FIITJEE – INTERNAL Phase Test

PHYSICS, CHEMISTRY & MATHEMATICS

QP CODE: 100940-0 Paper – 1

Time Allotted: 3 Hours Maximum Marks: 180

BATCHES: PANINI426-G1,A1,A2 & B1_Reshuffling Test

▪ 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 (01-04) – 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.
(ii) PART–A (05–07) 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.
(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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S
SEEC
CTTIIO
ONN –– II:: P
PHHY
YSSIIC
CSS
(PART – A)
(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.

1. Three identical rods, each of length x, are joined to form a rigid equilateral triangle. Its radius
of gyration about an axis passing through a corner and perpendicular to the triangle is :
x x 3 x
(A) (B) (C) x (D)
3 2 2 2
a (m/s2)
2. A racing motor boat speeds up in a straight line in a lake,
from rest. Referring to the acceleration displacement graph
for speeding boat, find speed of the motor boat when it has 8
maximum acceleration
(A) 64 m/s (B) 32 m/s
(C) 8 m/s (D) 4 m/s S(m)
O 8 16
3. Power applied to a particle varies with time as P = (3t2 – 2t + 1) W where t is in second. Find
change in its kinetic energy between time t = 2s and t = 4s.
(A) 32 J (B) 46 J (C) 61 J (D) 102 J
4. A particle is projected from the top of a tower of height 1500 37°
m and with a velocity v making an angle 37° with the 1500 m
horizontal and its vertically downward component is 100 m/s v
100 m/s
as shown in the figure. The distance from the foot of the
tower where it strikes the ground will be
 3
 g = 10 m / s , tan 37 = 4 
2

 
4000 5000
(A) m (B) m (C) 2000 m (D) 3000 m
3 3

(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.

5. A particle of mass m moves along a curve y = x2. When particle has x-co-ordinate as ½ and
x-component of velocity as 4 m/s then.
(A) the position coordinate of particle are (1/2, 1/4).
(B) the velocity of particle will be along the line 4x − 4y − 1 = 0 .
(C) the magnitude of velocity at that instant is 4 2 m/s.
(D) none of the above.
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6. A solid material is supplied heat at a constant rate. The y

temperature of material is changing with heat input as
E

Temperature
shown in the figure. Choose the correct options.
(A) CD represents latent heat of fusion.
(B) CD represents latent heat of vaporization. C D
(C) Slope of DE represent heat capacity of vapour.
A B
(D) Slope of DE represent inverse of heat capacity of
vapour O x
Heat Input

7. If no external force acts on a system, choose correct statement.

(A) velocity of centre of mass remains constant.
(B) velocity of centre of mass is not constant.
(C) velocity of centre of mass may be zero.
(D) acceleration of centre of mass is zero.

(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. Assume all the liquid drop or air bubble have surface tension T and radius R.

List–I List–II
(P) Excess pressure of liquid drop in air is (1) 4T
+ gh
R
(Q) Excess pressure of bubble in air is (2) 2T
+ gh
R
(R) Excess pressure of air bubble in liquid (3) 4T
at its free surface is R
(S) Excess pressure of air bubble in liquid (4) T
at depth h from free surface is 2
R
(5) 2T
− gh
R
The correct option is:
(A) P → 3, Q → 4, R → 4, S → 3 (B) P → 4, Q → 3, R → 4, S → 4
(C) P → 1, Q → 3, R → 5, S → 4 (D) P → 3, Q → 1, R → 4, S → 5
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1 m/s

9. Consider the system shown in the figure. S C

Here the pulleys can move in a vertical
A
plane, point A and B are on the rope,
point C is the centre of the indicated P B
pulley while point D is a point on the rope 2 m/s
1 m/s
near the bottom of the middle pulley. The R
string are taut
D

1 m/s
Q

List – I List – II
(P) 5 m/s (1) Speed of point A must be
(Q) 1.5 m/s (2) Speed of point B must be
(R) 3 m/s (3) Speed of point C must be
(S) 17 m/s (4) Speed of point D must be
(5) Speed of pulley S must be
The correct option is:
(A) P → 2, Q → 3, R → 1, S → 4 (B) P → 2, Q → 4, R → 3, S → 1
(C) P → 1, Q → 2, R → 5, S → 4 (D) P → 2, Q → 1, R → 3, S → 5

T
A
4T0
10. One mole of an ideal diatomic gas undergoes a cyclic
process as shown in Temperature-Pressure graph.
Temperature and pressure of gas at ‘A’ is 4T0 and P0
respectively and temperature in process BC is T0. The
process AB is given by TP2 = constant and the process B
T0 C
CA is given by TP4 = constant.

