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BRILLIA N TS
M O C K A LL-IN DIA TESTS (B.M A T)
N A TIO N A L SIT-D O W N
PRO G RESSIV E EV A LUA TIO N TEST 1FOR STUDENTS OF
OUR TWO-YEAR ELITE POSTAL COURSE
TOWARDS
IIT-JO INT EN TRA N C E EXA M INA TIO N , 2011
QUESTION PAPER CODE
Time: 3 Hours Maximum Marks: 240
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
INSTRUCTIONS:
Name: . Enrollment No.:
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1
A. General
1. This booklet is your Question Paper containing 57 questions. The booklet has 26 pages.
2. This question paper CODE is pr in ted on t he r igh t h an d t op cor ner of t his s heet a nd on t he ba ck pa ge
(pa ge no. 26) of t his booklet.
3. Th is q ues t ion pa p er con t a in s 6 b la n k pa g es f or y ou r r ou gh w or k. N o a d di t ion a l s heet s w i ll b e pr ovi dedfor rough work.
4. B la n k pa per s, clipb oa r ds , log t a bles , s lid e r ules , ca l cu la t or s, cellula r ph on es , pa g er s, a n d elect r on icgadgets in a ny form are not a llow ed to be car ried inside the examina tion hall.
5. F ill in t he boxes pr ovid ed below on t his pa ge a nd a ls o w r it e your Name a nd Enrollment No. in t hespa ce provided on the ba ck page (page no. 26) of this booklet.
6. The answ er sheet, a ma chine-readable Objective Response Sheet (ORS), is provided sepa ra tely.
7. DO NOT TAMPE R WITH /MU TILATE THE ORS OR THE B OOK LE T.
8. Do not break t he seals of the question-paper booklet before being inst ructed to do so by t he invigilators.
B. Filling the ORS
9. On t he low er pa rt of t he ORS , w rit e in ink, your na me in box L1, your E nr ollment No. in box L2 a ndNam e of the Centr e in box L3. Do not write these anywhere else.
10. The ORS has a CODE printed on its lower and upper parts.11. Ma ke sur e t he C OD E on t he ORS is t he sa me a s t ha t on t his booklet a nd put your signa tur e in ink in
box L4 on the ORS affirm ing tha t you have verified this.
12. IF THE CODE S D O NOT MATCH , ASK FOR A CHANG E OF THE BOOK LET.
C. Question paper format: Read the inst ructions printed on t he ba ck page (pa ge no. 26) of t his booklet.
D. Marking scheme: Read the instructions on the back page (page no. 26) of this booklet.
SEAL
S
EAL
DON
OTBREAKTHESEALSON
THISBOOKLET,
AWAITINSTRUCTIONSFROMT
HEINVIG
ILATOR
CHEMISTRY MATHEMATICS PHYSICSPAPER II
I have read all the instructionsand shall abide by them.
...............................................
Signature of the Candidate
I have verified all the informationsfilled in by the Candidate.
...............................................
Signature of the Invigilator
ELITE 2011
I PET/ C M P/ P( II) / Q NS
02 .08 .2009
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PART A : CHEMISTRY
SECTION I
Single 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 ONLYONE is correct.
1.An aqueous solution of 6.3 g of oxalic acid dihydrate is made up to 250 mL. Thevolume of 0.1 N NaOH required to neutralize 10 mL of this solution is
(A) 40 mL (B) 20 mL (C) 10 mL (D) 4.0 mL
2. The rms velocity of hydrogen is 7 times the rms velocity of nitrogen. If T is thetemperature of the gas then
(A)TH
2
= TN
2
(B)TH
2
< TN
2
(C)TH
2
> TN
2
(D)TH
2
= 7 TN
2
3. Given that the mass of an electron is 9.1 1031
kg and the velocity of electron is
2.2 106
ms1
. If the uncertainty in its velocity is 0.1%, the uncertainty in the
position would be
(A) 26 nm (B) 32 nm (C) 48 nm (D) 50 nm
4.A pair of compounds which have odd electrons in the group NO, CO, ClO2, SO
2
and O3
are
(A) NO, ClO2 (B) CO, SO
2 (C) ClO
2, CO (D) SO
2, O
3
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SECTION II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B),
(C) and (D) for its answer, out of which ONE OR MORE is/are correct.
