TIME : 3 HRS
A.I.T.S. # 1
DATE : 03/01/2010
IIT-JEE 2010
PAPER - II
MAX. MARKS : 240
I N S T R U C T I O N S T O C A N D I D AT E
1. This booklet is your question paper. Answers have to be marked on theprovided OMR sheets .
2. This question paper contains 57 questions. .
3. Blank sheets are provided for rough work alongwith the question paper. No additional sheet will be provided for rough work
4.
5. If a student is caught copying , he/ she will not be allowed to write the exam.
6. On the OMR sheet, write in ink your name, and name of the centre and put your signature in the appropriate boxes.
7.
For each question in Section - III , you will awarded 2 marks 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(s) for this section.
The question paper consists of 3 parts ( Physics , Chemistry & Maths ) Each part has 4 sections.
8.
Marking Scheme:
Physics :
Chemistry:
Maths :
Q.1 - Q.4 ( + 3, -1) ; Q.5 - Q.9 ( + 4,-1) ; Q.10 - Q.11 ( + 8, 0) ; Q.12 - Q.19 ( +4 ,-1) Q.20 - Q.23 ( + 3, -1) ; Q.24 - Q.28 ( + 4,-1) ; Q.29 - Q.30 ( + 8, 0) ; Q.31 - Q.38 ( + 4 ,-1) Q.39 - Q.42 ( + 3, -1) ; Q.43 - Q.47 ( + 4,-1) ; Q.48 - Q.49 ( + 8, 0) ; Q.50 - Q.57 ( +4 ,-1)Name :_____________________________________________________
Batch : ________________________ _____________________________
Centre : ____________________________________________________
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EDUCATION PVT LTD
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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 which ONLY ONE is correct.
1. At night approximately 500 photons per second must enter an unaided human eye for an object to be seen. A light bulb emits about 5.00 1018 photons per second uniformly in all directions. The
radius of the pupil of the eye is about 4 10-3 meters. What is the maximum distance from which
the bulb could be seen?
(A) 2.0 104m (B) 2.0 105m (C) 20 m (D) 5.0 103m
2. An infinitely long solenoid passes through the circuit as shown. The magnetic field of the solenoid, directed into the plane of the page, is weakening which produces a constant emf of magnitude for a closed loop around the outside of the solenoid. Once equilibrium is established in this circuit, what is the potential difference across the switch S?
(A) 0 (B) 1
3 (C)
4
3 (D) cannot be determined 3. Two particles A and B having equal charges after being accelerated through the same potential
difference, enter a region of uniform magnetic field and describe circular paths of radii R1 and R2
respectively. The ratio of mass of A to that of B is:
(A) (R1 / R2)2 (B) (R1 / R2)1/2 (C) (R2 / R1)3/2 (D) (R1 / R2)
4. Two spheres having masses m1 and m2 are kept on a on a inclined plane as shown. Both of them are
in equilibrium. What is a necessary condition for this? (1 is coefficient of friction between m1 and
inclined plane and 2 is coefficient of friction between m2 and inclined plane).
m1 m2 (A) m1 > m2 (B) m1 < m2 (C) 1 2 (D) 1 2
SECTION – I
SECTION –
II
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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 which ONE OR MORE is/are correct.
