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CODE : WHITE 26888/QB/HYD-SBD-C / IITJEE / 2-12-2010 / IITJEE

NARAYANA IIT ACADEMY ANDHRA PRADESH

GRAND TEST-2 PAPER-2 IITJEE MODEL Exam Date : 11-12-10

Time : 3:00 Max Marks : 240 ID.NO :

INSTRUCTIONS :

1)

This booklet of your Questions Paper contains 57 questions. Maximum marks: 240. The question paper consists of 3 parts (Chemistry, Mathematics and Physics). Each part has 4 sections.

2)

Section-I contains 4 multiple choice questions. Q.No: 1 to 4, 20 to 23 and 39 to 42. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section ¿ I, you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (-1) mark will be awarded.

3)

Section-II contains 5 multiple correct answer(s) type questions. Q.No: 5 to 9, 24 to 28 and 43 to 47. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. For each question in Section II, you will be awarded 4 marks s if you have darkened all the bubble(s) corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

4)

Section-III contains 2 questions. Q.No: 10,11,29,30,48 and 49. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. For each question in Section III, you will be awarded 2 for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marking for incorrect answer(s) for this section.

This Question paper contains 20 Pages GRAND TEST-2 PAPER-2_11-12-10

5)

Section-IV contains 8 questions. Q.No: 12 to 19, 31 to 38 and 50 to 57. The answer to each of the question is a single digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For each question in Section IV, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

CHEMISTRY

SECTION-1Section-I contains 4 multiple choice questions. Each question has 4 choices (A) , (B) , (C) and (D) , out of which ONLY ONE is correct. For each question in Section - I , you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer , minus one (-1) mark will be awarded.

1) At , the presence of a catalyst causes the activation energy of a reaction to decrease by 4.606K.cal. The rate of the reaction will be increased byA) 2 times B) 10 times C) 100 times D) 1000 times

2) When a solution of and is treated with an excess of KCN solution, then the most stable complex formed is.

A) B) C) D)

3) Identify the weakest acid from the followingA) Cyclopentadiene B) CycloheptatrieneC) 2,4,6 - Trinitrophenol D) Acetic acid

4) The major product obtained in the reaction is,

Space for rough work of 20


A) B) C) D)

SECTION-2Section-II contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A) , (B) , (C) and (D) , out of which ONE OR MORE is/are correct. For each question in Section II , you will be awarded 4 marks s if you have darkened all the bubble(s) corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases , minus one (-1) mark will be awarded. 5) Consider the cell

The cell reaction will be spontaneous ifA) and B) and C) and D) and

6) For the reaction the correct statements is / are:

A) B) C) D)7) The borax bead test can be used to detect the presence of

A) B) C) D)

8) The incorrect statement among the following are A) At high temperature dissociates into two neutral oxides of nitrogen.B) forms three acidic saltsC) is soluble in by forming a complex

D) Aqua regia is a mixture of 75% conc. and 25%. Conc. HCl.9) Which among the following molecule (s) or molecular ion (s) is /are planar ?

A) B) C) D)

SECTION-3



Section-III contains 2 questions. Each question contains statements given in two columns , which have to be matched. The statements in Column I are labeled A , B , C and D , while the statements in Column II are labeled p , q , r , s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. For each question in Section III , you will be awarded 2 for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus , each question in this section carries a maximum of 8 marks. There is no negative marking for incorrect answer(s) for this section. 10) Match the Following:

Column I Column II(a) (p)

(b) (q)

(c) (r)(d) (s)

11) Match the Following: Column I Column II

(a) (p) alc. KOH at room temperature

(b) (q) ethoxide in ethanol

(c) (r) + Raney Ni



(d) (s)

(t) in ether at

SECTION-4Section-IV contains 8 questions. The answer to each of the question is a single digit integer , ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For each question in Section IV , you will be awarded 4 marks if you darken the bubble corresponding to the correct answer , and zero mark if no bubble is darkened. In all other cases , minus one (-1) mark will be awarded. 12) A chemical reaction takes place in container of cross sectional area of 100 , the

container has a piston at one end. As a result of reaction, piston is pushed out against 100 kpa and 90J of work is performed on the surroundings. Then the distance (in cm) travelled by the piston is

13) 0.2 moles of gas at 0.4 atm diffuses in 4 sec. through a pin hole. Then the time

required in seconds for the diffusion of 0.1 moles of at 1.6 atm through the same hole is

14) A solution contains 500ml of 0.2M and 500ml of 0.1M . If 500ml of water is added to this, then pH after dilution is (pka of is 4.7)

15) Total number of nuclides that undergoes positron emission among are

16) In alkaline medium reacts with 30% and forms a red-brown complex compound. The oxidation state of Cr is + n in that complex. Then n value is.

