27-01-2014-20140127102544

Batch : Impulse & Momentum Date : 27/01/2014Time : 3 hour Max. Marks : 360

INSTRUCTIONS

Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages.If you found some mistake like missing questions or pages then contact immediately to theInvigilator.

1. The question paper contains 90 questions. All of them are compulsory.

Q.1 to Q.90 have only one correct alternative and carry 4 marks each.There is NEGATIVE marking and 1 mark will be deducted for each wrong answer.

2. Indicate the correct answer(s) for each question by filling appropriate bubble(s) in your OMR sheet.

3. Use only HB pencil for darkening the bubble(s).

4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.

5. For example if only 'B' choice is correct then, the correct method for filling the bubble isA B C D

For example if only 'B & D' choices are correct then, the correct method for filling the bubbles isA B C D

The answer of the question in any other manner (such as putting , cross , or partial shading etc.) will be treated as wrong.

USEFUL DATAAtomic Mass: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14,Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.4, Ba = 137,Co = 59, Hg = 200, Pb = 207, He = 4, F=19, Ar = 40.Radius of nucleus =1014 m; h = 6.626 1034 Js; me = 9.1 1031 kg, RH = 109637 cm1.Take g = 10 m/s2 where ever required.

TEST PAPER

A-49, Moulana Azad Sarani, City Centre, Durgapur-16, Ph: 7699999929 www.iitjeeguru.in

Q.1 If (1, 2) is one of the points of intersection of the graphs of ax2 + by2 = 5 and bx2 + ay2 = 5, thenfind a + b.(A) 2 (B) 3 (C) 4 (D) 5

Q.2 The continued fraction

...........212

12

12

, has the value equal to

(A) 1 (B) 5/4 (C) 3/2 (D) 7/4

Q.3 If 0 < x < 2 and 2tan x = 4sin x then the number of value of x is ________.(A) 1 (B) 2 (C) 3 (D) 4

Q.4 Given the following system of equations

31

y1

x1

; 51

z1

x1

; 71

z1

y1

The value of the ratio yz

is

(A) 17 (B) 23 (C) 29 (D) 31

Q.5 The equation 2x2 = 162x 3 has two solutions. Their sum is

(A) 0 (B) 2 (C) 6 (D) 8

Q.6 If sin2x + sin x cos x 6cos2x = 0 and 0x2

, then the value of tan x, is

(A) 0 (B) 3 (C) 2 (D) 6

Q.7 If sin = 135

and is in Quadrant III, then the value of

2

cos , is

(A) 136

(B) 261

(C) 12

5 (D)

2626

SPACE FOR ROUGH WORK

MATHEMATICS

Q.8 The value of the parameter m for which the equation 1x32x

= mx61x2

has no solution for x,

is(A) 12 (B) 18 (C) 14 (D) 13

Q.9 The value of x such that 4(1 + y)x2 4x + 1 y = 0 is true for all real values of y, is(A) 1/2 (B) 2/3 (C) 2/3 (D) 1/2

Q.10 Knowing that 2 is a solution of the equation 6x3 25x2 + 32x 12 = 0, the sum of the othertwo solutions, is(A) 12/5 (B) 12/5 (C) 13/6 (D) 13/6

Q.11 Suppose that x & y are numbers such that sin (x + y) = 3/10 and sin (x y) = 1/2. The value ofsinxcosy is(A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4

Q.12 If a + b = 1 and a2 + b2 = 85, then the value of (a3 + b3), is(A) 127 (B) 173 (C) 154 (D) 321

Q.13 The set of values of k for which the sum of the roots of P(x) = 4x2 + k2x + k is equal to twicethe product of the roots is(A) {2} (B) {2, 0} (C) {0} (D) {2}

Q.14 If ba = 43 and cb = 98 and dc = 32 , then 2bad is equal to

(A) 8164

(B) 8461

(C) 6481

(D) 6184

Q.15 Number of diagonals in a regular polygon with 20 sides, is(A) 170 (B) 180 (C) 190 (D) 200

Q.16 The value of m for the zeros of the polynomial P(x) = 2x2 mx 8 differ by (m 1) is

(A) 4, 310

(B) 6, 310

(C) 6, 310

(D) 6, 310

Q.17 If f(4) = g(4) = 2 ; f (4) = 9 ; g (4) = 6 then Limitx 4f x g x

x( ) ( )

