 20 units,respectively, are connected as shown in the

figure. Ends A and C are maintained at

constant temperatures of 100°C and 0°C,respectively. The rate at which the heat is

crossing junction B is :

A

B

C

(1) 5 units (2) 10 units

(3) 20 unites (4) 7.5 units

19. A wire carrying a current I is placed inside

a uniform magnetic field 0ˆB B k

. The

shape of the wire is parabolic and has

equation Y = 2x – x2. The force on the wirewill be :

A

y

Y

O

z× × × × × ×

× × ×

× × ×× × × × × ×

i i

(1) F = 2B0i, upwards

(2) F = 2B0i, downwards



20. There is a long cylindrical pipe wire of

internal radius r and external radius R

carrying current i along its length. The

variation of magnetic field with distance

from the axis of the wire can be represented

by the :-

(1)

y-axis

r R x-axis

(2)

y-axis

rRx-axis

(3)

y-axis

r Rx-axis

B

(4)

y-axis

rR x-axis

B

21. In a series R-L-C AC circuit, for a

particular value of R, L and C power

supplied by the source is P at resonance. If

the value of inductance is halved, then the

power from the source again at resonance

is P'. Then :

(1) P'

P2

(2) P = 2P'

(3) P = 4P' (4) P = P'

0000CT103116004E-6/18



22. Carefully analyses the diagram and choose

the correct option :

(i) PlaneWave

Thinlens

Focus

Sphericalwave

(ii) PlaneWave

Thinlens

Focus

Sphericalwave

(iii) PlaneWave

Thinlens

Focus

Sphericalwave

(iv) PlaneWave

Thinlens

Focus

Sphericalwave

(1) i and ii are true (2) i and iii are true

(3) i and iv are true (4) ii and iv are true

23. A point source of light is placed at a depth

h = 0.5 m below the surface of a liquid

5

4

. Then, the fraction of light energy

that escape directly from the liquid surface

is :-

(1) 0.1 (2) 0.2 (3) 0.3 (4) 0.4

24. Two radioactive elements R and Sdisintegrate as

R P + ; R = 4.5 × 10–3 years–1

S P + ; S = 3 × 10–3 years–1

Starting with number of atoms of R and Sin the ratio of 2 : 1, this ratio after the lapseof three half lives of R will be :

(1) 3 : 2 (2) 1 : 3 (3) 1 : 1 (4) 2 : 1

25. A hollow conducting sphere of inner radius

R and outer radius 2R is given a charge Q

as shown in the figure, then the :

R

2R

A

B

C

+Q

O

(1) potential at A and B is different

(2) potential at O and B is different

(3) potential at O and C is different

(4) potential at A, B, C and O is same

26. A liquid is kept in a cylindrical vessel.

When the vessel is rotated about its axis,

the liquid rises at its sides. If the radius of

the vessel is 0.05 m and the speed of

rotation is 2 revolutions per second, the

difference in the heights of the liquid at the

centre and at the sides of the vessels will

be (take g = 10 ms–2 and 2 = 10)

(1) 2 cm (2) 4 cm

(3) 1 cm (4) 8 cm

27. A uniform narrow 1.95 m long pipe is open

at both ends. It resonates at two successive

harmonic of frequency 275 Hz and 330 Hz.

The speed of sound in the tube is :

(1) 200 m/s (2) 205 m/s

(3) 210 m/s (4) 214.5 m/s


E-7/180000CT103116004


28. In the given figure a ring of mass m is kept

on a horizontal surface while a body of

equal mass 'm' attached through a string,

which is wounded on the ring. When the

system is released the ring rolls without

slipping. Consider the following

statements and choose the correct option.

m

m

(i) acceleration of the centre of mass of ring

is g

3

(ii) acceleration of the hanging particle is

2g

3

(iii) frictional force (on the ring) acts along

forward direction

(iv) frictional force (on the ring) acts along

backward direction

(1) statement (i) and (ii) only

(2) statement (ii) and (iii) only

(3) statement (iii) and (iv) only

(4) none of these

29. A ladder AP of length 5 m is inclined to a

vertical wall is slipping over a horizontalsurface with velocity of 2 m/s, when A is at

a distance 3m from ground what is thevelocity of C.M. at this moment :

(1) 1.25 m/s (2) 0 m/s

(3) 1 m/s (4) 2 m/s

30. Two identical adiabatic vessels are filledwith oxygen at pressure P

1 and P

2 (P

1 > P

2).

The vessels are interconnected with eachother by a nonconducting pipe. If U

01 and

U02

denote initial internal energy of oxygenin first and second vessel respectively and

1fU and

2fU denote final internal energy

values, than :

(1) 1 2

01 1f f

02 2

U P, U U

U P

(2) 1 2

01 2f f

02 1

U P, U U

U P

(3) 1 2

01 2f f

02 1

U P, U U

U P

(4) 1 2

01 1f f

02 2

U P, U U

U P

0000CT103116004E-8/18



PART B - CHEMISTRY

31. A solid element, (metal) crystallises in

ABABAB..... ...type packing in three

dimension. If the density of the element and

its atomic radius are 5.0 gm/cm3 and

100 2pm , the atomic mass of the element

is (NA = 6 × 1023)

(1) 48 (2) 72 (3) 96 (4) 32

32. In 20 ml 0.4 M-HA solution, 80 ml water is

added. Assuming volume to be additive, the

pH of final solution is

(Ka of HA = 4 × 10–7 , log2 = 0.3)

(1) 4.30 (2) 3.75 (3) 3.40 (4) 3.70

33. Which of the following aqueous solution has

highest freezing point ?

(1) 0.2 m-urea solution

(2) 0.15 m-NaCl solution

(3) 0.1 m CH3COOH solution

(4) 0.12 m-Ca(NO3)2 solution

34. 5 moles of an ideal gas is expanded from

(10L, 300K) to (20L, 300K) against a

constant external pressure of 1.0 bar. The

only incorrect value of physical quantities

for this change in state of the system, is-

(1) U = 0 (2) H = 0

(3) S = 0 (4) T = 0

35. For a first order reaction, the rate constant

is 0.04 min–1 at 27ºC and 0.08min–1 at 37ºC.

The activation energy of reaction is

(ln2 = 0.7)

(1) 13.02 kcal /mol (2) 139.86 kcal /mol

(3) 54.12 kcal /mol (4) 13020 kcal /mol

36. 20 gm iron pyrite, FeS2, is roasted

completely and SO2 gas produced is absorbed

completely in 400 ml NaOH solution. If only

50% NaOH is used in the reaction, the

molarity of NaOH solution was

(1) 5

M3

(2) 10

M3

(3) 5

M6

(4) 20

M3

37. Fe(OH)3 sol is prepared by the hydrolysis of

FeCl3 in a hot water. If the sol is electrolysed

using inert electrodes, the only correct

statement is -

(1) Coagulation will occur near anode

(2) Cl2 gas may be cathode product

(3) H2 gas may be anode product

(4) O2 gas may be anode product


E-9/180000CT103116004


38. Certain mass of an ideal gas is heated at

constant volume. Which of the following

parameter of gas will increase ?

