FIITJEE – INTERNAL Phase Test

PHYSICS, CHEMISTRY & MATHEMATICS

QP CODE: 100982 RIT – 2

Time Allotted: 3 Hours Maximum Marks: 180
BATCHES – Class – XII (CTY426 Batches)

▪ Please read the instructions carefully. You are allotted 5 minutes specifically for
this purpose.
▪ You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS
Caution: Question Paper CODE as given above MUST be correctly marked in the answer
OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Sections.
3. Section-I is Physics, Section-II is Chemistry and Section-III is Mathematics.
4. All the section can be filled in PART-A & B of OMR.
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed.

B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on
OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with Blue/Black Ball Point Pen for each
character of your Enrolment No. and write in ink your Name, Test Centre and other details at the
designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Two Parts.

(i) PART–A (01–03) contains (3) Multiple Choice Questions which have One or More Than One Correct
answer.
Full Marks: +4 If only the bubble(s) corresponding to all the correct options(s) is (are) darkened.
Partial Marks: +1 For darkening a bubble corresponding to each correct option, provided NO incorrect
option is darkened.
Zero Marks: 0 If none of the bubbles is darkened.
Negative Marks: −1 In all other cases.
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will
result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result
in −1 marks, as a wrong option is also darkened.
(ii) Part-A (04-07) – Contains Four (04) multiple choice questions which have ONLY ONE CORRECT answer
Each question carries +3 marks for correct answer and -1 marks for wrong answer.
(iii) Part-A (08-11) – This section contains Four (04) Matching List Sets. Each set has ONE Multiple Choice
Question. Each set has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II
has Five entries (1), (2), (3), (4) and (5). FOUR options are given in each Multiple Choice Question based
on List-I and List-II and ONLY ONE of these four options satisfies the condition asked in the Multiple
Choice Question. Each question carries +3 Marks for correct answer and -1 marks for wrong answer.
(iii) Part-B (01-06) This section contains SIX (06) questions. The answer to each question is a NON-
NEGATIVE INTEGER. For each question, enter the correct integer corresponding to the answer. Each
question carries +4 marks for correct answer. There is no negative marking.

Name of the Candidate: ____________________________________________

Batch: ____________________ Date of Examination: ___________________

Enrolment Number: _______________________________________________

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 2 IT−2026 (RIT-2)-(PCM)

S
SEEC
CTTIIO
ONN –– II :: P
PHHY
YSSIIC
CSS
(PART – A)
(One or More Than One Options Correct Type)
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. In the adjoining figure block A is of mass m and block B

is of mass 2m. The spring has a force constant k. All the A
surfaces are smooth and the system is released from
rest with spring unstretched B

4mg
(A) The maximum extension of the spring is
k
2mg 2m
(B) The speed of block A when extension in spring is , is 2g
k 3k
2
(C) Net acceleration of block B when the extension in the spring is maximum, is g.
3
2mg
(D) Tension in the thread for extension of in spring is mg.
k

2. A particle of mass 5 kg moving in the X-Y plane has its potential energy given by
U = ( −7x + 24y) Joule. The particle is initially at origin and has velocity u = (14.4iˆ + 4.2j)
ˆ m/s
(A) the particle has speed 25 m/s at t = 4 sec
(B) the particle has an acceleration 5 m / s2
(C) the acceleration of particle is normal to its initial velocity
(D) none of these

3. In the shown arrangement the blocks are released from rest and m
allowed to move through a distance of h. There is no friction and A
the string is light. Then
(A) total mechanical energy of the system is not conserved since
besides gravity tension also does work on each of the blocks. B m
(B) work done by tension on each block is separately zero.
(C) work done by tension on block A is positive and on block B it is negative.
(D) total mechanical energy is conserved.
Space For Rough Work

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 3 IT−2026 (RIT-2)-(PCM)

(Single Correct Answer Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

4. Two bodies of masses m and 4 m are attached with string as

shown in the figure. The body of mass m hanging from a 4m
string of length l is executing oscillations of angular amplitude 0
0, while the other body is at rest. The minimum coefficient of l
m
friction between the mass 4 m and the horizontal surface
should be
 2 − cos 0     1 − cos 0   3 − 2cos 0 
(A)   (B) 2cos2  0  (C)   (D)  
 3   2  2   4 

