APER--2 Academic Session: 2017-18 C 0 JEEPREPARATORYTEST …
Transcript of APER--2 Academic Session: 2017-18 C 0 JEEPREPARATORYTEST …
®
Academic Session: 2017-18
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PART - I : PHYSICS
SECTION – 1 : (Maximum Marks : 40)
This section contains TEN questions
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9 (1 or more
answers are there), both inclusive
For each question, darken the bubble corresponding to the correct integer in the ORS
Marking scheme :
+4 If the bubble corresponding to the answer is darkened
0 If none of the bubbles is darkened
–2 In all other cases
For example, if answer is 1, 4, 7 then OMR should look like0 1 2 3 4 5 6 7 8 9
then (+4) marks will be
given and if, left blank "0 marks" will given else (–2) marks will be given.
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1. In the figure shown, the entire arrangement is on smooth horizontal surface. The mass of rod OA
is negligible and it can freely rotate about O, block B of mass m is attached to spring (2). Spring
constants of springs are shown in figure. Now the block is slightly displaced along the length of the
spring (2) and released. Block performs simple harmonic motion with time periodCm
2K
, find C.
k(2)
massless rod
(1) k
/2 /2
m
O
A
B
2. A particle A is at origin, and another particle B is at x = 5m at t = 0 and they are moving with
constant velocities ˆ ˆ ˆ(2i 2 j k)m / s and ˆ ˆ ˆ( 2i j k)m / s respectively. What is the minimum
distance (in m) between these particle during the course of their motion ?
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3. Two small spheres of mass 1 kg each are connected to each other by means of an undeformed
spring of force constant k = 100 N/m and natural length 1 m. The system is placed on a smooth
horizontal surface and the two spheres are given velocities v0 along and perpendicular to the
spring, as shown in the figure. The maximum elongation in the spring is found to be 0.1 m during
the subsequent motion. The value of v0 is m/s. Find the integer next to .
v0
m mk
v0
4. A non-conducting rod AB of length 5m. having uniformly distributed charge of charge density
10-3 c/m is kept in x-y plane as shown. Electric field at origin due to rod is directed along the line
OC. If line OC makes an angle = (10a + b) degree with positive x-axis as shown. Find the value
of (a+b). (a & b are positive integers)
A
37º
X
Y
CB
O
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5. Two uniform rods AB and CD, each of length and mass m are fixed to two gears (Which are
discs pivoted to fixed points A and C at same horizontal level) as shown in figure. The system is in
vertical plane. When rod AB is slightly rotated by as small angle, rod CD rotates in the opposite
sense by another small angle such that there is no slipping and no dissipation of energy at the
point of contact of the gears due to their teeth in contact. Neglecting the mass of gears, the time
period of small oscillations of the system, is given by10
2ng
where n is a positive integer and g
is acceleration due to gravity. Find n ?
Gear2r
A C
D
B
6. There are 20 points on a circuit board. Each point is connected to each of the other points by a
wire of resistance r = 60Find the equivalent resistance R (In ) between any two points.
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7. Moment of inertia of a disc of mass M = 2 0.02 kg, inner radius a = 5 ± 0.05 cm, outer radiusb = 7 ± 0.07 cm, with respect to an axis passing through geometrical centre of the disc and
perpendicular to the plane of disc is given by (A0 ± B0 × 10–2) kg – cm2. Find the value of 0
0
B
A.
8. A glass sphere5
3
with an inbuilt point source of light P is placed on table. The source P is
just inside the surface of glass and lies on the lower end of vertical diameter. The apparatus isplaced in a dark room. The surface area of the glowing portion of the glass sphere as observed by
the eye is found to be2
2R
.Here and are integers. Find minimum value of – .
small point source of light
glass sphere
P
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9. A uniform disc of mass m and Radius R is to be kept in equilibrium such that its one surface is
touched at a horizontal wall, by irradiating a parallel beam of electromagnetic radiation of intensity
, at an angle with the vertical. Whole arrangement is shown in figure. Disc is perfectly absorbing.
