SEC: INC.JR_*CO-SC(MODEL-A)
Time: 3 Hrs
Date: 18-12-22
Max. Marks: 186
18-12-22_INC.JR.IIT_STAR CO-SC(MODEL-A)_JEE ADV_WAT-24_SYLLABUS
PHYSICS:
PRESENT WEEK (80%): Heat & Thermodynamics : Definition of
heat, Temperature, Scales of measurement of temperature, Thermal
Expansion of Solids & Liquids, Calorimety. (Experiment: Specific
heat of liquid using calorimeter)
PREVIOUS WEEK (20%): Error Analysis : Error Analysis of Physical
quantities, Significent figure, Rounding off of numbers, Accuracy,
Precision (All rules pertaining to above topics only as per NCERT text
book)
CHEMISTRY:
Experiment: Experiments based on using Vernier calipers and screw
gauge (micrometer)
PRESENT WEEK (80%): Strength of acids, strength of base,
Tautomerism
MATHEMATICS:
PREVIOUS WEEK (20%): Hyper conjugation, Reactive intermediates
homolytic and heteroltyic cleavage, stability of carbocation and
rearrangement, stability of carbanion and free radical, stability of
carbene and nitrene, electrophiles and nucleophiles
PRESENT WEEK (80%): AOD: Tangents & Normals, Rate measure,
Angle between the intersecting curves
PREVIOUS WEEK (20%): Differentiation: Solving functional
equation by using differentiation, Derivatives of implicit function,
Derivatives upto order two
Narayana IIT Academy
Time: 3HRS
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
IMPORTANT INSTRUCTIONS
PHYSICS:
Section
Question Type
Sec – I(Q.N : 1 – 5)
Questions with Single Correct Choice
Questions with Multiple Correct Choice
(Partial Marking +1)
Questions with Integer Answer Type
Sec – II(Q.N : 6 – 13)
Sec – III(Q.N : 14 – 18)
Max Marks: 186
+Ve
Marks
3
- Ve
Marks
-1
No.of
Qs
5
Total
marks
15
4
-2
8
32
3
0
5
15
18
62
Total
CHEMISTRY:
Section
Question Type
Sec – I(Q.N : 19 – 23)
Questions with Single Correct Choice
Questions with Multiple Correct Choice
(Partial Marking +1)
Questions with Integer Answer Type
Sec – II(Q.N : 24 – 31)
Sec – III(Q.N : 32 – 36)
+Ve
Marks
3
- Ve
Marks
-1
No.of
Qs
5
Total
marks
15
4
-2
8
32
3
0
5
15
18
62
Total
MATHEMATICS:
Section
Question Type
Sec – I(Q.N : 37 – 41)
Questions with Single Correct Choice
Questions with Multiple Correct Choice
(Partial Marking +1)
Questions with Integer Answer Type
Sec – II(Q.N : 42 – 49)
Sec – III(Q.N : 50 – 54)
INC.Jr.IIT_*CO SC
Total
+Ve
Marks
3
- Ve
Marks
-1
No.of
Qs
5
Total
marks
15
4
-2
8
32
3
0
5
15
18
62
Page No: 2
Narayana IIT Academy
PHYSICS
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Max Marks: 62
SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its
answer, out of which ONLY ONE option can be correct.
Marking scheme: +3 for correct answer, 0 if not attempted and –1 in all other cases.
1.
The least count of the main scale of a vernier calipers is 1 mm. Its vernier scale is
divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws
are touching each other, the 7th division of vernier scale coincides with a division of
main scale and the zero of vernier scale is lying right side of the zero of main scale.
When this vernier is used to measure length of a cylinder the zero of the vernier scale
between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The
length of the cylinder is : (VSD is vernier scale division)
A) 3.2 cm
2.
B) 0.50 mm
C) 0.75 mm
D) 0.80 mm
B) 1C
C) 2C
D) 2C
A piece of metal weighs 46g in the air. When it is immersed in the liquid of specific
gravity 1.24 at 270C, it weighs 30g. When the temperature of liquid is raised to 420C,
the metal piece weighs 30.5g. Specific gravity of the liquid at 420C is 1.20. The
coefficient of linear expansion of the metal will be
A) 3.316 105 / 0 C
5.
D) 2.99 cm
A Fahrenheit thermometer reads 113 F while a faulty Celsius thermometer reads 44C .
The correction required to be applied to the Celsius thermometer is
A) 1C
4.
C) 3.07 cm
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to
measure the thickness of a thin sheet of Aluminium. Before starting the measurement,
it is found that when the two jaws of the screw gauge are brought in contact, the 45th
division coincides with the main scale line and the zero of the main scale is barely
visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the
25th division coincides with the main scale line?
A) 0.70 mm
3.
B) 3.21 cm
B) 2.316 105 / 0 C
C) 4.316 105 / 0 C
D) 1.316 105 / 0 C
One kilogram of ice at 0C is mixed with one kilogram of water at 80C . The final
temperature of the mixture is (Take: specific heat of water  4200 J kg 1 K 1 , latent heat
of ice  336kJkg 1 )
A) 40C
INC.Jr.IIT_*CO SC
B) 60C
C) 0C
D) 50C
Page No: 3
Narayana IIT Academy
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
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.
A vessel is partly filled with liquid. When the vessel is cooled to a lower temperature,
the space in the vessel unoccupied by the liquid remains constant. Then the volume of
the liquid VL  volume of the vessel VV  , the coefficient of cubical expansion of the
material of the vessel  V  and of the liquid   L  are related as
A)  L   V
7.
B)  L   V
C)
 V VV