5. An electrostatic field line leaves at angle from point charge q1, and terminates at point charge – q2
at an angle (shown in figure). Then the relationship between and is:
1 q q2 (A) 2 2 1 2
q sin q sin (B) q tan1 q tan2
(C) q sin1 2 q sin2 2
2 2
(D) q cos1 q cos2
6. Two capacitor of 2 F and 3F are charged to 150 volt and 120 volt respectively. The plates of a capacitor are connected as shown in the figure. A discharged capacitor of capacity 1.5 F falls to the free ends of the wire. Then after the system comes in steady state :
(A) Charge on the 1.5 F capacitor will become 180 C (B) Charge on the 2 F capacitor will become 120 C
(C) + ve charge flows through A from left to right (D) +ve charge flows through A from right to left
7. A proton of charge ‘e’ and mass enters a uniform and constant magnetic field B Biˆ with an initial velocity V V i0XˆV j.0Yˆ Which of the following will be correct at any later time ‘t’
(A) x – component of velocity of the proton will be Vox cos qBt
m
(B) y – component velocity will be Voy cos qBt m
(C) z – component of velocity will be Voy sin qBt
m
along
ˆk diercetion (D) x – component of velocity will remains unchanged.8. Graphs shows a hypothetical speed distribution for a sample of N gas particle 150V
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(for V < V0 ; dN 0
dV )
(A) The value of aV0 is 2N (B) The ratio Vavg / V0 is equal to 2/3 . (C) The ratio Vrms / V0 is equal to 1/ 2
(D) Three fourth of the total particle has a speed between 0.5 V0 and V0 9. A U – shaped conducting frame is fixed in space. A conducting
rod CD lies at rest on the smooth frame as shown. The frame is in uniform magnetic field B0 , which is perpendicular to the plane of frame. At time t = 0, the magnitude of magnetic field begins to change with time t as , B B0 ,
1 kt
where k is a positive
constant. For no current to be ever induced in frame, the speed with which rod should be pulled starting from time t =0 is ( the rod CD
should be moved such that its velocity must be lie in the plane of frame and perpendicular to rod CD ) (A) ak (B) bk (C) a ( 1 + kt ) (D) b ( 1 + kt)
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Matrix – Match Type
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. One or more than one may be correct
10. For the situation shown in the figure below, match the entries of Column-I with entries of Column-II. r q1 q2 Hollow Neutral conductor Column – I Column – II
(A) In the situation shown (p) Distribution of charge on inner surface of conductor is uniform (B) If outside charge is not present (q) Distribution of charge on inner
surface of conductor is non-uniform
(C) If we displace the outside charge while the inside charge remains at centre
(r) Distribution of charge on outer surface of conductor is uniform (D) If the inside charge is displaced by
small amount from centre then
(s) Distribution of charge on outer surface of conductor is non-uniform
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11. Column-II gives four situations in which three or four semi infinite current carrying wires are placed in xy-plane as shown. The magnitude and direction of current is shown in each figure. Column-I gives statements regarding the x and y components of magnetic field at a point P whose coordinates are P(0, 0, d). Match the statements in column-I with the corresponding figures in column-II.
Column – I Column – II
(A) The x component of magnetic field at point P is zero in (P) x i/3 i/3 i i/3 y
(B) The z component of magnetic field at point P is zero in (Q) x i i/2 y 45o 45o i/2
(C) The magnitude of magnetic field at point P is 0i 4 d in (R) i/2 i/2 i x
(D) The magnitude of magnetic field at point P is less than 0i 2 d in (S) x i i/2 y 45o 45o i/2
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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.
12. In the figure ammeter (I) reads a current of 10mA , while the volt meter reads a potential difference of 3V. What does ammeter (II) ( in mA ) read? The ammeters are identical , the internal resistance of the battery is negligible. ( Consider all ammeters and voltmeters as non ideal ) ( round off the answer to the nearest integer)
13. Three identical large metal plates of area A are small at distances d and 2d from each other. Top metal plate is uncharged, while other metal plates have charges +Q and – Q. Top and bottom metal plates are connected by switch S through a resistor of unknown resistance. What energy is dissipated in the resistor when switch is closed? (x 10 J) 4
. Find x.
( Given : 0A 6 F, Q 60 C)
d
14. A uniform square plate of mass m = 100 gm and side a = 24 cm can rotate about a smooth vertical axis passing through one edge It is initially at rest . A particle of mass m =100 gm is moving horizontally and perpendicular to the plane of the plate with velocity u=70 cm/s. It collides with the plate elastically at the centre of the plate. Find the angular velocity ( in rad/s) of the plate just after collision?
15. In the circuit shown S1 and S2 are switches. S2 remains closed for a long time and S1 open. Now S1 is also closed . It is given that R = 10 , L = 1 mH and 3V. Just after S1 is
closed , find the magnitude of rate of change of current ( in ampere/sec) that is di
dt, in the inductor L is 1000 x. Find x. A A V I II 100 100 4V S A A A Q Q 2d d
SECTION –
IV
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16. Light is incident at an angle on one planar end of a transparent cylindrical rod of
refractive index . Determine the least value of so that the light entering the rod does not emerge from the curved surface of rod irrespective of the value of . Find 2
2 .