(1) Density

(2) Mean free path

(3) Collision frequency

(4) Molar mass of gas

39. Eºcell

for the cell :

Pt(s) |H2(g)|HCOOH(aq.)||CH

3COOH(aq.)|H

2(g)|Pt(s)

at 25ºC is (Ka of HCOOH = 2.4 × 10–4, K

a

of CH3COOH = 1.8 × 10–5, log2 = 0.3, log 0.48,

2.303 298 R0.06

F

)

(1) 0.0672V (2) –0.0672V

(3) –0.1344 V (4) –0.0336 V

40. The standard enthalpies of formation of

1, 3-butadiene (g), CO2(g) and H

2O(g) at

298K are –30, –94 and –68 kcal/ mol,

respectively. If the magnitude of resonance

enthalpies of 1,3-butadiene and CO2 are

10 and 20 kcal/mol, respectively, the

enthalpy of combustion of 1, 3-butadiene(g)

at 298K, is (enthalpy of vaporisation of

H2O(l) at 298K = 10 kcal/mol)

(1) –650 kcal / mol (2) +650 kcal / mol

(3) –680 kcal / mol (4) –620 kcal / mol

41. An octahedral complex with no chelate ring

of M+3 with NH3 and NO

2 ligands only have

four M–N linkage and two M–O linkage, then

such complex will show :-

(1) Geometrical isomerism

(2) Linkage isomerism

(3) Optical isomerism

(4) Both (1) and (2)

42.

yellowsolution

Identify (B), and F respectively :-

(1) AgCl , Cl2

(2) NH4Cl , NH

3

(3) Hg2Cl

2 , NH

3(4) CHCl

3 , NH

3

43. KMnO4 is the oxo-salt of the acid of following

oxide :-

(1) MnO (2) Mn2O

7

(3) MnO3

(4) MnO2

0000CT103116004E-10/18



44. E° for the conversion of Ce+4 into Ce+3 is

1.74V. It suggest that :-

(1) Ce+4 is more stable as compare to Ce+3

(2) Ce+4 will tend to change into Ce+3 although

Ce+4 have inert gas configuration

(3) Ce+4 compounds are neither good

oxidising nor good reducing agents

(4) Ce+3 will tend to change into Ce+4 because


45. Which of the following is mixed anhydride :-

(1) ClO2

(2) NO2

(3) ClO3

(4) All of these

46. Which of the following reaction represent the

redox reaction involving water :-

(1) SiCl4(l) + 2H

2O(l) SiO

2(s) + 4HCl(aq.)

(2) H2O(l) + NH

3(aq.) NH

4+(aq.) + OH

–(aq.)

(3) 2F2(g) + 2H

2O(l) 4H+(aq.) + 4F

–(aq.)

+ O2(g)

(4) P4O

10(s) + 6H

2O(l) 4H

3PO

4(aq.)

47. Which of the following species have all the

bond angles of X° and all the bond length of

'Y' Å :-

(1) S2O

32– (2) HCO

3

(3) CO32– (4) N

2O

5

48. Which set of quantum numbers is not

possible for last electron of 'Al' (Z = 13) :-

n l m s

(1) 3 1 –1 –1

2

(2) 3 0 0 1

2

(3) 3 1 0 1

2

(4) 3 1 1 –1

2

49. An ore of metal 'M' Metal oxideRoasting

(After crushing and grinding)

Carbon Reduction

'M' 'M' may be :-

(1) Al (2) Zn

(3) Hg (4) All of these

50. If X(OH) > Y(OH) (acidic strength)

'X' and 'Y' both belong to same group then

select the CORRECT statement :-

(1) Electron gain enthalpy of 'Y' must be

greater than 'X'

(2) Atomic size of 'X' must be greater than 'Y'

(3) O-H bond will be easily broken in case of

hydroxide of 'X'


hydroxide of 'Y'


E-11/180000CT103116004


51. Which of the following reaction will produces

primary alcohol ?

(1) Hydration of propene in the presence of

dilute sulphuric acid

(2) Reaction of propene with borane followed

by water

(3) Reaction of propanone with methyl

magnesium bromide followed by

hydrolysis

(4) Catalylic reduction of butanal

52. Which of the following is not used as

antispetic ?

(1) Soframicine (2) Furacine

(3) Iodoform (4) Prontosil

53. Which of the following is incorrectly

matched ?

(Formation of) (Best synthesis by)

(1) Alkyl fluoride Swarts reaction

(2) Alkyl chloride Darzen process

(3) Alkyl ether Williamson synthesis

(4) Alkyl iodide Wurtz reaction

54. Major product (R) of following reaction is :

NH2

CH COCl3

PyridineP

Br2

CH COOH3

Q

HO3

+

R

(1)

Br

NH2

(2) Br

NH2

Br

Br

(3)

NH2

Br

(4)

NH2

Br

55. Major product (Q) of following reaction is

used to form :

O

KMnO4

KOHP

dil. H SO2 4 Q

(1) Terylene (2) Bakelite

(3) Glyptal (4) Nylon-6,6

0000CT103116004E-12/18



56. Which of the following reaction will not

produce "Aniline"

(1)

NO2

H / Pd2

ethanol(2)

COOH

HN3

H SO2 4

(3)

CN

Na(Hg)C H OH2 5

(4)

C

Br /NaOH2

NH2O

57. Compound CH –C–CH –OH3 2

O

reduces :

(1) Tollen's reagent

(2) NaOH / I2 solution

(3) Fehling solution

(4) All of these

58. By passing vapours of phenol over heated

zinc dust will produce :

(1) Benzoic acid

(2) Quinone

(3) Benzene

(4) Malic acid

59. Major product obtained in following

reaction is :

CH –CH2 3

O N2

Br2hv

(1)

Br

NO2

(2)

Br

NO2

(3)

Br

NO2

(4) Br

NO2

60. Which of the following pyrimidine base

present in RNA ?

(1) Ademine (2) Guanine

(3) Uracil (4) All of these


E-13/180000CT103116004


61. If area of quadrilateral formed by tangents

drawn at ends of latus rectum of hyperbola

2 2

2 2

x y1

a b is equal to square of distance

between centre and one focus of hyperbola,

then e3 is (e is eccentricity of hyperbola)

(1) 2 2 (2) 2

(3) 3 (4) 8

62. Area bounded by curves x y 1 and

y = x + 1 is-

(1) 1

3 sq. unit (2)

8

3 sq. unit

(3) 1

6 sq. unit (4)

2

3 sq. unit

63. Solution of differential equation

2dyx sin y sin y cos y

dx is-

(1) tany = (x – 1) + Ce–x

(2) coty = (x – 1) + Ce–x

(3) tany = (x – 1)ex + C

(4) coty = (x – 1)ex + C

(where C is an arbitrary constant)

64. If n be the number of values of x for which

matrix (x) =

x x 2

2 x x

x 2 x

will be singular,

then det((n)) is (where det(B) denotes

determinant of Matrix B) -

(1) –8 (2) –6 (3) 0 (4) 10

65. A tetrahedron of volume 5 has three of its

vertices at the points A(2,1,–1), B(3,0,1) and

C(2,–1,3). If the fourth vertex D lies on the

y-axis, then sum of ordinates of all possible

points D is-

(1) –1 (2) 0 (3) 1 (4) 2

66. If be a non-real cube root of unity, then

the value of

2 2 2cos {(1 )(1 ) (2 )(2 ) .... (2017 )(2017 )}.2017

is-

(1) –1 (2) 0 (3) 1 (4) 3

2

PART C - MATHEMATICS

0000CT103116004E-14/18



67. Let N be the set of natural numbers greater

than 100. Define the relation R by :

R = {(x,y) N × N : the numbers x and y

have atleast two common divisors}. Then R

is-

(1) Reflexive, Symmetric and transitive

relation

(2) Symmetric, transitive and NOT

Reflexive relation

(3) Reflexive, transitive and NOT

Symmetric relation

(4) Reflexive, Symmetric and NOT

transitive relation

68. If 2017C0 + 2017C1 + 2017C2+......+ 2017C1008

= 2 ( > 0), then remainder when is divided

by 33 is-

(1) 8 (2) 13

(3) 17 (4) 25

69. Let distinct lines L1,L

2 belong to family of

lines (x – 2y – 3) + (x + 3y + 2) = 0 and B1 is

angle bisector of L1 and L

2 which passes

through point A(2,3), then equation of other

bisector of L1 and L2 is ( is a parameter)

(1) x + 4y + 3 = 0

(2) 4x + y – 3 = 0

(3) x + y = 5

(4) 2x – y = 1

70. If

2

2

2 2x a

b cos x aL lim

x a sin cx a

is non-zero

finite (a > 0), then-

(1) L = 2, b = 1, c = 1

(2) 1

L ,b 1,c 12

(3) L 4,b 1,c 1

(4) 1

L ,b 1,c 14

71. The solution of

1

2+cosx + cos2x + cos3x + cos4x = 0 is-

(1)

2n

x ,n I,n 9m9

, m I

(2)

2n

x ,n I,n 9m9

, m I

(3)

n

x ,n I9 2

(4)

