IIT-JEE 2002 Screening Paper With Answer Key

1

IIT-JEE 2002 Paper

IIT-JEE 2002 TEST PAPER SCREENING EXAMINATION T3 im .:0He0rs.

M aM x.a2rk 7: s 0

GENERAL INSTRUCTIONS 1.

This question paper has 90 objective type questions. Each question has four choices (A), (B), (C) and (D) out of which only one is correct.

2.

For each question you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.

PART-I (PHYSICS) Directions : Select the most appropriate alternative from A, B,

1.

C and D in questions.

A simple pendulum is oscillating without damping. When the displacements of the bob is less than maximum, !

its acceleration vector a is correctly shown in

!

(A)

(B) !

(C)

!

(D) !

2 2.

IIT-JEE 2002 Paper

A wooden block, with a coin placed on its top, floats in water as shown in figure. The distances " and h are shown there.

Coin

Aftersome timethe coin falls intothe water.Then

3.

"

(A) "d ecreasesandhincreases

(B)

" increases and h decreases

(C) both "a ndhincrease

(D)bothlandhdecrease

#

A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping throughout this motions). The directions of the frictional force acting on the cylinder are : (A) Up the incline while ascending and down the incline while descending (B) Up the incline while ascending as well as descending (C) Down the incline while ascending and up the incline while descending (D) Down the incline while ascending

4.

5.

as well as descending.

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of t he platform. Now the platform is given an angular velocity "0. When the tortoise moves along a chord of the platform with a constant velocity (with respe ct to the platform), the angular velocity of the platform "(t) will vary with time t as

(A)

(B)

(C)

(D)

Two blocks of masses 10kg and 4kg are connected by a spring of negligible mass and placed on a frictionles s horizontal surface . An impulse gives a velocity of 14 ms 1 to the heavier block in the direction of the lighter block. Then, the velocity of the centre of mass is –

6.

(A) 30 ms

–

1

(B) 20 ms

(C) 10 ms

–

1

–

(D) 5 ms

–

1

1

A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the srcin as F(x) = -kx + ax 3. Here k and a are positive constant. For x

# 0, the functional form of the potential energy U(x) of the particle is

(A)

(B)

(C)

(D)

3 7.

8.

IIT-JEE 2002 Paper

A siren placed at a railway platform is emitting sound o f frequency 5 kHz. A passenger sitting in a m oving train A records a fr equency of 5.5 kHz, while the train approaches the siren. During h is return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is (A)

242 252

(B) 2

(C)

5 6

(D)

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire . W hen this mass is replaced by a mass M, the wire resonates with the same tuning fork forming t hree antinodes for the same positions of the bridges. The value of M is (A) kg 25

kg (B) 5

(C) 12.5 kg 9.

(D) 1/25 kg

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is (A) Mg/k 4

(B) Mg/k 2

(C) Mg/k 10.

(D) Mg/2k

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a spy satellite orbiting a few hundred kilometers above the earth’s surface (REarth = 6400 km) will approximately be : (A) 1/2 hr

(B) hr 1

hr(C) 2 11.

11 6

hr(D) 4 2R

The effective resistance between points P and Q of the

2R

electricalcircuitshowninthefigureis 8R(R $ r ) (B) 3R $ r

2Rr (A) R$r

2R r

r

P

Q 2R

4R +(C) 2r 12.

5R + 2r 2

(D)

2R

2R

A particle of mass ‘ m ‘ and charge ‘ q ‘ moves with a constant velocity ‘ v ‘ along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is : (A)

qbB m

(B)

q(b % a )B m

(C)

qaB m

(D)

q(b $ a)B 2m

4 13.

IIT-JEE 2002 Paper

Two equal point charges are fixed at x = - a and x = + a on the x - axis. Another point charge Q is placed at the srcin. The change in the electrical potential energy of Q,

when it is displaced by a sm all distance

x along the x - axis, is approximately proportional to : x (A) 14.

