RBT 1

IIT2019, (Two Year CRP(17-19)-RBT-I-CPM-1
FIITJEE INTERNAL TEST

RANK BOOSTER TEST SERIES – I
Batches: All1719 (R & W)
IIT- JEE 2019
QP CODE: 118153
Time: 3 hours Maximum Marks: 228
 Please read the instructions carefully. You are allotted 5 minutes specially for this purpose.
 You are not allowed to leave the examination hall before end of the test.
 Use Blue/Black Ball Point Pen only for writing particulars on Side–1 and Side–2 of the
Answer Sheet. Use to Pencil is strictly prohibited.
Instructions
Note:
1. The question paper contains 3 sections (Sec-1, Chemistry, Sec-II, Physics & Sec-III, Mathematics.)
2. Each section is divided into three parts, PART-A, PART-B and PART-C.
3. PART – A contains 13 questions which are further divided as follows:
 Q. 1 – 5 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of
which only one is correct.
 Q. 6 – 13 are multiple correct answer type questions. Each question has four choices (A), (B), (C) and
(D), out of which one or more answer(s) is/are correct.
4. PART – B contains 1 Matrix Match Type Questions which have statements given in 2 columns.
Statements in the first column have to be matched with statements in the second column. There may be
One or More Than One Correct choices.
5. PART–C contains 5 Numerical Based questions with Single Digit Integer as answer, ranging from 0 to 9.
Marking Scheme
1. For each question in the group Q. 1 – 5 to PART – A you will be awarded 5 marks if you have darkened only
the bubble corresponding to the answer and zero marks if no bubble is darkened. In all other cases, minus
three (–2) mark will be awarded.
2. PART – A (06 – 13) contains 8 Multiple Choice Questions which have One or More Correct answer.
For each question in the group Q. 6 – 13 of PART – A you will be awarded
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: 2 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 2
marks, as a wrong option is also darkened.
3. PART – B contains 1 Matrix Match Type Questions which have statements given in 2 columns. Statements
in the first column have to be matched with statements in the second column. There may be One or More
Than One Correct choices. Each question carries +4 marks for all correct answer however for each correct
row +1 marks will be awarded. No negative marks will be awarded in this section.
4. PART-C (1 – 5) contains 5 Numerical Based questions with Single Digit Integer as answer, ranging from 0 to
9 and each question carries +3 marks for correct answer and –1 mark for wrong answer.
Name of the Candidate :
Enrolment Number :
FIITJEE Ltd., Punjabi Bagh Centre, 31, 32, 33 Central Market, West Avenue Road, Punjabi Bagh, New Delhi – 110026, Ph: 011 - 45634000
Section – I (Chemistry)
PART – A
(Single Correct Choice Type)
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which only
ONE option is be correct.
1. The equivalent weight of metal M is x and the formula of its oxide is M nOm. The atomic mass of metal
is
2n.x 2m.x 2mn mn
(A) (B) (C) (D)
m n x x
2. Equal no. of moles of NaOH and acidic KMnO4 are separately reacted with NaHC2O4 monosodium
oxalate. Ratio of no. of moles of NaHC2O4 reacted with NaOH and acidic KMnO4 respectively is
(A) 2 : 5 (B) 5 : 2 (C) 1 : 5 (D) None of these
3.
The boiling point of helium is more than hydrogen
4. Calculate relative rate of effusion of O2 to CH4 through a container containing O2 and CH4 in 3 : 2
mass ratio
3 2 3 3
(A) (B) (C) (D) none of these
4 4 2 2 2
5. The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a 0 is Bohr radius]
h2 h2 h2 h2
(A) (B) (C) (D)
42ma02 162ma02 322ma02 642ma02
space for rough work
(Multiple Correct Choice Type)

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which
ONE OR MORE may be correct.
6. In the figure representing variation of the compressibility factor Z of a real gas with pressure:
c
a
Z
b
P
Which of the following options are correct?
(A) ab shows that the gas is more compressible than ideal gas
(B) bc shows that the gas is more compressible than ideal gas
a
(C) ab may be explained by PV  RT 
V
(D) bc may be explained by PV  RT  Pb
7. The figure shows the effect of pressure on the compressibility factor, Z of a gas:
F
D
A
E
Z B C
P
The correct conclusion(s) is/are :
(A) The curve AE can be explained by PV = RT
(B) The curve AF and CD can be explained by PV = RT + Pb
a
(C) The curve AB can be explained by PV  RT 
V
(D) All the three curves AF, AE and CD shows the real behaviour
8. Which of the following orbital(s) have angular node at yz plane?