If the minimum coefficient of friction required between disc and horizontal wall for this propose is
2
2
R
R mgC
. Find minimum value of + + use4
.
R
g
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10. Four identical charges are fixed on the periphery of a non conducting ring of radius R as shown.
Ring is rotated with constant angular velocity w.r.t. an axis perpendicular to plane of the ring and
passing through the centre of the ring. Force acting on any of the charge particle only due to the
magnetic interaction between the charges is F =2 2
0q 1
4
Here is an integer. Find the
value of
+q
+q
+q
+qR
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SECTION – 2 : (Maximum Marks : 40)
This section contains FIVE paragraphs Based on each paragraph, there will be TWO questions. Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four option is correct For each question, darken the bubble corresponding to the correct option in the ORS Marking scheme :
+4 If only the bubble corresponding to the correct option is darkened 0 If none of the bubbles is darkened–2 In all other cases
Paragraph for Questions 11 and 12
Two wires 1 and 2 of the same cross-sectional area A = 10 mm2 and the same length but made ofdifferent materials are welded together and their ends are rigidly clamped between two walls asshown in the figure. The respective Young's Modulus and the linear coefficient of thermalexpansion are
Y1 = 109 Nm–1, Y2 = 2 × 109Nm–2
1 = 6×10–4°C, 2 = 3 × 10–4°CAnswer the following two questions.
1, Y1 2, Y2
00
O
11. If the temperature of the system is reduced by 20°C, then the tension in each wire (in N) and thedisplacement of the joint O (in cm) are respectively:(A) 120, Zero (B) 100, 0.7 (C) 150, 0.25 (D) 160, 0.7
12. Find the minimum frequency of the tuning fork that excite the system into vibration, if joint is a
node and the mass per unit length of the wires are 1 = 0.3 kgm–1 and 2 = 0.075 kgm–1 ; 0 = 1m
(A) 80Hz (B) 40Hz (C) 20Hz (D) 100Hz
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Paragraph for Questions 13 and 14
A charged particle of charge –q and mass m is projected with initial velocity 00
qQu
4 ma
from
distance a from a fixed charged Q at an angle of = 60° with the line joining the charges as shownin figure. It is found that charge moves along elliptical path. Answer the following two questions.
–q, m
u0
a
+Q
13. Then for elliptical path choose the correct option:
–q, m
u0
a
+Q
(A) The length of semi-major axis is ‘2a’ (B) The length of semi-minor axis is3
a2
(C) The length of semi-major axis isa
2(D) The length of semi-minor axis is
3a
4
14. Which of the following option is incorrect.(A) The time taken to complete one revolution will depend on angle .(B) if is less than 90° tangential acceleration of particle is positive.
(C) The time period of revolution for = 60° is3 3
016 ma
(D) Area of the ellipse followed will depend on angle .
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Paragraph for Questions 15 and 16
Figure shows variation of internal energy U with the density of one mole of ideal mono-atomicgas for a thermodynamics cycle ABCA. Here process AB is a part of rectangular hyperbola.answer the following two questions.
U
5U0
2U0
20 50
B
CA
15. Incorrect diagram for the above process is:
(A)
PC
B AV
(B)
P C
B
A
V
(C)
V
CB
A
T
(D)
P
AB
C
T
16. Which of the following options is incorrect:(A) Work done by gas in process AB is – 2U0
(B) Work done by gas in process BC is zero
(C) Net work done by the gas during one cycle is 010
n2.5 2 U3
(D) Heat supplied to the gas during process CA is 010
n2.5 1 U3
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Paragraph for Questions 17 and 18
In a hypothetical atom, negatively charged particle having a charge of magnitude 3e and mass 3m
revolves around a proton. Here, e is the magnitude of electronic charge and m is the electronic
mass. Mass of proton may be assumed to be much larger than that of the negatively charged
particle, thus the proton is at rest. This "atom" obeys Bohr's postulate of quantization of angular
momentum, that ish
mvr n2
. It is given that for the first Bohr orbit of hydrogen atom radius of
orbit is r0 speed of electron is V0, and total energy is – E0. Now answer the following questions.
