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Sec: SR.IIT_*CO-SC Date: 17-03-
Time: 3HRS Max. Marks: 198
Name of the Student: ___________________ H.T. NO:
17-03-24_SR.STAR CO-SUPER CHAINA_JEE-ADV_GTA-1(P1)_SYLLABUS
PHYSICS: TOTAL SYLLABUS
CHEMISTRY: TOTAL SYLLABUS
MATHEMATICS: TOTAL SYLLABUS
Time: 3HRS IMPORTANT INSTRUCTIONS Max Marks: 186
MATHEMATICS:
Section Question Type
+Ve
Marks
Marks
No.of
Qs
Total
marks
Sec – I(Q.N : 1 – 5) Questions with Single Correct Choice 3 -1 5 15
Sec – II(Q.N : 6 – 13)
Questions with Multiple Correct Choice
(Partial Marking +1)
Sec – III(Q.N : 14 – 18) Questions with Integer Answer Type 3 0 5 15
Total 18 62
PHYSICS:
Section Question Type
+Ve
Marks
Marks
No.of
Qs
Total
marks
Sec – I(Q.N : 19 – 23) Questions with Single Correct Choice 3 -1 5 15
Sec – II(Q.N : 24 – 31)
Questions with Multiple Correct Choice
(Partial Marking +1)
Sec – III(Q.N : 32 – 36) Questions with Integer Answer Type 3 0 5 15
Total 18 62
CHEMISTRY:
Section Question Type
+Ve
Marks
Marks
No.of
Qs
Total
marks
Sec – I(Q.N : 37 – 41) Questions with Single Correct Choice 3 - 1 5 15
Sec – II(Q.N : 42 – 49)
Questions with Multiple Correct Choice
(Partial Marking +1)
Sec – III(Q.N : 50 – 54) Questions with Integer Answer Type 3 0 5 15
Total 18 62
SECTION – II
(MULTIPLE CORRECT ANSWER 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 all correct options & +1 partial marks, 0 if not attempted and -2 in all wrong cases
6. Let f(x) =
3
x x 1 , suppose g(x) is a cubic polynomial such that g(0) = -1 and the roots
of g(x) are the square of the roots of f(x), then
A)
^
2 2
g x f x B)
^
2 2
g x f x C) g 1 3 D) g 4 99
7. Consider the following statement about the equation x x px q 0 , p,q Rthen
A) it has at most 3 real roots B) it has at least one real root
C) it has real roots only if
2
p 4q 0 D) it has 3 real roots if p<0 and q>
8. In a ABC ,if
1
A A
sec tan
2
B B
sec tan
3
C C
sec tan
, then
A)
1 2 2 3 3 1
=1 B)
2 2 2
1 2 3
C)
1 2 2 3 3 1
1 D)
2 2 2
1 2 3
9. If k is an integer such that 0
cos
lim cos
^
n n
n
k k
then which of the following
is/are possible
A) k is divisible neither by 4 nor by 6
B) k must be divisible by 12, but not necessarily by 24
C) k must be divisible by exactly one of 4 or 6 but not by both together
D) either k is divisible by 24 or k is divisible neither by 4 nor by 6
10. Let f: [2, 4] R is a continuous positive function, differentiable on (2, 4), then
A) there exists (2, 4) such that
2f ( )
f ( )
f(4)
e
f(2)
B) there exists (2, 4) such that f() =
f( ) f( )
C) there exists (2, 4) such that f() = 0
D) there exists (2, 4) such that f() = 2f()
11. If
3 2 3
f x 3x f x x 0 , then
f x
dx
x
is equal to
A) f x c B) f x c C) 2f x c D) xf ' x c
12. If
2 2 1
1
3
1
2x x x p 2 1
dx ln cos
q 3 m 6 1 x
^ ^
, p,q I
, HCF (p, q) = 1, then
A)
2
p m 1 B)
2
p m C) q m 1 D)
2
pq 4m
13. Consider the circle z 5 i 3 and two points
1
z and
2
z on it such that
1 2
z z , 1
arg z (^) 2
arg
z
. A tangent is drawn at
2
z which cuts the real axis at
3
z then
A)
3
2 3
arg
i z
z z
(^)
B)
3 2
z z 3 3 C)
3
z 5 i 6 D)
3
z 11
SECTION – III
(INTEGER ANSWER TYPE)
This section contains 5 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive).