2 is equal to :

(A) 3 2 (B) 32

(C) 0 (D) none

Q.18 The value of x satisfying the equation, x = x222 is

(A) 2 cos 10 (B) 2 cos 20 (C) 2 cos 40 (D) 2 cos 80


Q.19 log3 113

+ log3 1

14

+ log3 1

15

+ .............. + log3 1

1242

when simplified has the

value equal to(A) 1 (B) 3 (C) 4 (D) 5

Q.20 In the inequality below the value of the angle is expressed in radian measure. Which one of theinequalities below is true?(A) sin 1 < sin 2 < sin 3 (B) sin 3 < sin 2 < sin 1(C) sin 2 < sin 1 < sin 3 (D) sin 3 < sin 1 < sin 2

Q.21 The locus of z, for arg z = 3 is

(A) same as the locus of z for arg z = 32

(B) same as the locus of z for arg z = 3

(C) the part of the straight line yx3 = 0 with (y < 0, x > 0)

(D) the part of the straight line yx3 = 0 with (y > 0, x < 0)

Q.22 For Rx , the difference between the greatest and the least value of y = 1x

x2

is

(A) 1 (B) 2 (C) 3 (D) 21

Q.23 The equation (x R) xx

2

21 1

53

= x

(A) has no root (B) exactly one root (C) two roots (D) four roots

Q.24 Let f (x) =

2xif2x3x

4x

2xif22

622

2

x1x

x3x

then

(A) f (2) = 8 f is continuous at x = 2 (B) f (2) = 16 f is continuous at x = 2(C) f (2) f (2+) f is discontinuous (D) f has a removable discontinuity at x = 2


Q.25 Consider 8 vertices of a regular octagon and its centre. If T denotes the number of triangles andS denotes the number of straight lines that can be formed with these 9 points then T S has thevalue equal to(A) 44 (B) 48 (C) 52 (D) 56

Q.26n

rn

rn

rr

n CC C

10

1

is equal to :

(A) n2

(B) n n

n( )( )

12 1 (C)

n12

(D) n n( )1

2

Q.27 If the roots of the quadratic equation (4p p2 5)x2 (2p 1)x + 3p = 0 lie on either side ofunity then the number of integral values of p is(A) 0 (B) 1 (C) 2 (D) infinite

Q.28 The absolute term in the quadratic expression

n

1k 2k31x

1k31x as n is

(A) zero (B) 1 (C) 32

(D) 31

Q.29 Starting with a unit square, a sequence of square is generated. Each square in the sequencehas half the side length of its predecessor and two of its sides bisected by its predecessor'ssides as shown. This process is repeated indefinitely. The total area enclosed by all the squaresin limiting situation, is

(A) 45

sq. units (B) 6479

sq. units

(C) 6475

sq. units (D) 121

sq. units

Q.30 What is the radius of the smallest circle that contains both of the circles x2 + y2 = 4 and(x 3)2 + (y 3)2 = 9?

(A) 2

533 (B)

2733

(C) 2

523 (D)

2723


Q.31 Three projectiles A, B and C are thrown simultaneously from thesame point in the same vertical plane. Their trajectories are shownin the figure. Then which of the following statement is false.(A) The time of flight is the same for all the three.(B) The launch speed is greatest for particle C. (C) The vertical velocity component for particle C is greater than that for the other particles(D) Ycoordinate of all particles is always same

Q.32 Suppose a player hits several baseballs. Which baseball will be in the air for the longest time?(A) The one with the farthest range.(B) The one which reaches maximum height.(C) The one with the greatest initial velocity.(D) The one leaving the bat at 45 with respect to the ground.

Q.33 Two blocks are arranged as shown in the figure. Therelation between acceleration a1 and a2 is :

(A) a1 = a2 (B) a1 = 6a2 (C) a1 = 3a2 (D) a1 = 4a2

Q.34 To man running at a speed of 5 m/sec,the rain drops appear to be falling at an angle of 45 fromthe vertical. If the rain drops are actually falling vertically downwards, then velocity in m/s is(A) 5 (B) 5 3 (C) 5 2 (D) 4

Q.35 Three blocks are connected as shown in the figure, on a horizontalfrictionless table and pulled to the right with a force at 60N. ifM= 10kg, M2 = 20kg and M3 = 30 kg then the value of T2 is

(A) 40N (B) 30N (C) 20N (D) 10N

PHYSICS


Q.36 Find the time in which 2 kg mass will strikes the pulleyafter being released from rest.(A) 10 sec (B) 2 sec(C) 5 sec (D) 4 sec

Q.37 The wedge is moved with constant horizontal acceleration a. For whichof the following values of a will the acceleration of the block be differentfrom its acceleration in other three cases.

