IIT Full Test 2 Paper I_Test

7/29/2019 IIT Full Test 2 Paper I_Test

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IIT-JEE Full Test 3 (Paper I) A

CHEMISTRY

SECTION I

Single Correct Choice Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE iscorrect.

1. For reaction,2 2 4

2NO (g) N O (g) ,2 4p,m (N O )

C 2x 6xT ,2p,m (NO )

C x 2xT ,o

(1)H at T1 = +x kcal / mole then o(2)H at T2 = ?

(A) x (1 + 2T2 2T1) (B) x + xT2 xT1 (C) x (1 + T22 T1

2) (D) x (1 T2 T1)

2. What intermediate is expected to involve in the reaction?

HBr

H

OTsH

Br

(A)

H

H

(B)

H

(C) (D) None of these

3. H2A, is a weak dibasic acid with K1(H2A) = 2 103 and K2(H2A) = 2 10

7. Similarly, H2B is also a weak dibasic acid with K1(H2B) = 3 102 and K2 (H2B) = 3 10

5. The stability of HA with respect to HB in their respective solution is:(A) 101 times that of HB (B) 10 times that of HB

(C)53 10

4 times that of HB (D) 54 10

9

times that of HB

4.

Me

C

Me

CH

OH

+2

4

Hg(OAc) /THF

NaBH /OHA.

A is

(A)Me

C

Me

CH2

OHOH

(B)O

(C)

Me

CH

Me

CH

OH

OH

(D) none of these

5. A solution of a non-volatile solute in water has a boiling point of 375.3K. The vapour pressure of water above this solution at 338 K is[Given p0 (water) = 0.2467 atm at 338 K and Kb for water = 0.52 K kg mol

1](A) 0.18 atm (B) 0.23 atm (C) 0.34 atm (D) 0.42 atm

6. What is the product (D) of the following reaction?

3

(i)t BuO

(ii)H OD.

CH3

NH R

O

(A)

CH3

N R

O

t-BuOH

(B)

NH

R


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IIT-JEE Full Test 3 (Paper I)

Space for Rough Work

DEXLIIT-JEE Academy; Raja Park :DEXL House, 468-A, Gali No. 4, Raja Park, Jaipur Ph : 0141-4036660/4034848Vidyadhar Nagar : Office No. 102, 1st Floor, Shivam Apartment, P. No. 4, Central Spine, Vidyadhar Nagar, Jaipur Ph :

0141-6595558(2)

A

(C)

N

R

(D)

N

R

7. Which of the following statement(s) is/are correct(s)?

H

BrCl

H H

BrH

Cl Br

HH

Cl Br

HCl

H

(A) (B) (C) (D)

I. (A) and (B) are diastereomers II. (B) and (C) are enantiomersIII. (A) and (D) are geometric isomer IV. (A) and (C) are optical isomer(A) only I is true (B) I, II & III are true (C) I & II are true (D) I, III and IV are true

8. Among the following which has the highest spin magnetic moment(A) [CoF6]

3 (B) [NiF6]4 (C) [Co(SCN)6]

4 (D) [Mn(SCN)6]4

SECTION IIMultiple Correct Choice Type

This section contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MOREis/are correct.

9. Which among the following are true about compounds of Boron and Si(A) B2O3 and SiO2 are acidic in nature (B) Both B2O3 and SiO2 exist in two allotropic forms(C) Borate and silicates structural units are different in structure(D) Halides of both are easily hydrolysed except BF3

10. For a reaction in gaseous phase 2 A(g) 4B(g) + C(g)if initial pressure is P0, total pressure of the gaseous mixture at time t is P t and total pressure of the gaseous mixture at infinite time is P,reaction follows first order kinetic, then which of the following is correct?

(A)0

0 t

3PK t n

5P 2P

(B) t

3PK t n

5 P P

(C) 1/ 2K t 0.693 (D) pressure of A(g) at time t is t2 (P P )3

11. Which of the following reaction(s) is/are correct(s)?


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(A)O

CH3

conc.HI

OH

3CH I

(B)conc.HI

3 3 3 3(CH ) C O Pr (CH ) CI Pr OH

(C)HI

3 3 2 3 3 2(CH ) C CH O Pr (CH ) C CH OH Pr I

(D)

conc.HI

3 2 2

3 2 2

CH CH CH O CH CH CH

CH CH CH OH CH CH CH I

12. A metal A crystallizes into FCC lattice. B atoms are present in tetrahedral voids so as to form a perfect crystal. If the e dge length ofcube is x and rA and rB are radii of A and B, then

(A)A4r 2x (B) A Br r 3x (C) A B

3r r x

4 (D) B

A

r0.256

r

SECTION IIIComprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choice questions 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 Nos. 13 to 15

Aqueous 200 ml 0.1M H2A solution when titrated against 0.1 M NaOH shows different results in presence of different indicators. Forphenolphthalene indicator it is converted to Na2A and with methyl orange it is converted to NaHA.