2

x (B)

(C) x 3

(D) 1/x

A long straight wire along the z

% axis carries a current I in the negative z direction. The magnetic vector

!

field B at a point havin g coordinates (x, y) in the

15.

z = 0 plane i s:

(A)

' 0I 2&

( y i % x j) (x2 $y2)

(B)

' 0 I ( x i $ y j) 2& ( x 2 $ y 2 )

(C)

' 0I 2&

( x j% y i ) (x2 $y2)

(D)

' 0I ( x i % y j) 2& ( x 2 $ y 2 )

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

As shown in the figure, P and Q are two coaxial conducting loops

P Q

separated by some distance. When the switch S is closed, a clockwise current (P flows in P (as seen by E) and an induced

(Q1 flows in Q. The switch remains closed for a long time. When S is opened, a current (Q2 flows in Q. Then Battery the direction ( Q1 and ( Q2( asseenbyE)are-

E

current

(A) re specti vely clockw ise an d anti -clockw ise 16.

(C) both anti-clockwise A 100 W bulb B 1, and two 60 W bulbs B

S

(B) both cloc kwise

(D) respectivelyanti-clockwise and clockwise and B ,. are connected 2 3

to a 250 V source, as shown in the figure. Now W 1, W 2 and W 3 are the output powers of the bulbs B 1, B 2 and B 3, respectively. Then (A) W 1 > W 2 = W 3 17.

18.

(B) W 1 > W 2 > W 3

(C) W 1 < W 2 = W 3 (D) W 1 < W 2 < W 3 Two identical capacitors have the same capacitance C. One of them is charged to potential V1 and the other to V2. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is :

(A)

1 C (V 12 4

(C)

1 C (V 1 4

% V 22)

% V2) 2

(B)

1 C (V12 + V 22) 4

(D)

1 C (V 1 + V 2) 2 4

A short-circuited coil is placed in a time-varying magnetic f current induced in the coil. If the number of

ield. Electrical power is dissipated due to the

turns were to be quadrupled and the wire radius halved, the

electrical power dissipated would be (A) halved

(B) the same

(C) doubled

(D) quadrupled

5 19.

20.

IIT-JEE 2002 Paper

The magnetic field lines due to a bar magnet are correctly shown in :

(A)

(B)

(C)

(D)

An ideal gas is tak en through t he cycle A ! B ! C ! A as shown in the figure. If the net h eat supplied to the gas in the cycle is 5 J,the work done by the gas in the process C

21.

22.

–

5J

(B)

–

10 J

(C)

–

15 J

(D)

–

20 J

Which of the following graphs correctly represents the variation of at constant temperature ?

(A)

(B)

(C)

(D)

The potential difference applied to an X-ray tube is 5 kV number of electrons striking the target per second is:

(A) 2 * 1016

24.

) = –(dV/dP)/V with P for an ideal gas

and the current through it is 3.2 m A. Then the

* 1016 (D) 4 * 1015 (B) 5

(C) 1 * 10 An ideal black-body at room temperature is thrown into a furnace. It is observed that (A) initially it is the darkest body and at later times the brightest. (B) it is the darkest body at all times. (C) it cannot be distinguished at all times (D) initially it is the darkest body and at later times it cannot be distinguished. A hydrogen atom and a Li ++ ion are both in the second excited state. If l H & l Li are their respective electronic angular momenta and E H & ELi their respective energies, then: 17

23.

! A is :

(A)

(A) l H > lLi and (C) l H = lLi and

+EH+ > +ELi+ +EH+ > +ELi+

(B) l H = lLi and

+EH+ < +ELi+

(D) l H < lLi and + EH+ < + ELi +

6 25.

IIT-JEE 2002 Paper

The half life of

215

At is 100

's. The time taken f

or the radioactivity of a sample of

215

At to decay to 1/16

of its initial value is: (A) 400

's

26.

300 (D)

Which of the following processes represents a gamma decay? (A) AX Z + A

27.

's 's

6.3 (B)

(C) 40 's

, -! AXZ+% 1

b+a

A

(B)

A

X Z + 1n0 -! A % 3X Z % 2 + c

A

A

(C) XZ -! + XZ f (D) X Z + e%1 -! X Z % 1 + g An observer can see through a pinhole the top end of a thin rod of height h, placed as shown in the figure. The beake r height is 3h and its radius h. W hen the beaker is filled with a liquid up to a

height 2h,

he can see the lower end of the rod. Then the refractive index of the liquid is:

(A)

5 2

3 2

(C) 28.