17. The momentum of an emitted photon when it makes a transition from the second excited state to
ground state, is
(A) 08E
c(B) 0E
c(C) 0E81
4 c
(D) 024E
c
18. Radius of the 2nd orbit of this hypothetical atom is
(A) 04
r9
(B) 016
r9
(C) 04
r3
(D) 01
r9
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Paragraph for Questions 19 and 20
A uniform wire frame of linear mass density having three sides each of the length 2a is kept on a
smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the
midpoint of AB. Now answer the following questions.
x
y
J
A P B
g
19. The angular velocity of system just after the impulse
(A)2
3J
22 a(B)
2
3J
11 a(C)
2
J
11 a(D)
2
2J
11 a
20. The velocity of point P just after the impulse is :
(A)J
ja
(B)J
j6 a
(C)J 2 1ˆ ˆi ja 11 6
(D)J 1 1ˆ ˆi ja 11 6
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PART : II CHEMISTRY
Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,
P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,
Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]
SECTION – 1 : (Maximum Marks : 40)
This section contains TEN questions
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9 (1 or more
answers are there), both inclusive
For each question, darken the bubble corresponding to the correct integer in the ORS
Marking scheme :
+4 If the bubble corresponding to the answer is darkened
0 If none of the bubbles is darkened
–2 In all other cases
For example, if answer is 1, 4, 7 then OMR should look like0 1 2 3 4 5 6 7 8 9
then (+4) marks will be
given and if, left blank "0 marks" will given else (–2) marks will be given.
21. If P = total number of geometrical isomers of the octahedral complex [Ma2b2cd], where a, b, c and
d are monoatomic ligands and Q = total number of optical stereoisomers of the same complex,
then the values of P and Q are :
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22. The following wave function of an H-like species refers to nth excited state. The possible values of
n is/are :
=Zr
3 / 2 21Z (2 Zr)e
4 2
23. A first order reaction is completed by 20% in 2 minutes. How much time (in minute) can be further
elapsed so that its concentration does not reduce below 50% of initial concentration ? (Given : log
2 = 0.30, log 5 = 0.70)
24. 5.6 L of an unknown ideal gas at STP requires 7.5 calorie energy to rise its temperature from 300K
to 310K in an isochoric process. What is/are the possible value(s) of atomicity of the gas?
(Take R = 2 cal.mol–1.K–1)
25. A crystal is made up of atoms X, Y and Z. Atoms X are in FCC packing. Y atoms occupy all
octahedral voids and Z atoms occupy all tetrahedral voids. If all the atoms along two body
diagonals are removed, formula of the crystal becomes XaYb Zc, where a, b and c are simplest
possible integers. The values of a, b and c are:
26. When the following reaction in hot aqueous medium is completed and balanced with simplest
integer coefficients, the coefficient of the products X, Y and Z are:
Br2 (g) + Na2CO3 (aq) X (aq) + Y (aq) + Z (g)
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27 Consider the major organic product of the reaction when following compound is heated with
excess concentrated H2SO4.
OH
OHHO
H+ (excess)
If x = number of carbon atoms in cyclic ring of the major organic product and
y = number of pi bonds in the major organic product
write the number of (x+y) = ?
28. How many of the following favours nucleophilic addition reaction with 1 equivalent of CH3MgBr in
ether.
(i)
O
(ii)OO
(iii) (iv) C
O
H H
(v)
O
NH2(vi)
O C
O
H (vii)
OC
H
O
O
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29. How many hyperconjugable H-atoms are available in this species ?
CH–CH(CH3)2
+
C2H5
CH3
30. How many of the following are correctly matched :
S1 : Nylon-6,6 Condensation polymer
S2 : Cellulose triacetate Natural polymer
S3 : Polyisoprene Homopolymer
S4 : Sucrose Polysaccharide
S5 : Starch Polymer of -D-Glucose
S6 : Teflon Amide linkage
S7 : Nylon-6 Polymer of Caprolactum
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SECTION – 2 : (Maximum Marks : 40)
This section contains FIVE paragraphs
Based on each paragraph, there will be TWO questions.