17) The presence of nitrate ion is detected by brown ring test. The number of unpaired electrons present at the metal ion in that complex is.

18) The total number of lone pairs in triethylene tetramine (triene) is19) Give the number of carbon atom, attached to methyl group in the product formed,

as per the indicated numbering in the reactant, in the following reaction.



MATHEMATICSSECTION-1

Section-I contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section - I , you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (-1) mark will be awarded.

20) In the xy – plane, how many straight lines whose x-intercept is a prime number and

whose y-intercept is a positive integer pass through the point

A) B) C) D)

21) are all different and non zero real numbers which are in arithmetic progression. If

the roots of the quadratic equation are and such that

and are in geometric progression, then the value of is

A) B) C) D)

22) The point of intersection of the plane with the straight line passing

through the origin and perpendicular to the plane is



A) B) C) D)

23) An ellipse has foci at and in the xy – plane and is tangent to the x axis. The length of its major axis is

A) B) C) D)

SECTION-2Section-II contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. For each question in Section II, you will be awarded 4 marks s if you have darkened all the bubble(s) corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

24) Let be the point and be a point on the y axis such that has slope Then the locus of the mid point of as varies over all real values, is a

parabola, whoseA) Vertex is B) Latus – rectum is of length 2

C) Focus is D) Directrix is

25) For real number let denote the largest integer smaller than or equal to and

denote the smallest integer greater than or equal to Also, let

for Then

A) is not periodic B) is periodic with period 1

C) D)

26) Let be the three sets of complex numbers as defined below

and

Let be any point in and let be any point satisfying

Then lies between

A) B) C) D)



27) For the function

A)

B) For atleast one in the interval

C) For all in the interval

D) is strictly decreasing in the interval 28) Let and be two points on the x – axis. A point is moving in

the xy – plane in such a way that Then the point moves along a conic whose

A) Eccentricity is 2 B) Eccentricity is

C) Latus – rectum is of length 6 D) Directrices are

SECTION-3Section-III contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. For each question in Section III, you will be awarded 2 for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marking for incorrect answer(s) for this section.

29) Match the following:Column -I Column -II

(A) The parabola has vertex and y-intercept where The value of is not less than

(p)

(B) Two of the altitudes of a scalene triangle ABC have length 4 and 12. If the length of the third altitude is

which is also an integer, then can be

(q)

(C) The number of points in the complex plane satisfying and

(r)



is not more than(D) The straight line intersects the

ellipse at two points A and B. There is a

point on the ellipse such that area of is 3. The number of such points is not greater than

(s)

(t)30) Match the following:

Column -I Column -II

(A) If the equations

are consistent, then can be

(p)

(B) Number of solutions of the equation

in does not

exceed

(q)

(C) In triangle ABC, with usual notation, the value of

is not less than

(r)

(D) Let be complex numbers such that Then

cannot be less than

(s)

(t)

SECTION-4

Section-IV contains 8 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For each question in Section IV, you will be



awarded 4 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

31) If in triangle ABC, the line containing circumcentre and ortho–centre is parallel to then

32) If are non zero numbers such that are the roots of the equation

and are the roots of the equation then the value of

is

33) The value of the definite integral is

34) Suppose people are seated at a round table. If three people are selected at

random, and is the probability that atleast two of them are sitting next to each other,

then (when is expressed in lowest terms) where

35) Consider a triangle ABC. The median meets the side at A point on is chosen such that The straight line extended meets the side at

the point F. Then equals

36) Let where is an integer Then

37) If the function and then the value of is

38) When the terms in the binomial expansion of are arranged in decreasing

powers of the coefficients of the first three terms are in arithmetic progression. The number of terms in the expansion with integer powers of is