P0 P
List –I describe the name of thermodynamics process involve in the cyclic process and List-II
gives work done by gas in the process, charge in internal energy of the gas in the process
and heat given to the gas in the process.
List –I List –II
(P) In the thermodynamics process A → B (1) Work done by gas and
heat given to gas is
negative
(Q) In the thermodynamics process B → C (2) Work done by gas is
negative but heat given
to gas is positive
(R) In the thermodynamics process C → A (3) Work done by gas is
positive but heat given
to gas negative
(S) In the cyclic process (4) Work done by gas and
heat given to gas is
positive
(5) Work done by gas is
positive and change in
internal energy of gas is
negative
Which one of the following options is correct?
(A) P → 1 ; Q → 5 ; R → 4 ; S → 2 (B) P → 4 ; Q → 1 ; R → 2 ; S → 3
(C) P → 1 ; Q → 4 ; R → 4 ; S → 1 (D) P → 2 ; Q → 3 ; R → 4 ; S → 5

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11. A uniform rod of mass m & length  is released from rest in hinged
the position shown in figure. Rod is hinged at one end. It is m, 
free to rotate in vertical plane about hinge. Take length of
rod  = 1. Consider the case just after release.

List-I List-II
(P) Angular velocity of rod is (1) 3g
2

(Q) Angular acceleration of rod is (2) 0

(R) Acceleration of centre of mass of rod is (3) 3g
4

(S) Net force acting on rod is (4) 3g

(5) 3Mg
4

When rod is horizontal

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

(PART – B)
(Non – Negative Integer)

1. A ball falls from rest from a height h onto a floor, and rebounds to a height h/4. Find the
reciprocal of coefficient of restitution between the ball and the floor.

2. The escape velocity for a planet is Ve. A tunnel is dug along a diameter of the planet and a
small body is dropped into it at the surface. When the body reaches the centre of the planet,
V
its speed will be e , then find the value of ‘k’.
k
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x 3 9x 2
3. Potential energy of a particle moving along x-axis is given by U = − + 20x . Find out
3 2
position of stable equilibrium state.

4. A composite rod (formed by joining two rods of equal length  but

different materials) is held between two fixed supports as shown. R
If temperature of the system is lowered by , then the P A/2, 2Y,  A, Y, 2
 
displacement of the contact point R is , then find the value Q
n
of ‘n’. [Symbols are having their usual meanings]

5. Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side
length a. The only forces acting on the particles are their mutual gravitational forces. It is
desired that each particle moves in a circle while maintaining the original mutual separation
a. Find the initial velocity that should be given to each particle.  take a =
GM 
 16 

6. What is the speed of 10 kg block at the end of 3 second is  = 0.2 10 kg F = 5t N

3
. Find the value of ‘n’. =0 20 kg
n
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S
SEEC
CTTIIO
ONN –– IIII:: C
CHHE
EMMIIS
STTR
RYY
(PART – A)
(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.

1. The diatomic molecule of which element can be ionized easily into a cation than its
constituent atom according to molecular orbital theory?
(A) Nitrogen (B) Lithium
(C) Oxygen (D) Boron

2. Which atom has the highest value of first ionization energy?

(A) Lithium (B) Nitrogen
(C) Oxygen (D) Boron

1
3. In a first order chemical reaction, fraction of molecules cross the energy barrier when
10
they are heated at 500 K. What is the activation energy of the reaction in joule unit?
[R = 8 JK–1 mol–1][n 0.1 = -2.3]
(A) 4800 (B) 9200
(C) 8600 (D) 9680

4. Hydroboration oxidation converts an alkene into alcohol through syn-addition.

CH3
→ Product (P )
B H , THF
⎯⎯⎯⎯⎯⎯
2 6
NaOH, H2O2

In above reaction(P) is
CH3 CH3

(A) (B)
OH OH
CH3 CH3
(C) OH (D) OH

Space For Rough Work

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(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.