(A) dxy (B) dyz (C) dxz (D) dx2 – y2
9. Which is/are correct statement?

(A) There cannot be two probabilities for an electron at any position in atom
(B) Probability cannot change abruptly form one point to the other
(C) For large distance from the nucleus probability should be smaller
(D) The total probability of electron some where in space around the nucleus approaches to1
4
10. aFe  CN6  bCe4  cOH  dFe3  Ce3  CO32  NO3  H2O
Which of the following is/are correct about the above reaction?
(A) a = 1, b = 61, c = 250, d = 1 (B) a = 1, b = 61, c = 72, d = 1
(C) n-factor for Ce4+ is 61 (D) n-factor for Fe(CN)4-6 is 61.
11. One mole of KMnO4 is used for complete oxidation of FeSO4,FeC2O4 and H2C2O4 respectively and
separately. Pick up the correct statement:
(A) 5 mole of FeSO4 can be oxidized (B) 3/5 mole of FeC2O4 can be oxidized
5
(C) mole of FeC2O4 can be oxidized (D) 2.5 mole of H2C2O4 can be oxidized
3
12. Select the correct statement(s)
(A) In the reaction MnO2  4HCl  MnCl2  Cl2  2H2O. Eq. mass of HCl = 36.5
(B) In the reaction
K 2Cr2O7  14HCl  2KCl  2CrCl3  3Cl2  7H2O
7
Equivalent mass of HCl = molecular mass of HCl
3
7 4 6 3M
(C) 3Mn  Mn  2Mn , EMn7   where M is molar mass of Mn7+
5
(D) KClO3  KCl  O2 is a reaction in which oxygen acts as a reducing substance
13. Which of the following options are correct when a gas is at its critical point?
TC
P
 dP   d2P 
(A) Z = 1 (B) Z  1 (C)  0 (D)  2 
0
 dV   dV 
PART – B
(Matrix Match Type)
1.
PART – C
This section contains 05 multiple choice questions. The answer to each question is a single digit integer, ranging from 0
to 9 (both inclusive)
1. 8g of sulphur is burnt to form SO2 which is oxidised by Cl2 water. The solution is then treated with
1
BaCl2 solution. The moles of BaSO4 precipitated would be , value of n is
n
2. Number of electron in the orbitals of ‘Mn’ for which magnetic angular momentum vector is -h/2
3. The radial wave equation for ‘H’ atom is

3/2
1

1
 
16 4  a0     
 x  1 x 2  8x  12  e x / 2 , Where x  2r ;
a0
a0  radius of first
Bohr orbit
The maximum position of radial nodes from the nucleus is x a0 the value of ‘x’ is
4. How many fold of degeneracy is observed for the energy of electron in n = 3 of H atom.
5. Not considering the e– spin, the degeneracy of second excited state(n = 3) of H atom is 9, while the
degeneracy of the second excited state of H– is
Section – II (Physics)
PART – A
1. A 2m wide truck is moving with a uniform speed v0 = 8 m/s along a

straight horizontal road. A pedestrian starts to cross the road with a
2m Truck v0 v
uniform speed v when the truck is 4 m away from him. The
minimum value of v so that he can cross the road safely is man
4m
(A) 2.62 m/s (B) 4.6 m/s (C) 3.57 m/s (D) 1.414 m/s
2. A balloon start rising from the ground with an acceleration of 2.5 m/s 2. After 4 sec a stone is released
from the balloon. If g = 10 m/s2, the stone will
(A) have a maximum displacement of 20 m from ground.
(B) cover a total distance of 25 m after being released.
(C) reach the ground in 3.2 sec after being released.
(D) begin to move down after being released.
3. The graph which represents the variation of slope m of the trajectory of a projectile with horizontal
displacement s is
(A) (B)
m m
s
s
(C) (D)
m m
s
s
4. In curvilinear motion (Where atan – tangential acceleration )

vdv vdv
(A) atan  (B) atotal .dr  v . dv (C) atan  (D) atotal .dr  v.dv
dr dr
5. Two blocks of masses 10 kg and 5 kg are placed one over the other
on a horizontal plane as shown in the figure. If co-efficient of friction  = 0.2 5kg
is  = 0.2, and an external force F = 25 N is applied horizontally on
F = 25 N
the lower blocks, then, the force of friction between the two blocks is  = 0.2
10kg
(A) 30 N (B) 25 N
(C) zero (D) 20 N