 L VL
D)
 V VL

 L VV
A clock is calibrated at a temperature of 20C . Assume that the pendulum is a thin
brass rod of negligible mass with a heavy bob attached to the end  brass  19 106 / K 
A) On a hot day at 30C the clock gains 8.2 s
B) On a hot day at 30C the clock loses 8.2 s
C) On a cold day at 10C the clock gains 8.2 s
D) On a cold day at 10C the clock loses 8.2 s
8.
When the temperature of a copper coin is raised by 80C , its diameter increases by
0.2%.
A) Percentage rise in the area of a face is 0.4%
B) Percentage rise in the thickness is 0.4%
C) Percentage rise in the volume is 0.6%
D) Coefficient of linear expansion of copper is 0.25 104C 1
9.
A uniform cylinder of steel of mass M, radius R is placed on frictionless bearings and
set to rotate about its vertical axis with angular velocity 0 . After the cylinder has
reached the specified state of rotation it is heated without any mechanical contact from
temperature T0 to T0  T . If
I
is the fractional change in moment of inertia of the
I
cylinder and  be the fractional change in the angular velocity of the cylinder and 
0
be the coefficient of linear expansion, then
A)
I 2 R

I
R
C)   2T
0
INC.Jr.IIT_*CO SC
B) I  
I
D)
0
I
2R

I
R
Page No: 4
Narayana IIT Academy
10.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Two rods of length L1 and L2 are made of materials of coefficients of linear expansions
1 and  2 respectively such that L11  L2  2 . The temperature of the rods is increased
by T and correspondingly the change in their respective lengths be L1 and L2
A) L1  L2
B) L1  L2
C) Difference in length  L1  L2  is a constant and is independent of rise of temperature
D) Data is insufficient to arrive at a conclusion
11.
The temperature of an isotropic cubical solid of length l0 , density 0 and coefficient of
linear expansion  is increased by 200C. Then at higher temperature, to a good
approximation
A) Length is l0 1  20 
B) Total surface area is l02 1  40 
C) Total volume is l03 1  60 
D) Density is
12.
0
1  60
In a container of negligible heat capacity, 200 g ice at 0C and 100g steam at 100C are
added to 200g of water that has temperature 55C . Assume no heat is lost to the
surroundings and the pressure in the container is constant 1.0 atm.
 L  80cal / g , L  540 cal / g , s  1cal / g C 
f
v
W
A) The final temperature of the mixture is 100C
B) The final mass of the water present in the system is 483.3g
C) The final mixture will have 2g ice left in it
D) The final mass of the water present in the system is 398 g
INC.Jr.IIT_*CO SC
Page No: 5
Narayana IIT Academy
13.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Due to thermal expansion with rise in temperature ( Given  L   B )
A) Metallic scale reading does not change
B) Pendulum clock becomes fast
C) A floating body sinks a little more
D) The weight of a body in a liquid increases
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. Three students S1 , S2 and S3 perform an experiment for determining the acceleration due
to gravity (g) using a simple pendulum. They use different lengths of pendulum and
record time for different number of oscillations. The observations are as shown in the
table.
Student
Length of
No.of oscillations Total time for n
No.
pendulum (cm)
(n)
oscillations
1
64.0
8
128.0
2
64.0
4
64.0
3
20.0
4
36.0
(Least count of length  0.1m ; Least count for time  0.1s )
Time
period(s)
16.0
16.0
9.0
If E1 , E2 and E3 are the percentage errors in ‘g’ for students 1,2 and 3 respectively, then
the minimum percentage error is obtained by student no. ………….
15.
Two vessels connected at the bottom by a thin pipe with a sliding plug contain liquid at
3 1
20C and 80C respectively. The coefficient of cubic expansion of liquid is 10 K . The
ratio of heights of liquid columns in the vessel  h20 / h80  is nearest to which integer?
INC.Jr.IIT_*CO SC
Page No: 6
Narayana IIT Academy
16.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Three rods of equal length l are joined to form an equilateral triangle PQR. O is the
midpoint of PQ. Distance OR remains the same for small change in temperature.
Coefficient of linear expansion for PR and RQ is the same, i.e.,  2 but that for PQ is 1
. Then find
17.
1
2
A calorimeter of water equivalent 10g contains a liquid of mass 50g at 400C. When ‘m’
gram of ice at 100 C is put into the calorimeter and the mixture is allowed to attain
equilibrium, the final temperature was found to be 200C. It is known that specific heat
capacity of the liquid changes with temperature as S  1 