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four option is correct
For each question, darken the bubble corresponding to the correct option in the ORS
Marking scheme :
+4 If only the bubble corresponding to the correct option is darkened
0 If none of the bubbles is darkened
–2 In all other cases
Paragraph for Question Nos. 31 to 32
Compound A with formula M’(MO2)2 is a principle ore of metal M. M’ is another metal. When A is
fused with K2CO3 in air followed by acidification and filtration, a very common oxidizing agent B is
formed.
Aqueous solution of B is orange coloured which turns yellow in alkaline pH. When mixture of B and
NH4Cl is strongly heated a gas C is evolved leaving back a green coloured residue of M2O3. Metal
M can be extracted by thermite reduction of M2O3 by Aluminium.
31. Metal M is :
(A) Cu (B) Fe (C) Zn (D) Cr
32. The gas C is :
(A) O2 (B) N2 (C) NO (D) N2O
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Paragraph for Question Nos. 33 to 34
In quantum chemistry, the spin multiplicity is defined as (2S+1), where S is the total spin. States
with spin multiplicity 1, 2, 3, 4 are respectively called singlets, doublets, triplets, quartets. Total spin
S is modulus of summation of individual spins of all unpaired electrons.
For example, the ground state of the carbon atom is a triplet state. This is due to two unpaired
electrons with parallel spin in the ground state which makes total spin S =1 1
2 2 = 1 and spin
multiplicity = (2S+1) = (2×1 + 1) = 3.
33. Suppose two hypothetical states (the first and second states) of O2 molecule violate Hund's rule
(but not Pauli's principle) while filling its highest occupied molecular orbitals (HOMO). Which of the
following option is correct regarding these states ?
(A) Both states of O2 are triplet.
(B) One of the states of O2 is singlet, while other state is triplet.
(C) Both states of O2 are singlet.
(D) None of these.
34. Which of the following reaction(s) involves formation of a singlet carbon containing intermediate?
(I) Reimer-Tiemann formylation of phenol
(II) Acid catalysed dehydration of alcohol (E1 elimination)
(III) Carbylamine formation from primary amine
Correct answer is :
(A) I, II (B) I, III (C) I, II, III (D) I
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Paragraph for Question Nos. 35 to 36
Consider the following reaction sequence in which a coordination complex Z is formed:
Cyclopenta-1,3- →diene + Na NaY +1
2 H2
2 NaY + FeCl2 → Z + 2 NaCl
Compound Z has infinite possible conformations.
35. Which of the following is not true about the compound Z?
(A) It contains aromatic rings
(B) It is an organo-metallic compound
(C) Effective Atomic Number of central atom in Z is 34
(D) All Carbon–Carbon bonds in Z are of identical length
36. IUPAC name of the compound (Z) is :
(A) Bis(cyclopentadienyl)iron(0) (B) Bis(cyclopentadienyl)iron(II)
(C) Bis(cyclopentadienyl)ferrous(II) (D) None of these
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Paragraph for Question Nos. 37 to 38
(1) H3O
(2) OO
COOH(X)
Y + Z
Test Compound Y Compound Z
NaOI No reaction Yellow ppt
2. [Ag(NH3)2] No reaction Silver mirror
3. NaHCO3 No reaction No reaction
37. Compound Y is :
(A)O
OH
O
(B)O
O
(C) CH3–CH=O (D)OH OH
COOH
38. Choose the correct option
(A) Compound Z is CH3–CH=O
(B) Compound Y is formed due to decarboxylation
(C) Compound Y is formed due to esterification between –COOH & –OH group
(D) Both (A) & (C) are correct
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Paragraph for Question Nos. 39 to 40
Observe the following sequence of reaction:
O O
H /OH P
KOHCHCl3 Q 2Ac O / AcO /
Hydrolysis
R 2H /NiS /SOH 42 T
39. Choose the correct options :
(A) product Q isOH
CHO(B) product T is
O
O
(C) product T isO
(D) product S isOH
CH2OH
40. Compound P and R can be distinguished by
(A) Br2 / H2O test (B) Neutral FeCl3 test
(C) NaHCO3 test (D) Na metal test
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PART : III MATHEMATICS
SECTION – 1 : (Maximum Marks : 40)
This section contains TEN questions
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9 (1 or more
answers are there), both inclusive
For each question, darken the bubble corresponding to the correct integer in the ORS
Marking scheme :
+4 If the bubble corresponding to the answer is darkened
0 If none of the bubbles is darkened
–2 In all other cases
For example, if answer is 1, 4, 7 then OMR should look like0 1 2 3 4 5 6 7 8 9
then (+4) marks will be
given and if, left blank "0 marks" will given else (–2) marks will be given.