2
6. A train starts from rest at S = 0 and is subjected to acceleration as a(m/s)
shown 6
(A) Change in velocity at the end of 10 m displacement is 50 m/s.
(B) Velocity of the train for S = 10 m is 10 m/s. S(m)

30
(C) The maximum velocity attained by train is not greater than 10 3 m/s.
(D) The maximum velocity of the train is between 15 m/s and 16 m/s.
7. The force exerted by the floor of an elevator on the foot of a person standing there is more than the
weight of the person if the elevator is
(A) going up and slowing down (B) going up and speeding up
(C) going down and slowing down (D) going down and speeding up.
8. Two projectile are thrown at the same time from two different points. The projectile thrown from the
origin has initial velocity 3iˆ  3ˆj with respect to earth. The projectile has initial velocity aiˆ  bjˆ with
respect to earth thrown from the point (10, 5). ( î is a unit vector along horizontal, ĵ along vertical). If
the projectile collides after two second, then the
1 1
(A) value of a is -2 (B) value of a is (C) value of b is (D) value of b is –2
2 2
9. Three blocks a, b, and c of masses 10 kg, 10 kg and 20 kg are

arranged as shown in figure. All the surfaces are frictionless and
string is inextensible. Pulleys are light. A constant force
F = 20 N is applied on block a as shown. Pulleys and string are light.
Part of the string connecting both pulleys is vertical and part of the b
strings connecting pulleys with blocks a and b are horizontal. c a F
(A) Acceleration of mass blocks a, b and c is 0.5 m/s 2.
(B) Acceleration of mass block b is 1.
(C) Tension in the string is 10 N.
(D) Acceleration of mass block c is 0.5
10. Starting from rest a particle moves in a straight line with acceleration a  2  t  2   m/s . Velocity of
2
particle at the end of 4 sec will be

(A) 16 m/s (B) 20 m/s (C) 8 m/s (D) 12 m/s
11. In the system as shown in figure, all the surfaces are smooth. Rod of mass
5 kg is moved by external agent with acceleration 12 m/sec 2 vertically
downwards then
(A) Acceleration of 10 kg wedge is 10 m/sec2
(B) Acceleration of 10 kg wedge 16 m/sec2
(C) The force exerted by rod on the wedge is 100 N
800
(D) The force exerted by rod on the wedge is N
3
12. The contact force exerted by one body on another body is equal to the normal force between the
bodies. It can be said that
(A) The surface must be frictionless.
(B) The force of friction between the bodies is zero.
(C) the magnitude of normal force equals that of friction.
(D) It is possible that the bodies are rough and they do not slip on each other.
13. Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume
that the duration of collision is negligible and the collision with the plate is totally elastic. Then the
correct graph for velocity as a function of time the height as function of time are
v
(A) (B)
+v1
O t
–v1
(C) (D) None of these
PART – B
(Matrix Match Type)
1. A block of mass 1 kg is placed on a rough horizontal surface of coefficient friction  = 0.2.

A force is applied on the block horizontally whose variation with time is shown in the figure.
(g = 10 m/s2)
F(N)
1 Kg F
8
 = 0.2
2
1
t(s)
1 2 8 30
Match Column I with Column II
Column-I Column-II
(A) Velocity of particle is zero at (P) t=1s
(B) Acceleration of particle is zero at (Q) t=2s
(C) Friction force = 1 N (R) t = 27 s
(D) Friction fore  F (S) t = 30 s
PART – C
1. The pulley is light and frictionless. The thread is light and

inextensible. The force F is such that the acceleration of 3kg
block is zero. The acceleration of the pulley is g/n the find the
value of ‘n’.
2. A point P moves in counter-clockwise direction on a circular path