5. A container contains 10 moles of an ideal gas(NO) at 800 K. Then, [R = 8 JK–1 mol–1]

(A) the root mean square velocity of the gas is 800 ms–1
(B) the total kinetic energy of the gas is 96 kJ
(C) under identical conditions the relative rate of effusion of the gas with respect to neon gas
is 2 : 3
(D) the compressibility factor of the gas is 1

6. For which of the following reaction, Kp = Kc?

(A) N2 ( g) + O2 ( g) 2NO ( g) (B) H2 ( g) + Cl2 ( g) 2HCl ( g)
(C) S ( s) + O2 ( g) SO2 ( g) (D) 2CO ( g) + O2 ( g) 2CO2 ( g)

7. Which of the following compounds show position isomerism?

CH 3CH 2CHCH 3
(A) CH3 – CH = CH – CH3 (B)
OH
CH 3CHCH 3
(C) (D) CH3CH2C  CH
CH3
(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 lists.

List – I List– II
(Atomic orbitals) (Characteristics)
(P) 3px (1) Has four radial nodes

(Q) 4pz (2) The wave function can be expressed as

4, 1, 0
(R) 3dxy (3) Has double dumbbell shape

(S) 5s (4) Has one angular node or nodal plane

(5) Azimuthal quantum number is 3

(A) P → 1; Q → 2; R → 5; S → 4 (B) P → 3; Q → 2; R → 1; S → 5
(C) P → 4; Q → 2; R → 3; S → 1 (D) P → 5; Q → 2; R → 4; S → 1
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9. Match the lists.

List – I List– II
(Compounds) (Aromaticity)
(P) (1) Aromatic

(Q) (2) Quasi-aromatic

(R) CH2 - CH = CH 2 (3) Antiaromatic

(S) (4) Non-aromatic

(5) Pseudoaromatic

(A) P → 1; Q → 2; R → 3; S → 4 (B) P → 3; Q → 2; R → 1; S → 4
(C) P → 5; Q → 4; R → 2; S → 3 (D) P → 2; Q → 3; R → 4; S → 5
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10. Match the lists.

List– II
(Approximate quantity of PV-work
List – I done by one mole of an ideal gas)
(Reversible thermodynamic processes) [log 2 = 0.3010]
[R = 8.314 JK-1mol-1 = 0.0821 L atm K-1
mol-1]
(P) (1) Zero

P
(in atm)

2 6
V (in L)
(Q) (2) -561.59 joule

4
P
(in atm)
2

200 400
T (in K)
(R) (3) -16 L atm

V
(in L)

200 1000
T (in K)
(S) (4) -1152.65 joule
4

P
(in atm)
2

2 4
V(in L)
(5) +16 L atm

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

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11. Match the lists.

List – I List– II
(Compounds) (Characteristics)
(P) H3BO3 (1) Contains 3c – 2e bond

(Q) Na2B4O7 (2) Inorganic benzene

(R) B2H6 (3) Anhydrous form of borax

(S) B3N3H6 (4) Undergoes dehydration on heating to

produce finally B2O3
(5) Inorganic graphite

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

(PART – B)
(Non – Negative Integer)

AB ( g) ⎯⎯→ 2P ( g) + Q ( g) + R ( g)

1.
Above first order reaction starts by taking AB(g) in a container at 100 mm of Hg pressure.
After 12 minute from the start of the reaction, total pressure observed in the container in
250 mm of Hg. What is the half-life period of AB(g) in minute unit?
2. The pH of the saturated solution of a sparingly soluble base M(OH)2 is 13. If the solubility
product of the base is expressed as x  10–4, what is the value of x?
O
3. CH3CH = CH − CH = CHC2H5 ⎯⎯⎯⎯
3
→P + Q + R
Zn/H2O
If (P) is the simplest product of the reaction, what is the molar mass of Q in g mol–1 unit?
4. If the formula of sodium orthosilicate is NaxSiyOz, what is the value of (x + y + z)?
5.