Marking scheme +3 for correct answer, 0 if not attempted and 0 in all other cases.
14. The least natural number p for which the equation
2
cos p x 2 cos p x
3 x x
cos cos 2
2p 2p 3
=0 has a root is ____________.
- Let be the bigger root of the equation 4 2 8 0
2
f x ax ax where
a and
if the value of (^) 2 L
cot
cot 2 tan tan
1 1
then the value of
6 L
is ____________.
16. Let ABC be an acute angled triangle with circumradius and inradius 3 and 1
respectively. Let P
A
, Q
A
be the points in which the line AI meets the circumcircles of
ABC and IBC respectively. Similarly, P
B
, Q
B
; P
C
, Q
C
are also observed. (I is the
incentre of ABC) then
A A B B C C
2 2 2
A A B B C C
P B.P C P C.P A P A.P B
P Q P Q P Q
______
17. Let f: R R be a function defined as f(x + y) = f(x) + f(y) – 3xy(x + y) – 1 x, y R,
f(0) = –1. Find the least positive integer value of x which satisfies the inequality 1 – f(x)
3
(x) > f(1 – 5x).
18. Let n > m, and f(n, m) =
n n m
K r n r
r m
k 0 r 0
C C
and if f(100, 50) =
C
51
C
51
, then the
number of odd integral divisors of + + 3 is ______
22. The potentiometer wire AB in the figure has length ‘L’ and resistance ‘9r’. The cells
have emfs V and V/2 and internal resistance ‘r’ and ‘2r’ as marked. Mark the
INCORRECT options
A) The Galvanometer ‘G’ will show zero deflection, when the length of AJ equal to
L
B) The Galvanometer ‘G’ will show zero deflection, when 5r is in series to emf of ‘V’
then
L
AJ
C) The Galvanometer ‘G’ will show non zero deflection, when the length AJ is equal to
L
if 2r is in series with V/2 emf
D) Balancing length remains unchanged if any finite resistance is connected in series
with V/
23. A tube of uniform cross section ‘a’ and length L is rotating with a constant angular speed
in the vertical plane. End A is open to atmosphere. What is the angular speed required
just to stop water coming out from a very small opening present at the closed end B
when the hole is at the top most position. Atmospheric pressure is P
0
(pascal)
A
h
L
=constant
B
A)
2g
(2L h)
B)
0
2( hg p )
h(2L h)
C)
2 2
2gh
L h
D)
0
2 2
2( hg p )
(L h )
SECTION – II
(MULTIPLE CORRECT ANSWER 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 all correct options & +1 partial marks, 0 if not attempted and -2 in all wrong cases
24. A planet is moving around the sun in a circular orbit of radius R and with a time period
T. If the planet is suddenly stopped in its orbit then
A) the mechanical energy will decrease
B) the mechanical energy after the stopping will become twice the initial
C) Its angular momentum about the centre of the sun will become zero
D) It will fall onto the sun after a time
T
if released thereafter
25. In the given diagram three concentric conducting charged spherical shells are indicated.
Initially both the switches are open. Select the correct alternative(s).