41. If a, b, c are the sides of a triangle, then the least integral value ofa b c
c a b a b c b c a
is
greater than or equal to.
42. If a, b, c, d > 0; x R and 2 2 2 2 2 2 2(a b c )x 2(ab bc cd)x b c d 0, then
33 14 log a
65 27 log b
97 40 log c
= The value of (3 + 7) is divisible by
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43. Suppose that f(x) is a differentiable invertible function f '(x) 0 and h'(x) f(x) . Given that
f(1) f '(1) 1, h(1) 0 and g(x) is inverse of f(x) . Let 2G(x) x g(x) xh g(x) x R then values
of G'(1) , G''(1) are
44. A be a square matrix of order 2 with | A | 0 such that A | A |.adj(A) 0, where adj (A) is a
adjoint of matrix A, then the value of A | A |.adj(A) is divisible by
45. Two persons A and B get together once a week to play game. They always play 4 games. From
past experience Mr. A wins 2 of the 4 games just as often as he wins 3 of the 4 games. If the
probability of winning a game by Mr. A is (Given the probability of A’s winning a game is a non-
zero constant less than one), 1 210k k
100
(where k1, k2 are digits), then prime numbers which are
smaller than k1 are :
46. If the radius of the circle touching the pair of lines 2 27x 18xy 7y 0 and the circle
2 2x y 8x 8y 0 , and contained in the given circle is equal to k, then k2 is divisible by
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47. Possible value(s) of k for which equation x2 + (k – 3)x + 1 = 5|x| has 3 distinct real solutions is(are) ?
48. If the eccentric angles of two points P and Q on the ellipse2 2x y
128 7 whose center is C, differ
by a right angle, then the area of CPQ is 'k'. The value of k is greater than
49. The straight linex y
14 3 intersects the ellipse
2 2x y1
16 9 at two points A and B, there is a point
P on this ellipse such that the area of PAB is equal to 6( 2 1) . Then the number of such points
(P) is/are
50. Number of the solutions of equation 2 sin 11x cos 3x 3 sin 3x 0 in 0,4
, 0,2
,
– ,4 2
are respectively.
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SECTION – 2 : (Maximum Marks : 40)
This section contains FIVE paragraphs
Based on each paragraph, there will be TWO questions.