OH

CN
O Cl

How many asymmetric carbon atom(s) is/are present in above compounds?

6. Assume that the Lewis base ( CH3 ) C  P reacts with the Lewis acid B(CH3)3 to form an
 3 3
adduct or molecular compound.
( CH3 ) C P + B ( CH3 ) ⎯⎯→ ( CH3 ) C P ⎯⎯→ B ( CH3 )
 3 3 3  3 3 3
3
How many sp hybridized atoms are present in the adduct?
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S
SEEC
CTTIIO
ONN –– IIIIII:: M
MAAT
THHE
EMMA
ATTIIC
CSS
(PART – A)
(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.

1. If  = x1x2 x3 and  = y1y2 y3 are two 3 – digit numbers, then the number of pairs  and 
can be formed so that  can be subtracted from  without borrowing, is
(A) (44) (55)2 (B) (45) (55)2
2
(C) (45) (55) (D) (44)2 (55)

1+  1+  1+ 
2. If , , are roots of the cubic equation f ( x ) = 0 where , ,  are the roots of the
1−  1−  1− 
cubic equation 3x 3 − 2x + 5 = 0, then the number of negative real roots of the equation
f ( x ) = 0 is:
(A) 0 (B) 1
(C) 2 (D) 3

3. If sin ( e x ) = 2x + 2− x , then the number of real solutions is equal to

(A) 0 (B) 1
(C) 2 (D) none of these

4. From a point on the level ground, the angle of elevation of the top of a vertical pole is 30 .
On moving 20 meters nearer, the angle of elevation becomes 45 . The height of the pole in
meters is
(
(A) 10 3 − 1 ) (B) 10 3 + 1 ( )
(C) 15 (D) 20

(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.

5. Which of the following statement(s) is (are) correct?

100

 Cr ( x − 4 ) (5)
2 100 100 −r r
(A) The coefficient of x in the expansion of is equal to 4950.
r =0
8
 −38 
(B) If the sixth term in the expansion of  x + x log10 x  is 5600, then x is equal to 1000.
2

 
A 15
(C) Let A n = C0 C1 + C1 C2 + ... + Cn−1 Cn and n+1 =
n n n n n n
, then the sum of possible
An 4
values of n is equal to 6.
n n −1
Ck
(D) If A k = n
Ck + nCk +1
and 3
A
k =0
k = 4, then n is equal to 128.

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
6. The value of  cot (n
n=1
−1 2
)
+ n + 1 is also equal to:

(A) cot ( −1) + sec −1 (1) − cos ec −1 (1)

−1

(B) cot ( 2 ) + cot ( 3 )

−1 −1

 1 − x2 
(C) minimum value of the function f ( x ) = tan 
−1
2 
 1+ x 
−1  41 
(D) cos  cos
 4 

7. Let z1,z2 and z3 be three distinct complex numbers satisfying z1 = z2 = z3 = 1. Which of

the following is/are true?
z    z − z1  
(A) If arg  1  = then arg    where z  1
 z2  2  z − z2  4
(B) z1z2 + z2 z3 + z3 z1 = z1 + z2 + z3
 ( z + z2 )( z2 + z3 )( z3 + z1 ) 
(C) Im  1  = 0
 z1 .z2 .z3 
 z − z1 
(D) If z1 − z2 − 2 z1 − z3 = 2 z2 − z3 , then Re  3 =0
 z3 − z 2 

(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. If a, b, c are in H.P. then

List – I List – II
(P) a b c (1) H.P.
, ,
b +c −a c +a −b a +b −c
(Q) 1 1 1 (2) G.P.
, ,
b−a b b−c
(R) b b b (3) A.P.
a − , ,c −
2 2 2
(S) a b c (4) A.G.P.
, ,
b+c c +a a+b
(5) Binomial series
The correct option is
(A) P→(1) Q → (3) R→(2) S→(1) (B) P→(2) Q → (4) R→(1) S→(5)
(C) P→(3) Q → (3) R→(4) S→(4) (D) P→(1) Q → (5) R→(3) S→(4)
Space For Rough Work