1

3

a 2K H A 10 ,

2

6

a 2K (H A) 10

H2A + NaOH NaHA + H2O (Methyl orange)

H2A + 2NaOH Na2A + 2H2O (Phenalpthalene)

13. When 100 ml of NaOH is added in presence of methyl orange indicator, pH of solution is(A) 3.5 (B) 4.5 (C) 3 (D) 4

14. When 200 ml of NaOH is added in presence of phenolpthalene indicator, then pH of solution is(A) 3.5 (B) 4.5 (C) 3 (D) 4

15. When 200 ml of NaOH is added in presence of methyl orange indicator, pH of solution is(A) 4.5 (B) 5 (C) 4 (D) 3.5


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Paragraph for Questions Nos. 16 to 18To explain the nature of bonding beautifully in transition metal complexes, out of lot of theories, valence bond theory (VBT) has greatimportance, which is based on the theory of covalent bonding. It deals with electronic structures of central metal ion in its ground state, kinds ofgeometry and magnetic properties of the complex.According to VBT

(i) The central metal ion or atom contains a number of s, p and d atomic orbitals equal to its co-ordination number. First of all, these atomicorbital hybridise together to form hybrid orbital which are same in number as the atomic orbital hybridizing together. These are vacant,equivalent in energy and have definite geometry.

(ii) The complexes having unpaired electron is known as para-magnetic complex and having no unpaired electron is known as diamagnetic

complex.

Magnetic moment due to spin only = spin only = ( 2) . .n n B M where, n = no. of unpaired electron.

(iii) Nature of ligands also influences the nature of the complex compounds. Stronger ligands make pairing of electron against Hunds rule,and generally produces inner orbitals complex are complexes in which ligands use the inner d-orbital of central metal ion.

Weaker ligands does not make pairing of electron and obeys Hunds rule and generally produces outer d-orbital complexes.

Keep in mind that the chelated complex is more stable than that of the non-chelated complex..

16. Which of the following is not the square planar complex ?(A) [Ni(CN)4]

-2 (B) [Cu(NH3)4]2+ (C) [Pt(NH3)4]

2+ (D) [Ni(CO)4]

17. In square planar complex, which of the following d-orbitals are used up ?

(A) 2 2x y

d

(B) 2z

d (C) xyd (D) yzd

18. Which of the following complex is more stable ?(A) [Cr(en)3]

2+ (B) [Cr(CN)6]3- (C) [Cr(H2O)6]

3+ (D) [Cr(EDTA)]-


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SECTION IVMatrix-Match Type

This section contains 2 questions. Each question contains statements given in two columns,which have to be matched. The statements in Column I are labelled A, B, C and D, while thestatements in Column II are labelled p, q, r, s and t. Any given statement in Column I can havecorrect matching with ONE OR MORE statement(s) in Column II. The appropriate bubblescorresponding to the answers to these questions have to be darkened as illustrated in thefollowing example: If the correct matches are A p, s and t; B q and r; C p and q; and D sand t; then the correct darkening of bubbles will look like the following.

19. (i)

2 2

(i) Ozonolysis

5 8 3 3 4 2(ii)CH NA(C H O ) B(C H O )

OCH3

(ii) OCH3

2 2

(i) Ozonolysis

2 2 2 4 6 3(ii) CH NC(C H O ) D(C H O )

Match the following :

Column I (Different Tests/Reactions) Column II (Produced Compounds)(A) FeCl3 test (p) A

(B) Haloform test (q) B

(C) Tollens test (r) C

(D) Intramolecular cannizaro reaction (s) D

20. Consider the following 4 cellsCell A: Pt/H2(g, 1atm) | NH3 (aq, 0.1M) || CH3COOH (aq, 0.1M) | H2 (g, 1 atm)/Pt

Kb = 105 Ka = 10

5

Cell B:2 11 2 3Cu(s) | Cu (aq,10 M) || Cu (aq, 10 M) | Cu(s)