2n

x ,n I3 6


E-15/180000CT103116004


72. If

1 1 1 1tan x 2 tan x 2 tan

2,

then sum of value(s) of x is equal to-

(1) 1 (2) –5 (3) –4 (4) 1

2

73. x1,x2........x34 are numbers such that

xi = xi+1 = 150 i {1,2,3,......9} and

xi+1 – xi + 2 = 0 i {10,11,12,......33}, then

median of xi,x2,......x34 is-

(1) 150 (2) 140 (3) 135 (4) 137

74. Let A,B and C are three points on ellipse

2 2x y

125 16

where line joing A & C is parallel

to the x-axis and B is end point of minor axis

whose ordinate is positive then maximum

area of ABC, is-

(1) 12 3 (2) 20

(3) 15 3 (4) 20 3

75. If () be intersection point of linesx – 3y + 2z + 4 = 0 = 2x + y + 4z + 1 and

1x

y z38 3 6

, then ) is-

(1) –2 (2) –1 (3) 0 (4) 2

76. p q q ~ p is-

(1) equivalent to p q

(2) Tautology

(3) Fallacy

(4) Neither tautology nor fallacy

77. Minimum distance between parabola

y2 = 8x and its image with respect to line

x + y + 4 = 0 is-

(1) 2 2 (2) 3 2

(3) 4 2 (4) 5 2

78. Two numbers x and y are chosen at random

from the set of integers {1,2,3,4......15}. The

probability that point (x,y) lies on a line

through (0,0) having slope 2

3 is-

(1) 1

3(2)

1

15(3)

1

21(4)

1

42

79. The value of

1 1 1tan tan tan .....

4 8 8 16 16 32

terms

is equal to-

(1)

5 1

2(2)

3 1

2

(3)

2 1

2(4)

4 1

4

0000CT103116004E-16/18



80. Tangent to a non linear curve y = ƒ(x), at any

point P intersects x-axis and y-axis at A and

B respectively. If normal to the curve

y = ƒ(x) at P intersects y-axis at C such that

AC = BC, ƒ(2) = 3, then equation of curve is-

(1) 6

yx

(2) x2 + y2 = 13

(3) 2y2 = 9x (4) 2y = 3x

81. If

pn n m

3

r 1 p 1 m 1 r 1

r 1 80 , then possible value

of n can be-

(1) 3 (2) 4 (3) 5 (4) 6

82. If in ABC, AB = 4, BC = 6 and AC = 5,

h1,h2,h3 be the length of altitude of from

vertices A,B,C respectively, then value of

1 2 3

1 1 1

h h h is equal to-

(1) 7

15(2)

2 7

15(3)

4 7

15(4)

8 7

15

83.

2

2

2

4 x 6 2

6 9 x 3

2 3 1 x

; (x 0) is not divisible

by-

(1) x (2) x3 (3) 14+ x2 (4) x5

84. Two parallel towers A and B of different

heights are at some distance on same level

ground. If angle of elevation of a point P at

20m height on tower B from a point Q at

10m height on tower A is and is equal to

half the angle of elevation of point R at 50m

height on A from point P on B, then is-

(1) 30º (2) 45º

(3) 15º (4) 60º

85. Radius of circle touching y-axis at point

P(0,2) and circle x2 + y2 = 16 internally-

(1) 5

2(2)

3

2(3)

5

4(4) 2

86. AB,BC are diagonals of adjacent faces of a

rectangular box with its centre at the origin,

its edges parallel to the co-ordiantes axes.

If the angles BOC, COA and AOB are and

respectively, then cos + cos + cos is-

(1) –1 (2) 0

(3) 3

2(4) data insufficient

87. Number of solutions of the equation

x

2

0

6 t 1 nt dt 5|x|, x R0 is-

(1) 5 (2) 4 (3) 2 (4) 3


E-17/180000CT103116004


88. The shaded region in given figure is-

A

B C

(1) A B C (2) C A B

(3) C B C (4) C A B

89. The number of numbers between 1 and 1010

which contains digit 1, is-

(1) 1010 – 910 (2) 1010 – 910 + 1

(3) 109 (4) 10

10 rr

r 0

C 9

90. If ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆr 3i 2j 5k,a 2i j k,b i 3j 2k

and ˆˆ ˆc 2i j 3k such that

r a b c ,

then -

(1)

, ,2

are in A.P

(2) 2 are in A.P

(3) are in A.P

(4)

, ,3

are in G.P

0000CT103116004E-18/18




Test Type : ALL INDIA OPEN TEST Test Pattern : JEE-Main

TEST DATE : 19 - 03 - 2017

TARGET : JEE (MAIN) 2017

LEADER & ENTHUSIAST COURSE

Paper Code : 0000CT103116004Form Number :

CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)

HIN

DI

Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005

+91-744-5156100 [email protected] www.allen.ac.in

Your Target is to secure Good Rank in JEE (Main) 2017

Important Instructions

Do not open this Test Booklet until you are asked to do so.

1. Immediately fill in the form number on this page of the

Test Booklet with Blue/Black Ball Point Pen. Use of pencil

is strictly prohibited.

2. The candidates should not write their Form Number

anywhere else (except in the specified space) on the Test

Booklet/Answer Sheet.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum

marks are 360.

5. There are three parts in the question paper A,B,C

consisting of Physics, Chemistry and Mathematics

having 30 questions in each part of equal weightage.

Each question is allotted 4 (four) marks for correct

response.

6. One Fourth mark will be deducted for indicated incorrect

response of each question. No deduction from the total

score will be made if no response is indicated for an item

in the Answer Sheet.

7. Use Blue/Black Ball Point Pen only for writting

particulars/marking responses on Side–1 and Side 2 of

the Answer Sheet.

Use of pencil is strictly prohibited.

8. No candidate is allowed to carry any textual material,

printed or written, bits of papers, mobile phone any

electronic device etc, except the Identity Card inside the

examination hall/room.

9. Rough work is to be done on the space provided for this

purpose in the Test Booklet only.

10. On completion of the test, the candidate must hand over

the Answer Sheet to the invigilator on duty in the Room/

Hall. However, the candidate are allowed to take away

this Test Booklet with them.

11. Do not fold or make any stray marks on the Answer

Sheet.

1.

2.

3. 3 4. 90360

5. A, B, C 30 4

6.

7.

8.

9.

10.

11.


H-1/350000CT103116004

PART A - PHYSICS

BEWARE OF NEGATIVE MARKING

HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS

1. A charge particle q0 of mass m

0 is projected

along the y-axis at t = 0 from origin with a

velocity V0. If a uniform electron field E

0 also

exists along the x-axis, then the time at

which de-broglie wavelength of the particle

becomes half of the initial value is :-

(1) 0 0

0 0

m v

q E (2) 0 0

0 0

m v2

q E

(3) 0 0

0 0

m v3

q E (4) 0 0

0 0

m v3

q E

2. The charge flowing through a resistor R

varies with time t as Q = 3t – 6t2. The heat

produced in R till the current in it becomes

zero is :-

(1) 3R

4(2)

3R

2

(3) 4R

2(4)

9R

2

1. q0 m0 y

t = 0 V0

E0 x-

(1) 0 0

0 0

m v

q E (2) 0 0

0 0

m v2

q E

(3) 0 0

0 0

m v3

q E (4) 0 0

0 0

m v3

q E

2. R t

Q = 3t – 6t2 R

(1) 3R

4(2)

3R

2

(3) 4R

2(4)

9R

2

0000CT103116004H-2/35


3. A particle moves along a circle with a

constant angular speed . Its displacement,

with respect to this position of the particle

at time t = 0 is plotted against time. The

graph would look like :

(1)

t

S

circular

/

(2)

t

S

circular

2 /

(3)

t

S

sine curve

2 /

(4)

t

S

2 / /

4. A metallic rod is placed in a uniform

electric field. Select the correct option.

A B

E0

(1) Inside the rod there will be an induced

electric field from B to A.

(2) Free electrons will accumulate at the

end B of the rod.

(3) The potential of the end A will be more

than that at B.

(4) The electric field outside the rod will

not change due to the induced charged

in the rod.

3. t = 0

(1)

t

S

circular

/

(2)

t

S

circular

2 /

(3)

t

S

sine curve

2 /

(4)

t

S

2 / /

4.

