)0999DJA111521004) (0999DJA111521004) Test Pattern DISTANCE LEARNING PROGRAMME (Academic Session : 2021 - 2022) JEE(Advanced) TEST # 04 14-11-2021 JEE(Main + Advanced) : LEADER TEST SERIES / JOINT PACKAGE COURSE (PHASE-II) Test Type : Unit Test # 04 12 th Undergoing/Pass Students READ THE INSTRUCTIONS CAREFULLY GENERAL / lkekU ; % 1. This sealed booklet is your Question Paper. Do not break the seal till you are told to do so. 2. Use the Optical Response sheet (ORS) provided separately for answering the questions. 3. Blank spaces are provided within this booklet for rough work. 4. Write your name, form number and sign in the space provided on the back cover of this booklet. 5. After breaking the seal of the booklet, verify that the booklet contains 25 pages and that all the 20 questions in each subject and along with the options are legible. If not, contact the invigilator for replacement of the booklet. 6. You are allowed to take away the Question Paper at the end of the examination. OPTICAL RESPONSE SHEET : 7. The ORS will be collected by the invigilator at the end of the examination. 8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work. 9. Write your name, form number and sign with pen in the space provided for this purpose on the ORS. Do not write any of these details anywhere else on the ORS. Darken the appropriate bubble under each digit of your form number. DARKENING THE BUBBLES ON THE ORS 10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS. 11. Darken the bubble COMPLETELY. 12. The correct way of darkening a bubble is as : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way. 14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or "un-darken" a darkened bubble. 15. Take g = 10 m/s 2 unless otherwise stated. / g = 10 m/s 2 QUESTION PAPER FORMAT 16. The question paper has three parts : Physics, Chemistry and Mathematics. DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR Time : 3 Hours Maximum Marks : 252
JEE(Advanced) TEST # 04
Test Type : Unit Test # 04 12th Undergoing/Pass Students
READ THE INSTRUCTIONS CAREFULLY
GENERAL / lkekU; %
1. This sealed booklet is your Question Paper. Do not break the
seal till you are told to do so.
2. Use the Optical Response sheet (ORS) provided separately for
answering the questions.
3. Blank spaces are provided within this booklet for rough
work.
4. Write your name, form number and sign in the space provided on
the back cover of this booklet.
5. After breaking the seal of the booklet, verify that the booklet
contains 25 pages and that all the 20 questions in each subject and
along with the options are legible. If not, contact the invigilator
for replacement of the booklet.
6. You are allowed to take away the Question Paper at the end of
the examination.
OPTICAL RESPONSE SHEET :
7. The ORS will be collected by the invigilator at the end of the
examination.
8. Do not tamper with or mutilate the ORS. Do not use the ORS for
rough work.
9. Write your name, form number and sign with pen in the space
provided for this purpose on the ORS. Do not write any of these
details anywhere else on the ORS. Darken the appropriate bubble
under each digit of your form number.
DARKENING THE BUBBLES ON THE ORS
10. Use a BLACK BALL POINT PEN to darken the bubbles on the
ORS.
11. Darken the bubble COMPLETELY.
12. The correct way of darkening a bubble is as :
13. The ORS is machine-gradable. Ensure that the bubbles are
darkened in the correct way.
14. Darken the bubbles ONLY IF you are sure of the answer. There is
NO WAY to erase or "un-darken" a darkened bubble.
15. Take g = 10 m/s2 unless otherwise stated. / g = 10 m/s2
QUESTION PAPER FORMAT
16. The question paper has three parts : Physics, Chemistry and
Mathematics.
D O
N OT
B RE
A K
TH E
SE A
LS W
IT HO
U T
BE IN
G IN
ST RU
CT ED
T O
D O
SO B
Y TH
E IN
VI GI
LA TO
PART-1 : PHYSICS
SECTION-I (i) : (Maximum Marks: 18)
Full Marks
: +3 If ONLY the correct option
is chosen. Zero Marks
: 0 If none of
the options is chosen (i.e. the question is unanswered)
Negative Marks :
–1 In all other cases
1. Force acting on a particle is N. Work done by this force
is zero, when a particle is moved on
the line 3y + kx = 5. Here value of k is
(A) 2 (B) 4 (C) 6 (D) 8
2. A circular conducting loop of radius R carries a current I.
Another straight infinite conductor carrying current I
passes through the diameter of this loop as shown in the figure.