Cell C:3 3

2 2Pt / H (g,1atm) | NaOH(aq,10 M) || HCl(aq,10 M) | H (g,1atm) / Pt

Cell D:5

a(HCN) 10

4

2 2 4 2K

Pt / H (g,1atm) | CN (aq,0.1M) ||H SO (aq,5 10 M) | H (g,1atm)/ Pt

Match the following :

Column I Column II

(A) Cell A (p)o

cellE 0

(B) Cell B (q) cellE 0.4728 V

(C) Cell C (r) pH at anode is 11

(D) Cell D (s) pH at cathode is 3

MATHEMATICS

SECTION ISingle Correct Choice Type


21. If x2 + 9y2 = 1, then minimum and maximum value of 3x2 27y2 + 24xy is(A) 0, 5 (B) 5, 5 (C) 5, 10 (D) 0, 10

22. The harmonic mean of two numbers is 4 and their arithmetic mean and geometric mean satisfy the relation 2A + G2 = 27. The numbersare(A) 6, 3 (B) 5, 4 (C) 5,5/2 (D)3, 1

23. If A,B,C are any three events in a sample space, such that

P A B C P A P B P C , then the events A,B,C are(A) Pair wise independent (B) Exhaustive events(C) mutually independent (D) mutually exclusive


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24. For x2( + 2)|x| + 9 = 0 to have real solutions, the range of is(A) [, 4] (B) [4, ) (C) (, 7] [11, ) (D) [4, )

25. If is any complex number such that z = |z|2 and | z z | | | 4, then as varies, then the area of locus of z is(A) 4 sq. units (B) 8 sq. units (C) 16 sq. units (D) 12 sq. units

26. If a, b, c be three natural numbers in A.P. and a + b + c = 30, then the possible number of values of a, b, c is(A) 19 (B) 24 (C) 30 (D) 36

27. tan(cos1x) is equal to

(A)

21 x

x

(B)

2

x

1 x(C)

21 x

x

(D)

2

x

1 x

28. Let A(1,1, 1) and B(1, 1,1) be the vertices of triangle ABC such that A = B. The locus of the vertex C is(A) x + 2y + z = 0 (B) 2x + y z = 0 (C) x y + z = 0 (D) x 2y + z = 0



29. If in a ABC, C = 90 and b, sinA, cosA are rational numbers, then(A) a is rational (B) c is irrational (C) c is rational (D) a is irrational

30. If p and q are odd integers, then the equation x2 + 2px +2 q = 0(A) has no integral roots (B) has no rational roots(C) has no irrational roots (D) has no imaginary roots.

31. A line which makes an acute angle with the positive direction of xaxis is drawn the point A(4, 3) to meet the line x = 8 at B and y = 6at C, then(A) AB = 4 sec (B) AC = 3 cosec

(C)2 2

16 91

(AB) (AC) (D)

2(4sin 3cos )AB AC

sin2

32. Let a and b be odd integers such that 0 < a < b, let f(x) = xa/b for x R, then(A) f is differentiable everywhere (B) f(0) does not exist

(C) f increases on (0, ) (D) f increases on R


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A point P moves such that sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet ofnormals. The locus of P is a curve C.

33. The equation of the curve C, is(A) x2 = 4y (B) x2 = 16y (C) x2 = 12y (D) y2 = 8x

34. If the tangent to the curve C cuts the coordinate axes in A and B, then the locus of the middle point of AB, is(A) x2 = 4y (B) x2 = 2y (C) x2 + 2y = 0 (D) x2 + 4y = 0

35. Area of the equilateral triangle, inscribed in the curve C, having one vertex as the vertex of curve C.

(A) 772 3 sq. units (B) 776 3 sq. units (C) 760 3 sq. units (D) 768 3 sq. units


1. P(AB) = P(A) + P(B) P(AB)

2.A

P

B

means probability of occurrence of A given that B

has occurredA P(A B)

PB P(B)

3. P(AB) = P(A)P(B) Events A & B are independent.

A B B AA B

A B

Venn Diagram

4. If events A & B are independent, then A and B are also independent, A and B are also independent

36. If3 2 1 A A

P(A) ,P(B) , P(A B) , then P P4 3 12 B B

(A) 0 (B)

1

3 (C)1

2 (D)

3

4

37. If1 1

P(A) , P(B) ,3 2

then the range of P(A B) is

(A)1

0,3

(B)1 1

,6 2

(C)1 1

,3 2

(D)1 2

,3 3

38. If1 3

P(A) , P(B) ,3 4

then the range of P(A B) is

(A)1

0,

3

(B)1

0,

4

(C)1 3

,

3 4

(D)1 3

,

4 4



39. Match the following:


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(A) If x, y [5, 5], then number of solutions (x, y) of the inequation

