JEE-Adv Grand Test Question Paper (P 1) - 12-05-2014
-
Upload
ranjan-prasad -
Category
Documents
-
view
251 -
download
5
Transcript of JEE-Adv Grand Test Question Paper (P 1) - 12-05-2014
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Max. Marks: 252 Duration: 3 Hrs
1. This paper consists of 84 questions with 3 parts of Chemistry, Mathematics and Physics
Each Part consist of 4 sections
Section – I : 8 Multiple Choice Questions with one correct answer (with negative marks). A
correct answer carries 3 Marks. A wrong answer carries a penalty of 1 mark
Section – II : 5 Multiple Choice Questions with one or more correct answers (No negative
marks). A correct answer carries 3 Marks.
Section – III : 5 Comprehension Type questions. A correct answer carries 3 Marks. A wrong
answer carries a penalty of 1 mark
Section – IV : 10 Integer Type question with one correct answer. A correct answer carries 3
Marks. No negative mark.
2. Darken the appropriate bubble using a pen in the OMR sheet provided to you. Once entered,
the answer cannot be changed. Any corrections or modifications will automatically draw a
penalty of 1 mark.
3. Use of calculators and log tables is prohibited.
4. No clarification will be entertained during the examination. Doubts in the paper can be
reported to the coordinator after the exam.
All the best !!
Useful Data
At. Wt.:
N = 14; O = 16; H = 1; S = 32; Cl = 35.5; Mn = 55; Na = 23; C = 12; Ag = 108; K = 39; Fe = 56; Pb = 207
Physical constants:
346.626 10 J.sech , 23 -1
aN 6.022 10 mol , 8 -1C 2.998 10 ms , 31
em 9.1 10 kg
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 2
Chemistry
Section I
Multiple Choice Questions with one correct answer. A correct answer carries 3 marks. A wrong
answer carries a penalty of 1 mark 8 x 3 = 24
1. Identify the final product obtained in the following reaction.
(a) (b)
(c) (d)
O
O
O
O
OO
O
O
O
O
O
O
O
O
O
O
O
COOC2H5
O
1)NaH2)HCHO
X ; X is
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 3
2. The product formed in the reaction is
DHO
. OH18
H+
(a) (b)
(c) (d)
3. When sulphur is heated with aqueous NaOH , the compounds formed are
(a) 2 2Na S H O (b) 2 3 2Na SO H O
(c) 2 2 2 3 2Na S Na S O H O (d) 2 2 3 2Na S O H O
4. 2 .Zn
Ag S NaCN X Y If Y is a metal, then X and Y are respectively.
(a) 2 4,Na Zn CN Zn
(b) 2
,Na Ag CN Ag
(c) 2 4,Na Ag CN Ag
(d) 3 4,Na Ag CN Ag
. D
O18 O
.
O
.
18O
D.
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 4
5. A reaction proceeds at a rate five times more at 60 C than it does at 30 C . Then the energy of
activation is approximately
(a) 110.8K cal mol (b) 111.8K cal mol (c) 19.8K cal mol (d) 112.8K cal mol
6. A 500 0.01ml M aqueous solution of 3 2CH NH (methanamine) is titrated by a 0.005 M HCl solution at
25 C , bK of 3 2CH NH , at 25 C is 44 10 . Then, the pH of the solution at the equivalence point is
nearly
(a) 3.5 (b) 6.5 (c) 7.5 (d) 7
7. An endothermic reaction with high activation energy for the forward reaction is given by the
diagram:
R
P
Reaction coordinate
Potentialenergy
R
R R
P P
P
Reaction coordinate
Reaction coordinate Reaction coordinate
Potentialenergy
Potentialenergy
Potentialenergy
(a) (b)
(c) (d)
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 5
8. Which of the following volume V , temperature T plots represents the behaviour of an ideal gas
at one atmospheric pressure?
(a) (b)
(c) (d)
Section II
Multiple Choice Questions with one or more correct answer. A correct answer carries 3 marks.