5. The work done by tension in lowering down a block of mass = m kg

through a distance ‘d’ is
d d
(A) mg (B) 3mg m
4 4 g/4
d
(C) –3mg (D) mgd
4

6. A force F = -k(yi + xj) acts on a particle moving in xy plane. Starting from the origin, the
particle is taken along the positive x axis to the point (a, 0) and than parallel to the y-axis to
the point (a, a). the total work done by the force F on the particle is
(A) − 2ka 2 (B) 2ka 2
(C) – ka2 (D) ka 2

7. Two blocks of masses m1 and m2 are connected with a k

F2 F1
spring of string constant k. They are kept on a smooth m2 m1
horizontal surface as shown in figure. Initially, the blocks
are at rest and the spring is unstretched. If the blocks are
pulled by forces F1 and F2 as shown in figure, then
maximum extension in the spring will be
Fm + F m Fm + F2m
(A) 1 1 2 2 (B) 1 2
K(m + m2 ) K(m + m2 )
Fm + F2m1 Fm + F m
(C) 2 1 2 (D) 1 1 2 2
K(m1 + m2 ) 2K(m1 + m2 )

Space For Rough Work

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 4 IT−2026 (RIT-2)-(PCM)

(Matching List Sets)

This section contains FOUR (04) Matching List Sets. Each set has ONE Multiple Choice Question. Each set
has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1),
(2), (3), (4) and (5). FOUR options are given in each Multiple Choice Question based on List-I and List-II and
ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question.

8. When a body is moving vertically up with constant velocity, then match the following:

List-I List-II
(P) Work done by lifting force is (1) negative
(Q) Total work done by all the forces is (2) positive
(R) Work done by gravity (3) zero
(S) Work done by lifting force + work done by (4) Many positive values
gravity force
(5) Many negative values

The correct option is:

(A) P → 2 ; Q → 3 ; R → 5 ; S → 1 (B) P → 2 ; Q → 3 ; R → 1 ; S → 3
(C) P → 4 ; Q → 5 ; R → 2 ; S → 3 (D) P → 3 ; Q → 1 ; R → 4 ; S → 2

m1
9. A horizontal force F pulls a ring of mass m1 such that  remains F
constant with time. The ring is constrained to move along a
smooth rigid horizontal wire. A bob of mass m2 hangs from m1

by an inextensible light string. Then match the entries of List-I
with that of List-II. m2

List-I List-II
(P) F (1) (m1 + m2) g
(Q) Force acing on m2 is (2) m2g sec 
(R) Tension in the string is (3) F
m2
m1 + m2
(S) Force acting on m1 by the wire is (4) (m1 + m2) g tan 
(5) m1g sec 

The correct option is:

(A) P → 4 ; Q → 3 ; R → 2 ; S → 1 (B) P → 4 ; Q → 3 ; R → 1 ; S → 5
(C) P → 3 ; Q → 4 ; R → 2 ; S → 1 (D) P → 2 ; Q → 1 ; R → 5 ; S → 3
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 5 IT−2026 (RIT-2)-(PCM)

10. A man pushes a block of 30 kg along a level floor at a constant speed with a force directed
at 45° below the horizontal. If the coefficient of friction is 0.20, then match the following.
List-I List-II
(P) Work done by all forces exerted by the (1) zero
surface on the block in 20 m
(Q) Work done by the force of gravity (2) –1500 J
(R) Work done by the man on the block in (3) 750
pushing it through 10 m
(S) Net force on the block (4) 30 J
(5) 60 J

The correct option is:

(A) P → 2 ; Q → 1 ; R → 4 ; S → 3 (B) P → 4 ; Q → 2 ; R → 5 ; S → 3
(C) P → 2 ; Q → 1 ; R → 3 ; S → 1 (D) P → 3 ; Q → 5 ; R → 2 ; S → 1

11. A chain of length  and mass m lies on the surface of a smooth sphere of radius R >  with
one end tied to the top of the sphere.
List-I List-II
(P) Gravitational potential energy w.r.t. centre (1) Rg   
of the sphere 1 − cos  R  
  
(Q) The chain is released and slides down, its (2) 2Rg     
KE when it has slid by  sin  R  + sin  − sin   + R  
    
(R) The initial tangential acceleration (3) MR2g  
sin  
R
(S) The radial acceleration ar (4) MR2g     
sin  R  + sin  − sin   + R  
    

(5)   
Rg 1 − sin   
  R 

The correct option is:

(A) P → 3 ; Q → 4 ; R → 2 ; S → 5 (B) P → 4 ; Q → 1 ; R → 3 ; S → 2
(C) P → 2 ; Q → 5 ; R → 3 ; S → 2 (D) P → 3 ; Q → 4 ; R → 1 ; S → 2
Space For Rough Work

