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CHEMISTRY MATHEMATICS - mdpcos.files.wordpress.com€¦ · DEFINITE INTEGRATION: Introduction, Fundamental Theorem of Integral Calculus - I and II, Fundamental Theorem of Integral
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A) The net electric flux crossing the plane / 2x a= + is equal to the
net electric flux crossing the plane / 2x a= −
B) The net electric flux crossing the plane / 2y a= + is more than
the net electric flux crossing the plane / 2y a= −
C) The net electric flux crossing the entire origin is 0/q
D) The net electric flux crossing the plane / 2z a= + is equal to the
net electric flux crossing the plane / 2x a= +
14. An electric dipole is placed at the centre of a sphere. Then choose
correct options
A) The flux of the electric field through the sphere is zero
B) The electric field is zero at every point of the sphere
C) The electric field is not zero anywhere on the sphere
D) The electric field is zero an a circle on the sphere
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SECTION – III (15 TO 18) (PARAGRAPH TYPE)
This section contains 2 Paragraphs based on these 2 questions each given.
Each question has 4 options (A), (B), (C), (D). ONLY ONE of these four options
is CORRECT. Darken the bubble corresponding to the correction option in
ORS.
Marking scheme +3 for correct answer, 0 in all other cases.
Paragraph for Question no. 15 and 16
Two particles A and B, having opposite charges 62 10 C− and 62 10 C−−
are placed at a separation of 1cm. Then
15. The electric dipole moment of this pair is
A) 82 10 C m− B) 84 10 C m−
C) 0 D) 86 10 C m−
16. The electric filed at a point on the axis of the dipole 1m away from
the centre is
A) 300 N/C B) 360 N/C
C) 400 N/C D) 450 N/C
Paragraph for Question no. 17 and 18
If the flux of the electric field through a closed surface is zero, then
17. The charge inside the surface must be________
A) zero B) one
C) infinity D) 0.5
18. The electric field _________every where on the surface.
A) infinity B) may be zero
C) must be 1 D) must be 0.5
SZ1_JEE-ADV(2016-P2)_WAT-14_QP_Exam.Dt.17-05-2020
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SECTION – I (19 TO 24) (SINGLE CORRECT ANSWER TYPE)
This section contains 6 multiple choice questions. Each question has four choices (A), B), (C) and (D) out of which ONLY ONE OPTION IS CORRECT. Marking scheme +3 for correct answer, 0 if not darkened any bubble, -1 in all other cases.
19. The most stable oxidation state of lanthanoids is
A) +5 B) +2 C) +3 D) +4
20. The cumulative effect of the contraction of the lanthanoid series,
known as
A) Lanthanoid expansion B) Lanthanoid contraction
C) Actinoid contraction D) Actinoid expansion
21. Gadolinium belongs to 4f series. It’s atomic number is 64. Which of
the following is the correct electronic configuration of gadolinium?
A) 7 1 24 5 6Xe f d s B) 6 2 24 5 6Xe f d s
C) 8 24 6Xe f d D) 9 14 5Xe f s
22. When 4KMnO solution is added to oxalic acid solution, the
decolourisation is slow in the beginning but becomes instantaneous
after some time because
A) CO2 is formed as the product B) Reaction is exothermic
C) 4MnO− catalyses the reaction D) 2Mn + acts as autocatalyst
23. On addition of small amount of 4KMnO to concentrated 2 4H SO , a
green oily compound is obtained which is highly explosive in
nature. Identify the compound from the following.
A) 2 7Mn O B) 2MnO C) 4MnSO D) 2 3Mn O
24. Potassium permanganate used for the bleaching of
A) Wool B) Cotton C) Silk D) All of these
SZ1_JEE-ADV(2016-P2)_WAT-14_QP_Exam.Dt.17-05-2020
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SECTION – II (25 TO 32)
(MULTIPLE CORRECT CHOICE TYPE) This section contains 8 multiple choice questions. Each question has 4 options
(A), (B), (C) and (D) for its answer, out of which ONE OR MORE than ONE
option can be correct. Marking scheme: +4 for correct answer, Partial marking +1 for darkening a bubble
corresponding to each correct option (provided no incorrect option darkened), 0 if none of the
bubble is darkened, -2 in all other cases.
25. Identify the correct statement among the following
A) d-Block elements show irregular and erratic chemical
properties among themselves
B) La and Lu have partially filled d orbitals and no other partially
filled orbitals
C) The chemistry of various lanthanoids is very similar
D) 4f and 5f orbitals are equally shielded
26. There are 14 elements in actinoid series. Which of the following
elements belong to this series?
A) U B) Np C) Tm D) Fm
27. Which of the following actinoids show oxidation states upto +7?
A) Am B) Pu C) U D) Np
28. In context of the lanthanoids, which of the following statements is
correct?