A B

E0

(1) B A

(2) B (3) A B (4)


H-3/350000CT103116004

5. Calculate energy needed for moving a mass

of 4kg from the centre of the earth to its

surface (in joule), if radius of the earth is

6400 km and acceleration due to gravity at

the surface of the earth is g = 10 m/sec2.

(1) 1.28 × 108 J

(2) 1.28 × 106 J

(3) 2.56 × 108 J

(4) 2.56 × 1010 J

6. A ball of mass 'm' is released from the top

of a smooth movable wedge of mass 'm'.

When the ball collides with the floor,

velocity of the wedge is 'v'. Then the

maximum height attained by the ball after

an elastic collision with the floor is :

(Neglect any edge at the lower end of the

wedge).

45°

msmooth

m

(1)

22v

g(2)

2v

4g

(3)

24v

g(4)

2v

2g

5. 4kg

6400 km

g = 10 m/sec2 (1) 1.28 × 108 J

(2) 1.28 × 106 J

(3) 2.56 × 108 J

(4) 2.56 × 1010 J

6. 'm' 'm'

'v'

(

)

45°

msmooth

m

(1)

22v

g(2)

2v

4g

(3)

24v

g(4)

2v

2g

0000CT103116004H-4/35


7. A particle is acted upon by a force whose

component's variations with time are

shown in diagrams. Then the magnitude of

change in momentum of the particle

in 0.1sec will be :-

Fx

0 t=0.1 sec

30N

Fy

0 t=0.1 sec

80N

Fz

0

t=0.1 sec

–50N

(1) m

2kgsec

(2) m

10kgsec

(3) m

12kgsec

(4) m

5 2 kgsec

8. A steel rod is projecting out

A B

E

F

CD

of rigid wall. The shearing

strength of steel is 345 MN/m2.

The dimensions AB = 5 cm,

BC = BE = 2 cm. The

maximum load that can be

put on the face ABCD is

(neglect bending of the rod)

(g = 10 m/s2)

(1) 3450 kg (2) 1380 kg

(3) 13800 kg (4) 345 kg

7.

0.1 sec

Fx

0 t=0.1 sec

30N

Fy

0 t=0.1 sec

80N

Fz

0

t=0.1 sec

–50N

(1) m

2kgsec

(2) m

10kgsec

(3) m

12kgsec

(4) m

5 2 kgsec

8.

A B

E

F

CD

345 MN/m2 AB = 5 cm, BC = BE = 2 cm

ABCD ()(g = 10 m/s2)(1) 3450 kg (2) 1380 kg(3) 13800 kg (4) 345 kg


H-5/350000CT103116004

9. In a cylindrical container open to the

atmosphere from the top a liquid is filled

upto 10 m depth. Density of the liquid

varies with depth from the surface as

(h) = 100 + 6h2 where h is in meter and

is in kg/m3. The pressure at the bottom of

the container will be : (atmosphere pressure

= 105 Pa, g = 10 m/sec2)

(1) 1.7 × 105 Pa

(2) 1.4 × 105 Pa

(3) 1.6 × 105 Pa

(4) 1.3 × 105 Pa

10. A plane electromagnetic wave of angular

frequency propagates in a poorly

conducting medium of conductivity and

relative permittivity . Find the ratio of

conduction current density and

displacement current density in the

medium.

(1) 0

(2)

0

(3) 0

(4) 0

9.

10 m

(h) = 100 + 6h2

h , kg/m3

(

= 105 Pa, g = 10 m/sec2)

(1) 1.7 × 105 Pa

(2) 1.4 × 105 Pa

(3) 1.6 × 105 Pa

(4) 1.3 × 105 Pa

10.

(1) 0

(2)

0

(3) 0

(4) 0

0000CT103116004H-6/35


11. A screw gauge has some zero error but its

value is unknown. We have two identical

rods. When the first rod is inserted in the

screw, the state of the instrument is shown

by diagram (I). When both the rods are

inserted together in series then the state

is shown by the diagram (II). What is the

zero error of the instrument ?

1 msd = 100 csd = 1 mm :-

12

10

(1) –0.16 mm (2) +0.16 mm

(3) +0.14 mm (4) –0.14 mm

12. A transistor is operating in the active

mode. v1 is potential barrier across base

emitter junction and v2 is potential barrier

across collector base junction. b1 is width

of depletion layer of base emitter junction

and b2 is width of collector base junction.

(1) v1 > v

2, b

1 > b

2

(2) v1 < v

2, b

1 < b

2

(3) v1 > v

2, b

1 < b

2

(4) v1 < v

2, b

1 > b

2

11.

(I)

(II)

1 msd = 100 csd = 1 mm :-

12

10

(1) –0.16 mm (2) +0.16 mm

(3) +0.14 mm (4) –0.14 mm

12. v1

v2

b1 b2

(1) v1 > v2, b1 > b2

(2) v1 < v2, b1 < b2

(3) v1 > v2, b1 < b2

(4) v1 < v2, b1 > b2


H-7/350000CT103116004

13. Inside a closed furnace held at a

temperature of 400 K, we have a black body.

A hole of area 10 cm2 is opened in the

furnace so that sunlight starts falling on

black body. The intensity of sunlight is

2000 W/m2. In the steady state

(1) The black body and furnace can't be

distinguished.

(2) The black body will appear darker than

the furnace

(3) The black body will appear brighter

than the furnace

(4) Information insufficient

14. A thin rectangular magnet suspended

freely has a period of oscillation equal to

T. Now it is broken into two equal halves

(each having half of the original length) and

one piece is made to oscillate freely in the

same field. If its period of oscillation is T',

the ratio T'/T is :-

(1) 1

2 2(2)

1

2

(3) 2 (4) 1

4

13. 400 K

10 cm2

2000 W/m2

(1)

(2)

(3)

(4)

14.

T

T'

T'/T

(1) 1

2 2(2)

1

2

(3) 2 (4) 1

4

0000CT103116004H-8/35


15. For a GPS navigation to track a mobile

device, we use :-

(1) 3-satellites one for latitude, another for

longitude and third for altitude

(2) 4-satellites one for altitude and 3 for

position on ground.

(3) 2-satellites one for position on ground

on for altitude

(4) 1 satellite only.

16. Identify the terminals on this BJT, and alsothe type of BJT it is (NPN or PNP): (Startingfrom left). The multimeter reads resistanceand the black terminal is connected to thenegative terminal of the battery :-

AV

AV

OFF

com

AV

AV

OFF

com

0.623 0.625

RedRed

BlackBlack

(1) Emitter base collector NPN(2) Emitter base collector PNP(3) Collector base emitter NPN(4) Collector base emitter PNP

15. GPS navigation (1) 3-

(2) 4-

(3) 2-

(4) 16. BJT

BJT (NPN PNP)

AV

AV

OFF

com

AV

AV

OFF

com

0.623 0.625

RedRed

BlackBlack

(1) NPN

(2) PNP

(3) NPN

(4) PNP


H-9/350000CT103116004

17. A physical quantity A is dependent on

other four physical quantities p, q, r and s

as given below 2 3

pqA

r s . The percentage

error of measurement in p, q, r and s 1%,

3%, 0.5% and 0.33% respectively, then the

maximum percentage error in A is :

(1) 2% (2) 0%

(3) 4% (4) 3%

18. Three rods AB, BC and AC having thermal

resistances of 10 units, 10 units and 20 units,

respectively, are connected as shown in the

figure. Ends A and C are maintained at

constant temperatures of 100°C and 0°C,

respectively. The rate at which the heat is

crossing junction B is :

A

B

C



17. A p, q, r s

2 3

pqA

r s

p, q, r s 1%, 3%,

0.5% 0.33% A

(1) 2% (2) 0%

(3) 4% (4) 3%

18. AB, BC AC

10 10 20

A C 100°C

0°C

B

A

B

C



0000CT103116004H-10/35


19. A wire carrying a current I is placed inside

a uniform magnetic field 0ˆB B k

. The

shape of the wire is parabolic and hasequation Y = 2x – x2. The force on the wirewill be :

A

y

Y

O

z× × × × × ×

× × ×

× × ×× × × × × ×

i i





20. There is a long cylindrical pipe wire ofinternal radius r and external radius Rcarrying current i along its length. Thevariation of magnetic field with distancefrom the axis of the wire can be representedby the :-