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 6 IT−2026 (RIT-2)-(PCM)

(PART – B)
(Non – Negative Integer)

1. A particle of mass m is moving in a circular path of constant radius r(1m) such that it’s
centripetal acceleration ac is varying with time t as ac k 2rt 2 , where k is a constant, then
power delivered to the particle by the forces acting on it at t = 5 sec. (take mk 2 1 unit )

2. An object is displaced from point A(1m, 2m, 3m) to a point B(2m, 3m, 4m) under a constant
( )
force F = 2iˆ + 3jˆ + 4kˆ N . Find the work done by this force in this process. (in joule )

3. A system consists of two identical slabs each of mass m linked by

m
compressed weightless spring of stiffness k as shown in Figure. The
slabs are also connected by a thread, which is burnt at a certain
moment. If the value of  the initial compression of spring, the lower k
x mg
slab will bounce up after the thread is burned through is , then find
k
the value of ‘x’. m

4. A bead is free to slide down on a smooth wire 

tightly stretched between point A and B on a
vertical circle of radius 10 m. Find the time O
taken(in s) by the bead to reach the point B, if
the bead slide from rest from the highest point A
on the circle. (take g = 10 m/s2) B

5. A circular disc with a groove along its diameter is

placed horizontally. A block of mass 1kg is placed as
shown. The co efficient of friction between the block
a=20 m/s2
2
and all surfaces of groove in contact is . The disc
5
has an acceleration of 20 m/s2. Then acceleration of the 
block w.r.t disc will be in nearest integer.( = 370)

6. A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction
between the block and the surface is 0.6. If the acceleration of the truck is 5 m/s 2, then what
frictional force acting on the block (in newton).
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 7 IT−2026 (RIT-2)-(PCM)

S
SEEC
CTTIIO
ONN –– IIII :: C
CHHE
EMMIIS
STTR
RYY
(PART – A)
(One or More Than One Options Correct Type)
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1.
P Q
R
S
T
U
A
I.E 1 B
C
(kJ mol ) -1 D
E
F

2 3 4 5 6 7
Periods
The first ionization energies of the s-block elements are given above.
Choose the correct statements
(A) the second ionization energy of ‘B’ is higher than that of ‘Q’.
(B) the sulphate of ‘S’ is more soluble in water than that of ‘Q’.
(C) the iodide of ‘A’ is more soluble than that of ‘E’ in water.
(D) nitride of ‘Q’ has higher molar mass than that of ‘A’.

2. In which of the following option(s), the dipole moment(s) of the left side molecule(s) is/are
greater than that of the right side molecule(s)?
O
(A) Cis-XeCl2F2 and trans-XeCl2F2 (B) N and H 2O
O

Cl and Cl
(C) CH3Cl and CHCl3 (D)

Cl Cl

3. IF2+ (1) , IF2− ( 2)

Which of the following is/are correct for the species (1) and (2)?
(A) Bond angle: 2 > 1 (B) % of s-character in I – F bond: 1 > 2
(C) Number of lone pairs: 1 > 2 (D) Dipole moment: 2 > 1
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 8 IT−2026 (RIT-2)-(PCM)

(Single Correct Answer Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

4. The % ionic character in a covalent bond A – B is expressed as:

% Ionic character = 16|A - B| + 3.5|A - B|2
A = Electronegativity of A, B = Electronegativity of B
The electronegativity values of F = 4, O = 3.5, N = 3 and C = 2.1.
Choose the correct statement from the following
(A) The % ionic character of OF2 is 8.875.
(B) O2 contains 80% of covalent character.
(C) % ionic character of NO is greater than CO.
(D) The C – C sigma bond in CH2 = CH2 is more ionic than the C – C sigma bond in
HC  CH

5. Compounds Lattice energy in kJ mol–1

PF2 2906
QF2 2610
RF 703
SF 647

Ions Hydration energies in kJ mol–1

+
R -413
S+ -321
2+
P -1920
Q2+ -1650
F– -506
P, Q, R and S are s-block metals. The lattice energies of their fluorides and the hydration
energy of their ions are given above. Which salt can be easily crystallized from its saturated
solution?
(A) PF2 (B) QF2 (C) RF (D) SF

6. If the bond angles of MF2 = MCl2 = MBr2 = MI2 are identical and equal to 180o, which is M?
(A) Be (B) Mg (C) Ca (D) Sr

7. In the given substances carbon undergoes sp3 hybridization. The covalent bond of which
contains exactly 25% s-orbital character/
(A) CH2F2 (B) diamond (C) CF2Cl2 (D) CHCl3
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 9 IT−2026 (RIT-2)-(PCM)

(Matching List Sets)

This section contains FOUR (04) Matching List Sets. Each set has ONE Multiple Choice Question. Each set
has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1),
(2), (3), (4) and (5). FOUR options are given in each Multiple Choice Question based on List-I and List-II and
ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question.