The magnitude of force exerted by the straight conductor on the
loop is :-
(A) πµ I (B) µ I (C) (D)
BEWARE OF NEGATIVE MARKING
This section contains SIX (06) questions. Each question has FOUR
options. ONLY ONE of these four options is the correct answer. For
each question, choose the option corresponding to the correct
answer. Answer to each question will be evaluated according
to the following marking scheme :
(2 + 3 )i j
2π μ0 I 2
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
3. The potential energy of a particle varies according to the graph
shown. Force acting on it varies according to which of the
following graphs :-
(A) (B)
(C) (D)
4. Two bodies are connected by an elastic spring. A net external
force F acts on the system of bodies. The
(A) work done by F is equal to increase in kinetic energy of the
bodies.
(B) work done by F and spring force is equal to increase in kinetic
energy plus spring potential energy of bodies and spring
system
(C) work done by F and spring force is equal to increase in kinetic
energy of the two bodies.
(D) work done by spring force is always zero.
5. A force has components F = axy – by , F = –axy + bx where
a = 2 N/m and b = 2 N/m (figure).
Calculate the work done by the force on an object of mass 4kg if it
is moved on a closed path from (x, y) values of (0, 1) to (4, 1) to
(4, 3) to (0, 3) and back to (0, 1) (all coordinates in meters).
The path between the points is always the shortest straight one and
all the distances are given in meters :-
(A) 64 J (B) 0 J (C) 72 J (D) 18 J
6. An electron is revolving around a proton in a circular orbit of
diameter 1Å. If it produces a magnetic field of 14 wb/m at the
proton, then its angular velocity will be about :-
(A) 4.375 × 10 rad/s (B) 2.25 × 10 rad/s
(C) 4 × 10 rad/s (D) 8.75 × 10 rad/s
F x
2 y
SECTION-I (ii) : (Maximum Marks: 16)
Full Marks
: +4 If only (all) the correct
option(s) is (are) chosen. Zero
Marks : 0 In
all other cases.
7. A body of mass m is thrown at an angle θ above the horizontal
ground with the initial velocity v . Which of the following
statements is/are correct?
(A) Work done by the gravity up to the instant when speed is
minimum is
(B) Instantaneous power of gravity when speed is minimum is
zero.
(C) Instantaneous power of gravity as a function of time t is mg
(gt – v sinθ)
(D) Average power of gravity over the whole time of motion is
zero.
8. A block of mass 1.0 kg is pulled up on a rough slope of
inclination 37° with the horizontal. The coefficient of kinetic
friction between the block and the slope is 0.25. The block moves
with acceleration 2.0 m/s . After 5.0 s from the instant the block
starts, which of the following statements is/are true.
(A) Power delivered by the pulling force is 100 W.
(B) Power delivered by the weight of the block is –60
W.
(C) Power delivered by the friction between the slope and the block
is –20W.
(D) Power delivered by the contact force between the slope and the
block is –20W.
This section contains FOUR (04) questions. Each question has FOUR
options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is (are) correct option(s). For each question, choose the
correct option(s) to answer the question. Answer to each question
will be evaluated according to the following marking scheme:
0
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
9. A body starts from rest on a smooth horizontal surface under the
action of a constant horizontal force F and a resistance force F =
kv where k is a positive constant and v is instantaneous speed.
Choose the correct option as a function of time t :
(A) Velocity achieved by body at time t is
(B) Curve between velocity and time t and that between power of
force F and time t are both straight line
(C) Power of force F increase continuously and becomes constant
finally after long time
(D) Rate of change of power of force F decreases continuously and
becomes zero finally after long time
10. In the given diagram, there are two semicircular parts one
having radius ‘a’ and another having radius ‘3a’ as shown. If
resistance of ACB part is R and resistance of ADB part is 3R.
Select the correct option(s) :-
(A) Current through ACB is I/4
(B) Current through ADB is I/4
(C) Magnitude of at ‘O’ due to ACB part is
(D) Magnitude of at ‘O’ due to ADB part is
R
SECTION-I (iii) : (Maximum Marks: 12)
Full Marks
: +3 If ONLY the correct
option is chosen. Zero Marks
: 0 In all other
cases.