90
17. An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.0 F, and the resulting LC circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the capacitor, and I the current in the circuit. It is found that the maximum value of Q is 200 mC. When Q = 100 mC, the value of |dI/dt| is found to be 10x A/s. Find the value of x.
18. In Searle’s experiment, which is used to find Young’s Modulus of elasticity, the diameter of experimental wire is D = 0.05 cm (measured by a scale of least count 0.001 cm) and length is L = 110 cm (measured by a scale of least count 0.1 cm). A weight of 50 N causes an extension of X = 0.125 cm (measured by a micrometer of least count 0.001 cm). The
maximum possible error in the values of Young’s modulus is x 1010 N/m2. Find the value of x. Screw gauge and meter scale are free from error.( Round of to nearest integer)
19. Water at temperature 20o C flows from a tap T into a heated container C. The container has a heating element ( a resistor R) which is generating heat at the rate P, that may be varied. The rate of water in flow from tap is F = 0.021 litres per minute. The heat generated is sufficient so that the water in the container is boiling and getting converted into steam at a steady rate. What is the minimum power P ( in watt) that must be generated as heat in the steady state in resistor R so that the amount of liquid water in the container neither increases nor decreases with time? ( Neglect other losses of heat, such as conduction from the container to the air and heat capacity of container)For water , specific heat c = 4.2 kJ. Kg-1 , latent heat of vaporization Lvap= 2.3 MJ . kg-1, density = 1000 kg. m-3). Find P/100 .
IIT – ian’s PACE education Pvt. Ltd. : Andheri/Dadar/Chembur/Thane/Churchgate/Nerul/Powai PART – II
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 ONLY ONE is correct.
20. Which term does not describe the relationship between -D-glucopyranose and
-D-glucopyranose?
(A) diastereomers (B) epimers (C) enantiomers (D) anomers 21.
o
The products of above reaction are
(A) phenol and 2-iodopropane (B) iodobenzene and 2-propanol (C) iodobenzene & propene (D) p-isopropyl phenol
22. The IUPAC name of Na2[Fe(CN)5(NO)] is (A) Sodium pentacyanonitrosyl ferrate (III) (B) Sodium pentacyanonitrosyl ferrate (II) (C) Sodium pentacyanonitrosyl iron (III) (D) Sodium pentacyanonitrosyl iron (II)
23. Consider the cell described by the following reaction. Which of the changes listed will cause an increase in the cell voltage
2 (g ) (s) (s ) (aq ) (aq )
H 2AgCl 2Ag 2H 2Cl I. increase in H2(g) pressure
II. increase in the amount of AgCl(s) III. increase in pH
(A) I & III (B) II & III (C) I & II (D) II
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This section contains 5 multiple choice questions. Each question has 4 choices (A) , (B),(C) and (D) for its answers, out of which ONE OR MORE is/are correct .
24. C OH SOCl2 C H3 H C6H5 + Pyridine A + HCl + SO2
( ) - -Phenyl ethanol (optically pure)
Which of the following statement(s) are true regarding the above reaction. (A) Product ‘A’ has opposite configuration to alcohol
(B) Product ‘A’ has same configuration as alcohol (C) Product ‘A’ is leavo rotatory
(D) Product ‘A’ is dextro rotatory
25. Which of the following statement(s) is true?
(A) Lyophobic sol shows greater light scattering effect than lyophilic sol. (B) The stability of lyophobic sol is due to presence of charge on sol particles. (C) A catalyst increases the value of rate constant
(D) The absolute entropy of an element is zero at 25oC and 1 atm pressure 26. Pick out correct statements regarding Na2B4O7.10H2O
(A) It exists as Na2[B4O5(OH)4].8H2O
(B) It contain two tetrahedrons and two triangles
(C) Two boron atoms are sp3 hybridised and two boron atomis are sp2 hybridised (D) All boron atoms are sp2 hybridised
27. Which of the following statement(s) are correct regarding brown ring com complex [Fe(NO)(H2O)5]2+
(A) oxidation state of iron is + 1 (B) oxidation state of iron is + 2
(C) magnetic momentum ( is 3.9 B.M s) (D) magnetic momentum ( is 5.9 B.M s) 28. The ions which are planar are
(A) CO23 (B) NO23 (C) [I Cl ]4 (D) ClO3
SECTION - III Matrix - Match Type
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This section contains 2 questions. Each question constains 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 .