5 2

(B)

(D)

3 2

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surface of the lenses are as given in the diagrams.

(A)

R1

R2

(B)

R1¹ R2

(C)

29.

(D)

In the ideal double-slit experiment, when a glass-plate (refra ctive index 1.5) of thickness t is introduced in

/), the intensity at the position where the central

the path of one of the interfering beams (wavelength

maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is :

30.

(A) 2

(B) 2 / /3

(C)

/ //3

(D)

/

Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A li ght ray is incident at an angle of 30 º to a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the r ay undergoes reflecti ons (including the first one) before it emerges out is: 28 (A) 30 (B) 32 (C) 34 (D)

th

7

IIT-JEE 2002 Paper

PART-II (CHEMISTRY) IMPORTANT INFORMATION

Logarithmic table can be used. Use of Calculator is not allowed. Useful data Gas constant : R = 0.082 L atm K Atomic number : Be = 4;

–

1

mol 1 = 8.314 J K 1 mol –

–

B = 5; C = 6; N = 7;

–

1

O = 8; S = 16; Xe=54

Relative atomic mass ; H = 1.008; O = 16.00; S = 32.07 ; Se = 78.96 ; Te = 127.6 31.

Standard electrode potential data are useful for understanding the suitability of an oxidant in a redox titration. Some half cell reactions and their standard potentials are given below :

! Mn2+ (aq.) + 4H2O(") (aq.) + 6e ! 2Cr3+ (aq.) + 7H 2O(")

–

MnO4 (aq.) + 8H+ (aq.) + 5e 2–

+

–

Cr2O7 (aq.) + 14H

Fe (aq.) + e (! Fe 3+

2+

–

Cl2(g) + 2e ( ! 2Cl –

–

E0 = 1.51 V E0 = 1.38 V

–

aq.) aq.)

0

= 0.77 EV

0

= 1.40EV

Identify the onlyincorrect statement regarding the quantitative estimation of aqueous Fe(NO 3)2. –

(A) MnO4 c anbeusedinaqueousHCl

(B)Cr

–

(C) MnO4 can be used in aqueous H 2SO4 32.

(C)

can be used in aqueous H 2SO4

1

1

6.023 × 1054 9.108

(D) 9.108 * 6.023 × 108

One mole of a non-ideal gas undergoes a change of state (2.0 atm, 3.0 L, 95 K) ! (4.0 atm, 5.0 L, 245 K) with a change in internal energy, 0U = 30.0 L atm. The change in enthalpy (0H) of the process in L atm is : (B) 42.3

(C)44.0

35.

(D) Cr2O

2– 7

(B) 9.108 × 1031

(A) 40.0 34.

O72 can be used in aqueous HCl

How many moles of electron weigh one kilogram ? (A) 6.023 × 1023

33.

–

2

(D)notdefined,becausepressureisnotconstant

A substance Ax By crystallizes in a face centered cubic lattice in which atoms ‘A’ occupy each corner of the cube and atoms ‘B’ occupy the centres of each face of the cube. Identify the correct composition of the substance Ax By. (A) AB3

(B) A4 B3

(C) A3 B

(D)compositioncannotbespecified

Consider the following equilibrium in a closed container N2 O (g) 2NO 2 (g) 4 At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statements holds true regarding the equilibrium constant (KP) and degree of dissociation ( 1) ? (A) neither KP nor 1c

hanges

(C) KP changes, but 1d oesnotchange

(B)bothK (D)K

P

P

and 1 change

does not change but 1 changes

8 36.

37.

IIT-JEE 2002 Paper

Which of the following volume (v)-temperature (T) plots represent the behaviour of one mole of an ideal gas at one atmospheric pressure ?