5.A bond formed between two like atoms can be
(A) ionic (B) covalent (C) coordinate (D) metallic
6. Which of the following set of species have bond order more than 2.0:
O2
, NO, CO, O
2
2, O
2
(A) all (B)O2
, NO, CO
(C) O2
, O
2, O
2
2(D) O
2
, NO
7. Which of the following statements are true?
(A) The mean free path () of gas molecules is given by1
22N
.
(B) The relationship between average velocityv and root mean square velocity u
isv = 0.9213u.
(C) The root mean square velocity of the gas can be calculated by the formula
3RT
M
12
.
(D) Joule Thomson coefficient for a gas is zero at its critical temperature.
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8. For which of the following set of species Bohrs theory is applicable.
Be3+
, H+, Li
2+, He
2+, H, H
2
.
(A) Be3+
, Li2+
(B) H, H2
(C) H+, H, He
2+ (D) Be
3+, H, H
+
9. In a chemical reaction:
K2Cr
2O
7+ x H
2SO
4+ y SO
2 K
2SO
4+ z Cr
2(SO
4)3
+ H2O
The incorrect values of x, y and z are
(A) 4, 1, 4 (B) 1, 3, 1 (C) 3, 2, 3 (D) 2, 1, 2
SECTION III
Matrix-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 the statements in Column II are labelled 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. The appropriate bubbles correspondingto the answers to these questions have to be darkened as illustrated
in the following example:
If the correct matches are A p, s and t; B q and r; C p and q; and
D s and t; then the correct darkening of bubbles will look like the
following.
10. Column I Column II
(A) C2 (p) No antibonding orbital
(B) N2
(q) Highest bond dissociation energy
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(C) N2 (r) Bond order 1
2
(D) H2
(s) Diamagnetic
(t) Paramagnetic
11. Column I Column II
(A) Boyles law (p)
(B) Charles law (q) log P = log V + Constant
(C) Helium gas (r) log V= log T + Constant
(D) Hydrogen gas (s) PV = RT + Pb
(t) Heating effect on Joule Thomsonexperiment
SECTION IV
Integer Answer Type
This section contains 8 questions. The answer to each of the
questions 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 example, if the correct
answers to question numbers X, Y, Z and W (say) are 6, 0, 9
and 2, respectively, then the correct darkening of bubbles will
look like the following:
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12.A gas at T1
is heated in such a way that its pressure and volume both become
two times. The absolute temperature (T2) of the gas becomes __________ times
that of T1.
13. The frequency of the spectral line emitted when the electron is n = 3 in H atom
deexites to ground state is given as x 1015
sec1
as x approximately is _______ .
14. The maximum number of water molecules that one water molecule can hold
through hydrogen bonding is __________ .
15. The number of molecules which are linear among the following:
C2H
2, NO
3
, BF
3, BeH
2, HgCl
2is ________ .
16.At 200 K, the root mean square (rms) velocity of a gas A (Molecular weight = 40)
is equal to the most probable velocity of gas B at 30 K. The molecular weight of B
is ______ .
17. The number of half-filled orbitals in Fe3+
ion (Fe = 26) is ________ .
18.A neutral atom of an element has K2L
8M
11and N
2electrons. The total number of
s electrons in the atom is ________ .
19. The molecule SF6
has an octahedral shape. The total number of different orbitals
involved in the hybridisation is _________ .
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PART B : MATHEMATICS
SECTION I
Single 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 ONLYONE is correct.
20. If a, b, c, d > 0, k 0 anda bk
a bk=
b ck
b ck=
c dk
c dk, then a, b, c, d are in
(A) A.P (B) G.P (C) H.P (D) None of these
21. If a1, a
2, ..., a
nare in G.P with common ratio r, then
a1a
2
a1
2 a
2
2
a2a
3
a2
2 a
3
2 ...
an 1
an
an 1
2 a
n
2is
(A)n 1 r
1 r(B)
nr
1 r(C)
n1 r
1 r2
(D)nr
1 r2
22. If A = sin1
sin4
3, B = cos
1cos
5
3, then
(A) A = 2B (B) B = 2A (C) A > B (D) A = B
23.A point P is inside an equilateral triangle. If the distances of P from the sides are4, 5, 6 units, then the length of the side of the triangle is
(A) 5 (B)5 3 (C)10 3 (D)15 3
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SECTION II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B),
(C) and (D) for its answer, out of which ONE OR MORE is/are correct.