No negative mark 5 x 3 = 15
9. Identify correct statement (s) for the following reaction sequence
(a) The final product is a monohydric alcohol
(b) Same carbocation intermediate is formed in both the reactions
(c) Different carbocation intermediates are formed in two reactions
(d) The final product is a polyhydric alcohol
(36.8 L at 372K)
(22.4L
at 273K)
V(L)
T(K)
(28.6L at 373K)
(22.4L
at 273K)
T(K)
V(L)
(30.6L at 373K)
(22.4L
at 273K)
V(L)
T(K)
(14.2L at 373K)
(22.4L
at 273K)
V(L)
T(K)
HN
CF3
Cl
HBr H2OA B
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 6
10. The product(s) obtained in the following trifluoro acetolysis of given labelled phenethyl tosylate,
HH
DD
OTs
CF3COOH
?
(a) (b)
(c) (d)
11. Which of the following pairs are separable by using 4NH OH aq in excess ?
(a) 2 3,Zn Bi (b) 2 3,Sn Fe (c) 3 2, FeFe (d) 2 2, NiCr
12. In Mond’s process for the extraction of Nickel metal, a Nickel carbonyl complex is formed.
Hybridisation of Nickel in that complex is
(a) 3sp (b) 2sp (c) 2dsp (d) 2 3d sp
13. Radium has atomic mass 226 and half-life of 1600 years. The number of disintegrations per second
per gram are:
(a) 104.8 10 (b) 83.7 10 (c) 69.2 10 (d) 103.7 10
HH
DD
O CF3
O
DD
HH
O
CF3
DD
HH
O CF3
O
HH
DD
CF3
O
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 7
Section III
Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a
penalty of 1 mark 5 x 3 = 15
Comprehension – I
A leaving group in an alkylating agent can be displaced not only by a nucleophile added to the reaction
mixture but also by one in the alkylating agent itself. This holds for alkylating agents that contain a
nucleophilic electron pair at a suitable distance from the leaving group. This neighbouring group
displaces the leaving group stereoselectively through backside attack and this attack corresponds to that
of an SN2 reaction. The nucleophilic electron pairs of the neighbouring group can be non-bonding, or
they can be in a bond. The higher rate of reversal substitution reactions are explained using this
neighbouring group participation.
14. S 2 chloro- 3 -ethyl- 3 -pentanol undergoes 2NS hydrolysis with aq. KOH to give
(a) S 3 ethylpentane 2,3 - diol
(b) R 3 ethylpentane 2,3 diol
(c) 2R,3R 3 methylpentane 2,3 diol
(d) 2S,3S 3 .methylpentane 2,3 diol
15. The major product obtained in the following reaction is
|
3
.2 25H C S CH CH Cl
CH
aq KOH
(a) |
3
2 25H C S CH CH OH
CH
(b) |
3
2 25H C S CH CH OH
CH
(c) 5 2 3 2C S C CH OHH (d) 5 2 3C S CH CH CHH
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 8
16. The major product obtained in the given reaction is
EtN .
Et Cl
OH
2H O?
(a)
(b)
(c) (d)
Comprehension – II
When the solute undergoes dissociation or association in solution, the number of particles in solution
increases or decreases and thus, the colligative property changes accordingly. The extent of dissociation
or association of the solute in solution can be expressed in terms of Van’t Hoff factor, i.
In case of dissociation, 1i
1 1
1
ni
Similarly in case of association, 1i
11 1
1
ni
EtN .
Et OH
Et
N
Et
OH
.
EtN
.
Et OH
.
.Et
NOH
Et
. .
.
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 9
17. For the solution of benzoic acid in benzene is calculated using the expression
( is the degree of dissociation or association)
(a) 1
1
i
n
(b)
1
11
i
n
(c) 1
1
i
n
(d)
1
1
i
in
18. Which of the following solutions will exhibit highest boiling point
(a) 2 40.01 M Na SO (b) 30.01M KNO (c) 0.015 M urea (d) 0.015 M glucose
Section IV
Integer answers type questions. Each carries 3 marks. No negative marks 10 x 3= 30
19. At equimolar concentrations of 2Fe and 3Fe , what must Ag
be so that the voltage of the
galvanic cell made from /Ag Ag and electrodes equals zero? The reaction is
2 3Fe Ag Fe Ag . Determine the equilibrium constant at 25 C for the reaction. (Given:
0
/0.799
Ag AgE volt
and
3 20
/0.771
Fe FeE volt
)
20. 0.789g of crystalline barium hydroxide is dissolved water. For the neutralisation of this solution.