(A)

(B)

(C)

(D)

If nitrogen atom had electronic configuration 1s7, it would have energy lower than that of the normal ground state configuration 1s2 2s 2 2p 3, because the electrons would be close to nucleus, yet 1s 7 is not observed because it violates : (A) Heisenberg uncertaintyprinciple (C) Pauli’s exclusion principle

38.

(B) Hund ’s rule (D) Bohr’s postulate of stationary orbits.

Rutherford’s experiment, which established the nuclear model of the atom, used a beam of : (A) ) -particles, which impinged on a metal foil & got absorbed. (B) ,-rays, which impinged on a metal foil & ejected electrons. (C) helium atoms, which impinged on a metal foil & got scattered. (D) helium nuclei, which impinged on a metal foil & got scattered.

39.

40.

When the temperature is increased, surface tension of water : (A)increases

(B) decreases

(C)remainsconstant

(D)showsirregularbehaviour

Consider the chemical reaction, N2(g) + 3H2(g) --! 2NH3(g) The rate of this reaction can be expressed in terms of time derivatives of conc. of2N (g) , H2(g) or NH3(g). Identify the correct relationship amongst rate expressions : (A) Rate = %

(C) Rate = 41.

42.

d [N2 ] dt

d [N2 ] dt

2%

2%

1 d [H2 ] 3 dt

1 d [H2 ] 3 dt

2

2

1 d [NH3 ] 2 dt

1 d [NH3 ] 2 dt

(B) Rate =

d [N2 ] dt

(D) Rate = %

2 %3

d [N2 ] dt

2%

d [H2 ] dt

22

d [NH3 ] dt

d [H2 ] dt

2d

d [NH3 ] dt

Specify the coordination geometry around and hybridisation of N and B atoms in a 1 : 1 complex of BCl & NH3. 3 (A) N : tetrahedral sp3, B : tetrahedral sp3

(B) N : pyramidal sp3, B : pyramidal sp3

(C) N : pyramidal sp3, B : planar sp 2

(D) N : pyramidal sp3, B : tetrahedral sp3

Polyphosphates are used as water softening agents because they : (A) form soluble complexes with anionic species (B) precipitate anionic species (C) form soluble complexes with cationic species (D) precipitate cationic species

9 43.

44.

IIT-JEE 2002 Paper

Identify the correct order of acidic strengths of CO 2, CuO, CaO, H2O. (A) CaO < CuO < H 2O < CO2

(B) H2O < CuO < CaO < CO 2

(C) CaO < H2O < CuO < CO 2

(D) H2O < CO2 < CaO < CuO

Identify the least stable ion amongst the following. –

–

(A) Li

(B) Be

–

–

(C) B 45.

(D) C

Which of the following molecular species has unpaired electron(s) ? (A) N2 (B) F2 –

–

(D) O22

(C) O2 46.

A gas ‘X’ is passed through water to form a saturated solution. The aqueous solution on treatment with silver nitrate gives a white precipitate. Thesaturated aqueous solution also dissolves magnesiumribbon with evolution of a colourless gas ‘Y’. Identify ‘X’ and ‘Y’.

47.

(A) X = CO2 , Y = Cl2

(B) X = Cl 2, Y = CO2

(C) X = Cl 2 , Y = H2

(D) X = H2 , Y = Cl2

An aqueous solution of a substance gives a white precipitate on treatment with dilute hydrochloric acid, which dissolves on heating. When hydrogen sulfide is passed through the hot acidic solution, a black precipitate is obtained. The substance is a : (A) Hg s 22+ (C)sAg+

48.

2+ salt Cu (B)

alt

2+ salt Pb (D)

alt

Which of the following processes is used in the extractive metallurgy of magnesium ? (A)Fusedsaltelectrolysis

(B)Selfreduction

(C)Aqueous solution electrolysis 49.

(D) Thermite reduction

Identify the correct order of solubility of Na2S, CuS and ZnS in aqueous medium. (A) CuS > ZnS > Na2S

(B) ZnS Na >

(C) Na2CuS > ZnS S > 50.

(D) Na

2S 2S

< CuS

> ZnS > CuS

Anhydrous ferric chloride is prepared by : (A) heating hydrated ferric chloride at a high temperature in a stream of (B) heating metallic iron in a stream

air.

of dry chlorine.