8. Match the compounds mentioned in list-I with their characteristics mentioned in list-II.
List – I List – II
(P) CO2 (1) The solid form exists as three
dimensional network solid
(Q) SO2 (2) Contains one unpaired electron on
central atom
(R) NO2 (3) Has linear structure
(S) SiO2 (4) Central atom undergoes sp2
hybridization
(5) Contains only sigma bonds
(A) P → 3; Q → 2; R → 4; S → 5 (B) P → 3; Q → 4; R → 2; S → 1
(C) P → 2; Q → 4; R → 3; S → 5 (D) P → 3; Q → 1; R → 4; S → 1

9. Match the compounds mentioned in list-I with their characteristics mentioned in list-II.
List – I List – II
(P) COH2 (1) Has the smallest bond angle formed by
only single bonds out of the four
compounds
(Q) COF2 (2) Highest dipole moment among the four
compounds
(R) COCl2 (3) The central atom bonded with second
and third period elements
(S) COBr2 (4) Contains the longest single bonds
among the four compounds
(5) In the compound the single bonds
contain maximum s-character of central
atom
(A) P → 1; Q → 3; R → 2; S → 4 (B) P → 2; Q → 1; R → 3; S → 4
(C) P → 5; Q → 2; R → 3; S → 4 (D) P → 2; Q → 3; R → 1; S → 4
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 10 IT−2026 (RIT-2)-(PCM)

10. Match the compounds mentioned in list-I with their characteristics mentioned in list-II.
List – I List – II
(Compound) (Reaction with H2O)
(P) Mg3N2 (1) A volatile acidic gas is produced
(Q) KO2 (2) A basic gas is produced
(R) BeCl2 (3) A neutral homonuclear gas is produced
(S) CaC2 (4) A gas with molar mass 26 g mol–1 is
produced
(5) A gas with molar mass 28 g mol–1 is
produced
(A) P → 3; Q → 2; R → 1; S → 5 (B) P → 2; Q → 1; R → 3; S → 4
(C) P → 3; Q → 2; R → 5; S → 1 (D) P → 2; Q → 3; R → 1; S → 4

11. Match the homonuclear diatomic molecules mentioned in list-I with their characteristics
mentioned in list-II.
List – I List – II
(Compound) (Reaction with H2O)
(P) N2 (1) Bond order = 0.5
(Q) O2 (2) Lowest energy differences between
HOMO and LUMO
(R) F2 (3) Loss of electrons from ground state
increases stability
(S) Be+ (4) Loss of electrons from ground state
2
decreases stability
(5) Paramagnetic in ground state
(A) P → 4; Q → 3; R → 5; S → 1 (B) P → 4; Q → 2; R → 3; S → 1
(C) P → 3; Q → 4; R → 2; S → 1 (D) P → 4; Q → 3; R → 2; S → 1

(PART – B)
(Non – Negative Integer)

1. The number of valence electrons of a homonuclear diatomic molecule(X2) is equal to twice

the number of valence electrons of atom X. If X is a second period element and the number
of valence electron of X2 is 10. What is the bond order of X2?

2. AB is a covalent compound. The A – B bond length is 2.3 pm and the covalent radius of A is
1.4 pm. The electronegative difference between A and B is 0.1. If the covalent radius of B in
pm unit is x, what is the value of 10x?
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 11 IT−2026 (RIT-2)-(PCM)

3. X+ is the simplest group-1 cation which forms stable complex with 12 crown 4 ether.
If a = Atomic number of X
b = Coordination number of X
What is the value of (a + b)?

4. Both BeCl2 and Be(CH3)2 forms polymers.

x = Maximum number of covalent bonds present around each Be atom in BeCl2 polymer.
y = Coordination number of Be in BeCl2 polymer + coordination number of Be in Be(CH3)2
polymer
z = Coordination number of carbon in Be(CH3)2 polymer
What is the value of (x + y + z)?