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9. Consider the circles C1 of radius a and C2 of radius b, b > a both lying in the first quadrant
b
and touching the coordinate axes. Find the value of if
a
LIST – I LIST – II
(P) C1 and C2 touch each other (1) 2+ 2
(Q) C1 and C2 are orthogonal (2) 3
(R) C1 and C2 intersect so that the common chord is (3) 2+ 3
longest
(S) C2 passes through the centre of C1 (4) 3+2 2
(5) 3− 2
The correct option is
(A) P → 4; Q → 2; R → 1; S → 1 (B) P → 4; Q → 3; R → 2; S → 1
(C) P → 4; Q → 2; R → 1; S → 3 (D) P → 4; Q → 3; R → 2; S → 5

10. Normals are drawn at points A, B, C lying on the parabola y2 = 4x which intersect at (3, 0).
Then
List – I List – II
(P) Area of ABC is (1) 2
(Q) Centroid of ABC is (2) 5 
 2 , 0
 
(R) Circumcentre of ABC is (3) 2 
 3 , 0
 
(S) Circumradius of ABC is (4) 5
2
(5) 3
2
The correct option is
(A) P → 4; Q → 2; R → 1; S → 1 (B) P → 3; Q → 3; R → 4; S → 5
(C) P → 1; Q → 3; R → 2; S → 4 (D) P → 4; Q → 3; R → 1; S → 5

11. Match the following

List – I List – II
(P) If the line x + 2ay + a = 0, x + 3by + b = 0 and (1) A.P.
x + 4cy + c = 0 are concurrent, then a, b, c are
(Q) The points with the co – ordinates (2a, 3a), (3b, 2b) and (2) G.P.
(c, c) are collinear then a, b, c are in
(R) If the lines, ax + 2y + 1 = 0; bx + 3y + 1 = 0 and (3) H.P.
cx + 4y + 1 = 0 passes through the same point then a, b,
c are in
(S) Let a, b, c be distinct non – negative numbers. If the (4) neither A.P. nor G.P.
lines ax + ay + c = 0, x + 1 = 0 and cx + cy + b = 0 pass nor H.P.
through the same point then a, b, c are in
(5) A. G. P.
The correct option is
(A) P → 3; Q → 4; R → 1; S → 2 (B) P → 3; Q → 3; R → 4; S → 5
(C) P → 1; Q → 3; R → 2; S → 4 (D) P → 4; Q → 3; R → 1; S → 5
Space For Rough Work

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 15 IT−2026- PANINI426-G1,A1,A2 & B1_RT-Paper-1-SET-A-(PCM)

(PART – B)
(Non – Negative Integer)

1 1
1. If o
+ o
= , then the value of 9 4 + 812 + 97 must be
cos 290 3 sin 250

k
2. If 498 16cos x + 12sin x  = 2k + 60, then the maximum value of is
10

3. Let Pi and P 'i be the feet of the perpendiculars drawn from foci S,S ' on a tangent Ti to an
10
ellipse whose length of semi – major axis is 20. If  (SP )(S 'P ' ) ,
i=1
i i then find the value of

100e. (Where e denotes eccentricity).

4. Let P and Q be two circles externally tangent at point X. A straight line is tangent to P at
point A and is tangent to Q at point B ( A  B ) . The line tangent to P and Q at X intersects
line AB at a point Y. If AY = 10 and the radius of P is 9. If the radius of the circle Q can be
a
expressed as a rational number in the lowest form, find the value of ( a + b) .
b

5. A cricket player played n (n > 1) matches during his career and made a total of
(n2 − 12n + 39 )( 4.6n − 5.3n + 1) runs. If T represent the runs made by the player in r th
r
5
match such that T1 = 6 and Tr = 3Tr −1 + 6r , 2  r  n then n will be

6. Real number x, y satisfies x2 + y2 = 1. If the maximum and minimum values of the

4−y
expression z = are M and m respectively then find the value (2M + 6m)
7−x
Space For Rough Work

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