Paragraph for Questions 11 and 12
A person wants to roll a solid non-conducting spherical ball of
mass m and radius r on a surface whose coefficient of static
friction is µ. He placed the ball on the surface wrapped with n
turns of closely packed conducting coils of negligible mass at the
diameter. By some arrangement he is able to pass a current i
through the coils in the anticlockwise direction as seen from
+y-axis. A constant horizontal
magnetic field is present throughout the space as shown in
the figure. (Assume µ is large enough to
help rolling motion)
11. If current i is passed through the coils the maximum torque in
the coil is :-
(A) –πnir B (B) πnir B
(C) (D)
12. The angular velocity of the ball when it has rotated through an
angle θ is (θ < 180°) is :-
(A) (B)
(C) (D)
This section contains FOUR (04) questions. This section contains
TWO paragraphs. Based on each paragraph, there are TWO questions.
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of
these four options is correct. For each question, choose the option
corresponding to the correct answer. Answer to each question will
be evaluated according to the following marking scheme:
B
sin θ 10 7
Paragraph for Questions 13 and 14
Two labour Raju & Anil constructed two parallel walls each
consisting of 96 bricks [Weight 500 gm & size 8" × 4" × 2"].
The length of the wall made is 4' but the height is different as
Raju made 4" thick wall but Anil made 2" thick wall. If Raju
completed the work in 2hr & Anil in 3hr then [take g = 10m/s ,
1'' = 2.5 cm & 1' = 30 cm]
13. The difference in work performed by Raju & Anil is–
(A) 384 J (B) 192 J
(C) 200 J (D) 0
14. The work get stored in the form of potential energy in walls
made by Raju & Anil are respectively–
(A) 192 J, 384 J (B) 192 J, 292 J
(C) 192 J, 392 J (D) 192 J, 192 J
2
SECTION-I (iv) : (Maximum Marks: 6)
Full Marks
: +3 If ONLY the
correct option is chosen. Zero
Marks :
0 If none of the options is chosen (i.e.
the question is unanswered)
Negative Marks :
–1 In all other cases
15. There exists uniform magnetic field in space. A particle
of mass m = 10 kg and charge q = πC is
projected from origin with velocity m/s. The position of
particle is observed at t = 0.5 sec,
1 sec and 2 sec respectively. Following table coordinates of the
particles at given moments
x-coordinate y-coordinate z-coordinate
(P) x (1) 0
(Q) x (2) 1
(R) y (3) 2
(S) z (4) 4
(A) P → 3;Q → 2;R → 1;S → 1 (B) P → 2;Q → 3;R → 1;S → 1
(C) P → 1;Q → 3;R → 2;S → 4 (D) P → 1;Q → 2;R → 3;S → 4
This section contains TWO (02) questions. Each question
has matching lists. The codes for the lists have choices (A), (B),
(C) and (D) out of which ONLY ONE is correct For each question,
marks will be awarded in one of the following categories :
Space for Rough Work
1 1 1
2 2 2
3 3 3
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
16. A lift of mass m kg has to be taken through a height h from
state of rest to state of rest. This process is done in
shortest possible time with the help of cables which can bear a
tension 0 ≤ T ≤ 3 mg. In list-I are given statements regarding
variation of a given quantity with respect to time and in list II
are given some graphs showing variation of these quantities with
time. Match the List-I with List-II.
List–I List–II
(P) Variation of velocity of lift with time (1)
(Q) Variation of power delivered by tension in cable with
time.
(2)
(3)
(S) Variation of acceleration of lift with time (4)
(A) P → 3;Q → 2;R → 1;S → 4 (B) P → 3;Q → 2;R → 4;S → 1
(C) P → 2;Q → 3;R → 4;S → 1 (D) P → 2;Q → 3;R → 1;S → 4
Space for Rough Work
SECTION-III : (Maximum Marks: 24)
Full Marks
: +4 If only the
correct answer is given. Zero
Marks : 0
In all other cases
1. A small object can move in a vertical plane along a semi–circle
of radius 0.1 m without friction. The speed at which the ball must
be launched from point A so that its acceleration is 3g at point B
is given by 'v' m/s. Find the value of v (in m/s).
2. In a region, magnetic field along X-axis changes with time
according to the given graph. A charged
particle of mass 1 kg & charge 1C is located at origin starts
moving with initial velocity
m/s. It completes one revolution in T time. Find the
displacement (in m) of particle at time .