A) All the members exhibit +3 oxidation state
B) Because of similar properties the separation of lanthanoids is
not easy.
C) Availability of 4f electrons results in the formation of compounds
in +4 state for all the members of the series.
D) There is a gradual decrease in the radii of the members with
increasing atomic number in the series.
29. Which of the following statements is/are correct?
A) Both the manganate and permanganate ions are tetrahedral
B) The green manganate is paramagnetic
C) The permanganate is diamagnetic
D) The permanganate is paramagnetic
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30. Which of the following statements is/are correct?
A) Sodium and potassium dichromates are strong oxidising agents
B) Sodium dichromate is used as an oxidising agent in organic
chemistry
C) Potassium dichromate is used as a primary standard in
volumetric analysis
D) The acidified potassium dichromate will oxidise iodides to iodine
31. Although +3 is the characteristic oxidation state for lanthanoids but
cerium also shows +4 oxidation state because
A) it has variable ionisation enthalpy
B) it has a tendency to attain noble gas configuration
C) it has a tendency to attain 0f configuration
D) it resembles 4Pb +
32. Acidified permanganate solution oxidizes
A) oxalates to carbon dioxide B) iron(II) to iron(III)
C) nitrites to nitrates D) iodides to free iodine
SECTION – III (33 TO 36)
(PARAGRAPH TYPE) This section contains 2 Paragraphs based on these 2 questions each given. Each question has 4 options (A), (B), (C), (D). ONLY ONE of these four options
is CORRECT. Darken the bubble corresponding to the correction option in ORS. Marking scheme +3 for correct answer, 0 in all other cases.
Paragraph for Question no. 33 and 34
Dichromates are generally prepared from chromate, which in turn are
obtained by the fusion of chromite ore ( )2 4FeCr O with sodium or
potassium carbonate in free access of air. The yellow solution of sodium
chromate is filtered and acidified with sulphuric acid to give a solution
from which orange sodium dichromate, 2 2 7 22Na Cr O . H O can be
crystallised.
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33. During the conversion of chromate to dichromate the oxidation
state of chromium is
A) Decreased B) Increased
C) Does not change D) does not predict
34. The chromates and dichromates are
A) interconvertible in aqueous solution depending upon pH of the
solution
B) interconvertible in aqueous solution independent of pH of the
solution
C) Only chromates converts into dicromates
D) Only dichromates converts into cromates
Paragraph for Question no. 35 and 36
The lanthanoids resemble one another more closely than do the members
of ordinary transition elements in any series. They have only one stable
oxidation state and their chemistry provides an excellent opportunity to
examine the effect of small changes in size and nuclear charge along a
series of otherwise similar elements
35. The electronic configuration of lanthanoids having
A) 26s common B) 25s common
C) 24s common D) 27s common
36. The correct statement about lanthanides is/ are?
A) All the lanthanoids are silvery white soft metals
B) The hardness increases with increasing atomic number
C) Lanthanoids have typical metallic structure
D) All of these
SZ1_JEE-ADV(2016-P2)_WAT-14_QP_Exam.Dt.17-05-2020
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SECTION – I (37 TO 42) (SINGLE CORRECT ANSWER TYPE)
This section contains 6 multiple choice questions. Each question has four
choices (A), B), (C) and (D) out of which ONLY ONE OPTION IS CORRECT.
Marking scheme +3 for correct answer, 0 if not darkened any bubble, -1 in all other cases.
37. If ( )/ 2
1
0
ln sinI x dx
= and ( )/ 4
2
/ 4
ln sin cos ,I x x dx
−
= + then
A) 1 22I I= B)
1 2I I= C) 1 24I I= D)
1 22I I=
38. Let ( ) ( ), , 0.xf x e g x x x= = If ( ) ( ) ( )0
,
t
F t f t x g x dx= − then
A) ( ) ( )1tF t e t= − + B) ( ) tF t te=
C) ( ) tF t te−= D) ( ) ( )1 1tF t e t= − +
39. The value of
5 1
22
4 2
1
1 1ln 1
1
xx dx
x x x
+
+ + −
− +
A) ln 24
B) ln 2
2
− C) ln 2
4
D) ln 2
8
40. If ( )
2
0
cos,
2
xA dx
x
=+
then / 2
0
sin 2
1
xdx
x
=+
A) 1 1
2 2A− +
+ B)
1 1
2 2A+ −
+
C) 1
2A−
+ D)
1 1
2 2A− −
+
41. Let ( )f x be a monotonic differentiable function on , .a b Then
( ) ( )( )
( )1
f bb
a f a
f x dx f x dx−+ =
A) ( ) ( )af b bf a− B) ( ) ( )f b f a
b a
−
−
C) ( ) ( )
2
f a f b+ D) ( ) ( )bf b af a−
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42. Given a function : 0,4f R⎯⎯→ is differentiable. Then for some
( ), 0,2 , ( )4
0
f t dt =
A) ( ) ( )2 2f f + B) ( ) ( )2 22 f f +
C) ( ) ( )2 22 f f +
D) ( ) ( ) ( ) ( )f f f f +
SECTION – II (43 TO 50)
(MULTIPLE CORRECT CHOICE TYPE)
This section contains 8 multiple choice questions. Each question has 4 options
(A), (B), (C) and (D) for its answer, out of which ONE OR MORE than ONE
option can be correct. Marking scheme: +4 for correct answer, Partial marking +1 for darkening a bubble
corresponding to each correct option (provided no incorrect option darkened), 0 if none of the
bubble is darkened, -2 in all other cases.