(C) reaction of metallic iron with hydrochl oric acid. (D) reactrion of m etallic iron with nitric acid. 51.

Identify the correct order of reactivity in electrophilic substitution reactions of the following compounds.

1

2 3

4

(A)1>2 >3>4

(B)4>3>2>1

(C)2> 1>3 >4

(D)2 >3> 1> 4

10 52.

IIT-JEE 2002 Paper

Consider the following reaction

Identify the structure of the major product ‘X’.

53.

54.

(A)

(B)

(C)

(D)

Which of the following acids has the smallest dissociation constant? (A) CH3CHFCOOH

(B) FCH

(C) BrCH2CH2COOH

CH (D)

CH2COOH

2

CHBrCOOH

3

The nodal plane in the p-bond of ethene is located in : (A) the molecular plane (B) a plane parallel to the molecular plane (C) a plane parallel to the molecular plane which bisects the carbon-carbon 3 –bond at right angle (D) a plane perpendicular to the molecular plane which contains the carbon-carbon 3 –bond

55.

Identify the correct order of boiling points of the following compounds. CH3 CH2CH2 CH2OH 1

56.

CH3 CH2 CH2CHO 2

3>(A) 2>1

2>(B) 1>3

2>(C) 3>1

1>(D) 2>3

Which of the following hydrocarbons has the lowest dipole moment ? (B) CH3C 4 CCH3

(A) (C) CH3CH2C 4 CH 57.

58.

CH3 CH2CH2COOH 3

CH (D)

2=

CH – C

4

CH

Identify a reagent from the following list which can easily distinguish between 1-Butyne and 2-Butyne. (A) Bromine, CCl4

(B) H2, Lindlar catalyst

(C) Dilute H2SO4, HgSO4

(D) Ammonical Cu2Cl2 solution

Identify the set of reagents/reaction conditions ‘X’ and ‘Y’ in the following set of transformations. CH3

–

CH2

–

X

CH2Br

--!

Y

product

--!

CH3

CH3 % CH | % Br

(A) X = concentrated alcoholic NaOH, 80°C ; Y = HBr acetic acid, 20°C (B) X = dil. aq. NaOH, 20°C, Y = HBr / acetic acid, 20°C (C) X = dil. aq. NaOH, 20°C, Y = Br2 / CHCl3 , 0°C (D) X = conc. alc. NaOH, 80 °C, Y = Br2 / CHCl3 , 0°C

11 59.

60.

IIT-JEE 2002 Paper

Which of the following compounds exhibits stereoisomerism ? (A)2-Methylbutene-1

(B)3-Methylbutyne-1

(C)3-Methylbutanoicacid

(D)2-Methylbutanoicacid

Compound 'A’ (molecular formula C3H8O) is treated with acidified potassium dichromate to form a product 'B' (mol. Formula C3H6O). 'B' forms a shining silver mirror on warming with ammonical AgNO3 . 'B' when treated with an aqueous solution of H2NCONHNH2, HCl & sodium acetate gives a product'C'. Identify the structure of 'C ’. CH | 3

(A) CH3CH2CH = NNHCONH2

(B) CH3 % C 2 N % CONHNH2

(C) CH3 – CH = N.NH – CONH2

(D) CH3CH2CH = NCONHNH2

PART-III (MATHEMATICS) 61.

The area bounded by the curves y = | x | – 1 and y = 1 (A)

–

| x | + 1 is

2 (B)

(C) 2 2

(D) 4 m

62.

The sum

;10 8 ; 20 8 , (where ;9 p 86 = 0, if p < q), is maximum when ' 99 66 99 66 5 9 q6 : 7 i20 : i 7 : m % i 7

5 (A) 63.

64.