(1)

y-axis

r R x-axis

(2)

y-axis

rRx-axis

(3)

y-axis

r Rx-axis

B

(4)

y-axis

rR x-axis

B

19. I

0ˆB B k

Y = 2x – x2

A

y

Y

O

z× × × × × ×

× × ×

× × ×× × × × × ×

i i

(1) F = 2B0i,

(2) F = 2B0i,

(3) F = 4B0i,

(4) F = 4B0i,

20. r R i

(1)

y-axis

r R x-axis

(2)

y-axis

rRx-axis

(3)

y-axis

r Rx-axis

B

(4)

y-axis

rR x-axis

B


H-11/350000CT103116004

21. In a series R-L-C AC circuit, for a

particular value of R, L and C power

supplied by the source is P at resonance. If

the value of inductance is halved, then the

power from the source again at resonance

is P'. Then :

(1) P'

P2

(2) P = 2P'

(3) P = 4P' (4) P = P'

22. Carefully analyses the diagram and choose

the correct option :

(i) PlaneWave

Thinlens

Focus

Sphericalwave

(ii) PlaneWave

Thinlens

Focus

Sphericalwave

(iii) PlaneWave

Thinlens

Focus

Sphericalwave

(iv) PlaneWave

Thinlens

Focus

Sphericalwave

(1) i and ii are true

(2) i and iii are true

(3) i and iv are true

(4) ii and iv are true

21. R-L-C AC R, L C

P

P'

(1) P'

P2

(2) P = 2P'

(3) P = 4P' (4) P = P'

22.

(i) PlaneWave

Thinlens

Focus

Sphericalwave

(ii) PlaneWave

Thinlens

Focus

Sphericalwave

(iii) PlaneWave

Thinlens

Focus

Sphericalwave

(iv) PlaneWave

Thinlens

Focus

Sphericalwave

(1) i ii

(2) i iii

(3) i iv

(4) ii iv

0000CT103116004H-12/35


23. A point source of light is placed at a depth

h = 0.5 m below the surface of a liquid

5

4

. Then, the fraction of light energy that

escape directly from the liquid surface is :-

(1) 0.1 (2) 0.2 (3) 0.3 (4) 0.4

24. Two radioactive elements R and Sdisintegrate as

R P + ; R = 4.5 × 10–3 years–1

S P + ; S = 3 × 10–3 years–1

Starting with number of atoms of R and Sin the ratio of 2 : 1, this ratio after the lapseof three half lives of R will be :

(1) 3 : 2 (2) 1 : 3 (3) 1 : 1 (4) 2 : 1

25. A hollow conducting sphere of inner radius

R and outer radius 2R is given a charge Q

as shown in the figure, then the :

R

2R

A

B

C

+Q

O

(1) potential at A and B is different

(2) potential at O and B is different

(3) potential at O and C is different

(4) potential at A, B, C and O is same

23. 5

4

h = 0.5m (1) 0.1 (2) 0.2

(3) 0.3 (4) 0.4

24. R S

R P + ; R = 4.5 × 10–3 years–1

S P + ; S = 3 × 10–3 years–1

R S 2 : 1

R

(1) 3 : 2 (2) 1 : 3 (3) 1 : 1 (4) 2 : 1

25. R 2R

Q

R

2R

A

B

C

+Q

O

(1) A B

(2) O B

(3) O C

(4) A, B, C O


H-13/350000CT103116004

26. A liquid is kept in a cylindrical vessel.

When the vessel is rotated about its axis,

the liquid rises at its sides. If the radius of

the vessel is 0.05 m and the speed of

rotation is 2 revolutions per second, the

difference in the heights of the liquid at the

centre and at the sides of the vessels will

be (take g = 10 ms–2 and 2 = 10)

(1) 2 cm

(2) 4 cm

(3) 1 cm

(4) 8 cm

27. A uniform narrow 1.95 m long pipe is open

at both ends. It resonates at two successive

harmonic of frequency 275 Hz and 330 Hz.

The speed of sound in the tube is :

(1) 200 m/s

(2) 205 m/s

(3) 210 m/s

(4) 214.5 m/s

26.

0.05 m

2

(g = 10 ms–2 2 = 10)

(1) 2 cm

(2) 4 cm

(3) 1 cm

(4) 8 cm

27. 1.95 m

275 Hz 330 Hz

(1) 200 m/s

(2) 205 m/s

(3) 210 m/s

(4) 214.5 m/s

0000CT103116004H-14/35


28. In the given figure a ring of mass m is kept

on a horizontal surface while a body of

equal mass 'm' attached through a string,

which is wounded on the ring. When the

system is released the ring rolls without

slipping. Consider the following

statements and choose the correct option.

m

m

(i) acceleration of the centre of mass of ring

is g

3

(ii) acceleration of the hanging particle is

2g

3

(iii) frictional force (on the ring) acts along

forward direction

(iv) frictional force (on the ring) acts along

backward direction

(1) statement (i) and (ii) only

(2) statement (ii) and (iii) only

(3) statement (iii) and (iv) only

(4) none of these

28. m

m

m

m

(i) g

3

(ii) 2g

3

(iii) ()

(iv) ()

(1) (i) (ii)

(2) (ii) (iii)

(3) (iii) (iv)

(4)


H-15/350000CT103116004

29. A ladder AP of length 5 m is inclined to a

vertical wall is slipping over a horizontalsurface with velocity of 2 m/s, when A is at

a distance 3m from ground what is thevelocity of C.M. at this moment :

(1) 1.25 m/s (2) 0 m/s

(3) 1 m/s (4) 2 m/s

30. Two identical adiabatic vessels are filled

with oxygen at pressure P1 and P

2 (P

1 > P

2).

The vessels are interconnected with each

other by a nonconducting pipe. If U01

andU

02 denote initial internal energy of oxygen

in first and second vessel respectively and

1fU and

2fU denote final internal energy

values, than :

(1) 1 2

01 1f f

02 2

U P, U U

U P

(2) 1 2

01 2f f

02 1

U P, U U

U P

(3) 1 2

01 2f f

02 1

U P, U U

U P

(4) 1 2

01 1f f

02 2

U P, U U

U P

29. 5 m

AP 2 m/s

A 3m

(1) 1.25 m/s (2) 0 m/s

(3) 1 m/s (4) 2 m/s

30. P1

P2 (P

1 > P

2)

U

01 U

02

1f

U 2f

U

(1) 1 2

01 1f f

02 2

U P, U U

U P

(2) 1 2

01 2f f

02 1

U P, U U

U P

(3) 1 2

01 2f f

02 1

U P, U U

U P

(4) 1 2

01 1f f

02 2

U P, U U

U P

0000CT103116004H-16/35


PART B - CHEMISTRY

31. A solid element, (metal) crystallises in

ABABAB..... ...type packing in three

dimension. If the density of the element and

its atomic radius are 5.0 gm/cm3 and

100 2pm , the atomic mass of the element

is (NA = 6 × 1023)

(1) 48 (2) 72 (3) 96 (4) 32

32. In 20 ml 0.4 M-HA solution, 80 ml water is

added. Assuming volume to be additive, the

pH of final solution is

(Ka of HA = 4 × 10–7 , log2 = 0.3)

(1) 4.30 (2) 3.75 (3) 3.40 (4) 3.70

33. Which of the following aqueous solution has

highest freezing point ?

(1) 0.2 m-urea solution

(2) 0.15 m-NaCl solution

(3) 0.1 m CH3COOH solution

(4) 0.12 m-Ca(NO3)2 solution

34. 5 moles of an ideal gas is expanded from

(10L, 300K) to (20L, 300K) against a

constant external pressure of 1.0 bar. The

only incorrect value of physical quantities

for this change in state of the system, is-

(1) U = 0 (2) H = 0

(3) S = 0 (4) T = 0

31. () ABABAB........