29. Column – I Column – II
(A) Extracted by electrolytic reduction (p) Pb (B) Metal dissolved in acids & bases (q) Mg (C) Metal used as reducing agent in the
extraction of Cr and Mn from their oxides.
(r) Cu
(D) Metal extracted by self reduction (s) Al
30. Column – I Column – II (A) C O H O CH3 & (p) Fehling reagent (B) H C OH & H C CH 3 O O (q) [Ag(NH3)2]+ (C) H 3C C H + H3C C CH3 O O (r) FeCl3 (D) OH C2H5 & HO CH CH3 (s) I2 + NaOH SECTION - IV
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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 darking of bubbles will look like the following:
31. The number of isomeric disubstituted products formed by Borazole (Inorganic benzene) are _______ 32. The normality of 22.4 volume H2O2 is ________
33. The total number of and bonds present in XeO4 are ________
34. 20 ml 5.6 volume H2O2 completely reduces 20 ml of KMnO4 in acid solution. The molarity of KMnO4 _______ x 10-1
35. The total number of isomers (structural as well as stereo) possible for dichlorocyclopentane are ____ 36. For sublimation of iodine crystals I2 (s ) I2(g ) at 25oC and atmospheric pressure
H 10
K.cal/mole and S 20 cal/K-mole. The temperature at which solid I2 be in equilibrium with gaseous I2 is _________ x 102 K
37. If 36.8% of initial amount of a radioactive substance is left after 43.2 minutes, the time taken for 99.9% disintegration of initial amount is ______ hours.
38. The potential of the cell
2 2 0.1MBCl Cu Pt, H (1atm) Cu 0.2M BOH (1M) is 0.88 V at 25oC
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PART III : MATHEMATICS
SECTION – I
Single Correct Choice Type
This section contains 4 multiple choice questions. Each question has 4 options of which
ONLY ONE is correct.
39.
cos sin cos x x x dx x x
equals
(A)
x
cos
x
C
(B)
x
sin
x
C
(C)
2
x
cos
x
C
(D)
C
2
x
cos
x
40.
Chord AB of the circle
2 2100
x
y
passes through the point(7,1) and subtends an angle of
60
at the circumference of the circle. If m
1and m
2are the slopes of two such chords then the
value of m
1m
2, is
(A)
1(B) 1
(C) 7/12
(D)
3
41.
Statement 1 : Consider the cubic equation
f
x
x
3
nx
1 0
where
n
3,
n
N
,
then
x
0
f
has at least one root in (0,1).
because
Statement 2 : If g(x) is a differentiable function such that
g x
'
0
at
x
a
and
x
b
and
0
g a g b
then the equation
g x
0
has atleast one root in (a,b).
(A) Statement-1 is true, statment-2 is true and statment-2 is correct explanation for statement-1.
(B) Statement-1 is true,Statement-2 is true and Statement-2 is not the correct explanation for
Statement-1.
(C) Statement-1 is true,Statement-2 is false
(D) Statement-1 is false,Statement-2 is true
42.
Let
g R: Rdefined by
g x
ex ,where {x} denotes fractional part function.
Statement 1 : g(x) is periodic function
because
Statement 2 : {x} is periodic function.
(A) Statement-1 is true, statment-2 is true and statment-2 is correct explanation for statement-1.
(B) Statement-1 is true,Statement-2 is true and Statement-2 is not the correct explanation for
Statement-1.
(C) Statement-1 is true,Statement-2 is false
(D) Statement-1 is false,Statement-2 is true
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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 the function
f R
:
R
defined as
f
x
x
sin .
x
Which of the following are
correct
statements ?