A) If only switch S
2
is closed then the charge transferred through this switch
will be
Q
B) If only switch S
2
is closed then the charge transferred through this switch
will be
Q
C) If only switch
1
S is closed then the charge transferred through this switch
will be Q/
D)If only switch
1
S is closed then the charge transferred through this switch
will be
Q
26. A ring of mass M, radius R, cross section area ‘a’ and Young’s modulus Y is kept on a
smooth cone of base radius 2R and semi vertex angle 45
0
, as shown in figure. Assume
that the extension in the ring is small. Pick the correct alternative(S)
Ring
2R
45°
29. Choose the correct statement(s):
A) In a reversible adiabatic expansion, the product of pressure and volume decrease.
B) The rms translational speed for all ideal gases at the same temperature is not the same
but it depends on the molecular mass.
C) If temperature of an ideal gas is doubled from 100 C to 200 C , the average kinetic
energy of each particle is also doubled.
D) The magnitude of momentum of a Helium atom in a sample of Helium gas at 200K
will be less than the magnitude of momentum of a Hydrogen molecule in a sample of
Hydrogen gas at 400K
30. In the arrangement shown, the small spherical object of mass m is at rest on a smooth
floor at
R
x
and it is connected to a spring of force constant k. At t = 0, it was given
a velocity
R k
v i
4 m
. Then
R/
x=
concave mirror of R
radius of curvature
i
j
A) At
3 m
t
4 k
, the velocity of object is towards the concave mirror
B) At
3 m
t
4 k
, the speed of object is
R k
4 2m
C) At
3 m
t
4 k
, the speed of image of this object is
2k
R
m
D) At
3 m
t
4 k
, the image is virtual, erect & magnified
31. X ray from a tube with a target A of atomic number Z shows strong K lines for target A
and weak K lines for impurities. The wavelength of K
is
z
for target A and,
1
and
2
for two impurities.
z
1
and
z
2
. Consider screening constant of K
lines to be unity. Select the correct
statement(s)
A) The atomic number of first impurity is 2Z-
B) The atomic number of first impurity is 2Z+
C) The atomic number of second impurity is
(Z 1)
D) The atomic number of second impurity is
Z
SECTION – III
(INTEGER ANSWER TYPE)
This section contains 5 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive).
Marking scheme +3 for correct answer, 0 if not attempted and 0 in all other cases.
32. A neutron is scattered through (=deviation from its old direction) degree in an elastic
collision with an initially stationary deuteron. If the neutron loses
of its initial K.E,
to the deuteron then find the value of
( In atomic mass unit , the mass of a neutron is
lu and mass of a deuteron is 2u)
33. The heat capacity in a process of 0.5 moles of a diatomic gas, if it does work of Q/
when a heat of Q is supplied to it ,is
R
x
. The value of x is
34. A radioactive material consists of nuclides of 3 isotopes which decay by emission,
emission and deuteron emission respectively. Their half-lives are
1 2 3
T 400sec,T 800sec and T 1600secrespectively. At t=0, probability of getting , and
deuteron from radio nuclide are equal. If the probability of emission at t=
seconds is
n
, then find the value of ‘n’
35. The values of two resistors are (5.0^ ^ 0.2)k^ and (10.0^ ^ 0.1)k^. What is percentage error in
the equivalent resistance when they are connected in parallel?
36. In a car race sound signals emitted by the two cars are detected by the detector on the
straight track at the end point of the race. Frequency observed are 330 Hz & 360 Hz and
the original frequency is 300 Hz of both cars. Race ends with the separation of 100 m
between the cars. Assume both cars move with constant velocity and velocity of sound is
330 m/s. Find the time taken by winning car (in sec)
41. The emf of the given cell is -0.46 V
(^)
3 2
2 2 4 4
1atm
1L solution
Pt H H PO 0.4 M , HPO 6.4 10 M M 0.81M M s
If (^)
0 2
E M M 0.76V log 3 0.477,log 2 0.
and temperature is
0
25 C.
a
pK for reaction
2
2 4 4
H PO HPO H
is?
A) 5.9 B) 4.57 C) 7.9 D) 6.