(A) 2 g (B) 3 g (C) g (D) 10g

Q.38 A trolley is accelerating down an incline of angle withacceleration g sin. Which of the following is correct.( is the angle made by the string with vertical).(A) = (B) = 00(C) Tension in the string, T = mg (D) Tension in the string, T = mg sec

Q.39 Which of the following is correct about kinetic friction?(A) Always acts in opposite direction of the applied force.(B) total work done by this force on the system may be zero.(C) direction of friction is always apposite to direction of velocity.(D) it can increase velocity.

Q.40 The net contact force on the 1 kg block is

(A) 54 N (B) 10 3 N

(C) 20 3 N (D) 10 N


Q.41 An object moves counter-clockwise along the circular path shown below.As it moves along the path its acceleration vector continuously points towardspoint S. The object(A) speeds up at P, Q and R(B) slows down at P, Q and R(C) speeds up at P and slows down at R.(D) slows down at P and speeds up at R.

Q.42 The work done by a force )ix6(F 3

N in displacing a particle from x = 4 m to x = 2 m is(A) 240 J (B) 360 J (C) 420 J (D) will depend upon the path

Q.43 Consider the configuration (shown below) of a rope that is halfhanging over the edge of a frictionless table. Suppose the ropehas a mass per unit length of kg/m. How much work is doneby a force that slowly pulls the entire rope up onto the table?Select the correct answer.

(A) L2 g (B) 8gL2

(C) 4gL2

(D) None

Q.44 A particle parallel to x-axis as shown in the figure such that at all instantthe y-axis component of it's position vector is constant and is equal to'b'. The angular velocity of the particle about the origin is

(A) bv

sin2 (B) bv

(C) bv

sin (D) vb

Q.45 A particle of mass m rotates in a circle of radius R with a uniform angular speed . It is observedfrom a frame rotating about the same axis with a uniform angular speed 0 in same sense. Theacceleration of particle as observed in the rotating frame is

(A) 2R R20 (B) (0)2R (C) R20 (D)

2R


Q.46 A particle of mass m is going along surface of smooth hemisphere ofradius R. At the moment shown its speed is v.Choose correct option.

(A) mg Nsin = m(gcos2 Rv2

sin) (B) mg Nsin = 0

(C) mg Nsin = R

mv2(D) None of these

Q.47 Which of the following best illustrates the acceleration of a pendulum bob at points a throughe?

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

Q.48 Three men A, B & C of mass 40kg, 50kg & 60kg are standingon a plank of mass 90kg, which is kept on a smooth horizontalplane. If A & C exchange their positions then mass B will shift(A) 1/3m towards left (B) 1/3m towards right (C) will not move w.r.t. ground (D) 5/3 m towards left

Q.49 A ball is thrown downwards with initial speed =6 m/s, from a point at height =3.2 m above ahorizontal floor. If the ball rebounds back to the same height then coefficient of restitution equalto(A) 1/2 (B) 0.75 (C) 0.8 (D) None

Q.50 A ball of mass 1kg strikes a heavy platform, elastically, moving upwardswith a velocity of 5m/s. The speed of the ball just before the collision is10m/s downwards. Then the impulse imparted by the platform on theball is(A) 15 N s (B) 10 N s (C) 20 N s (D) 30 N s


Q.51 A small ball is dropped from a height h onto a rigid frictionless plate atB and rebounds. Find the maximum height reached after rebound if thecoefficient of restitution between the ball and the plate is e = 0.75:(A) 0 (B) 3h /25(C) 3h/125 (D) 9h/625

Q.52 AB and CD are two identical rods each of length L and mass Mjoined to form a cross. Find the M.I. of the system about abisector of the angle between the rods (XY)

(A) 12

ML2 (B) 6

ML2 (C) 3

ML2 (D) 3

ML4 2

Q.53 A wheel is made to roll without slipping, towards right, by pullinga string wrapped round a coaxial spool as shown in figure. Withwhat velocity the string should be pulled so that the centre of thewheel moves with a velocity of 3 m/s?