20mL of 34
NHNO is required. How many molecules of water are present in one g mole of this base?
137.4, 16, 14, 1Ba O N H
21. A current of 2amp when passed for 5 hour through a molten salt deposits 22.2g of metal of atomic
mass 177 . The positive oxidation state of the metal in the metal salt is:
22. The dissociation constant of a substituted benzoic acid at 25 C is 41 10 . The pH of a 0.01M
solution of its sodium salt is:
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 10
23. At 400K , the root mean square (rms) speed of gas X (molecular mass 40 ) is equal to the most
probable speed of gas Y at 60K . The molecular mass of the gas Y is
24. For a liquid the vapour pressure is given by: 10400
log 10PT
. Vapour pressure of the liquid is
10x mm Hg . The value of x will be
25. 2 2SO Cl and 2Cl are introduced into a 3L vessel. Partial pressure of 2 2SO Cl and 2Cl at equilibrium
are 1atm and 2atm respectively, the value of pK for the following reaction is10 .
2 2 2 2SO Cl g SO g Cl g . The total pressure in atm at equilibrium would be
26. Nitrobenzene 6 5 2C H NO can be reduced to aniline 6 5 2C H NH by electrolytic reduction; the
equivalent mass of nitrobenzene will be equal to molecular mass
n
. The value of n is
27. 1.2kg ethylene lycol was added in a car radiator containing 9 litre water.
The freezing of water was just prevented when car was running in the Himalayan valley at
temperature 4 C . Sudden thunderstorm in the valley lowered the temperature to 6 C . Calculate
the amount of ice separated.
28. At 10 C , the osmotic pressure of urea solution is 500mm . The solution is diluted and the
temperature is raised to 25 C , when the osmotic pressure has to be 105.3mm . Determine extent of
dilution.
CH2OH
CH2OH
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 11
Mathematics
Section I
Multiple Choice Questions with one correct answer. A correct answer carries 3 marks. A wrong
answer carries a penalty of 1 mark 8 x 3 = 24
29. The area of the triangle formed by the complex numbers , ,z iz z iz in the Argand plane is
(a) 21
2z (b)
2z (c)
23
2z (d) none of these
30. If the line 3y x intersects the curve 21 2y x in exactly one point, then belongs to
(a) 2 (b) 2 (c) 2, 2 (d) 1
31. A triangle is constructed by joining the vertices of a regular polygon of 10 sides. The number of
ways in which this can be done so that no side of the triangle coincides with a side of the polygon is
(a) 45 (b) 50 (c) 10 (d) 120
32. Let
1sin , 0
0 , 0
nx xf x x
x .
Then f x is continuous but not differentiable at 0x , if
(a) 0, 1n (b) 1,n (c) , 0n (d) 0n
33. The area of the triangle formed by the positive x axis, the normal and tangent to the circle
2 2 4x y at the point 1, 3 is
(a) 3 sq. units (b) 2 3 sq. units (c) 4 3 sq. units (d) none of these
34. A ray of light coming from the point 1, 2 is reflected at a point A on x axis and then passes
through the point 5, 3 . The coordinates of the point A are
(a)
13, 0
5 (b)
5, 0
13 (c) 7, 0 (d) none of these
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 12
35. The length of latus rectum of the parabola whose parametric equations are
2 21, 1,x t t y t t where t R , is equal to
(a) 2 (b) 4 (c) 8 (d) none of these
36. The equation cos2 sin 2 7x a x a possesses a solution for
(a) all a (b) 6a (c) 2a (d) 2, 6a
Section II
Multiple Choice Questions with one or more correct answer. A correct answer carries 3 marks.
