VITEEE Past Year Paper With Solutions - 2021 | VITEEE: Subject Wise and Full Length MOCK Tests - JEE PDF Download

 Page 1


SOLVED PAPER
VITEEE
2021
(memory based)
GENERAL INSTRUCTIONS
• This question paper contains total 80 questions divided into four parts :
Part I : Physics Q. No - 1 to 25
Part II : Chemistry Q. No - 26 to 50
Part III : Mathematics Q. No - 51 to 75
Part IV : English & Logical reasoning Q. No - 76 to 80
• All questions are multiple choice questions with four options, only one of them is correct.
• For each correct response, the candidate will get 1 mark.
• There is no negative marking for the wrong answer.
• The test is of 1½ hours duration.
(a) r
2
 + r
2 (b)
21
12
rr
rr
-
(c)
12
21
rr
rr -
(d)
22
12
rr +
5. A charge q is moving with a velocity v parallel to
a magnetic field B. Force on the charge due to
magnetic field is
(a) q v B (b) q B/v
(c) zero (d) B v/q
6. Two spheres A and B of masses m and 2m and
radii 2R and R  respectively are placed in contact
as shown. The COM of the system lies
A
B
2R R
(a) inside A
(b) inside B
(c) at the point of contact
(d) None of these
PART - I (PHYSICS)
1. The distance of the centres of moon and earth is
D. The mass of earth is 81 times the mass of the
moon. At what distance from the centre of the
earth, the gravitational force will be zero?
(a)
2
D
(b)
2
3
D
(c)
4
3
D
(d)
9
10
D
2. T wo wires A and B are of the same material. Their
lengths are in the ratio of 1 : 2 and the diameter
are in the ratio 2 : 1. If they are pulled by the
same force, then increase in length will be in the
ratio of
(a) 2 : 1 (b) 1 : 4
(c) 1 : 8 (d) 8 : 1
3. If x = at + bt
2
, where x is the distance travelled
by the body in kilometers while t is the time in
seconds, then the unit of b is
(a) km/s (b) kms
(c) km/s
2
(d) kms
2
4. A soap bubble of radius r
1
 is placed on another
soap bubble of radius r
2
 (r
1
 < r
2
). The radius R
of the soapy film separating the two bubbles is
Page 2


SOLVED PAPER
VITEEE
2021
(memory based)
GENERAL INSTRUCTIONS
• This question paper contains total 80 questions divided into four parts :
Part I : Physics Q. No - 1 to 25
Part II : Chemistry Q. No - 26 to 50
Part III : Mathematics Q. No - 51 to 75
Part IV : English & Logical reasoning Q. No - 76 to 80
• All questions are multiple choice questions with four options, only one of them is correct.
• For each correct response, the candidate will get 1 mark.
• There is no negative marking for the wrong answer.
• The test is of 1½ hours duration.
(a) r
2
 + r
2 (b)
21
12
rr
rr
-
(c)
12
21
rr
rr -
(d)
22
12
rr +
5. A charge q is moving with a velocity v parallel to
a magnetic field B. Force on the charge due to
magnetic field is
(a) q v B (b) q B/v
(c) zero (d) B v/q
6. Two spheres A and B of masses m and 2m and
radii 2R and R  respectively are placed in contact
as shown. The COM of the system lies
A
B
2R R
(a) inside A
(b) inside B
(c) at the point of contact
(d) None of these
PART - I (PHYSICS)
1. The distance of the centres of moon and earth is
D. The mass of earth is 81 times the mass of the
moon. At what distance from the centre of the
earth, the gravitational force will be zero?
(a)
2
D
(b)
2
3
D
(c)
4
3
D
(d)