(A) 3 m/s (B) 1 m/s (C) 3/2 m/s (D) 2 m/s

Q.54 If 100 g of ice at 0C is mixed with 100 g of boiling water at 100C, which of the followinggraphs would best represent the temperature v/s time of the two components of the mixture?

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

Q.55 Suppose there is a hole is a copper plate. Upon heating the plate, diameter of hole, would :(A) always increase (B) always decrease(C) always remain the same (D) none of these


Q.56 A particle moves along the x-axis according to : x = A.[1 + sin t]. What distance does is travelbetween t = 0 and t = 2.5/?(A) 4A (B) 6A (C) 5A (D) None

Q.57 An infinite number of masses, each of one kg are placed on the +ve X axis at 1m, 2m, 4m,______ from the origin. The magnitude of the gravitational field at origin due to this distributionof masses is:

(A) 2G (B) 3G4

(C) 4G3

(D)

Q.58 Two point masses of mass 4m and m respectively separated by d distance are revolving undermutual force of attraction. Ratio of their kinetic energies will be :(A) 1 : 4 (B) 1 : 5 (C) 1 : 1 (D) 1 : 2

Q.59 A simple harmonic motion having an amplitude A and time period T is represented by theequation y = 5 sin (t + 4) m Then the values of A (in m) and T (in sec) are :(A) A = 5; T = 2 (B) A = 10 ; T = 1 (C) A = 5 ; T = 1 (D) A = 10 ; T = 2

Q.60 A composite rod made of three rods of equal length and cross-section as shown in the fig. Thethermal conductivities of the materials of the rods are K/2, 5K and K respectively. The end Aand end B are at constant temperatures. All heat entering the face A goes out of the end Bthere being no loss of heat from the sides of the bar. The effective thermal conductivity of thebar is

BA

K5KK/2

(A) 15K/16 (B) 6K/13 (C) 5K/16 (D) 2K/13.


Q.61 2Pentene contains(A) 15 & one bonds (B) 14 & one bonds(C) 13 & two bonds (B) 14 & no bonds

Q.62 The number of isomers of formula C4H10 is(A) 1 (B) 2 (C) 3 (D) 4

Q.63 An isomer of propanal is(A) Acetone (B) Propane (C) Ethanol (D) Propanol

Q.64 Which one of the following is strongest acid(A) 2chloropentanoic acid (B) 3chloropentanoic acid(C) 5chloropentanoic acid (D) 4chlorpentanoic acid

Q.65 For which carboxylic acid, the pKa value is the lowest:(A) CH3CH2COOH (B) CH CCOOH(C) CH3CH2CH2COOH (D) CH2=CHCOOH

Q.66 The correct arrangement of acid strength in decreasing order is (A) (CH3)3CCOOH > CH3COOH > CCl3 COOH > O2NCH2COOH(B) CH3COOH > (CH3)3CCOOH > O2NCH2COOH > CCl3COOH(C) O2NCH2COOH > (CH3)3CCOOH > CH3COOH > CCl3 COOH(D) CCl3 COOH > O2NCH2COOH > CH3COOH > (CH3)3CCOOH

Q.67 Basic strength of CH C, CH2 = C H

(II), CH3 C H

2 (III) will be in order :(A) I < II < III (B) II < III < I (C) III < II < I (D) III < I < II

Q.68 What is the correct order of acidity of the following hydra-acid?(A) HF > HCl > HBr > HI (B) H2O > H2S > H2Se > H2Te(C) H2O < H2S < H2Se < H2Te (D) HI > HBr > HCl > HF

Q.69 Which of the follwing acting as electrophile?(A) H (B) NH3 (C) H2O (D) BF3

CHEMISTRY


Q.70 24 mL of HI are produced from the reaction of 15 mL of 2H and 17.1 mL of 2I vapour at 444oCThe equilibrium constant for the reaction H2 + I2 = 2HI at 444

oC(A)27.5 (B)37.647 (C)73.647 (D) 57.25

Q.71 For the gas phase reaction, C2H4 + H2 C2H6 (H = 32.7 kcal), carried out in a closed vessel,the equilibrium concentration of C2H4 can be increased by(A) increasing the temperature (B) decreasing the pressure(C) removing some H2 (D) adding some C2H6