24. The series of natural numbers is divided into groups as 1; 2, 3, 4; 5, 6, 7, 8, 9;10, 11, 12, 13, 14, 15, 16; ... . Then the sum of the numbers in the nth group is
(A) n3 3n
2+ 3n + 1 (B) n
3+ (n 1)
3
(C) (2n 1) (n2 n + 1) (D) (2n 1) n
2
25. If 3 sin = sin (2 + ), then
(A) sin = cos ( + ) sin (B) tan ( + ) = 2 tan
(C) 2 sin = sin ( + ) cos (D) None of these
26. If tan1
x, tan1
y, tan1
z are in A.P. and x, y, z are in A.P. (y 1, 1, 0), then
(A) (x y)2
+ (y z)2
+ (z x)2
= 0
(B) x = 2y = z
(C) x = y = z
(D) x = y = 2z
27. In a ABC, cos A cos B + sin A sin B sin C = 1, then the triangle is
(A) obtuse-angled (B) right-angled
(C) isosceles (D) equilateral
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28. If sin1
x + sin1
y =2
3, cos
1x cos
1y =
3, then
(A) x =
1
2 (B) y =
1
2 (C) x = 1 (D) y = 1
SECTION III
Matrix-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 the statements in Column II are labelled 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. The appropriate bubbles corresponding
to the answers to these questions have to be darkened as illustratedin the following example:
If the correct matches are A p, s and t; B q and r; C p and q;
and D s and t; then the correct darkening of bubbles will look like
the following.
29. The value of x when
Column I Column II
(A) sin1
x + cot1
1
2=
2is (p)
1
3
(B) 2 cos1
x + sin1
x = cos1 2 6
5is (q)
1
6
(C) 3 sin1 2x
1x2 4 cos
1 1x2
1 x2 2 tan
1 2x
1 x2
=
3is (r)
1
5
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(D) tan1
2x + tan1
3x =
4is (s)
1
5
(t)1
3
30. The solutions of the trigonometric equations
Column I Column II
(A) 4 cot 2 = cot2 tan
2 (p) n +
4, n I
(B) sin4
x + cos4
x = sin x cos x (q) n
4, n I
(C) The common root of the equations (r) n, n I2 sin
2x + sin
22x = 2; sin 2x + cos 2x = tan x
(D) tan2
x sec10
x + 1 = 0 (s) (2n + 1)
4, n I
(t) (n + 1)
4, n I
SECTION IV
Integer Answer TypeThis section contains 8 questions. The answer to each of the
questions 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 example, if the correct
answers to question numbers X, Y, Z and W (say) are 6, 0, 9
and 2, respectively, then the correct darkening of bubbles will
look like the following:
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31. In a ABC, r1
= 1, r2
= 2 and C =
2, then area ofABC is ________ .
32. The value of tan 20 + 2 tan 50 tan 70 is ______
33. If the area of a ABC is 2 square units, then b2
sin 2C + c2
sin 2B is equal to
______ .
34. The sum of the first 10 terms of a G.P is equal to 244 times the sum of its first
five terms. Then the common ratio is ____________ .
35. For an A.P, S2n
= 3Sn. Then the value of
S3n
Sn
is ______ .
36. If the positive numbers a, x, y, z, b are such that when they are in A.P
x + y + z = 15 and when their reciprocals are in A.P 1
x
1
y
1
z=
5
3, then ab equals
___________ .
37. In a ABC, a = 5, b = 4 and cos (A B) =31
32, then the side c is _________ .
38. In a ACB, if 3b = c + a, cotC
2cot
A
2equals _______ .
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PART C : PHYSICS
SECTION I
Single Correct Choice TypeThis section contains 4 multiple choice questions. Each question has 4 choices (A), (B),
(C) and (D) for its answer, out of which ONLYONE is correct.