(A) The function is strictly increasing at every point on R except at ‘x’ equal to an odd
integral multiple of
where the derivative of f(x) is zero and where the function f is not
strictly increasing.
(B) The function is bounded in every bounded interval but unbounded on whole real line.
(C) The graph of the function y = f(x) lies in the first and third quadrants only.
(D) The graph of the function y = f(x) cuts the line y = x at infinitely many points.
44.
Let f(x) be a non constant twice diffrentiable function defined on R such that
2
x
f
2
x
f
and
1 0 ' 1 .
2'
ff
Then which of the following alternatives are correct?
(A)
f
4
f
8 .
(B) Minimum number of roots of the equation
f
"
x
0
in (0,4) are 4.
(C)
4 42
sin
0.
f
x
x dx
(D)
2 4 cos cos 0 25
t4
5
t.
f t
dt
f
t
dt
45.
Let
2
1
2
1
4
1
1 cos
1 cos
1 cos
1 cos
4
4
4
4
k
k
k
P k
k
k
k
k
then which of
the following is/are correct?
(A)
3 3 16 P (B)
4 2 2 16 P (C)
5 3 5 32 P (D)
6 2 3 32 P 46.
If the function f(x) defined as
2
for
0
2
1
sin
for
0
nx
x
f x
x
x
x
is continuous but not derivable at
0
x
then n can not be
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47.
A twice differentiable function f(x) is defined for all real numbers and satisfies the following
conditions
f
0
2;
f
' 0
5
and
" 0
f
3.
The function g(x) is defined by
ax
,
g x
e
f x
x
R
where ‘a’ is any constant. If
g
' 0
g
" 0
0
then ‘a’ can be
equal to
(A) 1
(B)
1(C) 2
(D)
2SECTION – III
Matrix – Match Type
This section contains 2 questions. Each question contains statements given in two
columns, which are 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.
48.
Column I
Column II
(A)
A rectangle is of width
4
.
3
One vertex is taken and folded
(P)
1
over to touch the opposite edge on the rectangle (length not
(Q)
2
specified). the minimum length of the crease, is
(B)
The number of solutions of the equation
log 3
x
5
x
7,
(R)
3
(C)
As ‘x’ range over the interval
0,
, the function
2 29
173
900
9
77
900
f x
x
x
x
x
range over (0,M).
The possible integral value(s) in the range of f(x) is
(S)
4
(D)
The possible real number ‘k’ for which
2 2 2
2
4 4 4
x y z k x y z
(T)
5
holds for
x y z, , R,is
49.
Column I
Column II
(A)
The value of the integer
x x
2
satisfying
n n 1 ... n 120
2 !
l x l x le
x
is
(P) 1
(B)
The number of solution of the equation,
tan 1
4
cot 1
, 2x x x
is
(Q)
2
(where [] denotes greatest integer function and {} denotes fractional
part function)
(R)
3
(C)
If the equation
2 22
2
2
4
0
x
y
xy
gx
fy
represents a pair of real
straight lines, then the possible value of ‘g’ can be
(S)
4
(D)
Let A and B are two points in x-y plane which are d units apart
where
d
5, 6
. The number of lines that are 2 units away from A
A
(T)
5
and 3 units away from B can be
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SECTION – IV
Integer Answer Type
This section contains 8 questions. The answer to each of the questions is a integer type
ranging . The appropriate bubbles below the respective question numbers in the ORS
have to be darkened.
50.
Line l is a tangent to a unit circle S at a point P. Point A and the circle S are on the same side
of l , and the distance from A to l is 3. Two tangent form point A intersect line l at the point B
and C respectively. Find the value of (PB)(PC).
51.
Consider two lines
17 7 3 : 3 2 1 x y z
L
and
2: 1 1 1. 2 4 3 x y zL
If a line L whose
di-rection ratios are 2, 2,1
intersect the line
L and
1L at A and B, then find the distance AB.
2AB.
52.
Let
a
3
2231
1
and for all
n
3,
let
1 2 3
1 0 0 1 2 .... 1 1 . n n n n n n n n n n C a C a C a C af
If the value of
f
2007
f
2008
9
k
where k N
, then find k.