 
1 0  1
C where  is
 cal g
500 
temperature is 0C. The specific heat capacity of ice, water and the calorimeter remain
constant and their values are Sice  0.5cal g 1 0C1; Swater  1.0 cal g 1 0C1 and latent heat of
fusion of ice is Lf  80cal g 1 . Assume no heat loss to the surrounding. Ifthe value of m
is 4x grams, then the value of x is…..
18.
What is heat capacity of 1 L water  in kcal C 1  ? Specific heat capacity of water is 1.0
cal g 1 C 1 .
INC.Jr.IIT_*CO SC
Page No: 7
Narayana IIT Academy
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
CHEMISTRY
Max Marks: 62
SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its
answer, out of which ONLY ONE option can be correct.
Marking scheme: +3 for correct answer, 0 if not attempted and –1 in all other cases.
19.
Which of the following will racemise in in dilute basic medium?
Me
Me
A)
B)
O
O
Me
Me
C)
D)
D
20.
Ph
O
O
Which is the strongest acid?
O
A)
21.
C ) CH 3  CH 2  OH
D)
Which is the strongest base?
A) NH 3
22.
B ) CH 3  CHO
O
B) CH 3  NH 2
C)  CH 3 3 N
D) C6 H 5  NH 2
Which of the following carbocations will not show rearrangement?
Ph
A)
23.
B)
Ph
C)
OH
D ) Ph
Which of the following electron delocalization is not an example of hyperconjugation?
A)  (fully filled) to  * (vacant)
B)  (fully filled) to  * (vacant)
C)  (fully filled) to  * (vacant)
D)  (fully filled) to  * (vacant)
INC.Jr.IIT_*CO SC
Page No: 8
Narayana IIT Academy
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
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.
Which of the following will have higher heterolytic bond dissociation energy for the C
–X bond than
Br ? (X = halogen)
Cl
A)
Br
B)
Br
D)
C)
Br
25.
Which of the following orders are correct regarding stability of carbanions?
A) Ph  CH 2  CH 3  C  CH 2
B) MeO  CH 2  C  CH 2  CH 3  C  CH 2
O
O
C ) MeO  C  CH 2  CH 3  C  CH 2
O
26.
O
O
D ) CH 3  C  CH 2  CH  C
O
Which of the following statements is not true about carbenes?
A) Carbenes are always diamagnetic.
B) Carbenes are always paramagnetic.
C) Triplet carbenes are always more stable than singlet carbenes.
D) For difluorocarbene, singlet carbene is more stable than triplet carbene.
27.
Which of the following are stronger acids than HCOOH?
A) Cl  CH 2  COOH
B) Cl  CH 2  CH 2  COOH
C) Ph  COOH
D) Br  CH 2  COOH
INC.Jr.IIT_*CO SC
Page No: 9
Narayana IIT Academy
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
O
O
?
28. Which of the following will have more enol content than
O
O
O
A)
B)
Ph
Which of the following reactions are favourable in the forward direction?
NH 2
NH 3
NH 3
NH 2

A)
CH 3
CH 3
NH 2
NH 3
NH 3
NH 2

B)
CH 3
NH 2
CH 3
NH 3
NH 3
NH 2

C)
OCH 3
NH 2
OCH 3
NH 3
NH 3
OCH 3
NH 2
OCH 3

D)
30.
D)
O
O
O
29.
C)
O
Which cannot show tautomerism?
O
O
O
A)
B)
C)
O
D)
O
INC.Jr.IIT_*CO SC
Page No: 10
Narayana IIT Academy
31.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Which is/are correct for acidic strength order?
COOH
COOH
COOH
COOH
CH 3

A)