2cos ec x 1 232 2y 4y 14

(p) 1

(B) The number of solutions of the system of equations Re(z ) = 1,|z| = 1, is

(q) 2

(C) The least +ve integral value of for which the equation

4 3 24x x 4x 4 03

has no real root (r)3

(D) If f(x) = tanx + 2tan2x + 2 tan (2 x) + .. + 2n tan(2n x) + 2n (cot2nx), then thevalue off(/6), is

(s) 4

40. Match the following:

Column I Column II

(A) The number of integral solutions of the equationx + 2y = 2xy is

(p) 1

(B) The number of real solutions of the system of equations2 2 2

2 2 2

2z 2x 2yx , y , z

1 z 1 x 1 y

(q)

2

(C) If a(y + z) = x, b(z + x) = y, c(x + y) = z, where a 1, b 1,

c 1 admit non-trivial solutions, then1 1 1

1 a 1 b 1 c

is

(r) 0

(D) The number of solutions of the equation

2 2 23x 6x 7 5x 10x 14 4 2x x is(s)

Infinite


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PHYSICS

SECTION ISingle Correct Choice Type


41. A monochromatic beam of width t is incident at 45 on an air water interface as shown in

the figure. The refractive index of water is and that of air is 1. The width of the beam inwater is,(A) ( 1) t (B) t

(C)

21

t

(D)

22 1t

.

t

Air

Water

42. The variation of gravitational intensity g for a uniform solid sphere of mass M and radius R is given by

(A)

r=R

r

g

O

(B)

r=R

r

g

O

(C)

r=R

r

g

O

(D)

r=R

r

g

O 43. Which one of the following processes represents a gammadecay ?

(A)A AZ Z 1X X a b (B)

A 1 A 3Z 0 Z 2X n X c

(C)A 0 AZ 1 Z 1X e X g (D)

A * AZ ZX X f

44. An organ pipe filled with oxygen gas at 47C resonates in its fundamental mode at a frequency of 300 Hz. If it is now filled with nitrogengas, at which temperature will it resonate at the same frequency, in the fundamental mode ?(A) 7C (B) 41.1C (C) 280C (D) 92.7C

45. A projectile is projected in the earths gravitational field with initial kinetic energy E. The horizontal of the projectile range is R. If the massof the projectile is 1 kg, then the angle of projection of the projectile will be equal to

(A) E2/gRsin 1 (B) E2/gRsin2 1 (C) E2/gRsin5.0 1 (D) E2/gRsin4 1

46. A small cube of mass m slides down a circular path of radius R cut into a larger block of mass M,as shown in the figure. M rests on a table and both blocks move without friction. The blocks areinitially at rest and m starts from the top of the path. The velocity v of the cube as it leaves theblock is

m

R

M

(A)2mgR

M(B) 2gR (C)

2mgR

m M(D)

2MgR

m M

47. One end of a spring of force constant k is fixed to a vertical wall and the other to a body of mass m resting on a smooth horizontalsurface. There is another wall at a distance x0 from the body. The spring is then compressed by 2x0 and released. The time taken tostrike the wall is

(A)

m

6 k

(B)

m

k (C)2 m

3 k

(D)

m

4 k

48. A parallel plate capacitor has a capacitance C and charge Q. Another plate is inserted in between the plates of the capacitor at thecenter and is connected by a long wire to another far off spherical conductor of radius R. What is the potential difference between theedge of the sphere and one of the outer plates ?

(A)Q

C(B)

4

Q

C(C)

2

Q

C(D)

2Q

C



49. A thin convex lens made up of refractive index 0 is immersed in liquid 1 then which statement is wrong

(A) Lens will be converging if1 > 0 (B) Lens will be convex only if1 < 0(C) Lens will become convex only if1 > 0 (D) Lens will be diverging if1 > 0


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50. A dipole of dipole moment p is placed at a distance rfrom a point charge Q (as shown infigure). Choose the correct statement.(A) Torque acting on the dipole is zero (B) Force acting on the dipole due to the electric field produced by Q is zero.

(C) Potential energy of the dipole due to the point charge Q is2

o

Qp

4 r

(D) Force acting on the dipole due to the point charge Q is3o

Qp

2 r

p

Q r

51. A particle of mass m is doing horizontal circular motion with the help of a string (conicalpendulum) as shown in the figure. If speed of the particle is constant then,(A) the angular momentum of the particle about O is changing(B) magnitude of angular momentum about O remains constant(C) Z component of the angular momentum remains conserved(D) Z component of torque is always zero.