SECTION – II
(MULTIPLE CORRECT ANSWER 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 all correct options & +1 partial marks, 0 if not attempted and -2 in all wrong cases
42. Incorrect matching(s) is/are:
A)
don't neutralize
3
dil.HNO :
2
SiO , CO
B) reacts with HF :
2
SiO ,SnO
C) Solid at room temperature: 3
LiHCO , NaCl
D) act as reducing agent: CO, SnO
43. Identify the incorrect statement(s)
A) Combustion of methane in an adiabatic rigid container will cause no change in
temperature of the system.
B) Dimerization of acetic acid causes an increase in entropy of the system
C) It is possible to have both adiabatic reversible and adiabatic irreversible processes
between two states.
D) P – V work is always non – zero when there is a change in volume
44. Which of the following statement(s) is/are correct?
A) Tetracyanocuprate (I) is a tetrahedral complex
B) Tetracyanonickelate (II) is a square planar complex
C) Tetrachloridopatinate (II) is a tetrahedral complex
D) Tetraamminecopper (II) sulphate is a square planar complex
2 2
CaC N X Y
, X contains Calcium, then identify correct statement(s) regarding
'X' & ‘Y’?
A) Anion of 'X' is isoelectronic and isostructural with CO
2
B) Hydrolysis of X gives melamine
C) both of the hydrolysis products of X formed are highly water soluble
D) Y is amorphous form of carbon
46. Which of the following reaction is not an example of redox reaction?
A) Hydrolysis of
2
XeF B) Hydrolysis of
6
XeF
C) Reaction of
4
XeF with
2 2
O F D) Reaction of
2
XeF with
5
PF
47. Observe the following reaction:
H C 3
CH 2
NBS
hν
Pick the correct statement (s)
A) 6 optically active products are formed
B) All products formed in the reaction show geometrical isomerism
C) 4 chiral and 2 achiral products are formed
D) 4 Fractions are obtained on fractional distillation
48. The time required for an electron to make one complete revolution around nucleus of H-
atom in a higher orbit
2
n is 8 times to that of a lower orbit
1
n. Therefore
1
n and
2
n are
A) 1 and 2 B) 2 and 3 C) 2 and 4 D) 3 and 6
52. How many of the following amino acids when fused with sodium followed by addition
of aq. Sodium nitroprusside give purple colour solution?
Arginine, Lysine, Serine, Aspargine, isoleucine, Tyrosine
53. Identify the number of correct statements out of the given?
1. Cl
2
and SO
2
both are bleaching agents. Bleaching of flowers by Cl
2
is permanent
while by SO
2
is temporary
2. We have PCl
3
and PH
3
but there is no PH
5
though we have PCl
5
3. HNO
3
releases NO
2
gas when reacted with metals like Zn, Fe etc under concentrated
conditions but HNO
3
with same metals releases N
2
O under diluted conditions.
4. Ability to form negative oxidation states decreases down in the group VA.
5. For titrating boric acid with NaOH in presence of phenolphthalein, we add catechol.
6. Nitric acid is only oxidising agent but Nitrous acid is both oxidising as well as
reducing.
7. Dipole moment of NF
3
is less than NH
3
though F is more electronegative than H.
8. Na
2
CO
3
is stable while Li
2
CO
3
and MgCO
3
are less stable and decompose on heating
while Al
2
CO
3
doesn’t even exist.
9. Cl forms only HOCl, HClO
3
and HClO
4
while Br forms HOBr, HBrO
2
, HBrO
3
and
HBrO
4
10. In permanganometry titrations we use H
2
SO
4
to provide acidic conditions but not
HNO
3
or HCl
54. If 4 atoms of same radius are placed at the alternate corners of a cube touching each
other, and if the length of body diagonal of the cube is equal to x R, where R is the
radius of atom. Find the value of x?