43. Let ( ) ( )1
F x f x fx
= +
where ( )
1
ln,
1
xt
f x dtt
=+
then
A) ( )1 0F = B) ( )1
2f e = C) ( )
1
8F e = D) ( )2 2F e =
44. 2 2
1 1
0 0
Tan x dx Cot x dx− − + = ( )Where . denotes . .G I F
A) 2 tan1 cot1− + B) 2 tan1 cot1+ −
C) ( )2 1 cot 2+ D) ( )2 1 cot 2−
45. Which of the following statement(s) is/are true?
A) If ( )1
0
1, 0,
ln
xI dx
x
− = then ( ) ( )ln 1I = +
B) If ( )f x and ( )g x are continuous functions and ,a R then
( ) ( )( ) ( ) ( )( ). 0
a
a
f x f x g x g x dx−
+ − − − =
C) For ( )
0
1, ;
2
n n nn N x dx
− = ( ). . .denotes G I F
D) For 0
, ;2
nn
n N x dx = ( )where denotes fractional part function
SZ1_JEE-ADV(2016-P2)_WAT-14_QP_Exam.Dt.17-05-2020
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46. If ( ) ( ) ( )( )0
cos sin cos cos ,
x
f x t t dt= + then ( )f x+ =
A) ( ) ( )2f x f+ B) ( ) ( )f x f+
C) ( ) 22
f x f
+
D) ( )2
f x f
+
47. If ( ) ( ) ( )1
0
,f x x t x t f t dt= + + then
A) ( )1
0
42
23f x dx = B) ( )
24 18
23 23f x x= +
C) ( )1
1
36
23f x dx
−
= D) ( )48 18
23 23f x x= +
48. If ( ) ( )2 2f x f x− = + and ( ) ( )4 4 ,f x f x− = + x R and ( )f x is a
function for which ( )2
0
5,f x dx = then
A) ( )50
0
120f x dx = B) ( )100
0
250f x dx =
C) ( ) ( )50 54
0 4
f x dx f x dx= D) ( ) ( )52 46
2 4
f x dx f x dx−
=
49. If 2 7 6 5 3 2
2
2
2 3 10 7 12 1,
2 2 2
x x x x x x a bdx
x c−
+ − − − + + = −
+
where , , ; ,a b c N b c are different primes, then
A) 16a = B) 6a bc− = C) 48ab = D) 2 6a c− =
50. For 0, ,4
x
let ( )/ 4
tan
1
0
tan ,x
I x dx
= ( )/ 4
cot
2
0
tan ,x
I x dx
=
( )/ 4
tan
3
0
cot ,x
I x dx
= ( )/ 4
cot
4
0
cot ,x
I x dx
= then
A) 4 3I I B) 3 1I I C) 1 2I I D) 1 4I I
SECTION – III (51 TO 54)
SZ1_JEE-ADV(2016-P2)_WAT-14_QP_Exam.Dt.17-05-2020
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(PARAGRAPH TYPE) This section contains 2 Paragraphs based on these 2 questions each given. Each question has 4 options (A), (B), (C), (D). ONLY ONE of these four options
is CORRECT. Darken the bubble corresponding to the correction option in ORS. Marking scheme +3 for correct answer, 0 in all other cases.
Paragraph for Question no. 51 and 52
Let ( )f x be a continuous function such that ( )1
2 ,4
f x f x x R
+ + =
then answer the following
51. ( )f x is
A) even B) odd C) periodic D) non-periodic
52. ( )1000
0
f x dx =
A) 500 B) 1000 C) 2000 D) 4000
Paragraph for Question no. 53 and 54
Let ( ) ( ) ( )/ 2
/ 2
sin sin cosf x x x t x f t dt
−
= + + then answer the following
53. The range of ( )f x is
A) 3 3
,2 2
−
B) 5 5
,2 2
−
C) 2 2
,3 3
−
D) 5 5
,3 3
−
54. The value of ( )/ 2
0
f x dx
=
A) –1 B) 1 C) – 2 D) 2
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