as shown in the figure. The movement of ‘P’ is such that it
sweeps out a lengths s = t3 + 5, where s is in metres an t is in
seconds. The radius of the path is 20 m. The acceleration of ‘P’
x
when t = 2s is nearly x then is
2
3. Two cars leave one after the other and travel with an acceleration of 0.4 m/s 2. Two minutes after the
departure of the first, the distance between the cars becomes 1.9 km. If time interval between the
a
departure of the cars is min, then a =
6
4. A block of mass 5 kg is kept on the floor of an elevator at rest. As a=12 m/s2

the elevator starts descending with an acceleration of 12 m/s2,
5 kg
(Taking g = 10 m/s2) the displacement of the block during the first 2
sec is 4x. Then the value of ‘x’ is
5. A rod AB of length 5 2 m is attached to two sliders at A VA A

and B moving on the guide bars as shown in the figure. 5m
l= 5 2m
1
The velocity of the slider B is VB  (in m), when vA = 0.2 y
n
m/s. Find the value of ‘n’.
3m
B
x
Section – III (Mathematics)

PART – A
1. Consider z  t 2  1  t 4  t 2 , where t  R is a parameter

If t 2  1 then locus of z is
(A) Ellipse (B) Parabola (C) Circle (D) none of these
z1  z2 z  4
2. If z  2  2 and  then z1, z2 , z3 will be vertices of
z1  z3 z
(A) Equilateral Triangle (B) Acute Angled triangle
(C) Right Angled Triangle (D) None of these
3. All three roots of az3  bz2  cz  d  0, have negative real part,  a,b,c  R  then:
(A) All a, b, c, d have the same sign (B) a, b, c have same sign
(C) a, b, d have same sign (D) b, c, d have same sign
4. If in ABC , AC  3, BC  4, medians AD and BE are perpendicular then area of ABC must be

equal to
(A) 7 (B) 2 5 (C) 11 (D) None
5. A variable triangle is inscribed in a circle of radius R. If rate of charge of a side is R times the rate of
change of the opposite angel, then length of that side is
(A) R (B) 3R (C) 2R (D) None

6. If  be the complex nth root of unity then     2

      .........    is equal to
3 4 n1
(A) 1 (B) 1  2  32  43  .....  n  1 n2
(C) 1    2  ....  n1 (D)

1  n1

n  1 n1
1   2 1   
7. If the complex numbers z1, z2, z3, z4, taken in that order, represent the vertices of a rhombus, then
(A) z1 + z3 = z2 + z4 (B) |z1 – z2| = |z2 – z3|
z1  z3
(C) is purely imaginary (D) none of these
z2  z 4
8. The centre of a square ABCD is at z = 0. If A is z1 , then which of the following may represent the
centroid of ABC?
z1 z1 z1 z1
(A) (B) i (C)  (D)  i
3 3 3 3
3 i  1
9. Let w 
2

and P  w n : n  1,2,3,  . Further, H 1  z  C : Re z 

 and
2
 1
H2  z  C : Re z    , where C is the set of all complex numbers. If z1  P  H1 , z2  P  H2
 2
and O represents the origin, then z1Oz2 =
 5 2
(A) (B) (C) (D) 
6 6 3
A
In a triangle ABC with fixed base BC, the vertex A moves such that cosB  cosC  4 sin
2
10. . If a,b
2
and c denote the lengths of the sides of the triangle opposite to the angle A, B and C respectively,
then
(A) b  c  4a (B) b  c  2a
(C) locus of point A is an ellipse (D) locus of point A is a pair of straight lines
2
11. The triangle formed by the complex numbers z, iz, i z is:
(A) Equilateral (B) Isosceles (C) Right angled (D) Obtuse Angled
12. A circle of radius 4 inscribed in ABC which touches side BC at D. If BD = 6 and DC= 8 then
A 4 B 4
(A) perimeter = 42 (B) tan  (C) tan  (D) perimeter = 24
2 7 2 6
1 1 1 2
13. If h1,h2 ,h3 are length of altitudes of a triangle and    where R is the radius of
h1 h2 h3 R
circumcircle then
(A) 2h1  3R (B) 3h1  2R (C) 2h2  3R (D) 3h2  2R
PART – B
(Matrix Match Type)
1. In ΔABC, r  2, r1  4, S  12 and a  b  c
Column A Column B
(A) Area of ΔABC (P) 22
(B) 4  4R (Q) 24
(C) A (R) 4