10(B)

15 (C) 20 (D) If the tangent at the p oint P on the circle x 2 + y 2 + 6x + 6y = 2 meets the straight line 5x a point Q on the y-axis, then the length of PQ is 4 (A)

2 (B)

5

5 (C)

3 (D)

5

If a > 2b > 0, then the positive value of m for which y = mx x 2 + y 2 = b 2 and (x

–

(C)

a

2

% 4b

For all complex numbers z

7 (C)

(B)

2

2b a % 2b

|z1 – z 2| is 0 (A)

–

–

2y + 6 = 0 at

2 b 1 $ m is a common tangent to

a) 2 + y 2 = b 2 is

2b (A)

65.

m ' is:

(D) 1

, z 2 satisfying |z 2 (B) 17(D)

1

a2

% 4b 2 2b

b a % 2b

| = 12 and |z

2

–

3 – 4i| = 5, the minimum value of

12

66.

IIT-JEE 2002 Paper

Let

"=%

(A) 3 (C) 3

67.

1 2

1

3

+

2

1

i. Then the value of the determ inant

1

" "2

(B) 3 (D) 3

1

is:

" ( " % 1) " (1 % ")

A tan %1 x > @ 1 ? 2

The domain of the derivative of the function f(x) =

1

% 1%" 2 " 2 "2 "4

(A) R

–

{0}

(B) R

–

{1}

(C) R

–

{–1}

(D) R

–

{–1, 1}

, if | x | C 1 , if | x | B 1

is

1

68.

Let f : R

; f (1 $ x ) 8 x 9 6 ! R be such that f(1) = 3 and f D(1) = 6. Then xlim !0 9 f (1) 6 equals : 7 1

1 (A)

e2

(B)

(C) e 2 69.

(D) e 3

Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all x T

f(x + T) = f(x). If ( =

3 $3T

F f (x) dx , then the value of F f (2x) dx is 0

(A)

3 2

3

(

(B) 2(

(C) 3(

(D) 6( x

70.

Let f (x) =

F

2 % t 2 d t. Then the real roots of the equation x2 % f D (x) = 0 are :

1

(A) ± 1 (C) ±

(B) ±

1

The integral 1(A) % (C) 1

2

(D) 0 & 1

2 1/ 2

71.

1

F

% 1/ 2

; 1 x 8 9: [x] $ " n 9;: 1 $% x 687 67

d x equals:

/2

0 (B) (1/2) ln(D) 2

E

R,

13 72.

73.

IIT-JEE 2002 Paper

Let function f : R

! R be defined by f

(x) = 2 x + sin x for x

(B)onetoonebutnotonto

(C) ontobutnot one to one

(D)neitheronetoonenor onto

The equation of the common tangent to the curve y (A)3y =9x + 2

75.

2 (B)

3 (C)

4 (D)

The length of a longest interval in which the function 3

&

(B)

3

3& 2

(D)

40 (A)

60 (B)

80 (C)

sin x

–

4 sin 3x is increasing is

& 2

&

100 (D)

The locus of the mid point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix –

(B) x =

a

0 = x(C)

The set of all real numbers x for which x

G, – 2 ) H (2, G) (C) ( – G, – 1) H (1, G)

%

a 2

a 2 |x + 2| + x > 0 is x2

(D)

(A) ( – 79.

1 is

The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is

(A) x =

78.

–

(D) 2 +x=y

1 (A)

(C)

77.

= 8x and xy =

(cosx %1) (cos x % e x ) The integer ' n ' for which Limit is a finite non-zero number is: x !0 xn

(A)

76.

2

(B) = y2x + 1

(C) 2y 8 +x= 74.

E R. Then f is:

(A)onetooneandonto

2

–

( (B)

–

( (D)

G, – 2 , G)

2)

H(

2,

G)

If a 1, a 2, a 3, ........., a n are positive real numbers whose product is a fixed number value of a 1 + a2 + a3 + .... + a n 1 + 2a n is

c, then the minimum

–

80.

(A) n(2c) 1/n

(B) (n + 1) c

(C) 2nc 1/n

(D) (n + 1)(2c)

1/n 1/n

Suppose a, b, c are in A.P. and a 2, b2, c2 are in G.P. if a < b < c and a + b + c =

3 2

(A)

(C)

1

(B)

2 2 1 2

–

1 3

(D)

1 2 3 1 2

–

1 2

, then the value of a is

14 81.