PHYSICSSECTION-1

Section-I contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. For each question in Section - I, you will be awarded 3 marks if you have darkened only the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (-1) mark will be awarded. 39) In the figure shown the pulleys are light and frictionless and the strings light and

inextensible. Initially the system is in equilibrium. If m is now pushed downward and released it executes simple harmonic motion. Assuming during the motion there are no collisions and the spring is ideal, the maximum possible amplitude we can give to ‘m’(from the equilibrium position) such that the motion is still simple harmonic is (g = acceleration due to gravity)

A) B) C) D)

40) A triangular wedge of mass ‘M’ is placed on a smooth horizontal surface. A block of mass ‘m’ is placed on the wedge. The coefficient of friction between the block and the wedge is 0.6. The horizontal acceleration ‘a’ of the wedge such that ‘m’ moves up the wedge is



am

M60

A) B)

C) D) Such a value for ‘a’ is not possible

41) In a photo electric experiment I(current)-V (voltage) graph is as shown. Curves a,b,c correspond to three different metal surfaces irradiated with monochromatic light of same frequency. Assuming the ratio of number of electrons emitted per second to the number of photons incident per second is the same for all the three surfaces, choose the INCORRECT statement :

A) the work function of metals b and c are equal

B) the intensities of light incident on a and b are same

C) the work functions of metals a and b are not equal

D) the intensities of light incident on a, b and c are all different

42) The time period of oscillation of a thin uniform rod when suspended from a point P and when suspended from the point Q, P and Q being on opposite sides of the centre of mass, is same and is equal to T. If the distance between P and Q is l, the acceleration due to gravity

A) B) C) D)



SECTION-2

Section-II contains 5 multiple correct answer(s) type questions. Each question has 4 choices (A) , (B) , (C) and (D) , out of which ONE OR MORE is/are correct. For each question in Section II , you will be awarded 4 marks s if you have darkened all the bubble(s) corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases , minus one (-1) mark will be awarded.

43) A short electric dipole is placed in the electric field due to a point charge. Then

A) The dipole must experience a force

B) The dipole may experience a force

C) The dipole must experience a torque

D) The dipole may experience a torque

44) Charge ‘Q’ is uniformly spread on a circular disc, of mass ‘m’ radius ‘R’ which is free to rotate in horizontal plane about vertical axis. Initially the disc is at rest in a uniform vertical magnetic induction field ‘B’ which covers its entire area. Now the field is switched off. The angular velocity gained by the disc depends on

A) Q B) R C) m D) B

45) We have two equal size boxes, A and B. Each box contains gas that behaves as an ideal gas. The pressure of the gas in box A is 0.20 atm and the pressure of the gas in box B is 0.04 atm. This is all we know about the gas in the boxes. Which of the following statements MUST be true?

A) There are more molecules in A than in B

B) The molecules in A are moving faster than those in B

C) The temperature in A is higher than in B



D) The total translational kinetic energy of all molecules is greater in gas A than in gas B

46) A solid sphere of mass ‘m’ is rolling down an inclined surface inclined at an angle to the horizontal without slipping. Then

A) the frictional force acting on the sphere is ( coefficient of static friction)

B) ‘f ’ is dissipative force

C) Friction will increase the sphere’s angular velocity and decrease its linear velocity

D) If decreases, friction will decrease

47) A student performed the experiment to measure the focal length of convex (converging) lens by lens displacement method.(First an approximate estimate of the focal length was obtained by distant object method in which a distant object was focused on the screen using the lens and the distance between lens and screen noted as ‘f’, the focal length of the lens). The distance between the object and screen is adjusted to be a value ‘ l’. Now the lens, was moved from the object to the screen and clear images are obtained for two positions of the lens, the first position L1, which is closer to object and 2nd position L2

which is closer to screen. The distance between the two position i.e . Let

the focal length obtained be

A) the values of used are

B) the image for position of lens is diminished and that for position of lens is magnified

C) As l is increased (for more number of trials), ‘d’ also increases

D)



SECTION-3Section-III contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, B, C and D , while the statements in Column II are labeled p , q , r , s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. For each question in Section III, you will be awarded 2 for each row in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of 8 marks. There is no negative marking for incorrect answer(s) for this section.

48) Column II gives information of a capacitor undergoing a certain process. Column I suggests changes in some of the parameters related to the circuit the capacitor is in. Match the statements in Column I to the appropriate processes from Column II.