sin1  
5
(D) B (S) 3

sin1  
5
PART – C
 z1  z2  is equal to
2
 z1  
1. If z1,z2 lies on z  r and arg    then
 z2  3 z1z2
2. Sum of least and greatest value of z which satisfies 2z  1  i 3  2 is
3. Let z1  3 and z2  7 represent two points A and B respectively on complex plane. Let the curve C1
2 2
be the locus of point P(z) satisfying z  z1  z  z2  10 and the curve C2 be the locus of points
2 2
P (z) satisfying z  z1  z  z2  16 . Least distance between curves C1 and C2 is:
4. If lengths of the sides AC, AB of a triangle ABC are 8 cm and 4 cm respectively and BAC = 600 then
circum radius of the triangle is
5. In a triangle ABC, b  c  2a and A  60o . Let O be an interior point and its distance from
three sides 3,4,5 units , then circum radius of triangle ABC is
FIITJEE INTERNAL TEST

RANK BOOSTER TEST SERIES – I
Batches: All1719 (R & W)
IIT- JEE 2019
ANSWERS
QP CODE: 118153
SECTION – I (Chemistry)
Part – A
1. B 2. A 3. A 4. B
5. C 6. ACD 7. ABC 8. AC
9. ABCD 10. BD 11. ACD 12. BCD
13. BCD
Part – B
1. A  QS BR C  PT D T
Part – C
1. 4 2. 5 3. 3 4. 9
5. 3
SECTION – II (Physics)
Part – A
1. C 2. C 3. C 4. D
5. C 6. BC 7. BC 8. AC
9. BC 10. D 11. BD 12. BD
13. AC
Part – B
1. A  PQRS B  PQRS C  PRS D  PQRS
Part – C
1. 4 2. 7 3. 5 4. 5
5. 4
SECTION – III (Mathematics)

Part – A
1. D 2. C 3. A 4. C
5. B 6. BD 7. ABC 8. BD
9. BCD 10. BC 11. BC 12. ABC
13. AC
Part – B
1. AQ BQ C S DR
Part – C
1. 3 2. 2 3. 1 4. 4
5. 8

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What are the different sections in the test paper?

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What are the types of questions asked in Part A of each section?

What are the types of questions asked in Part A of each section?

IIT2019, (Two Year CRP(17-19)-RBT-I-CPM-1

FIITJEE INTERNAL TEST

Name of the Candidate :

The boiling point of helium is more than hydrogen

(Multiple Correct Choice Type)

8. Which of the following orbital(s) have angular node at yz plane?

9. Which is/are correct statement?

3. The radial wave equation for ‘H’ atom is

space for rough work

1. A 2m wide truck is moving with a uniform speed v0 = 8 m/s along a

4. In curvilinear motion (Where atan – tangential acceleration )

(Multiple Correct Choice Type)

(B) Velocity of the train for S = 10 m is 10 m/s. S(m)

9. Three blocks a, b, and c of masses 10 kg, 10 kg and 20 kg are

particle at the end of 4 sec will be

(C) (D) None of these

space for rough work

1. A block of mass 1 kg is placed on a rough horizontal surface of coefficient friction  = 0.2.

1. The pulley is light and frictionless. The thread is light and

2. A point P moves in counter-clockwise direction on a circular path

4. A block of mass 5 kg is kept on the floor of an elevator at rest. As a=12 m/s2

5. A rod AB of length 5 2 m is attached to two sliders at A VA A

space for rough work

Section – III (Mathematics)

1. Consider z  t 2  1  t 4  t 2 , where t  R is a parameter

4. If in ABC , AC  3, BC  4, medians AD and BE are perpendicular then area of ABC must be

(Multiple Correct Choice Type)

6. If  be the complex nth root of unity then     2

(A) 1 (B) 1  2  32  43  .....  n  1 n2

(C) 1    2  ....  n1 (D)

space for rough work

(A) Area of ΔABC (P) 22

(C) A (R) 4

(D) B (S) 3

2. Sum of least and greatest value of z which satisfies 2z  1  i 3  2 is

FIITJEE INTERNAL TEST

SECTION – III (Mathematics)

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