This section contains SIX (06) questions. The answer to each
question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive. For each question, enter the correct integer value of
the answer in the place designated to enter the answer. For each
question, marks will be awarded in one of the following categories
:
( + 2 )2 π i 3–√ j
0 5T0
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
3. The chain of length L is released from rest on a smooth fixed
incline with x = 0 as shown in the figure.
Determine velocity v of the chain when a half of the length has
fallen (Take L = ) in m/s. (Neglect
edge effect of inclined)
4. Find the magnetic field (in µT) at point A. (Given : Amp,
R = 1m)
5. Figure shows a square loop 10 cm on each side in the x-y plane
with its centre at the origin. An infinite wire is at z = 12 cm
above y-axis. What is torque on loop due to magnetic force? If
torque is expressed as 12x ×10 N-m, fill value of x.
6. Suppose a hypothetical magnetic field exists in space
above the earth surface where is a
unit vector directed radially outward from origin. Origin is on
surface of earth. A light charged particle has to perform uniform
circular motion in the combined uniform (vertical) gravitational
field of earth and magnetic field with speed v and radius r. Height
of the plane of motion from earth surface will be
. Find n.
h = nv2
SECTION-IV : (Maximum Marks: 8)
For each entry in Column-I
Full Marks
: +2 If only the
option(s) corresponding to all the correct match(es) is (are)
chosen Zero Marks
: 0
In all other cases
(A) At point O (0, 0, 0) (P)
(B) At point P (a, 0, 0) (here a > > L) (Q)
(C) At point P (0, a, 0) (here (a > > L) (R)
(D) At point P (a, a, 0) (here a > > L) (S)
(T)
This section contains ONE (01) question. Question contains two
columns, Column-I and Column-II. Column-I has four entries (A),
(B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and
(T) Match the entries in Column-I with the entries in Column-II.
One or more entries in Column-I may match with one or more entries
in Column-II. For each entry in Column-I, darken the options
of all the matching entries. For example, if entry (A) in Column-I
matches with entries (Q), (R) and (T), then chosen these three
options. Similarly, for entries (B), (C) and (D). For each
question, marks will be awarded in one of the following categories
:
Space for Rough Work
PART-2 : CHEMISTRY
SECTION-I (i) : (Maximum Marks: 18)
Full Marks
: +3 If ONLY the correct option
is chosen. Zero Marks
: 0 If none of
the options is chosen (i.e. the question is unanswered)
Negative Marks :
–1 In all other cases
1. In which of the following species presence of double bond does
not affect idealised bond angle :- (I) POCl (II)
XeO F (III) XeO F (IV)
XeO
(A) II, III, IV (B) I, II only (C) III, IV only (D) I, II,
III
2. In which of the following reactions is Incorrect according to
its products formed.
(A) PCl + 3H O → H PO + 3HCl (B) NCl + 3H O → NH + 3HOCl
(C) ICl + H O → HClO + HI (D) N O + H O → HNO + HNO
3. The CORRECT order of hybridisation of the N, P and B in the
following species is respectively N(SiH ) , PCl , H BO
(A) sp , sp , sp (B) sp , sp , sp (C) sp , sp , sp (D) sp , sp ,
sp
4. Radius of cation and anion are 2.5 Å & 2.6 Å
respectively. If a cubic crystal system is prepared by combination
of above cation and anion then edge length of unit cell is (Take
)
(A) 2.7 Å (B) 2 Å (C) 3 Å (D) 6 Å
5. A cubic unit cell contains manganese ions at the corners and
fluoride ions at the centres of each edge. The coordination number
of maganese ion is-
(A) 8 (B) 2 (C) 4 (D) 6
6. The decomposition of a gaseous substance (A) to yield gaseous
products (B), (C) follows first order kinetics. If initially only
(A) is present and l0 minutes after the start of the reaction the
pressure of (A) is 200 mm Hg and that of total pressure is 300 mm
Hg, then the rate constant for A → B + C is
(A) (1/600) n 1.25 sec (B) (2.303/10) log 1.5 min
(C) (1/10) n 1.25 sec (D) sec
This section contains SIX (06) questions. Each question has FOUR
options. ONLY ONE of these four options is the correct answer. For
each question, choose the option corresponding to the correct
answer. Answer to each question will be evaluated according
to the following marking scheme :
3 3 2 2 4 4
3 2 3 3 3 2 3
2 2 4 2 3 2
3 3
3 3 3
3 3 2 2 3 3 2 3 2 3 2 2
= 1.73–√
–1
SECTION-I (ii) : (Maximum Marks: 16)
Full Marks
: +4
If only (all) the correct option(s) is (are) chosen.