53.
If the value of the definite integral
2 1 1 1 2 2 1 1 cot cot 1 1 x a b x dx c x x
where , ,
a b c
N
in their lowest form, then find the value of
a b c
.
54.
The sides of a triangle have the combined equation
2 23
2
8
4
0.
x
y
xy
y
The third side,
which is variable always passes through the point
5, 1 .
If the range of values of the
slope of the third line so that the origin is an interior point of the triangle, lies in the
interval (a,b) then
find
2 1 . a b 55.
Number of ways in which 5A’s and 6B’s can be arranged in a row which reads the same
beckwards and forwards, is
56.
If
1 1 5 52x
y
y
then
2 2 21
d y
dy
,
x
x
ky
dx
dx
then find the value of ‘k’.
57.
Find the value of
5 3 3
2 0
1 cos
cos 2 cos 3
lim
.
xx
x
x
x
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1. (B) Photons per area per second at a distance r are 5.001018/4r2. Photons per second
entering the eye, radius R is then this times 2
R
. Set this product equal to 500 per second and solve for r. The result is [B].
2. (C) (O) R ( iR) S (O) R R i 3R S S 4 V iR V 3 3 3. (A) 2 mv qvB r r mv 2m(KE) 2mqV 2mv 1 qB qB qB q B 2 1 1 1 1 2 2 2 2 2 R M M R R M M R 4. (B) (m1 + m2) g sin 2f3 fs N f2 f1 N fs N + m1 g sin f1 m g sin2 Nf2 2 1 m g sin NNm g sin m2m1
5. (C) Flux passing through the cone will remain same for both Thus, 1 2
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali 1 q 1 q or 1 2 0 0 q q (1 cos ) (1 cos )
2 2 (using solid angle)
2 2 1 2 q sin q sin 2 2
6. (ABC) In the initial state, charge on each capacitor is shown in figure-1
figure 1 2 F 300 C 1.5 F 3 F 360 C figure2 2 F 300 q 3 F 360 q 1.5 F A q q
Let charge q flow anticlockwise in the circuit before it achieves steady state as shown in figure.-2. Applying KVL to figure 2.
(360 q) q (300 q)
0
3 1.5 2
or 180 C
final charge on 1.5 F capacitor is q = 180 C and final charge on 2F capacitor is 300- q = 120 C
7. (B,D)The x – component of velocity being parallel to magnetic field , shall remain unchanged. The component of velocity perpendicular to x – axis will always have magnitude Voy, and at any time t it shall make an angle = t with y – axis as shown .
z y t oy v
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali
at any time t is Voy sint. Where
qB m
8. (a,b,c,d) Area under the curve is equal to number of molecules of the gas sample. Hence
0 1 N a V aV0 2N 2 0 V avg 0 0 0 1 1 a V V N(V)dV V V dV N N v
avg 0 0 V 2 2 V 3 V 3 0 V 2 2 2 2 0 rms 0 0 0 V 1 1 a V V N(V)dV V V dV N N V 2
rms 0 V 1 V 2 Area under the curve from 0.5 V0 to V0 is
3
4 of total area.