39. Which of the following is the most precise device for measuring length?
(A)A vernier callipers with 20 divisions on the sliding scale.
(B)An optical instrument that can measure length to within a wavelength oflight.
(C)A screw gauge of pitch 1 mm and 100 divisions on the circular scale.
(D)A spherometer of pitch 1 mm and 250 divisions on the head scale.
40.A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 m/s.
The magnitude of its momentum is recorded as
(A) 17.56 kg m/s (B) 17.57 kg m/s
(C) 17.6 kg m/s (D) 17.565 kg m/s
41. The vernier of a circular scale is divided into 30 divisions which coincide against
29 main scale divisions. Each main scale division is1
2
. The least count of the
instrument is
(A) 30 (B) 10 (C) 1 (D) 0.1
42. The mass of a box is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are
added to the box. The total mass of the box correct to relevant significant figuresis
(A) 2.3 kg (B) 2.34 kg (C) 2.3432 kg (D) 2.31 kg
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SECTION II
Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B),
(C) and (D) for its answer, out of which ONE OR MORE is/are correct.
43. Consider a rubber ball freely falling from a height h onto a horizontal elastic
plate. Assume that the duration of collision is negligible and the collision with
the plate is totally elastic. Then which of the following graphs best describe the
velocity as a function of time and the height as a function of time?
(A) (B)
(C) (D)
44.A body A is at rest at x = 0. At t = 0, it starts moving in the positive x-direction
with constant acceleration 1 m/s2. At the same instant another body B passes
through x = 0 moving in the positive x-direction with a constant speed v = 2 m/s.
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The position of the first body is given by x1
(t) after time t and that of the second
body by x2
(t) after the same time interval. Then
(A) The relative displacement (x1 x2) is zero at t = 4 s.
(B) The relative displacement attains the minimum value at t = 4 s.
(C) The relative velocity (v1 v
2) is zero at t = 2 s.
(D) The body B overtakes the body A at t = 4 s.
45. For a particle projected at an angle with the ground, which of the following
statements are correct?
(A) The angle of projection at which the range and the maximum height attained
by a projectile are equal is tan1 4.
(B) The motion of a projectile as observed from another projectile is a straightline.
(C) The projectile motion is a free motion and a projectile is a freely falling body.
(D) Radius of curvature of the projectile at the highest position is equal to itsmaximum height.
46.A particle is projected on an inclined plane which is
inclined at an angle to the horizontal with a constantspeed at an elevation , then
(A) its acceleration is always directed vertically down.
(B) if the direction of velocity is changed, the force acting on it does not change inmagnitude and direction.
(C) if the direction of velocity is changed, the force acting on it does not change inmagnitude but changes its direction.
(D) the linear momentum continuously changes.
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47.A painter is applying force himself and the crate moves upward
with an acceleration of 5 m/s2
by a massless rope and pulleyarrangement. Mass of painter is 100 kg and that of crate is 50 kg. If
g = 10 m/s2, then
(A) tension in the rope is 1125 N.
(B) tension in the rope is 2250 N
(C) force of contact between the painter and the floor is 375 N.
(D) force of contact between the painter and the floor is 750 N.
SECTION III
Matrix-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 the statements in Column II are labelled 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. The appropriate bubbles
corresponding to the answers to these questions have to be
darkened as illustrated in the following example:
If the correct matches are A p, s and t; B q and r; C p and q;
and D s and t; then the correct darkening of bubbles will look like the following.
48. Column I gives a list of possible set of parameters measured in someexperiments. The variations of the parameters in the form of graphs are shown in
Column II. Match the set of parameters given in Column I with the graphsgiven in Column II.