Zero Marks
: 0 In all
other cases.
7. Which among the following molecule(s) have peroxy linkage
:-
(A) CrO (B) H P O (C) H S O (D) HClO
8. Which of the following statement(s) is/are CORRECT -
(A) [B O ] ion is non-planar but B N H is planar
(B) (H Si) N is planar but (SiH ) P is pyramidal
(C) H C – NCS is bent but SiH - NCS is linear
(D) (CH ) N is pyramidal but (GeH ) N is planar
9. Potassium crystallizes in a body centred cubic lattice with edge
length a = 5.0 Å. Then choose the correct statements in given
option -
(A) The number of nearest neighbour to any K atom is 8
(B) The number of next nearest neighbour to any K atom is 6
(C) Distance between nearest neighbours is 4.33 Å
(D) Distance between next nearest neighbours is 5.0 Å
10. For the reaction 2A(g) B(s) + 2C(g) + 3D(g)
Volume of C collected at t = 70 sec is 37.5 ml and volume of D
collected after sufficient time is 112.5 ml, then which of the
following are correct (ln2 = 0.7) [A follows first order
kinetics]
(A) Rate constant of reaction is 5 × 10 sec (B) Half life time of A
is 70 sec
(C) Volume of C at t = 140 sec is 56.25 ml (D) Volume of D at t =
140 sec is 75 ml
This section contains FOUR (04) questions. Each question has
FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are)
correct answer(s). For each question, choose the option(s)
corresponding to (all ) the correct answer(s) Answer to each
question will be evaluated according to the following marking
scheme:
5 4 2 8 2 2 8 4
3 6 –3
3 3 6
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
SECTION-I (iii) : (Maximum Marks: 12)
Full Marks
: +3 If ONLY the correct
option is chosen. Zero Marks
: 0 In all other
cases.
Paragraph for Questions 11 and 12
Qualitatively, the formation of molecular orbitals can be
understood in terms of the constructive or destructive
interference of the electron waves of the combining atoms. In the
formation of bonding molecular orbital, the two electron waves of
the bonding atoms reinforce each other due to constructive
interference while in the formation of antibonding molecular
orbital, the electron waves cancel each other due to destructive
interference.
11. Which of the following combinations give(s) antibonding sigma
molecular orbital if z-axis is the internuclear axis ?
(A) (B)
(C) (D)
(A) HeH (B) Be (C) C (D) NO
This section contains FOUR (04) questions. This section contains
TWO paragraphs. Based on each paragraph, there are TWO questions.
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of
these four options is correct. For each question, choose the option
corresponding to the correct answer. Answer to each question will
be evaluated according to the following marking scheme:
+ 2 2
ALLEN Leader Test Series/Joint Package
Course/Phase-II/14-11-2021
Paragraph for Questions 13 and 14
Consider the reaction represented by the equation : CH Cl(g) + H
O(g) —→ CH OH(g) + HCl(g) These kinetic data were obtained for the
given reaction concentrations :
Initial conc. (M) Initial rate of disappearance of
CH Cl M s [CH Cl] [H O]
0.2 0.2 1 0.4 0.2 2 0.4 0.4 8
Answer the following question based on these data :
13. The rate law for the reaction will be
(A) r = k[CH Cl] [H O] (B) r = k[CH Cl] [H O]
(C) r = k[CH Cl] [H O] (D) r = k[CH Cl] [H O]
14. Unit of rate constant will be :
(A) sec (B) litre mol sec
(C) litre mol sec (D) mol litre sec
3 2 3
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
SECTION-I (iv) : (Maximum Marks: 6)
Full Marks
: +3 If ONLY the
correct option is chosen. Zero
Marks :
0 If none of the options is chosen (i.e.
the question is unanswered)
Negative Marks :
–1 In all other cases
15.