IIT-JEE 2002 Paper

Which of the following pieces of data does NOT uniquely determine an acute - angled triangle ABC (R being the radius of the circumcircle ) ? (A)asin , A,sinB

(B)a,b,c

(C)a,sinB,R 82.

(D)a,sinA,R

Let 0 < 1 <

& 2

be fixed angle. If P = (cos I, sin I) and Q = (cos(1 – I), sin (1 – I)), then Q is obtained from P by

(A) clockwise rotation around srcin through an angle 1 (B) anticlockwise rotation around srcin through an angle

1 1 (D) reflection in the line through srcin with slope tan ( 1/2) (C) reflection in the line through srcin with slope tan

83.

Let P = (–1, 0), Q = (0, 0) and R = (3, 3 3 ) be three points. Then the equation of the bisector of the angle PQR is

3 (A)0= y +x 2

(C) 84.

+(B) x

+x0 = y 3

A straight line through the srcin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segement PQ in the ratio 4 : 3 (B) 3 : 4 (D)

The point(s) on the curve y

(A)

; 99 J :

4 3

3

+ 3x 2 = 12y where the tangent is vertical, is (are)

8 7

, % 2 66

(B)

0) (C) (0, 86.

(D)

The number of integral values of ' 4 (A) !

; 9J 9 :

11 86 ,1 6 3 7

; 99 J :

4 3

8 7

, 2 66

k ' for which the equation, 7 cos

x + 5 sin x = 2 k + 1 has a solution is:

8 (B)

10 (C) 87.

3 y=0 2

+ (D) x

2 : 1 (A) 1 : 2 (C) 85.

3y = 0

12 (D) !

!

!

!

If a & b are two unit vectors such that a + 2 b & 5 a !

%1

1/3)

are perpendicul ar to each other , then the

!

angle between a & b is: (A) 45 º (C) cos(

!

% 4b

(B) 60 º (D) cos %1 (2/7)

15

IIT-JEE 2002 Paper !

88.

!

Let V = 2ˆi $ ˆj % kˆ & W = $i

!

$ 3 k$ . If U

is a unit vector, then the maximum value of the scalar triple produc t

!! !

KUV W L is: 1

(A)

% 59

(C) 89.

10 $ (B) 6 (D)

(k + 1) x + 8y = 4k, kx + (k + 3) y = 3k 0 (A)

–

1 has infinitely many solutions, is

1 (B)

(C) 2 90.

60

The number of values of k, for which the system of equations

(D) infinite

Suppose f(x) = (x + 1) 2 for x # – 1. If g(x) is the function whose graph is reflectio n of the graph of f(x) with respect to the line y = x, then g(x) equals (A) (C)

–

x

01, x

–

x $1, x

1 (B) , x > ( x $ 1)2

#

#–1

(D)

x

–

1, x

–

1

#0

ANSWER KEY TO IIT-JEE 2002 TEST PAPER SCREENING EXAMINATION 1.

C

2.

D

3.

B

4.

C

5.

C

6.

D

7.

B

8.

A

9.

B

10.

C

11.

A

12.

B

13.

B

14.

A

15.

D

16.

D

17.

C

18.

B

19.

D

20.

A

21.

A

22.

A

23.

A

24.

B

25.

A

26.

C

27.

B

28.

C

29.

A

30.

B

31.

A

32.

D

33.

C

34.

A

35.

D

36.

C

37.

C

38.

D

39.

B

40.

A

44.

A

42.

C

43.

A

44.

B

45.

C

46.

C

47.

D

48.

A

49.

D

50.

B

51.

C

52.

B

53.

C

54.

A

55.

B

56. 61.

B B

57. 65.

D C

58. 63.

A C

59. 64.

D A

60. 65.

A B

66.

B

67.

D

68.

C

69.

C

70.

A

71.

A

72.

A

73.

D

74.

C

75.

A

76.

A

77.

C

78.

B

79.

A

80.

D

81.

D

82.

D

83.

C

84.

B

85.

D

86.

B

87.

B

88.

C

89.

B

90.

D