9
10
D
2. T wo wires A and B are of the same material. Their
lengths are in the ratio of 1 : 2 and the diameter
are in the ratio 2 : 1. If they are pulled by the
same force, then increase in length will be in the
ratio of
(a) 2 : 1 (b) 1 : 4
(c) 1 : 8 (d) 8 : 1
3. If x = at + bt
2
, where x is the distance travelled
by the body in kilometers while t is the time in
seconds, then the unit of b is
(a) km/s (b) kms
(c) km/s
2
(d) kms
2
4. A soap bubble of radius r
1
 is placed on another
soap bubble of radius r
2
 (r
1
 < r
2
). The radius R
of the soapy film separating the two bubbles is
7. Identify the correct statement.
(a) Static friction depends on the area of
contact
(b) Kinetic friction depends on the area of
contact
(c) Coefficient of kinetic friction is more than
the coefficient of static friction
(d) Coefficient of kinetic friction is less than
the coefficient of static friction
8. The distance travelled by a particle starting from
rest and moving with an acceleration 
2
4
ms
3
-
, in
the third second is:
(a) 6 m (b) 4 m
(c)
10
m
3
(d)
19
m
3
9. Photoelectric work function of a metal is 1eV.
Light of wavelength l = 3000 Å falls on it. The
photo electrons come out with a maximum
velocity of :
(a) 10 metres/sec (b) 10
2
 metres/sec
(c) 10
4
 metres/sec (d) 10
6
 metres/sec
10. The coefficient of apparent expansion of mercury
in a glass vessel is 153 × 10
–6
/ºC and in a steel
vessel is 144 × 10
–6
/ºC. If  a for steel is 12 × 10
–
6
/ºC , then that of glass is
(a) 9 × 10
–6
/ºC (b) 6 × 10
–6
/ºC
(c) 36 × 10
–6
/ºC (d) 27 × 10
–6
/ºC
11. A step-up transformer operates on a 230 V line
and supplies a load of 2 ampere. The ratio of
the primary and secondary windings is 1 : 25.
The current in the primary is
(a) 15 A (b) 50 A
(c) 25 A (d) 12.5 A
12. Two bodies of same mass are projected with the
same velocity at an angle 30° and 60°
respectively . The ratio of their horizontal ranges
will be
(a) 1 : 1 (b) 1 : 2
(c) 1 : 3 (d) 2 : 2
13. Two point charges +3µC and +8µC repel each
other with a force of 40N. If a charge of –5µC is
added to each of them, then the force between
them will become
(a) –10N (b) +10N
(c) +20N (d) –20N
14. A sphere rolls down on an inclined plane of
inclination q. What is the acceleration as the
sphere reaches the bottom?
(a)
5
sin
7
g q (b)
3
sin
5
g q
(c)
2
sin
7
g q (d)
2
sin
5
g q
15. A given ray of light suffers minimum deviation
in an equilateral prism P . Additional prisms Q
and R of identical shape and of same material as
that of P are now combined as shown in figure.
The ray will now suffer
Q
P R
(a) greater deviation
(b) no deviation
(c) same deviation as before
(d) total internal reflection
16. The current in the W 1 resistor shown in the
circuit is
6V
W 1
W 4
W 4
(a)
3
2
 AA (b) 3 A
(c) 6 A (d) 2 A
17. The root mean square velocity of hydrogen
molecules at 300 K is 1930 metre/sec. Then the
r.m.s velocity of oxygen molecules at 1200 K will
be
(a) 482.5 metre/sec (b) 965 metre/sec
(c) 1930 metre/sec (d) 3860 metre/sec
18. Lenz’s law gives
(a) the magnitude of the induced e.m.f.
(b) the direction of the induced current
(c) both the magnitude and direction of the
induced current
(d) the magnitude of the induced current
Page 3


SOLVED PAPER
VITEEE
2021
(memory based)
GENERAL INSTRUCTIONS
• This question paper contains total 80 questions divided into four parts :
Part I : Physics Q. No - 1 to 25
Part II : Chemistry Q. No - 26 to 50
Part III : Mathematics Q. No - 51 to 75
Part IV : English & Logical reasoning Q. No - 76 to 80
• All questions are multiple choice questions with four options, only one of them is correct.
• For each correct response, the candidate will get 1 mark.
• There is no negative marking for the wrong answer.
• The test is of 1½ hours duration.
(a) r
2
 + r
2 (b)
21
12
rr
rr
-
(c)
12
21
rr
rr -
(d)
22
12
rr +
5. A charge q is moving with a velocity v parallel to
a magnetic field B. Force on the charge due to
magnetic field is
(a) q v B (b) q B/v
(c) zero (d) B v/q
6. Two spheres A and B of masses m and 2m and
radii 2R and R  respectively are placed in contact
as shown. The COM of the system lies
A
B
2R R
(a) inside A
(b) inside B
(c) at the point of contact
(d) None of these
PART - I (PHYSICS)
1. The distance of the centres of moon and earth is
D. The mass of earth is 81 times the mass of the
moon. At what distance from the centre of the
earth, the gravitational force will be zero?