(Q) XeO F (2) orbital participated
in hybridisation
(R) (3) Maximum lone pair of electron present on central atom
out of given species
(S) (4) Only orbital participated in
(A) P → 2;Q → 4;R → 3;S → 1 (B) P → 3;Q → 4;R → 2;S → 1
(C) P → 2;Q → 4;R → 1;S → 3 (D) P → 4;Q → 3;R → 2;S → 1
16.
List-II (Nearest distance between two cations in terms of
edge
length (a) of unit cell)
(P) NaCl (1)
(S) Na O (4) a
(A) P → 1;Q → 1;R → 4;S → 2 (B) P → 2;Q → 3;R → 1;S → 4
(C) P → 1;Q → 2;R → 3;S → 2 (D) P → 4;Q → 3;R → 2;S → 1
This section contains TWO (02) questions. Each question
has matching lists. The codes for the lists have choices (A), (B),
(C) and (D) out of which ONLY ONE is correct For each question,
marks will be awarded in one of the following categories :
5
NH⊕4
SECTION-III : (Maximum Marks: 24)
Full Marks
: +4 If only the
correct answer is given. Zero
Marks : 0
In all other cases
1. Find the number of chemical species, in which 2pπ–3dπ back bond
is present B(OH) , N(SiH ) , P(CH ) , N(GeH ) , BeCl , O(SiH ) ,
OCl , BCl
2. Which of the following pairs have dipole-dipole
interaction (BF + BF ), (CCl + Na ) (HCl + HCl), (CHCl + CHCl
), (K + HCl), (Na + Cl )
3. Calculate the number of σ bond in given compound C N (N ) . Fill
your answer as sum of digits (excluding decimal places) till you
get the single digit answer.
4. An element A (molecular weight 80 gm/mole) crystallize in BCC
and FCC lattice. If density of FCC lattice is 4 gm/cm and distance
between next nearest neighbour in BCC is d than what is
(in
cm).
5. In first order reaction (A → P) calculate if
fraction of reactant is decayed in 't' time where t is
half life.
6. The energy of activation for a reaction is 10 kJ/mol. The
presence of catalyst lowers the energy of activation by 75%. Find
the factor by which rate of reaction increases at 27ºC due to
catalyst. (Take R = 25/3 J/mol-k) If your answer is e then fill x
in OMR sheet
This section contains SIX (06) questions. The answer to each
question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive. For each question, enter the correct integer value of
the answer in the place designated to enter the answer. For each
question, marks will be awarded in one of the following categories
:
3 3 3 3 3 3 3 2 3 2 2 3
3 3 4 +
SECTION-IV : (Maximum Marks: 8)
For each entry in Column-I
Full Marks
: +2 If only the
option(s) corresponding to all the correct match(es) is (are)
chosen Zero Marks
: 0
In all other cases
1. Column-I Column-II
(B) Frenkel defect (Q) Conductivity increases
(C) Metal deficiency defect (R) F-centre appears
(D) Metal excess defect (S) Stoichiometry changes
(T) Density remains same
This section contains ONE (01) question. Question contains two
columns, Column-I and Column-II. Column-I has four entries (A),
(B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and
(T) Match the entries in Column-I with the entries in Column-II.
One or more entries in Column-I may match with one or more entries
in Column-II. For each entry in Column-I, darken the options
of all the matching entries. For example, if entry (A) in Column-I
matches with entries (Q), (R) and (T), then chosen these three
options. Similarly, for entries (B), (C) and (D). For each
question, marks will be awarded in one of the following categories
:
Space for Rough Work
PART-3 : MATHEMATICS
SECTION-I (i) : (Maximum Marks: 18)
Full Marks
: +3 If ONLY the correct option
is chosen. Zero Marks
: 0 If none of
the options is chosen (i.e. the question is unanswered)
Negative Marks :
–1 In all other cases
1. The line joining A(3,1) and B(5,3) is rotated about the mid
point C of AB in the anticlockwise direction through 135º. The
coordinates of B in the new position are-
(A) (B) (C) (D)
2. is equal to
(A) (B)
(C) (D)
4. If the variable line (a + 2b)x – (a – b)y + (3a + 6b) = 0 (a, b
∈ R) passes through a fixed point, then co- ordinates of fixed
point is :-
(A) (–3, 0) (B) (3, 0) (C) (1, 0) (D) (0, 3)
5. If , (where c is constant of integration), where , then
is equal to
(A) (B) x sec(logx). tan(logx)
(C) (D) x sec(log x)
This section contains SIX (06) questions. Each question has FOUR
options. ONLY ONE of these four options is the correct answer. For
each question, choose the option corresponding to the correct
answer. Answer to each question will be evaluated according
to the following marking scheme :
(4, 2 + )2–√ (4 − , 2)2–√ (3 − 2 , 1)2–√ (4, 2 − )2–√
∫ (1 − x). cosec2xdxtan 2
2
x + 4
+ + C+ 8x + 15x2− −−−−−−−−−√ tan −1 + 8x + 15x2− −−−−−−−−−√ − + C+
8x + 15x2− −−−−−−−−−√ tan −1 + 8x + 15x2− −−−−−−−−−√
+ + Cx + 4− −−−√ tan −1 + 8x + 15x2− −−−−−−−−−√ − + Cx + 4− −−−√
tan −1 + 8x + 15x2− −−−−−−−−−√
∫ = g(x) + c xdxsec2
n2 100
1 + sec(log x)
2 tan(log x)
1 + sec(log x)
x tan(log x)
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
SECTION-I (ii) : (Maximum Marks: 16)
Full Marks
: +4
If only (all) the correct option(s) is (are) chosen.