5.0 gm/cm3

100 2pm ,

(NA = 6 × 1023)

(1) 48 (2) 72 (3) 96 (4) 32

32. 20 ml 0.4 M-HA 80 ml

pH (HA Ka = 4 × 10–7 , log2 = 0.3)

(1) 4.30 (2) 3.75 (3) 3.40 (4) 3.70

33. ?(1) 0.2 m- (2) 0.15 m-NaCl (3) 0.1 m CH

3COOH

(4) 0.12 m-Ca(NO3)2

34. 5 1.0 bar (10L, 300K) (20L, 300K) -(1) U = 0 (2) H = 0

(3) S = 0 (4) T = 0


H-17/350000CT103116004

35. For a first order reaction, the rate constant

is 0.04 min–1 at 27ºC and 0.08min–1 at 37ºC.

The activation energy of reaction is

(ln2 = 0.7)

(1) 13.02 kcal /mol (2) 139.86 kcal /mol

(3) 54.12 kcal /mol (4) 13020 kcal /mol

36. 20 gm iron pyrite, FeS2, is roasted

completely and SO2 gas produced is absorbed

completely in 400 ml NaOH solution. If only

50% NaOH is used in the reaction, the

molarity of NaOH solution was

(1) 5

M3

(2) 10

M3

(3) 5

M6

(4) 20

M3

37. Fe(OH)3 sol is prepared by the hydrolysis of

FeCl3 in a hot water. If the sol is electrolysed

using inert electrodes, the only correct

statement is -

(1) Coagulation will occur near anode

(2) Cl2 gas may be cathode product

(3) H2 gas may be anode product

(4) O2 gas may be anode product

35. 27ºC

0.04 min–1 37ºC 0.08min–1

(ln2 = 0.7)

(1) 13.02 kcal /mol (2) 139.86 kcal /mol

(3) 54.12 kcal /mol (4) 13020 kcal /mol

36. 20 gm FeS2

SO2 400 ml NaOH

50% NaOH NaOH

-

(1) 5

M3

(2) 10

M3

(3) 5

M6

(4) 20

M3

37. Fe(OH)3 FeCl

3

-

(1)

(2) Cl2

(3) H2

(4) O2

0000CT103116004H-18/35


38. Certain mass of an ideal gas is heated at

constant volume. Which of the following

parameter of gas will increase ?

(1) Density

(2) Mean free path

(3) Collision frequency

(4) Molar mass of gas

39. Eºcell

for the cell :

Pt(s) |H2(g)|HCOOH(aq.)||CH

3COOH(aq.)|H

2(g)|Pt(s)

at 25ºC is (Ka of HCOOH = 2.4 × 10–4, K

a

of CH3COOH = 1.8 × 10–5, log2 = 0.3, log 0.48,

2.303 298 R0.06

F

)

(1) 0.0672V (2) –0.0672V

(3) –0.1344 V (4) –0.0336 V

40. The standard enthalpies of formation of

1, 3-butadiene (g), CO2(g) and H

2O(g) at

298K are –30, –94 and –68 kcal/ mol,

respectively. If the magnitude of resonance

enthalpies of 1,3-butadiene and CO2 are

10 and 20 kcal/mol, respectively, the

enthalpy of combustion of 1, 3-butadiene(g)

at 298K, is (enthalpy of vaporisation of

H2O(l) at 298K = 10 kcal/mol)

(1) –650 kcal / mol (2) +650 kcal / mol

(3) –680 kcal / mol (4) –620 kcal / mol

38. (parameter) ?(1) (2) (3)

(4)

39. 25ºC Pt(s) |H

2(g)|HCOOH(aq.)||CH

3COOH(aq.)|H

2(g)|Pt(s)

Eºcell

(HCOOH Ka = 2.4 × 10–4,

CH3COOH K

a = 1.8 × 10–5, log2 = 0.3,

log 0.48, 2.303 298 R

0.06F

)

(1) 0.0672V (2) –0.0672V

(3) –0.1344 V (4) –0.0336 V

40. 298K 1, 3-(g), CO2(g) H

2O(g)

–30, –94

–68 kcal/ mol 1,3-CO2

10

20 kcal/mol 298K 1, 3-

(g) (298K H2O(l)

= 10 kcal/mol )

(1) –650 kcal / mol (2) +650 kcal / mol

(3) –680 kcal / mol (4) –620 kcal / mol


H-19/350000CT103116004

41. An octahedral complex with no chelate ring

of M+3 with NH3 and NO

2 ligands only have

four M–N linkage and two M–O linkage, then

such complex will show :-

(1) Geometrical isomerism

(2) Linkage isomerism

(3) Optical isomerism

(4) Both (1) and (2)

42.

yellowsolution

Identify (B), and F respectively :-

(1) AgCl , Cl2

(2) NH4Cl , NH

3

(3) Hg2Cl

2 , NH

3(4) CHCl

3 , NH

3

43. KMnO4 is the oxo-salt of the acid of following

oxide :-

(1) MnO (2) Mn2O

7

(3) MnO3

(4) MnO2

41. NH3 NO

2 M+3

M–N M–O :-(1) (2) (3)

(4) (1) (2)

42.

(HCl)

(B) F :-

(1) AgCl , Cl2

(2) NH4Cl , NH

3

(3) Hg2Cl

2 , NH

3(4) CHCl

3 , NH

3

43. KMnO4 ,

:-

(1) MnO (2) Mn2O

7

(3) MnO3

(4) MnO2

0000CT103116004H-20/35


44. E° for the conversion of Ce+4 into Ce+3 is

1.74V. It suggest that :-

(1) Ce+4 is more stable as compare to Ce+3

(2) Ce+4 will tend to change into Ce+3 although


(3) Ce+4 compounds are neither good

oxidising nor good reducing agents

(4) Ce+3 will tend to change into Ce+4 because


45. Which of the following is mixed anhydride :-

(1) ClO2

(2) NO2

(3) ClO3

(4) All of these

46. Which of the following reaction represent the

redox reaction involving water :-

(1) SiCl4(l) + 2H

2O(l) SiO

2(s) + 4HCl(aq.)

(2) H2O(l) + NH

3(aq.) NH

4+(aq.) + OH

–(aq.)

(3) 2F2(g) + 2H

2O(l) 4H+(aq.) + 4F

–(aq.)

+ O2(g)

(4) P4O

10(s) + 6H

2O(l) 4H

3PO

4(aq.)

47. Which of the following species have all the

bond angles of X° and all the bond length of

'Y' Å :-

(1) S2O

32– (2) HCO

3

(3) CO32– (4) N

2O

5

44. Ce+4 Ce+3 E°, 1.74V

:-

(1) Ce+3 Ce+4

(2) Ce+4 Ce+4, Ce+3

(3) Ce+4

(4) Ce+3Ce+4 Ce+4

45. :-

(1) ClO2

(2) NO2

(3) ClO3

(4)

46.

:-

(1) SiCl4(l) + 2H

2O(l) SiO

2(s) + 4HCl(aq.)

(2) H2O(l) + NH

3(aq.) NH

4+(aq.) + OH

–(aq.)

(3) 2F2(g) + 2H

2O(l) 4H+(aq.) + 4F

–(aq.)

+ O2(g)

(4) P4O

10(s) + 6H

2O(l) 4H

3PO

4(aq.)

47. X°

'Y' Å :-

(1) S2O

32– (2) HCO

3

(3) CO32– (4) N

2O

5


H-21/350000CT103116004

48. Which set of quantum numbers is not

possible for last electron of 'Al' (Z = 13) :-

n l m s

(1) 3 1 –1 –1

2

(2) 3 0 0 1

2

(3) 3 1 0 1

2

(4) 3 1 1 –1

2

49. An ore of metal 'M' Metal oxideRoasting

(After crushing and grinding)

Carbon Reduction

'M' 'M' may be :-

(1) Al (2) Zn

(3) Hg (4) All of these

50. If X(OH) > Y(OH) (acidic strength)

'X' and 'Y' both belong to same group then

select the CORRECT statement :-

(1) Electron gain enthalpy of 'Y' must be

greater than 'X'

(2) Atomic size of 'X' must be greater than 'Y'


hydroxide of 'X'


hydroxide of 'Y'

48. 'Al' (Z = 13) :-

n l m s

(1) 3 1 –1 –1

2

(2) 3 0 0 1

2

(3) 3 1 0 1

2

(4) 3 1 1 –1

2

49. 'M'

(

)

'M' 'M' :-(1) Al (2) Zn

(3) Hg (4)

50. X(OH) > Y(OH) ()

'X' 'Y'

:-

(1) 'Y' 'X'

(2) 'X' 'Y'

(3) 'X' O-H

(4) 'Y' O-H

0000CT103116004H-22/35


51. Which of the following reaction will produces

primary alcohol ?