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four option is correct
For each question, darken the bubble corresponding to the correct option in the ORS
Marking scheme :
+4 If only the bubble corresponding to the correct option is darkened
0 If none of the bubbles is darkened
–2 In all other cases
Paragraph for Question Nos. 51 to 52
If a, b, c, d
be vectors such that [ a b c
] = 2 and
(a b) ( c d) (b c) (a d) (c a) (b d) xa yb zc d
, (x, y, z, are scalars), then
51. [ a b b c c a
] is equal to
(A) 4 (B) 16 (C) 0 (D) 2
52. If xa yb zc md
, then m is equal to
(A) 2 (B) 4 (C) 6 (D) 8
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Paragraph for Question Nos. 53 to 54
Consider a differentiable function f : R R for which f(1) 2 and x yf(x y) 2 f(y) 4 f(x) x, y R
53. The value of f(4) is
(A) 160 (B) 240 (C) 200 (D) none of these
54. The minimum value of f(x) is
(A) 1 (B)1
2 (C)
1
4 (D) none of these
Paragraph for Question Nos. 55 to 56
If2 2n 2
2nn
(x ax 1) x (2x x b)f(x) lim
1 x
and
x 1lim f(x)
exists, then
55. The value of a is
(A) – 1 (B) 1 (C) 0 (D) 2
56. The value of b is
(A) – 1 (B) 1 (C) 0 (D) 2
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Paragraph for Question Nos. 57 to 58
Consider two functions y = f(x) and y = g(x) defined as2ax b; 0 x 1
f(x) bx 2b; 1 x 3
(a 1)x 2c 3; 3 x 4
and2
cx d; 0 x 2
g(x) ax 3 c; 2 x 3
x b 1; 3 x 4
57. Let f be differentiable at x = 1 and g(x) be continuous at x = 3. If the roots of the quadratic equation2x (a b c) x 49(k k ) 0 are real distinct for all values of the possible values of k will be
(A) k ( 1, 0) (B) k ( , 0) (C) k (1, 5) (D) k ( 1, 5)
58.x 2
f(x)lim
| g(x) | 1 exists and f is differentiable at x = 1. The value of limit will be
(A) – 2 (B) – 1 (C) 0 (D) 2
Paragraph for Question Nos. 59 to 60
Incircle of ABC touches AB, BC, CA at R, P, Q, respectively. If2 5 5 6
AR BP CQ r and the
perimeter of the triangle is the smallest integer also the sides of triangle are of integral length, thenanswer the following questions:
59. ABC is(A) scalene (B) isosceles (C) equilateral (D) right angled
60. The inradius of incircle of ABC is(A) 4 (B) 3 (C) 2 (D) 1
Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
GENERAL %
1. The sealed booklet is your Question Paper. Do not break the seal till you are instructed to do so.
2. The question paper CODE is printed on the right hand top corner of this sheet and the right hand top corner of the back cover of
this booklet.
3. Use the Optical Response Sheet (ORS) provided separately for answering the question.
4. Blank spaces are provided within this booklet for rough work.
5. Write your Name and Roll Number in the space provided on the below cover.
6. After the open booklet, verify that the booklet contains all the 60 questions along with the options are legible.
QUESTION PAPER FORMAT AND MARKING SCHEME :
7. The question paper has three parts : Physics, Chemistry and Mathematics. Each part has two sections.
8. Each section as detailed in the following table :
Full Marks Partial Marks Zero MarksNegative
Marks
1Single digit Integer(1 or more answer
are there)10
+4If only the bubbles
corresponding to the correctanswer is darkened
–0
if notattempted
–2In all other
cases40
2Comprehension(Single Correct
Option)10
+4If only the bubble
corresponding to all thecorrect option is darkened
–
0If none of
the bubblesis darkened
–2In all other
cases40
Section Question TypeNumber ofQuestions
Category-wise Marks for Each Question MaximumMarks of
the Section
OPTICAL RESPONSE SHEET :
9. Darken the appropriate bubbles on the original by applying sufficient pressure.
10. The original is machine-gradable and will be collected by the invigilator at the end of the examination.
11. Do not tamper with or mutilate the ORS.
12. Write your name, roll number and the name of the examination centre and sign with pen in the space provided for this purpose on
the original. Do not write any of these details anywhere else. Darken the appropriate bubble under each digit of your roll
number.
DARKENING THE BUBBLES ON THE ORS :
13. Use a BLACK BALL POINT to darken the bubbles in the upper sheet.
14. Darken the bubble COMPLETELY.
15. Darken the bubble ONLY if you are sure of the answer.
16. The correct way of darkening a bubble is as shown here :
17. There is NO way to erase or "un-darkened bubble.
18. The marking scheme given at the beginning of each section gives details of how darkened and not darkened bubbles are
evaluated.
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NAME OF THE CANDIDATE : ………………………………………………………………..………………………
ROLL NO. : ………………………..………………………
I have read all the instructions I have verified the identity, name and roll numberand shall abide by them of the candidate.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Signature of the Candidate Signature of the Invigilator
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