5. In interstitial hydrides of some 3d-transition series elements, the interaction takes place
between H2 molecules and metal atoms. The H2 molecules can gain and donate electrons by
the overlap of 1s and 1s
*
molecular orbitals with the metal d-orbitals
If x = Number of electrons donated by one H2 molecule.
and y = Number of electrons are gained by one H2 molecule
What is the value of (x + y)?

o
6. The bond length of B – F bond in BF3 is assumed to be 0.4 A . If the longest distance

( )
o
between any two fluorine atoms in the molecule is expressed as y 3 A , what is the value
of 10 y?
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 12 IT−2026 (RIT-2)-(PCM)

S
SEEC
CTTIIO
ONN –– IIIIII:: M
MAAT
THHE
EMMA
ATTIIC
CSS
(PART – A)
(One or More Than One Options Correct Type)
This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

1. If a, b, c are real numbers such that a2 + 4b2 − c 2 + 4ab = 0 , then the distance between any
two lines in the family of lines ax + by + c = 0 can be
(A) 2 (B) 13
(C) 8 (D) 4

2. The area of the region bounded by the straight lines x = K, x − 3y = 0, x + y = 2 and by x –

11
axis is , then the value of K is/are
32
9 9
(A) (B)
4 2
1 −9
(C) (D)
16 4

3. Let L 1 be a straight line passing through the origin and L 2 be the straight line x + y = 1 . If the
intercepts made by the circle x2 + y2 − x + 3y = 0 on L 1 and L 2 are equal, then which of the
following equations can represent L 1
(A) x + y = 0 (B) x − y = 0
(C) x + 7y = 0 (D) x − 7y = 0

(Single Correct Answer Type)

This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

4. A light ray emerging from the point source placed at P(2, 3) is reflected at a point Q on the
y – axis and then passes through the point R(5, 10). Coordinate of Q is:
(A) (0, 3) (B) (0, 2)
(C) (0, 5) (D) None of these

5. The equation of the circle passing through the point of intersection of the circles
x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 6y - 6 = 0 and having its centre on y = 0 is
(A) 2x2 + 2y2 – 8x + 3 = 0 (B 3x2 + 3y2 – 6x + 2y = 0
2 2
(C) x + y – 8x – y – 12 = 0 (D) none of these
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 13 IT−2026 (RIT-2)-(PCM)

6. If the lines 2x − 3y + 5 = 0, 9x − 5y + 14 = 0 and 3x − 7y +  = 0 are concurrent, then the

value of  is equal to
(A) 7 (B) 8
(C) 10 (D) 9

7. Let P be the point (–3, 0) and Q be a moving point (0, 3t). Let PQ be trisected at R so that R
is nearer to Q. RN is drawn perpendicular to PQ meeting the x-axis at N. The locus of the
midpoint of RN is
(A) (x + 3)2 –3y = 0 (B) (y + 3)2 –3x = 0
2
(C) x –y = 1 (D) y2 –x = 1

(Matching List Sets)

This section contains FOUR (04) Matching List Sets. Each set has ONE Multiple Choice Question. Each set
has TWO lists: List-I and List-II. List-I has Four entries (P), (Q), (R) and (S) and List-II has Five entries (1),
(2), (3), (4) and (5). FOUR options are given in each Multiple Choice Question based on List-I and List-II and
ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question.

8. Match each entry in List – I to the correct entries in List – II.

Each side of a square has lengths 4 units and its centre is at (3, 4). If one of the diagonal is
parallel to the line if y = x, then match the following.
List – I List – II
(P) Equation of one of the sides is (1) y−x=1
(Q) Equation of one of the diagonals is (2) y=6
(R) One of the vertices of the square is (3) x+y=7
(S) Midpoint of the one of the sides is (4) (1, 4)
(5) (1, 2)
(A) P→ (3); Q → (2) ; R→(1); S→(4)
(B) P→ (3); Q → (2) ; R→(5); S→(4)
(C) P→ (2); Q → (1) ; R→(5); S→(4)
(D) P→ (2); Q → (1) ; R→(1); S→(3)
Space For Rough Work

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9. Match each entry in List – I to the correct entries in List – II.