(1) Hydration of propene in the presence of

dilute sulphuric acid

(2) Reaction of propene with borane followed

by water

(3) Reaction of propanone with methyl

magnesium bromide followed by

hydrolysis

(4) Catalylic reduction of butanal

52. Which of the following is not used as

antispetic ?

(1) Soframicine (2) Furacine

(3) Iodoform (4) Prontosil

53. Which of the following is incorrectly

matched ?

(Formation of) (Best synthesis by)

(1) Alkyl fluoride Swarts reaction

(2) Alkyl chloride Darzen process

(3) Alkyl ether Williamson synthesis

(4) Alkyl iodide Wurtz reaction

51.

(1)

(2)

(3)

(4)

52.

(1) (2)

(3) (4)

53.

(1)

(2)

(3)

(4)


H-23/350000CT103116004

54. Major product (R) of following reaction is :

NH2

CH COCl3

PyridineP

Br2

CH COOH3

Q

HO3

+

R

(1)

Br

NH2

(2) Br

NH2

Br

Br

(3)

NH2

Br

(4)

NH2

Br

55. Major product (Q) of following reaction is

used to form :

O

KMnO4

KOHP

dil. H SO2 4 Q

(1) Terylene (2) Bakelite

(3) Glyptal (4) Nylon-6,6

54. (R)

NH2

CH COCl3

PyridineP

Br2

CH COOH3

Q

HO3

+

R

(1)

Br

NH2

(2) Br

NH2

Br

Br

(3)

NH2

Br

(4)

NH2

Br

55. (Q)

O

KMnO4

KOHP

dil. H SO2 4 Q

(1) (2)

(3) (4) -6,6

0000CT103116004H-24/35


56. Which of the following reaction will not

produce "Aniline"

(1)

NO2

H / Pd2

ethanol(2)

COOH

HN3

H SO2 4

(3)

CN

Na(Hg)C H OH2 5

(4)

C

Br /NaOH2

NH2O

57. Compound CH –C–CH –OH3 2

O

reduces :

(1) Tollen's reagent

(2) NaOH / I2 solution

(3) Fehling solution

(4) All of these

58. By passing vapours of phenol over heated

zinc dust will produce :

(1) Benzoic acid

(2) Quinone

(3) Benzene

(4) Malic acid

56. " "

(1)

NO2

H / Pd2

ethanol(2)

COOH

HN3

H SO2 4

(3)

CN

Na(Hg)C H OH2 5

(4)

C

Br /NaOH2

NH2O

57. CH –C–CH –OH3 2

O

(1)

(2) NaOH / I2

(3)

(4)

58.

(1)

(2)

(3)

(4)


H-25/350000CT103116004

59. Major product obtained in following

reaction is :

CH –CH2 3

O N2

Br2hv

(1)

Br

NO2

(2)

Br

NO2

(3)

Br

NO2

(4) Br

NO2

60. Which of the following pyrimidine base

present in RNA ?

(1) Ademine (2) Guanine

(3) Uracil (4) All of these

59.

CH –CH2 3

O N2

Br2hv

(1)

Br

NO2

(2)

Br

NO2

(3) Br

NO2

(4) Br

NO2

60. RNA

(1) (2)

(3) (4)

0000CT103116004H-26/35


PART C - MATHEMATICS

61. If area of quadrilateral formed by tangents

drawn at ends of latus rectum of hyperbola

2 2

2 2

x y1

a b is equal to square of distance

between centre and one focus of hyperbola,

then e3 is (e is eccentricity of hyperbola)

(1) 2 2 (2) 2

(3) 3 (4) 8

62. Area bounded by curves x y 1 and

y = x + 1 is-

(1) 1

3 sq. unit (2)

8

3 sq. unit

(3) 1

6 sq. unit (4)

2

3 sq. unit

63. Solution of differential equation


dx is-

(1) tany = (x – 1) + Ce–x

(2) coty = (x – 1) + Ce–x

(3) tany = (x – 1)ex + C

(4) coty = (x – 1)ex + C

(where C is an arbitrary constant)

61. 2 2

2 2

x y1

a b

e3 (e )

(1) 2 2 (2) 2

(3) 3 (4) 8

62. x y 1 y = x + 1

-

(1) 1

3 (2)

8

3

(3) 1

6 (4)

2

3

63.


dx -

(1) tany = (x – 1) + Ce–x

(2) coty = (x – 1) + Ce–x

(3) tany = (x – 1)ex + C

(4) coty = (x – 1)ex + C

(C )


H-27/350000CT103116004

64. If n be the number of values of x for which

matrix (x) =

x x 2

2 x x

x 2 x

will be singular,

then det((n)) is (where det(B) denotes

determinant of Matrix B) -

(1) –8 (2) –6 (3) 0 (4) 10

65. A tetrahedron of volume 5 has three of its

vertices at the points A(2,1,–1), B(3,0,1) and

C(2,–1,3). If the fourth vertex D lies on the

y-axis, then sum of ordinates of all possible

points D is-

(1) –1 (2) 0

(3) 1 (4) 2

66. If be a non-real cube root of unity, then

the value of

2 2 2cos {(1 )(1 ) (2 )(2 ) .... (2017 )(2017 )}.2017

is-

(1) –1 (2) 0

(3) 1 (4) 3

2

64. n, x (x)

=

x x 2

2 x x

x 2 x

det((n))

(det(B), B) -

(1) –8 (2) –6 (3) 0 (4) 10

65. 5

A(2,1,–1), B(3,0,1) C(2,–1,3)

D, y-

D -

(1) –1 (2) 0

(3) 1 (4) 2

66.

2 2 2cos {(1 )(1 ) (2 )(2 ) .... (2017 )(2017 )}.2017

-

(1) –1 (2) 0

(3) 1 (4) 3

2

0000CT103116004H-28/35


67. Let N be the set of natural numbers greater

than 100. Define the relation R by :

R = {(x,y) N × N : the numbers x and y

have atleast two common divisors}. Then R

is-

(1) Reflexive, Symmetric and transitive

relation

(2) Symmetric, transitive and NOT

Reflexive relation

(3) Reflexive, transitive and NOT

Symmetric relation

(4) Reflexive, Symmetric and NOT

transitive relation

68. If 2017C0 + 2017C1 + 2017C2+......+ 2017C1008

= 2 ( > 0), then remainder when is divided

by 33 is-

(1) 8 (2) 13

(3) 17 (4) 25

69. Let distinct lines L1,L

2 belong to family of

lines (x – 2y – 3) + (x + 3y + 2) = 0 and B1 is

angle bisector of L1 and L

2 which passes

through point A(2,3), then equation of other

bisector of L1 and L2 is ( is a parameter)

(1) x + 4y + 3 = 0

(2) 4x + y – 3 = 0

(3) x + y = 5

(4) 2x – y = 1

67. N, 100 :R = {(x,y) N × N : x y } R R

(1)

(2)

(3)

(4)

68. 2017C0 + 2017C1 + 2017C2+......+ 2017C1008

= 2 ( > 0) 33 -(1) 8 (2) 13

(3) 17 (4) 25

69. L1,L2 (x – 2y – 3) +

(x + 3y + 2) = 0 B1 L1 L2 A(2,3)L1 L2 ( )

(1) x + 4y + 3 = 0

(2) 4x + y – 3 = 0

(3) x + y = 5

(4) 2x – y = 1


H-29/350000CT103116004

70. If

2

2

2 2x a

b cos x aL lim

x a sin cx a

is non-zero

finite (a > 0), then-

(1) L = 2, b = 1, c = 1

(2) 1L ,b 1,c 1

2

(3) L 4,b 1,c 1

(4) 1

L ,b 1,c 14

71. The solution of

1

2+cosx + cos2x + cos3x + cos4x = 0 is-

(1)

2n

x ,n I,n 9m9

, m I

(2)

2n

x ,n I,n 9m9

, m I

(3)

n

x ,n I9 2

(4)

2n

x ,n I3 6

70.