9.(A) The magnetic flux must remain constant
0 m 0 B B ab bx 1 kt B0 C D x b Where x is as shown x = a (1 + kt) or v = dx ak dt 10. (A – p,s ; B – p, r ; C – p, s; D – q, s) 11. (A – p,q,r ; B – p,q,r,s ; C – r ; D – p,q,r,s)
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali (P) i/3 i/3 i/3 i not is downward 0i 0i / 3 0i ( i) 4 d 4 d 3 d (Q) 0i / 2 4 d 0i / 2 4 d 0i 4 d 2 0i cos 45 0i 0i 1 1 ( j) 8 d 4 d 4 d 2 (R) 0i / 2 4 d 0i / 2 4 d 0i 4 d 0i ( j) 4 d (S) 0i / 2 4 d 0i 4 d 0i / 2 4 d 0i 4 d 0i 4 2 d 0i ( j) 0i ( j) 4 d 4 2 d 12. (7) RA = resistance of ammeter
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali 1 1 1 A 4 V V 1 V 0 ...(1) 100 R 100 1V – 0V = ( 10 mA) RA RA = 100 1 1 1 4 V V 1 V 0 100 10Q 100
( By using equation (1) and (2) V1 = 5/3 V 1 A V 1 R
( current in ammeter (II) 5 / 3 1 6.67mA 100 = 7 13. (1) 2 i 0 Q d u 2 A then VC = VA ( At equilibrium condition) VAB = VBC
2 2 2 1 1 f 0 0 0 Q Q 2d Q d Q d U A A 3 A 1 1 0 0 Q d Q Q (2d) A A Q1 = 2(Q –Q1) 3Q1 = 2Q
2 2 1 1 f 0 0 0 Q Q 2d Q d Q d U A A 3 A
2 2 2 2 u 0 0 0 60 Q d Q d Q d 0.1mJ 2 A 3 A 6 A 6(6) . So x = 114. (5) The plate is free to rotate about vertical axis yy’.
y y ' C u m y y ' cm v v m C
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali angular velocity of plate just after collision.
From conservation of angular momentum about vertical axis passing though O is
2
a a ma
mu mv
2 2 3 … (1)
Since the collision is elastic, the equation of coefficient of restitution is
cm v v e 1 u … (2) But vcm a 2 … (3)
Solving equation (1), (2) and (3) we get 12 u
7 a
= 5 rad/s
15.(2) When S2 is closed current in inductor remains, i
2R 1 1 1 V V 2 V R 2R 2R 3 2R R 0 0 0 1 v i 2R 1 S Potential difference (V) 2 3 3 Ans. And Ldt 2 dt 3 di 2 dt 3L = 2000 ; X = 2
16.(4) The light entering the rod does not emerge from the curved surface of the rod when the angle 90 – r is greater than the critical angle.
i.e., 1
sin C
where C is the critical angle. Here C = 90 – r
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali 1 1 sin(90 r) cos r As a limiting case 1 cos r … (i) Applying Snell’s law at A
sin sin sin r sin r … (ii)
The smallest angle of incident on the curve surface is when 2
. This can be taken as a limiting case for angle of incidence on plane surface.
Form (ii) sin / 2 1 sin r sin r … (iii)
Form (i) and (ii) sin r = cos r r = 45o
1 1
cos 45 1/ 2
2 2 4
This is the least value of the refractive index of rod for light entering the rod and not leaving it form the curved surface.
17. Here Q0 = maximum value of Q = 200 C = 210-4 C 4 1 3 6 1 1 10 s LC (2 10 H) (5.0 10 F) Let at t = 0, Q = Q0 then … (1)
Q(t) = Q0 cos t I(t) dQ Q0 sin t dt … (2) 2 0 dI(t) Q cos( t) dt … (3) For 0 Q Q 100 C or 2
From (1) 100 = 200 cos t or cos( t) 1, 2
From equation (3):
L2.0mH
IIT – ian’s PACE Education Pvt. Ltd. ; Andheri/Dadar/Chembur/Thane/Nerul / Powai/ Kandivali 1 4 1 2 dt 1 (2.0 10 C) (10 s ) dt 2 4 dI 10 A / s dt But dI x 10 A / s dt x = 7 18. (1) Maximum percentage error in Y is given by Y W2 L
D X 4 max Y D X L 2 Y D X L 0.001 0.001 0.1 2 0.0489 0.05 0.125 110
So maximum percentage = 4.89% It is given that
2 W50N; D0.05cm; 0.05 10 m; X = 0.125 cm = 0.125 x 10 -2 m ; L = 110 cm = 110 x 10 -2 m
2 2 2 50 4 110 10 Y 3.14 0.05 10 0.125 10 = 2.24 x 10 11 N/m2 Y0.0489 2.24 10 111.09 10 N / m 10 2 9 2 11 10 N / m x = 1119. Rate of water coming from Tap T is 0.021 x 10 -5 m3 / minute 5 3 2.1 10 F m / sec 60 5 3 2.1 10 F m / sec 60
same amount of water should be ejected in from of steam.