No negative mark 5 x 3 = 15
37. If , , a b c are in H.P, then the value of 1 1 1 1 1 1
b c a c a b
is
(a) 2
2 1
bc b (b)
2 2
1 3 2 1
4 cac a
(c)
2
3 2
abb (d) none of these
38. If n is a positive integer and 2 1
3 3 5n
, where is an integer and 0 1, then
(a) is an even integer
(b) 2
is divisible by 2 12 n
(c) the integer just less than 2 1
3 3 5n
is divisible by 3
(d) is divisible by 10
39. A bag contains four tickets marked with 112, 121, 211 and 222 . One ticket is drawn at random
from the bag. Let 1, 2, 3iE i denote the event that the thi digit on the ticket is 2 . Then
(a) 1E and 2E are independent (b) 2E and 3E are independent
(c) 3E and 1E are independent (d) 1 2 3, , E E E are independent
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 13
40. A parallelogram is constructed on the vector 3 , 3a b .
If 2
and angle
between and is
3
, then the length of the diagonal of the parallelogram is
(a) 4 5 (b) 4 3 (c) 4 7 (d) none of these
41. If 2 3 2 3
1 1 2 2
1 2 3 4
0 0 1 1
2 , 2 , 2 and 2x x x xI dx I dx I dx I dx , then
(a) 1 2I I (b) 2 1I I (c) 3 4I I (d) 4 3I I
Section III
Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a
penalty of 1 mark 5 x 3 = 15
Comprehension – I
Let p be a prime number and n be a positive integer. If the exponent of p in !n is denoted by !PE n ,
then
2!p K
n n nE n
p p p
where 1k kp n p and x denotes integral part of x .
Every natural number n can be uniquely expressed as 31 22 3 5 , in are whole numbers.
On the basis of above information answer the following
42. The exponent of 7 in 10050C
is
(a) 0 (b)1 (c) 2 (d) 3
43. The number of zeros at the end of 108! is
(b) 10 (b)13 (c) 25 (d) 26
44. The last nonzero digit in 20! must be equal to
(a) 2 (b) 4 (c) 6 (d) 8
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 14
Comprehension – II
The differential equation corresponding to 31 21 2 3
m xm x m xy C e C e C e , where 1 2 3, , C C C are arbitrary
constants and 1 2 3, , m m m are roots of 3 7 6 0m m is
3 2
3 20, , , ,
d y d y dya b c d a b c d
dxdx dx are constants, then
45. The order and degree of the differential equation respectively are
(a) 3, 2 (b) 3, 1 (c) 3, 3 (d) 1, 3
46. The value of a b d
(a) 0 (b) 6 (b) 7 (d) 5
Section IV
Integer answers type questions. Each carries 3 marks. No negative marks 10 x 3= 30
47. If 1z and 2z are complex numbers such that
2 2 2 21 2 1 2 1 215 13 13 15z z z z z z , then the
value of must be equal to 197 k , where k
48. The coefficient of 50x in the polynomials after like terms have been collected in the expansion
1000 999 9982 10001 1 1x x x x x x is
!,
! !
mp n
n p. Then the value of 2 3m n p is
659k , where k
49. Suppose a matrix A satisfies 2 5 7 0A A I . If 5A aA bI , then the value of 2 3a b is equal to
207k , where k
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 15
50. A polynomial f x satisfies the condition
1 1f x f f x f
x x and 10 1001f .
Then
20f is 8000k , where k
51. Let
3
2
2
1 sin,
23cos
,2
1 sin
22
xx
x
f x a x
b xx
x
If ( )f x is continuous at 2
x
, then the value of
5/31
8
b
a is
52. If cos sin , sin cosx a t t t y a t t t , and
2
2
3t
d yb
dx, then the value of 120 ab
is 1440k ,
where k
53. Let the greatest and least values of the function 3 26 9 1f x x x x on the interval 0, 2
be
and respectively. If the value of 4 8 is 313k , then k
54. If
1
1, , >0 , 1, 2, 3, 4i
i
m m im
are four distinct points on a circle, then the value of
4
1i
i
m is
equal to
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 16
55. If the lines 1
4 6 1:
3 5 2
x y zL
and 2 : 3 2 5 0 2 3 4L x y z x y z k
are coplanar, then k is
equal to
56. If 1 1 1 3sin sin sin
2x y z
,
then the value of 3 3 3
2162500 x y z
x y z
is 2476 k . The value
of k is
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 17
Physics
Section I
Multiple Choice Questions with one correct answer. A correct answer carries 3 marks. A wrong
answer carries a penalty of 1 mark 8 x 3 = 24
57. A liquid of density and surface tension T is filled in the tube and the tube is rotated with angular
velocity about the given axis. Contact angle is 0 . The difference in heights of liquid in two
columns is
(a)
2 2
2
l w R T
Rg
(b)
2 2 4
4
l w R T
Rg
(c)
2 2 4
2
l w R T
Rg
(d)