O

Z (vertical)

Y

X g

52. The network shown in the figure is part of a complete circuit. If at a certain instant, the

electric current i is 10 A(A) if electric current is increasing at a rate of 103 A/s, then

VA VB is zero

A

10mH

20Vi

10mH

(B) if electric current is increasing at a rate of 103 A/s, then time rate of increase of magnetic energy in one of the inductors is 10 J/s(C) if electric current is increasing at a rate of 103 A/s then time rate of increase of the total magnetic energy stored in both the inductors

is 200 J/s(D) none of these




Figure shows a self-excited magneto-hydrodynamic (MHD) generator in which an electrically conducting gas of electrical conductivity moves

with speed along a duct with a square cross section of dimension a.


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duct

electrode

solenoid

p1

p2

The gas is driven by a pressure difference p = p1 p2. Metal electrodes of length are set in the top and bottom walls of the duct while amagnetic field exists perpendicular to the insulated side walls of the duct. An emf is therefore set up between the electrodes which drives acurrent through a long solenoid of n turns per unit length and negligible resistance which in turn provides the magnetic field.

53. The induced emf, is equal to

(A) Ba (B) B a (C)2

B

a

(D)

B

a

54. The resistance R in the path provided by the gas between the electrodes is

(A)a

(B)1

a(C)

1

(D)

1

55. The current generated is given by

(A) i a P (B)1

2a( P ) (C)1

2(a P ) (D)1

2P(a )


Spectral lines in the atomic spectra result due to downward transition of electron from some excited state (principal Q.N. (n+x)) to less excitedstate or ground state (principal Q.N. n). The wave numbers of spectral lines in the spectra of atom or ion containing only one electron fit into theempirical equation

2

H 2 2

1 1 1V R Z

n (n x)

where = 1, 2, 3 and 4 for the lines of Lyman, Balmer, Paschen and Brackett series respectively and it remain the same for all the lines of agiven series whereas x = 1, 2, 3, . for successive lines

2 2 4

H 3

2 K eR

h C

Rydberg constant of hydrogen

= reduce mass of atom or ion =mass of electron mass of nucleus

mass of electron + mass of nucleus

Mass of electron (me) being negligible in comparison to that of nucleus, Mass comes to be almost and taking this approximation RH iscalculated to be 109677 cm1.In an atom or ion the energy of electron is quantized and lowest possible energy state is known as ground state. The energy state just abovethe ground state is called 1st excited state and so on. The amount of energy required to remove the most loosely bound electron in an atom orion in its gaseous state is called IP. All the other terms in above equation have their usual meanings.

56. The wavelength of photon ( e hc / ) corresponding to the 3rd I P of Li atom (z = 3) in its 2nd excited state is(A) 911.7 (B) 101.5

(C) 100.3 (D) cannot be calculated with the above equation applicable for one electron system

57. The wave number of the spectral line of H atom corresponding to longest wave length transition of the Lyman series is

(A) RH (B) H3

R4

(C) H5

R36

(D) HR

2

58. Suppose electron in H atom is replaced by negative meson () having the same charge as that of electron but almost 200 times asheavier as electron. The wave number of the second line of Balmer series of this mesonic H atom ignoring nuclear motion will be

(A)8 14.113 10 m

(B) 8 141.13 10 m (C) 8 1411.3 10 m (D) 6 14.113 10 m



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59. A charge q is placed inside a spherical cavity, made in an uncharged conducting sphereof radius R as shown. A point charge Q is placed at a separation d from the centre ofsolid sphere as shown in the figure.

aO d

rR

X

rq

Column A Column B

(A) Electrostatic potential at point X inside theconductor

(p) kQ kq kq kQ

d R r ' r

(B) Electrostatic potential at point O (q)

2

kQ

r (C) The magnitude of the electrostatic field at point

X inside the conductor due to the chargesinduced at the outermost surface only

(r) kQ

r

(D) Electrostatic potential due to all the inducedcharges at point X inside the conductor

(s) kQ kq

d R

60. Column I contains some equation of motion along x axis w.r.t. time and column II measures distance, speed and acceleration at t = 1sec.

Column I Column II

(A) x = 5t2 + 6t + 1 m (p) Distance = 12 m

(B) x = 8t + 8 m (q) Speed = 16m/s(C) x = 3t + t + 5t (r) Acceleration = 10m/s

(D) x = t + 2t + 9t (s) Parabolic path


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IIT Full Test 2 Paper I_Test

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