Zero Marks
: 0 In all
other cases.
7. If area of the triangle formed by the points A(3, 0), B(0, 3)
& P(a, b) is sq. units, then identify the
correct statement(s)
(A) Locus of P will be a union of two parallel lines
(B) Locus of P will be a union of two perpendicular lines
(C) Locus of P is given by x + y + 2xy – 6(x + y) + 8 = 0
(D) Locus of P is given by x – y + 2y – 6x + 8 = 0
8. If = = , where C is constant of integration and p,q
N, then (p – q – 8)
is equal to
(C) (D)
9. A variable line segment PQ of length 2 moves in xy plane such
that the end P always lies on x-axis and Q lies
on the line y = 2x. If locus of mid point of PQ is S(x,y) =
0 where S(x,y) = x + by + 2hxy + 2gx + 2ƒy + c, then-
(A) S(1,1) > 0 (B) S(1,1) = 0 (C) b + c = 1 (D) g = ƒ = 0
10. Coordinates of point A is (1,2) and P(α,β) lies on the line L :
2x + 3y + 5 = 0. Point B(γ,δ) is point
of intersection of L : 3x – 2y = 0 & L : λx + 2y = 10, λ ∈ R
such that γ & δ are positive
integers. Let s = α + β + γ + δ + λ , then which of following
is/are correct-
(A) If |PA – PB| is minimum, then s = 11 (B) If |PA – PB| is
maximum, then 5s = 24
(C) If |PA + PB| is minimum, then 31s = 156 (D) If |PA + PB| is
minimum, then 5s = 24
This section contains FOUR (04) questions. Each question has
FOUR options. ONE OR MORE THAN ONE of these four option(s) is (are)
correct answer(s). For each question, choose the option(s)
corresponding to (all ) the correct answer(s) Answer to each
question will be evaluated according to the following marking
scheme:
3 2
2 2
2 2
2
SECTION-I (iii) : (Maximum Marks: 12)
Full Marks
: +3 If ONLY the correct
option is chosen. Zero Marks
: 0 In all other
cases.
Paragraph for Questions 11 and 12
Let ƒ,g,h be 3 functions such that ƒ'(x) > 0 & g(x) > 0 ∀
x ∈ R where &
, x ≠ 0.
On the basis of above information, answer the following questions
:
11. is equal to -
12. ƒ(x), g(x), h(x) are in -
(A) A.P. (B) G.P. (C) H.P. (D) None of these
Paragraph for Questions 13 and 14
If the lines ax + by + c = 0, bx + cy + a = 0 and cx + by + a = 0
are concurrent (a, b, c are distinct and non-zero real numbers). On
the basis of above information answer the following.
13. If the point of concurrency is (α, β), then (α + β ) is
:-
(A) 0 (B) 1 (C) 2 (D) 3
14. For quadratic equation ax + bx + c = 0, which of the following
is always true :-
(A) Both roots are imaginary (B) Both roots are negative
(C) At least one root is positive (D) Both roots are
equal
This section contains FOUR (04) questions. This section contains
TWO paragraphs. Based on each paragraph, there are TWO questions.