So heat supplied must be Q mS T mL or Rate of heat transfer
Q m m S T L t t t P FS T FL m F t P =
5 1000 2.1 10 [4.2 100 20 2300]kJ / sec 60 P = 922.6 (J/sec. or watt). P/100 = 9.22 = 9IIT – ian’s PACE education Pvt. Ltd. : Andheri/Dadar/Chembur/Thane/Churchgate/Nerul/Powai
Paper – II
Solution
20. C
21. A
22. B
23. A
24. A
25. A,B,C
26. A,B,C
27. A,C
28. A,B,C
29. A – q,s; B – p,s; C – s ; D – p,r
30. A-q,s; B-p,q,s; C-p,q; D-r
31. 4
32. 4
33. 8
34. 2
N1V1 = N2V2
1
20 = 20
N2
N2 = 1 = 5
M M = 0.2 = 2
10
-135. 7
Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl Cl36. 5 At equilibrium
G
= 0
H T S
2 H 10 1000 T 500K 5 10 K S 20 37. 5 Average life T = 1.44
t
1/2=
43.2 0.72 h 60 1/ 2 0.72 1 t h 1.44 2 Time for 99.9% disintegration 10
t1/2
=
10 1 5 h 2 38. 5
0.88 = 0.34 – (
0.059 pH)
pH =
0.54 9 0.0595 = pKb +
log0.1 0.25 =
pKb 0.3pKb = 5.3
pH =
7 1 5.3 log 5 10 2 2 =
7 1
5.3 0.7 2
2 = 5
Solution Paper # 2
39.
(C)
40.
(A)
41.
(B)
42.
(D)
43.
(B,C,D)
44.
(A,B,C,D)
46.
(C,D)
47.
(A,D)
51.
(18)
54.
(24)
55.
(10)
IIT-ian’s PACE Education Pvt .Ltd ; Andheri / Dadar / Chembur / Thane / Churchgate / Powai / Nerul
IIT-JEE 2010
A.I.T.S # 1 (Answers Key)
Date : 03/01/2010
ANSWERS KEY
Paper I
Que. 1 2 3 4 5 6 7 8 9 10 Ans. B C D D D D D B A,B,C,D A,C Que. 11 12 13 14 15 16 17 18 19 20 Ans. ABCD A B C B B A A A-q; B- r; C-s A-p,q; B-r,s;
C-p,q Que. 21 22 23 24 25 26 27 28 29 30 Ans. B C A D B C B D A,B A,B,C Que. 31 32 33 34 35 36 37 38 39 40 Ans. A,B A,B B C A A B A A-p,s; B-p,q,r
C-p,q; D-p,s A-q,r,s; B-p; C-q,r,s; D-q Que. 41 42 43 44 45 46 47 48 49 50 Ans. A C C B A A A D B,C A,B,D Que. 51 52 53 54 55 56 57 58 59 60 Ans. A,C A,B,C A C B A,D A,D A,C,D A-s; B-r;
C-q; D-p
A-r; B-t; C-q;D-q
Paper II
Que. 1 2 3 4 5 6 7 8 9 10 Ans. B C A B C A,B,C B,D A,B,C,D A A-p,s; B-p,r;
C-p,s; D-q,s Que. 11 12 13 14 15 16 17 18 19 Ans. A-p,q,r; B-p,q,r,s; C-r; D-p,q,r,s 7 1 5 2 4 7 1 9 Que. 20 21 22 23 24 25 26 27 28 29 Ans. C A B A A A,B,C A,B,C A,C A,B,C A-q,s; B-p,s;
C-s; D-p,r Que. 30 31 32 33 34 35 36 37 38 Ans. A-q,s; B-p,q,s; C-p,q; D-r 4 4 8 2 7 5 5 5 Que. 39 40 41 42 43 44 45 46 47 48 Ans. C A B D B,C,D A,B,C,D B,C C,D A,D A-r; B-q;
C-p,q,r,s,t; D-r,s,t Que. 49 50 51 52 53 54 55 56 57 Ans. A-t; B-q; C-q,r,s,t; D-r,s 3 18 2187 7 24 10 25 22