Q.72 An exothermic reaction is represented by the graph :

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

Q.73 The correct relationship between free energy change in a reaction and the corresponding equilibriumconstant K is(A) G = RT ln K (B) G = RT ln K (C) G = RT ln K (D) G = RT ln K

Q.74 The conjugate acid of 2NH is

(A) NH3 (B) NH2OH (C) 4NH (D) N2H4

Q.75 pH of an aqeous solution of NaCl at 85C should be(A) 7 (B) > 7 (C) < 7 (D) 0

Q.76 1 CC of 0.1 N HCl is added to 99 CC solution of NaCl. The pH of the resulting solution will be(A) 7 (B) 3 (C) 4 (D) 1

Q.77 10 ml of 200M

H2SO4 is mixed with 40 ml of 200M

H2SO4. The pH of the resulting solution is

(A) 1 (B) 2 (C) 2.3 (D) none of these

Q.78 The pH of an aqueous solution of 1.0 M solution of a weak monoprotic acid which is 1% ionisedis(A) 1 (B) 2 (C) 3 (D) 11


Q.79 If K1 & K2 be first and second ionisation constant of H3PO4 and K1 >> K2 which is incorrect.

(A) [H+] = [ 42POH ] (B) [H+] = ]POH[K 431

(C) K2 = ]HPO[ 4 (D) [H+] = ]PO[3 34

Q.80 The compound whose 0.1 M solution is basic is(A) Ammonium acetate (B) Ammonium chloride(C) Ammonium sulphate (D) Sodium acetate

Q.81 Which of the following solution will have pH close to 1.0?(A) 100 ml of M/100 HCl + 100 ml of M/10 NaOH(B) 55 ml of M/10 HCl + 45 ml of M/10 NaOH(C) 10 ml of M/10 HCl + 90 ml of M/10 NaOH(D) 75 ml of M/5 HCl + 25 ml of M/5 NaOH

Q.82 The partial pressure of CH3OH, CO and H2 in the equilibrium mixture for the reactionCO + 2H2 CH3OH at 427

0C are 2.0, 1.0 and 0.1 atm. respectively. The value of kP forthe decomposition of CH3OH to CO and H2 is(A) 1 X 10-2 atm (B) 2 X 102 atm-1 (C) 50 atm2 (D) 5 X 10-3 atm2

Q.83 From separate solution of four sodium salts NaW, NaX, NaY and NaZ had pH 7.0, 9.0,10.0and 11.0 respectively. When each solution was 0.1M, the strongest acid is

(A) HW (B)HX (C)HY (D)HZ

Q.84 To prepare a buffer of pH 8.26, amount of (NH4)2SO4 to be added into 500 ml of 0.01 MNH4OH solution [pKa (NH4

+) = 9.26] :

(A) 0.05 mol (B) 0.025 mol (C) 0.10 mol (D) 0.005 mol

Q.85 The pH of the solution when 0.2 mole of HCl is added to one litre of a solution containing0.1 M CH3COOH and 0.1 M CH3COO

is (A) 0.7 (B) 4.57 (C) 3.8 (D) 1.0


Q.86 When 0.4 g of NaOH is dissolved in one litre of solution, the pH of the solution is (A) 12 (B) 2 (C) 6 (D) 10

Q.87 pH of the solution obtain on mixing 300 ml of solution having pH = 2, 800 ml of solutionhaving pH = 12 and 900 ml of solution having pH = 13 is(A) 12.67 (B) 2 (C) 11.67 (D) 13

Q.88 How many times (approximately) should an extremely weak monobasic acid, HA, be diluted,

so that the hydrogen ion concentration is reduced to 41

of that in the original solution?(A) 16 (B) 2 (C) 4 (D) 8

Q.89 If 50 ml of 0.2 M KOH is added to 40 ml of 0.5 M HCOOH, the pH of the resulting solutionis : (Ka = 1.8 10

4)(A) 3.75 (B) 5.6 (C) 7.5 (D) 3.4

Q.90 Among the following compounds which has the largest dipole moment(A) CH3OH (B) CH4 (C) CF4 (D) CH3F


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27-01-2014-20140127102544