Column I Column II(a) The energy of the capacitor

decreases(p) A parallel plate capacitor is charged

and isolated. Now the distance between the plates is slowly increased till it is doubled

(b) Force on the plates due to the field of the capacitor remains the same

(q) A parallel plate capacitor is connected across a battery. Now the distance between the plates is slowly increased till it is doubled

(c) Work is done by the battery (r) A parallel plate capacitor is charged and isolated. A dielectric slab is introduced completely filling the gap between the plates

(d) Charge stored in the capacitor remains the same

(s) A parallel plate capacitor is connected across a battery. A dielectric slab is introduced completely filling the gap between the plates

(t) A parallel plate capacitor is charged to a potential difference of V volts. Now its polarity is reversed by connected it to a battery of V volts.



49) Column II shows the position of object OB with respect to an optical entity which is a convex mirror or refracting surface or a thin lens. Consider only paraxial rays. Column I gives possible properties of the image formed or optical entity involved. Match them

Column I Column II(a) Image is virtual (p)

(b) Image is magnified (q)

(c) Image lies below the principal axis

(r)

(d) The mirror / Refracting surface/Thin lens / acts as a converging system.

(s)



(t)

SECTION-4

Section-IV contains 8 questions. The answer to each of the question is a single digit integer , ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORS have to be darkened. For each question in Section IV, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer, and zero mark if no bubble is darkened. In all other cases, minus one (-1) mark will be awarded.

50) One experimental method of measuring an insulating materials thermal conductivity is to construct a box of the material and measure the power input to an electric heater inside the box that maintains the interior at a measured temperature above the outside surface. Suppose that in such an apparatus a power input of 180 W is required to keep the interior surface of the box above the temperature of the outer surface. The total area of the box is 2.18 m2 and the wall thickness is 3.9cm. The thermal conductivity of material is

. Find x to nearest integer.

51) Water level is maintained in a cylindrical vessel placed on horizontal floor up to a fixed height ‘H’. A tiny hole of area ‘A’ is punched in the side wall at a height from the bottom of the vessel equal to y. The emerging stream strikes the ground at a horizontal distance from cylinder. To maintain the level in the vessel at ‘H’, the rate

(volume /sec) of addition of water is A . Find n

52) A vertical capillary with inner diameter 0.50mm is submerged into water so that the length of its part protruding over the water surface in 25mm. The radius of curvature of the meniscus is . Find x to nearest integer. (Surface tension of water

)



53) A particle of mass ‘m’ having collided with a stationary particle of mass ‘M’ deviated by

an angle rad where as the particle of mass ‘M’ recoiled at an angle of to the

direction of the initial motion of the particle ‘m’. If after the collision there is 40% loss in kinetic energy of the two particle system, find M/m

54) The magnetic induction at the centre of a rectangular wire frame whose diagonal is equal to 16cm and the smaller angle between the diagonals is is . The current flowing in the frame is 5A. Find x.

55) In the figure shown, string is light and inextensible, spring is light and ideal, the pulleys are light and frictionless. Initially the spring is in its natural length and the string just taut. Now the system is released from rest. The maximum extension in the spring during

consequent motion is Find n

mk

2m

56) In the circuit shown in the adjacent diagram initially switch K1 is closed and switch K2 is open. After long time, K2 is also closed. The current through the cell of emf E

immediately after K2 is closed is . Find x.



E3R

2R

2ER

C1K

2K

57) A stretched string of length ‘l’ is excited by plucking the string at right angles to its

length at a point which is a distance of from one end and stopping the vibration at the

centre of the string with a finger. Find the number of antinodes for the vibration corresponding to the first overtone.

IF YOU HAVE GENUINE ACADEMIC PROBLEMSPAPERS SETTERS : HYD-SBD-C

MATHS : MR.APN-9440386328 : : MR.G.N.V.RAMA KRISHNA-9912343870PHYSICS : MR.JOE VINCENT-9885480554 : : MR.SRIHARI PATNAIK-9912346089CHEMISTRY: MR.ETV SHARMA (ORGANIC)-8019948755 : : MR.SUBBA RAO (IN-ORGANIC)-9912343970 : : DR.R.V.S.MURTHY-9949187103.

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ONLINE : 20-12-201010-04-2011

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