2 2l w R
Rg
58. A particle of mass ' 'm is attached to a massless spring of initial length 0 '' L and spring constant ''K .
Now it is rotated in a horizontal plane with an angular velocity ' ' by fixing its other end. The
tension in the spring is given by
(a) 2
02
m KL
K m
(b)
2
20
K m
m KL
(c)
202
m KL
K m
(d)
2
20
K m
m KL
59. A capacitor ' 'C is connected to a conducting rod of length
l the loop starts entering a transverse magnetic field ' 'B as
shown in diagram, when the loop is entering the field,
what will be the charge developed across the capacitor?
(a) zero (b) BlvC (c) 2
BlvC (d)
3
BlvC
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 18
60. If at 0t the switch wS is closed, then the charge on capacitor in the given circuit (initially
uncharged) when the current through battery becomes 50% of its
maximum value is (assume battery is ideal)
(a) 3
CE (b)
2
CE
(c) 4
CE (d) CE
61. Starting from one corner of a cube an insect has to travel to the diagonally opposite corner. The
insect travels along the edges. It traverses the first edge AB with constant velocity 1V , the second
edge BC with constant velocity 2V and the third edge CD with constant velocity
3V . The average
velocity of the whole path.
(a)
1 2 3
3
1 1 1
V V V
(b) 1 2 3
3
V V V
(c)
1 2 3
3
1 1 1
V V V
(d)
1 2 3
2
1 1 1
V V V
62. In a series LCR circuit, as the frequency of the voltage source increases, the magnitude of phase
difference between current and voltage.
(a) increases
(b) decreases
(c) first decreases, then becomes zero at a particular frequency, then increases
(d) remains constant
63. One mole of an ideal monoatomic gas undergoes process 2T V and temperature of gas changes
from 300 K to 1200 K . Then Work done by the gas is ( R is universal gas constant)
(a) 400 R (b) 450 R (c) 900 R (d) 600 R
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 19
64. A block of mass ' 'm is being pulled up the rough incline by an agent delivering constant power p .
The coefficient of friction between the block and the incline during the course of ascent is
(a)
sin cos
pv
mg mg
(b) sin cos
pv
mg mg
(c) 2
sin cos
pv
mg mg
(d) 3
sin cos
pv
mg mg
Section II
Multiple Choice Questions with one or more correct answer. A correct answer carries 3 marks.
No negative mark 5 x 3 = 15
65. A positively charged ring having uniform charge density is
shown in the figure. Two elements of ring of length 1l and
2l
subtend same angle (very small)at a point A point A is in the
plane of ring but not at the centre. The elements 1l and
2l are
at distance 1r and
2r respectively from the point A
(a) The ratio of charges of elements 1l and
2l is 1
2
r
r
(b) Net electric field at point is zero
(c) The elements 1l and
2l produce same potential at A
(d) The direction of net electric field at A towards 2l
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 20
66. A bent conducting rod ( )PQR PQ QR l is rotating about its end P , with equal speed ω in a
region of transverse magnetic field of strength B
(a) emf induced across the rod is 2
2
Bwl
(b) emf induced across the rod is 2
8
Bwl
(c) Potential difference between points Q and R on the rod is 2
2
Bwl
(d) Electric field from P to Q is 8
Bwl
67. In an organ pipe (which may be closed or open) of 99cm length, standing wave is set up whose
equation is given by longitudinal displacement.
0.3X mm cos 2 / 0.8 0.01 ] cos 400z m t
Where z measured from the top of tube in meters and t is in
seconds.