2

2

2 2x a

b cos x aL lim

x a sin cx a

(a > 0)

(1) L = 2, b = 1, c = 1

(2) 1

L ,b 1,c 12

(3) L 4,b 1,c 1

(4) 1

L ,b 1,c 14

71.1

2+cosx + cos2x + cos3x + cos4x = 0

-

(1)

2n

x ,n I,n 9m9

, m I

(2)

2n

x ,n I,n 9m9

, m I

(3)

n

x ,n I9 2

(4)

2n

x ,n I3 6

0000CT103116004H-30/35


72. If


2,

then sum of value(s) of x is equal to-

(1) 1 (2) –5 (3) –4 (4) 1

2

73. x1,x2........x34 are numbers such that

xi = xi+1 = 150 i {1,2,3,......9} and

xi+1 – xi + 2 = 0 i {10,11,12,......33}, then

median of xi,x2,......x34 is-

(1) 150 (2) 140 (3) 135 (4) 137

74. Let A,B and C are three points on ellipse

2 2x y

125 16

where line joing A & C is parallel

to the x-axis and B is end point of minor axis

whose ordinate is positive then maximum

area of ABC, is-

(1) 12 3 (2) 20

(3) 15 3 (4) 20 3

75. If () be intersection point of linesx – 3y + 2z + 4 = 0 = 2x + y + 4z + 1 and

1x

y z38 3 6

, then ) is-

(1) –2 (2) –1 (3) 0 (4) 2

72.


2

x

(1) 1 (2) –5 (3) –4 (4) 1

2

73. x1,x

2........x

34

xi = x

i+1 = 150 i {1,2,3,......9}

xi+1

– xi + 2 = 0 i {10,11,12,......33}

xi,x2,......x34

(1) 150 (2) 140 (3) 135 (4) 137

74. A,B C

2 2x y

125 16

A C

x B ABC -

(1) 12 3 (2) 20

(3) 15 3 (4) 20 3

75. () x – 3y + 2z + 4 = 0

= 2x + y + 4z + 1

1x

y z38 3 6

) -

(1) –2 (2) –1 (3) 0 (4) 2


H-31/350000CT103116004

76. p q q ~ p is-

(1) equivalent to p q

(2) Tautology

(3) Fallacy

(4) Neither tautology nor fallacy

77. Minimum distance between parabola

y2 = 8x and its image with respect to line

x + y + 4 = 0 is-

(1) 2 2 (2) 3 2

(3) 4 2 (4) 5 2

78. Two numbers x and y are chosen at random

from the set of integers {1,2,3,4......15}. The

probability that point (x,y) lies on a line

through (0,0) having slope 2

3 is-

(1) 1

3(2)

1

15(3)

1

21(4)

1

42

79. The value of

1 1 1tan tan tan .....

4 8 8 16 16 32

terms

is equal to-

(1)

5 1

2(2)

3 1

2

(3)

2 1

2(4)

4 1

4

76. p q q ~ p

(1) p q (2) (3) (4)

77. y2 = 8x x + y + 4 = 0

(1) 2 2 (2) 3 2

(3) 4 2 (4) 5 2

78. {1,2,3,4......15} x y (x,y) (0,0) 2

3

(1) 1

3(2)

1

15(3)

1

21(4)

1

42

79.1 1 1

tan tan tan .....4 8 8 16 16 32

(1)

5 1

2(2)

3 1

2

(3)

2 1

2(4)

4 1

4

0000CT103116004H-32/35


80. Tangent to a non linear curve y = ƒ(x), at any

point P intersects x-axis and y-axis at A and

B respectively. If normal to the curve

y = ƒ(x) at P intersects y-axis at C such that

AC = BC, ƒ(2) = 3, then equation of curve is-

(1) 6

yx

(2) x2 + y2 = 13

(3) 2y2 = 9x (4) 2y = 3x

81. If

pn n m

3

r 1 p 1 m 1 r 1

r 1 80 , then possible value

of n can be-

(1) 3 (2) 4 (3) 5 (4) 6

82. If in ABC, AB = 4, BC = 6 and AC = 5,

h1,h2,h3 be the length of altitude of from

vertices A,B,C respectively, then value of

1 2 3

1 1 1

h h h is equal to-

(1) 7

15(2)

2 7

15(3)

4 7

15(4)

8 7

15

83.

2

2

2

4 x 6 2

6 9 x 3

2 3 1 x

; (x 0) is not divisible

by-

(1) x (2) x3 (3) 14+ x2 (4) x5

80. y = ƒ(x) P x-y-A B y = ƒ(x) P y- C AC = BC, ƒ(2) = 3 -

(1) 6

yx

(2) x2 + y2 = 13

(3) 2y2 = 9x (4) 2y = 3x

81.

pn n m

3

r 1 p 1 m 1 r 1

r 1 80 n

-(1) 3 (2) 4 (3) 5 (4) 6

82. ABC , AB = 4, BC = 6 AC = 5,

A,B,C h1,h2,h3

1 2 3

1 1 1

h h h -

(1) 7

15(2)

2 7

15(3)

4 7

15(4)

8 7

15

83.

2

2

2

4 x 6 2

6 9 x 3

2 3 1 x

; (x 0)

-(1) x (2) x3 (3) 14+ x2 (4) x5


H-33/350000CT103116004

84. Two parallel towers A and B of different

heights are at some distance on same level

ground. If angle of elevation of a point P at

20m height on tower B from a point Q at

10m height on tower A is and is equal to

half the angle of elevation of point R at 50m

height on A from point P on B, then is-

(1) 30º (2) 45º

(3) 15º (4) 60º

85. Radius of circle touching y-axis at point

P(0,2) and circle x2 + y2 = 16 internally-

(1) 5

2(2)

3

2(3)

5

4(4) 2

86. AB,BC are diagonals of adjacent faces of a

rectangular box with its centre at the origin,

its edges parallel to the co-ordiantes axes.

If the angles BOC, COA and AOB are and

respectively, then cos + cos + cos is-

(1) –1 (2) 0

(3) 3

2(4) data insufficient

87. Number of solutions of the equation

x

2

0

6 t 1 nt dt 5|x|, x R0 is-

(1) 5 (2) 4 (3) 2 (4) 3

84. A B A 10 Q B 20P B P A 50 R

(1) 30º (2) 45º

(3) 15º (4) 60º

85. y-P(0,2) x2 + y2 = 16 -

(1) 5

2(2)

3

2(3)

5

4(4) 2

86. AB,BC BOC, COA AOB

cos + cos + cos -(1) –1 (2) 0

(3) 3

2(4)

87.

x

2

0

6 t 1 nt dt 5|x|, x R0

-

(1) 5 (2) 4 (3) 2 (4) 3

0000CT103116004H-34/35


88. The shaded region in given figure is-

A

B C

(1) A B C (2) C A B

(3) C B C (4) C A B

89. The number of numbers between 1 and 1010

which contains digit 1, is-

(1) 1010 – 910 (2) 1010 – 910 + 1

(3) 109 (4) 10

10 rr

r 0

C 9

90. If ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆr 3i 2j 5k,a 2i j k,b i 3j 2k

and ˆˆ ˆc 2i j 3k such that

r a b c ,

then -

(1)

, ,2

are in A.P

(2) 2 are in A.P

(3) are in A.P

(4)

, ,3

are in G.P

88. -

A

B C

(1) A B C (2) C A B

(3) C B C (4) C A B

89. 1 1010 1-

(1) 1010 – 910 (2) 1010 – 910 + 1

(3) 109 (4) 10

10 rr

r 0

C 9

90. ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆr 3i 2j 5k,a 2i j k,b i 3j 2k

ˆˆ ˆc 2i j 3k

r a b c

(1)

, ,2

(2) 2

(3)

(4)

, ,3


H-35/350000CT103116004

(Academic Session : 2016 - 2017) LEADER & ENTHUSIAST COURSE · 2018-10-21 · ALL INDIA OPEN...

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Transcript of (Academic Session : 2016 - 2017) LEADER & ENTHUSIAST COURSE · 2018-10-21 · ALL INDIA OPEN...