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Column I Column II
(A) Range of a projectile (y-axis) as a function of
its velocity (x-axis) when projected at a fixed
angle
(p)
(B) Displacement (y-axis) as a function of time
(x-axis) for one dimensional motion at zero or
constant acceleration when the body is movingalong the positive x-direction
(q)
(C) Speed (y-axis) as a function of time (x-axis)
of the ball during its flight when it is thrown
vertically upwards (constant air resistance isassumed)
(r)
(D) Velocity (y-axis) with displacement (x
-axis) of
a body starting from rest along a straight linewith zero or constant acceleration
(s)
(t)
49. Column I Column II
(A) A body is in translatory equilibrium if (p) it may be at rest(B) If the velocity of a body is always (q) resultant force on it
perpendicular to its acceleration may be zero
(C) If the magnitude of the velocity of a (r) it may be in uniform linearparticle is constant and equal to its speed motion
(D) If a particle has zero displacement (s) it may be in circularmotion
(t) it may be thrown verticallyupward
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SECTION IV
Integer Answer Type
This section contains 8 questions. The answer to each of the
questions 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 example, if the correct
answers to question numbers X, Y, Z and W (say) are 6, 0, 9
and 2, respectively, then the correct darkening of bubbles will
look like the following:
50.At certain moment of time, velocities of block A and block B both are 1 m/s
upwards, find the magnitude of velocity of block C at that moment in m/s.
51.An elevator starts from rest at the ground floor of a building. It can accelerate at
1.5 m/s2
and then decelerate at 0.5 m/s2. Find the shortest time in s, it takes to
reach a floor 12 m above the ground.
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52.An aeroplane lands on the straight runway, originally at 48 m/s when s = 0. If it
is subjected to the decelerations shown, the time needed to stop the plane is given
as t = 10x s. Find x.
53.A ball falls for 6 s under gravity. It passes through a cardboard which is 58.8 m
above the ground. After passing through the cardboard its velocity is reduced to
one third. Find the time taken to reach the ground.
54. Figure shows a block of m1
= 2.5 kg sliding on a
block of m2
= 0.5 kg which is placed on a smooth
inclined plane of inclination = 30. Find
tension in the string in newton.
55. Maximum range R1
down the inclined plane of
inclination 30 for a projectile is times the
maximum range R2
up the same inclined plane
for a given velocity of projection. Find .
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56. Two blocks of mass m = 15 kg and M = 10 kg are connected by a string passing
over a pulley B as shown. Another string connects the centre of the pulley B to
mass C = 30 kg and passes over another pulley A as shown. All masses are placed
on the ground. If a upward force F = 500 N is applied at the centre of pulley A,
(Both the pulleys are massless) the initial acceleration of mass M in m/s2
is
57.A passenger is walking on an escalator at a speed of 5 km/hr relative to escalator.
The escalator is moving at 4 km/hr relative to ground and a total length of 300 m.
How long does it take him to reach the escalator? (Express in minute)
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Name: . Enrollment No.:
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
B illi t T t i l P t Ltd EELP/I PET/CMP/P(II) 26
C. Question paper format:
13. The question paper consists of 3 parts (Part A: Chemistry, Part B: Mathematics and Part C: Physics).Each part has 4 sections.
14. Section I contains 4 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its
answer, out of which only one is correct.
15. Section II contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its
answer, out of which one or more is/are correct.
16. Section III contains 2 questions. Each question has four statements (A, B, C and D) given in Column Iand five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct
matching with one or more statement(s) given in Column II. For example, if for a given question,statement B matches with the statements given in q and r, then for that particular question, againststatement B, darken the bubbles corresponding to q and r in the ORS.
17. Section IV contains 8 questions. The answer to each of the questions is a single-digit integer,
ranging from 0 to 9. The answer will have to be appropriately bubbled in the ORS as per theinstructions given at the beginning of the section.
D. Marking scheme:
18. For each question in Section I, you will be awarded 3 marks if you darken 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.
19. For each question in Section II, you will be awarded 4 marks if you darken the bubble(s)
corresponding to the correct choice(s) for the answer, and zero mark if no bubble is darkened. In allother cases, minus one (1) mark will be awarded.
20. For each question in Section III, you will be awarded 2 marks for each row in which you havedarkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries amaximum of8 marks. There is no negative markingfor incorrect answer(s) for this section.
21. For each question in Section IV, you will be awarded 4 marks if you darken the bubble correspondingto the correct answer, and zero mark if no bubble is darkened. In all other cases, minus one (1)
mark will be awarded.