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of
these four options is correct. For each question, choose the option
corresponding to the correct answer. Answer to each question will
be evaluated according to the following marking scheme:
∫ ƒ(x). g(x)dx = + Cx4
g(x)
g(x)
h(x)
ALLEN Target : JEE(Main + Advanced) 2022/14-11-2021
SECTION-I (iv) : (Maximum Marks: 6)
Full Marks
: +3 If ONLY the
correct option is chosen. Zero
Marks :
0 If none of the options is chosen (i.e.
the question is unanswered)
Negative Marks :
–1 In all other cases
15. Match List-I with List-II and select the correct answer using
the code given below the list.
List-I List-II
(P)
An equilateral triangle has one vertex at (0,0) and another
at
the x-coordinate of third
vertex is
(1) 1
(Q) (1,–2), (3,6), (5,10), (3,y) in order are the vertices of
a parallelogram, then y is
(2) 2
(R) x-coordinate of circumcentre of triangle with
vertices (–2,–3), (–1,0), (7,–6) is
(3) 3
(S)
y-coordinate of a point which divides the line segment joining
(5,– 2) and (9,6) internally in the ratio 3 : 1, is
(4) 4
(A) P → 1;Q → 4;R → 3;S → 2
(B) P → 4;Q → 3;R → 1;S → 2
(C) P → 3;Q → 2;R → 3;S → 4
(D) P → 3;Q → 1;R → 4;S → 2
This section contains TWO (02) questions. Each question
has matching lists. The codes for the lists have choices (A), (B),
(C) and (D) out of which ONLY ONE is correct For each question,
marks will be awarded in one of the following categories :
Space for Rough Work
16. List I List II
(P) (1)
(Q) (2)
(R) (3)
(S) (4)
Where C is the constant of integration.
(A) P → 4;Q → 1;R → 2;S → 3 (B) P → 4;Q → 1;R → 3;S → 2
(C) P → 1;Q → 2;R → 3;S → 4 (D) P → 1;Q → 3;R → 4;S → 2
∫ dx 1 + x2− −−−−√
1 2
2 2–√
SECTION-III : (Maximum Marks: 24)
Full Marks
: +4 If only the
correct answer is given. Zero
Marks : 0
In all other cases
1. Let , (,m,n ∈ R), then is equal to
2. Let m and m are slopes of lines represented by the line pair qx
– 2pxy + y – 2x + 3y + λ = 0, then value
of is
3. If = ,
where C is constant of integration, then is equal
to
4. Sum of slopes of all possible lines passing through origin (O)
and intersecting the lines x + y = 1 & x + 2y = 1 at A & B
respectively such that , is
5. The point (x,y) lies on line 3x + 4y = 6, such that the smallest
value of 25|x – 2x + y +1| is m, then the
value of is
6. If (where c is integration constant & , m, n ∈
N), then ( – m – n)
is equal to
This section contains SIX (06) questions. The answer to each
question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both
inclusive. For each question, enter the correct integer value of
the answer in the place designated to enter the answer. For each
question, marks will be awarded in one of the following categories
:
∫ = + C ( − 4) dxx6
.( + 2)x6 1/4 x4
( + 2)x6 m
xn n m
2 2 2
1− 9x2− −−−−−√ ( + )+C1
(α + 3β)
SECTION-IV : (Maximum Marks: 8)
For each entry in Column-I
Full Marks
: +2 If only the
option(s) corresponding to all the correct match(es) is (are)
chosen Zero Marks
: 0
In all other cases
1. Column-I Column-II
is equal to (P) 1
(B) If then km is
equal to (Q) 3
(D) Let , then [g (1)] is
equal to (where [.] denotes greatest integer function) (where C is
constant of integration)
(S) Rational number
(T) Irrational number
This section contains ONE (01) question. Question contains two
columns, Column-I and Column-II. Column-I has four entries (A),
(B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and
(T) Match the entries in Column-I with the entries in Column-II.
One or more entries in Column-I may match with one or more entries
in Column-II. For each entry in Column-I, darken the options
of all the matching entries. For example, if entry (A) in Column-I
matches with entries (Q), (R) and (T), then chosen these three
options. Similarly, for entries (B), (C) and (D). For each
question, marks will be awarded in one of the following categories
:
Space for Rough Work
tan m
1
x m