B)
OCH 3
COOH
COOH
COOH

C)
COOH

D)
CH 3
OCH 3
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.
OD / D2O
CH 2  CH  CH  C  CH 3 

excess
32.
O
What is the maximum number of D- atoms that can be obtained in one molecule of the
stable product?
33.
How many of the following will give effervescence of CO2 when reacted with NaHCO3 ?
OH
a)
OH
c)
b)
NO2
g)
COOH
d)
e)
f)
COOH
NO2
COOH
OH
OH
O
h)
O
INC.Jr.IIT_*CO SC
CH 2OH
NO2
O
O
CH 2OH
j)
i)
OH
Cl
Cl
Page No: 11
Narayana IIT Academy
34.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
How many of the following are stronger bases than aniline?
H
NMe2
NH 2
NMe2
N
a)
c)
b)
N
d)
f)
e)
CONH 2
H
N
g)
35.
CH 2  NH 2 h)
j)
i ) NH 3
NH
How many of the following bases are stronger bases then  CH 3 3 N ?
a) CH 3  NH 2
b) Ph  NH 2
f ) CH 2  CH  NH 2
c)  CH 3 2 NH
g ) HN  CH  NH 2
d) Ph2 NH
e) NH 3
i ) O  CH  NH 2
h)
N
36.
How many of the following are stronger acids than acetic acid?
a) HCl
O
b) HBr
INC.Jr.IIT_*CO SC
d) HCN
e) HCOOH
f) Ph  COOH
OH
OH
O
OH
OH
O
OH
NO2
O2 N
i ) CH 3  SO3 H
h)
g)
O
c) HI
j)
NO2
Page No: 12
Narayana IIT Academy
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
MATHEMATICS
Max Marks: 62
SECTION – I
(SINGLE CORRECT ANSWER TYPE)
This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its
answer, out of which ONLY ONE option can be correct.
Marking scheme: +3 for correct answer, 0 if not attempted and –1 in all other cases.
37. If f  x    2x  3  
5
4
x  cos x and g is the inverse function of f, then g   2  is equal
3
to
7
A)
3
38.
3
B)
7
304  4
C)
3
D)
3
304  4
2x  2
Let  be the acute angle between the curves y  x ln x and y 
at their point of
ln 2
x
intersection on the line y  0. Then tan   2 tan 2  4 tan 4  8tan8  16cot16 is
equal to
A)
39.
1
2
B) 2
C)
1
3
If equation of tangent drawn to the curve y  log 2 x at x 
D) 3
1
is
3
px  yln  q   ln  3e   0 , then  p  q  is equal to
A) 3
B)
5
2
C) 5
D)
7
2
40.
A man walks along a straight path at a speed of 4ft/sec. A search light is located on the
ground 20ft from the path and is kept focused on man. At what rate is the search light
rotating when the man is 15ft from the point on the path closest to the search light?
A) 0.128 rad/sec
B) 1.6 rad/sec
C) 0.8 rad/sec
D) 0.24 rad/sec
41.
A particle moves along the curve y  x 2 in the first quadrant in such a way that its x 
coordinates (measured in metres) increases at a rate of 10 m/sec. Given that the angle
of inclination  of the line joining the particle to the origin changes, when x  3m , at
the rate of k rad/sec. If Pj  k j , j k  are three points for j = 1,2,3, such that the sum of
algebraic length of perpendicular from these points to a variable line
L  ax  by  c  0 vanishes then L = 0 always passes through a fixed point given as
A) 1, 2
INC.Jr.IIT_*CO SC
B) 2,1
C) 2,3
D) 1,3
Page No: 13
Narayana IIT Academy
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
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.
43.
The straight line which is both tangent and normal to the curve parametrically defined
as x  3t 2 , y  2t 3 is
A) y  3  x  1  0
B) y  3  x  1  0
C) y  2  x  2   0
D) y  2  x  2   0
Consider a differentiable function f : R  R for which f   0   n2 and
f  x  y   2 x f  y   4 y f  x   x, y  R . Which of the following is/are correct?
A) f  4   240
B) f   2   24n2
C) the minimum value of y  f  x  is 
1
4
D) the number of solution of f  x   2 is 1
44.
Which of the following statement is/are true for the curve  y  2   2x 3  4 ?
2
A) y  2 3 x  2  2 3 is tangent at 1,2 
B) y  2 3 x  2 3  2 is tangent from 1,2 
C) No tangent can be drawn from 1,2 
D) Exactly two tangents can be drawn from 1,2 
45.
Tangent at a point P1 [other than (0, 0)] on the curve y = x3 meets the curve again at P2.
The tangent at P2 meets the curve at P3 and so on. Then
A) Abscissae of P1, P2, P3, ……Pn are in A. P.
B) Abscissae of P1, P2, P3, …. Pn form a G. P.
C) Area  P2 P3 P4   16 area  P1P2 P3 
D) Area  P1P2 P3   16 area  P2 P3 P4 
INC.Jr.IIT_*CO SC
Page No: 14
Narayana IIT Academy
46.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
If the tangent to the curve 2 y 3  ax 2  x 3 at the point  a, a  cuts off intercepts  and 
on the coordinate axes, (Where  2   2  61) then the value of a is
A) –30
47.
B) 10
C) 20
D) 30
x3
 3a 
Given f  x     x 2 sin    x sin  a   sin  2a   5sin 1  a 2  8a  17  then
3
 2
A) f '  x    x 2  2x  sin 6    sin 4  sin8
B) f '  sin 8   0
C) f '  x  is not defined at x = sin 8
D) f '  sin 8   0
48.
Which of the following is/are correct?
A) A particle’s velocity v at time t is given by v  2e2t cos
which the acceleration becomes zero is
t
. Then one value of t , at
3
3
6
tan 1 .