Sec: OSR.IIT_*CO-SC GTA-1(P1) Date: 17-03-
Time: 3HRS 2016_P1 Max. Marks: 198
KEY SHEET
MATHEMATICS
1 B 2 C 3 A 4 D 5 D
6 CD 7 AB 8 AD 9 AD 10 AB
11 AD 12 BCD 13 ABCD 14 6 15 3
16 3 17 3 18 6
PHYSICS
19 D 20 B 21 B 22 C 23 A
24 ABCD 25 A 26 ABC 27 BD 28 AD
29 AB 30 BCD 31 AC 32 9 33 3
34 1 35 3 36 4
CHEMISTRY
37 D 38 B 39 B 40 C 41 D
42 C 43 ABCD 44 ABD 45 AD 46 BD
47 AD 48 ACD 49 A 50 3 51 7
52 0 53 9 54 6
Narayana IIT Academy 17-03-24_OSR.IIT_*CO-SC_JEE-ADV_GTA-1(P1)_KEY&SOL
SR.IIT_*CO-SC Page NO: 3
Eqn. (i),
2
x f x f
x
Now,
1 x
x
f t dt I
Replace x 1 x
2 2
1 x x
t
t
I f dt f dt
t (^) t t t
1 x
2
x
2I f t f t dt 0
t
from (*)
i.e., I^ ^0 f 1
cos x sin x cos 2x
f x g x h x tan x sin 3x cos 4x
cos 3x sin 5x cos 6x
0 0
f, g, h x dx f, g, h x dx
1 1
0 0
f, g, h dx f, g, h dx C C
0
f, g, h dx 0
1
a a, b
2 ^
a a 2, b 5
3 ^
a a 2, b 5
Area of , whose vertices are
1 2 3
a , a and a
, is
2
1 a b
1 a 2 b 5
1 a 2 b 5
1 a b 1 a b
1 a 2 b 5 1 a 2 b 5
1 a 2 b 5 1 a 2 b 5
and
1 2 1 3 2 3
a a 3, a a 3, a a 4
1 1 1 2 1 3 2
2 1 2 2 2 3
3 1 3 2 3 3
1 a .a 1 a .a 1 a .a
2 5 1 a .a 1 a .a 1 a .a
1 a .a 1 a .a 1 a .a
Required answer = 4 x 5 x 4 = 80
^ ^ ^
2
g x f x f x
1
A
tan tan
2
B
tan tan
3
C
tan tan
Narayana IIT Academy 17-03-24_OSR.IIT_*CO-SC_JEE-ADV_GTA-1(P1)_KEY&SOL
SR.IIT_*CO-SC Page NO: 4
9. Either
& cos
cos
k k
both lie in (–1, 1) or both together can be 1 or –1.
10. (A) Apply LMVT on ln (f(x))
(B) Apply LMVT on (x – 2) (x – 4) f(x).
3 2 3 y 3x y x 0
2 2
2 2 2 2
6xy 3x 3 2xy x dy y
dx x 3y 3x 3 y x
dy y
dx i.e., dx y c
dx x
f x cor xf ' x c
2
2
3 2 3 2 2
x 2x dx 2x x
xdx x x
dx
1 x x x 1 x
x
2 1 3 2
ln x tan x
x 3
^ ^
2 2
1
3
1
2x x
9 2 1 x dx ln cos
1 x
13. Origin,
2
5 ,i z and
3
z lies on a circle whose end points of diameter are 5 i and
3
z.
- (^)
^
2 3 x x
cos p x 1 cos cos 1 0
2p 2p 3
x p 2n, x 2p k
6n
p
6k 5
least
p 6
- f 2 0 The other root
a
lies between 2 and 3 as 2
a
So 2 , 3
a
2 tan 0
2 L
cot
tan
2 tan
tan
cot
cot 2 tan tan
1 1 1 1
^
^
So
6 L
is equal to 3
16. P
A
B = P
A
C = P
A
I.
Similarly, P
B
C = P
B
A = P
B
I
And PCA = PCB = PCI