List – I List – II
(P) The value of K for which x2+y2=4 and (1)
2 2
x +y –2x+2ky=k cut orthogonally is –35

(Q) The value of k for which the lines 2x–ky+3=0, 4x+y+5=0 (2)
cut axes in concyclic points is 5

(R) The value of k so that length of tangent from origin to the (3)
circle x2+y2–2x–4y–k=0 is 2 units is –4

(S) The value of k so that length of chord made by line (4)

3x+4y+k=0, to the circle x2+y2–10x=0 is of length 6 is –8

(5) 0
(A) P→ (3); Q → (4) ; R→(3); S→(1)
(B) P→ (3); Q → (2) ; R→(5); S→(4)
(C) P→ (2); Q → (1) ; R→(4); S→(5)
(D) P→ (2); Q → (1) ; R→(1); S→(3)

10. Match each entry in List – I to the correct entries in List – II.
List – I List – II
(P) If a circle passes through the points of intersection of the (1) 0
lines
2x – y + 1 = 0 and x − y − 3 = 0 with the coordinate axes,
then  is
(Q) A circle circumscribes a triangle whose sides are given (2) 1
by the joint equation (x + y − 4)(xy − 2x − y + 2) = 0 . The
diameter of the circle is equal to
(R) The number of points on the circle 2x2 + 2y2 – 3x = 0, (3) 2
which are at a distance 2 unit from the point (-2, 1) is
equal to
(S) If the angle between the tangents drawn from the origin (4) 2
2
to the circle (x − 7)2 + (y + 1)2 = 25 is , then k is
k
(5) 4
(A) P→ (3); Q → (4) ; R→(3); S→(4)
(B) P→ (3); Q → (2) ; R→(5); S→(4)
(C) P→ (2); Q → (1) ; R→(4); S→(5)
(D) P→ (4); Q → (3) ; R→(1); S→(5)
Space For Rough Work

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11. Match each entry in List – I to the correct entries in List – II.
Let C1 and C2 be 2 circles whose equations are x 2 + y 2 − 2x = 0 and x 2 + y 2 + 2x = 0
respectively. P ( ,  ) is a variable point
List – I List – II
(P) P lies inside C1 but outside C2 (1)   ( −, − 1)  (0, )

(Q) P lies inside C2 but outside C1 (2)   ( −, − 1)  (1, )

(R) P lies outside C1 but inside C2 (3)   ( −1, 0)

(S) P does not lie inside C2 (4)   (0, 1)

(5)   (0, 1) U (1, 2)

(A) P→ (3); Q → (2) ; R→(3); S→(4)
(B) P→ (3); Q → (2) ; R→(5); S→(4)
(C) P→ (4); Q → (3); R→(3); S→(1)
(D) P→ (2); Q → (1) ; R→(1); S→(3)

(PART – B)
(Non – Negative Integer)

1. The number of common tangents to the circle x2 + y2 − 4x − 6x − 12 = 0 and

x + y + 6x + 18y + 26 = 0 , is
2 2


2. If the straight lines ax + by + p = 0 and x cos  + y sin  = p are inclined at an angle and
4
concurrent with the straight line x sin  − y cos  = 0 , then a2 + b2 is :

3. If a line lies between the circles x 2 + y 2 − 2x − 2y + 1 = 0 and

3x + 4y −  = 0
x 2 + y 2 − 18x − 2y + 78 = 0 without touching or intersecting either circle, then the number of
integral values '  ' can assume is

4. If a straight line through P ( )

3, 2 and inclined at an angle

6
with x - axis meets the line

3x − 4y + 8 = 0 at Q, then PQ is

5. Let C1 and C2 be the centrex2 + y2 − 2x − 2y − 2 = 0 and

of the circle
x2 + y2 − 6x − 6y + 14 = 0 respectively. If P and Q are the points of intersection of these
circles, then the are (in sq. units) of the quadrilateral PC1QC2 is

6. Two circles in the first quadrant of radii r1 and r2 touch the coordinate axes. Each of them
cuts off an intercept of 2 units with the line x + y = 2 . Then r12 + r22 − r1r2 is equal to

Space For Rough Work

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 16 IT−2026 (RIT-2)-(PCM)

FIITJEE INTERNAL TEST

BATCHES: Class – XII
Code: 100982
JEE ADVANCED LEVEL
ANSWER KEY
ANSWER KEYS
Physics
PART – A
1. ABC 2. ABC 3. CD 4. D
5. C 6. C 7. C 8. B
9. A 10. C 11. D
PART – B
1. 5 2. 9 3. 3 4. 2
5. 7 6. 5

Chemistry
PART – A
1. ACD 2. ABCD 3. AB 4. A
5. A 6. A 7. B 8. B
9. B 10. D 11. D
PART – B
1. 3 2. 18 3. 7 4. 17
5. 4 6. 4

Mathematics
PART – A
1. ABCD 2. AD 3. BC 4. C
5. A 6. C 7. D 8. C
9. A 10. D 11. C
PART – B
1. 3 2. 2 3. 8 4. 6
5. 4 6. 7

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