B) A man of height 2m walks directly away from a lamp at a height of 5m, on a level
road at 3m/s. The rate at which the length of his shadow is increasing is 2m/s
C) If k is the diameter of a fixed circle and A is the area of a sector of the circle whose
vertical angle  varies, then
dA k 2  d 
 

8  dt 
dt
D) A point is moving along y 3  27 x . The interval of x in which the abscissa changes at
slower rate than ordinate is  , 1  1,  
INC.Jr.IIT_*CO SC
Page No: 15
Narayana IIT Academy
49.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Which of the following is/are False ?
A) If t , n, t1 & n1 are length of tangent, normal, sub tangent and sub normal respectively
1 1
1
at P  x, y  on a curve y  f  x  , then 2  2  1 1  0
t
n tn
B) If t , n, t1 & n1 are length of tangent, normal, sub tangent and sub normal respectively
1 1
1
at P  x, y  on a curve y  f  x  , then 2  2  1 1  1
t
n tn
C) If the tangent to the curve parametric equation given by
x  t 2  3t  8, y  2t 2  2t  5 at the point (2,-1) makes y-intercept ‘k’ then  k   2
(where  denotes G.I.F)
D) If the tangent to the curve parametric equation given by
x  t 2  3t  8, y  2t 2  2t  5 at the point (2,-1) makes y-intercept ‘k’ then  k   1
(where  denotes G.I.F)
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.
50.
Let f  x  


 x 
 sgn  tan 1 
tan 1 x, where sgn (y) denotes signum function of
2 
2
1 x 

y, and g(x) is the inverse of f(x). If the complete set of values of k for which the
equation 2g  x   k    2x   0 has three distinct solutions, is  a,  then find ‘a’.
51.
Let f  x  be a differentiable function on R defined by f  x   5   x  1 , and A be the
2
point of intersection where the tangent line drawn to the graph of y  f  x  at the point
P  x,f  x   intersects with x-axis and B be the intersection point where the tangent line
intersects with y-axis. If S  x  denotes the area of OAB where O is the origin, and the
minimum value of S  x  in the interval  0,1 is equal to
p
(where p and q are coprime).
q
Then the sum of digits of  p  q  is equal to
INC.Jr.IIT_*CO SC
Page No: 16
Narayana IIT Academy
52.
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
The parametric equations of a curve are x  sec 2 t and y  cot t . If the tangent, drawn



5 , where ,  are
to the curve at P  t   meets the curve again at Q, and if PQ 

4

co-prime then, the numerical value of    is
53.
Let f  x  
sin x
, x   0,   and g  x  be inverse of f  x  . The slope of tangent to the
x
b
curve y  g  x  , x   0,   at the point where it meets the curve xy  1 is 
where
a
a, b  N . The value of 2a  b is equal to ____
54.
Let f  x  be a continuous function which satisfies, f 3  x   5 f 2  x   10 f  x   12  0 ,
f 2  x   4 f  x   3  0, f 2  x   6 f  x   8  0 .
If the equation to the tangent drawn from (2,0) to the curve y  x 2 f  sin x  is of the
form y  ax  2a, a  R  , then the numerical value of
INC.Jr.IIT_*CO SC
a
is ____
6
Page No: 17
Narayana IIT Academy
INC.Jr.IIT_*CO SC
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Page No: 18
Narayana IIT Academy
INC.Jr.IIT_*CO SC
18-12-22_INC.JR.IIT_*CO-SC(MODEL-A)_JEE-ADV_WAT-24_Q’P
Page No: 19