Take end correction 1 cm choose the correct statements
(a) The upper end and lower end of tube are open and closed respectively
(b) The upper end and lower end of tube are closed and open respectively
(c) The air column is vibrating in third harmonic
(d) The air column is vibrating in second overtone
68. The path of a ray is shown in the figure. It could be the path of a wave whose
(a) Velocity in water is less than velocity in air
(b) Velocity in air is less than velocity in water
(c) Frequency does not change
(d) Wave length changes
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 21
69. A particle excretes S.H.M according to sinx A t . The time taken by it to move from 0x to
2x A is 1T and from 2x A to 2x A is
2T then
(a) 1 2 T T (b)
1 2 T T (c) 1 22 T T (d)
2 1 2 T T
Section III
Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a
penalty of 1 mark 5 x 3 = 15
Comprehension – I
A ring of mass m and radius R rests in equilibrium on a smooth cone of semi vertical angle 45 as
shown. The radius of the cone is 2R , the radius of circular cross section of the ring is r r R
Answer the following questions
70. What will be the tension in the ring?
(a) 2 2
mg
(b)
2
mg
(c) 2
mg
(d)
2 mg
71. What will be the speed of transverse wave on the ring
(a) gR (b) 2gR (c) 1
2gR (d) 2 gR
72. If the cone is rotated about its axis with angular velocity ω. what will be the tension in the ring now ?
(a) 2( )2
mg w R
(b) 2( )
2
mg w R
(c) / 2mg (d) 2mgw R
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 22
Comprehension – II
When a progressive wave enters from one medium to another medium, some of its energy gets
transmitted and the remaining of its energy reflected at the boundary of separation.
The energy of incident wave = The energy of reflected wave + The energy of transmitted wave
A progressive wave travels in a medium 1S and enters into another medium
2S in which its speed
decreases to 75% . What is the ratio of the amplitude of the
73. Reflected and the incident waves
(a) 1: 7 (b) 1:1 (c) 6 : 7 (d) 8 : 7
74. Transmitted and the incident waves
(a) 1:1 (b) 1: 7 (c) 8 : 7 (d) 6 : 7
Section IV
Integer answers type questions. Each carries 3 marks. No negative marks 10 x 3= 30
75. A metallic block of mass 1 kg and specific heat 1 cal gm C is connected to
three identical rods as shown in diagram. Temperature of ,A B and C are
maintained at 10 , 5C C and 3 C respectively. Find the final temperature of
1 kg block on Celsius scale. (Neglect any heat loss due to radiation)
76. A siren placed at a railway platform is emitting sound of frequency 5 KHz . A passenger sitting in a
moving train A records a frequency of 5.5 KHz while the train approaches the siren. During his
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?
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 23
77. In the network of capacitor and resistances shown in figure,
steady current I enters at junction (a) and same current leaves
junction (b) charge on capacitor 3C with shown polarity is
4
KIRCfind K . Initially all capacitors were uncharged
78. The capacitor is charged by closing the switch ' '.S The switch is then opened and the capacitor is
allowed to discharge. 1t and
2t be the time constant of
the circuit during the charging and discharging of the
capacitor( 1 2 3R R R R ).
If the ratio of 1
2 1
t n
t n
, then the value of n is?
79. In double slit experiment, the slits are 0.5 mm apart and interference is observed on a screen placed
at a distance of 100cm from slits. It is found that 9th bright fringe is at a distance of 8.835 mm from
the 2nd dark fringe from the centre of fringe pattern. If the wavelength of light used is 73.398 10n m
then ?n
80. A single electron orbits a stationary nucleus of charge Ze where Z is a constant and e is the
magnitude of the electronic charge. It acquires 47.2 eV to excite the electron from the second Bohr
orbit to third Bohr orbit. Find the value of Z .
81. Potential difference C BV V in volts is
IIT Section
Subject Topic Grand Test – Paper I Date
C + M + P Grand Test – 08 IIT – GT – 08
12th May 2014 I20140508
Ace Insignia Rough Work Page 24
82. A mono chromatic light is just able to ionise a hypothetical one electron atom in its ground state
having energy levels defined by2
17nE
n
eV where n is principal quantum number. In an
experimental set-up same light is incidents on a metal plate and it was found out that electrons have
2eV as maximum kinetic energy. If the work function of metal is 5K eV. Find the value of K.
83. Three metallic blocks A, B and C have same specific heats and
masses m, 2m and 2m respectively. Initial temperatures of A, B and
C are 10 , 5C C and 5 C respectively. Now the 3 blocks are
connected by 3 identical rod is shown. Find the final temperature of
block A on Celsius scale (neglect any heat loss due to radiation)
84. A plane concave lens is placed on a paper on which
a flower is drawn. Above its actual position does
the flower appear to be 10V cm x then find x ?
=3/2
Radius of curvature = 20cm