(a)
2
D
(b)
2
3
D
(c)
4
3
D
(d)
9
10
D
2. T wo wires A and B are of the same material. Their
lengths are in the ratio of 1 : 2 and the diameter
are in the ratio 2 : 1. If they are pulled by the
same force, then increase in length will be in the
ratio of
(a) 2 : 1 (b) 1 : 4
(c) 1 : 8 (d) 8 : 1
3. If x = at + bt
2
, where x is the distance travelled
by the body in kilometers while t is the time in
seconds, then the unit of b is
(a) km/s (b) kms
(c) km/s
2
(d) kms
2
4. A soap bubble of radius r
1
 is placed on another
soap bubble of radius r
2
 (r
1
 < r
2
). The radius R
of the soapy film separating the two bubbles is
7. Identify the correct statement.
(a) Static friction depends on the area of
contact
(b) Kinetic friction depends on the area of
contact
(c) Coefficient of kinetic friction is more than
the coefficient of static friction
(d) Coefficient of kinetic friction is less than
the coefficient of static friction
8. The distance travelled by a particle starting from
rest and moving with an acceleration 
2
4
ms
3
-
, in
the third second is:
(a) 6 m (b) 4 m
(c)
10
m
3
(d)
19
m
3
9. Photoelectric work function of a metal is 1eV.
Light of wavelength l = 3000 Å falls on it. The
photo electrons come out with a maximum
velocity of :
(a) 10 metres/sec (b) 10
2
 metres/sec
(c) 10
4
 metres/sec (d) 10
6
 metres/sec
10. The coefficient of apparent expansion of mercury
in a glass vessel is 153 × 10
–6
/ºC and in a steel
vessel is 144 × 10
–6
/ºC. If  a for steel is 12 × 10
–
6
/ºC , then that of glass is
(a) 9 × 10
–6
/ºC (b) 6 × 10
–6
/ºC
(c) 36 × 10
–6
/ºC (d) 27 × 10
–6
/ºC
11. A step-up transformer operates on a 230 V line
and supplies a load of 2 ampere. The ratio of
the primary and secondary windings is 1 : 25.
The current in the primary is
(a) 15 A (b) 50 A
(c) 25 A (d) 12.5 A
12. Two bodies of same mass are projected with the
same velocity at an angle 30° and 60°
respectively . The ratio of their horizontal ranges
will be
(a) 1 : 1 (b) 1 : 2
(c) 1 : 3 (d) 2 : 2
13. Two point charges +3µC and +8µC repel each
other with a force of 40N. If a charge of –5µC is
added to each of them, then the force between
them will become
(a) –10N (b) +10N
(c) +20N (d) –20N
14. A sphere rolls down on an inclined plane of
inclination q. What is the acceleration as the
sphere reaches the bottom?
(a)
5
sin
7
g q (b)
3
sin
5
g q
(c)
2
sin
7
g q (d)
2
sin
5
g q
15. A given ray of light suffers minimum deviation
in an equilateral prism P . Additional prisms Q
and R of identical shape and of same material as
that of P are now combined as shown in figure.
The ray will now suffer
Q
P R
(a) greater deviation
(b) no deviation
(c) same deviation as before
(d) total internal reflection
16. The current in the W 1 resistor shown in the
circuit is
6V
W 1
W 4
W 4
(a)
3
2
 AA (b) 3 A
(c) 6 A (d) 2 A
17. The root mean square velocity of hydrogen
molecules at 300 K is 1930 metre/sec. Then the
r.m.s velocity of oxygen molecules at 1200 K will
be
(a) 482.5 metre/sec (b) 965 metre/sec
(c) 1930 metre/sec (d) 3860 metre/sec
18. Lenz’s law gives
(a) the magnitude of the induced e.m.f.
(b) the direction of the induced current
(c) both the magnitude and direction of the
induced current
(d) the magnitude of the induced current
3
19. A parallel plate capacitor with air between the
plates has a capacitance of 8 pF. Calculate the
capacitance if the distance between the plates is
reduced by half and the space between them is
filled with a substance of dielectric constant. (k
= 6)
(a) 72 pF (b) 81 pF
(c) 84 pF (d) 96 pF
20. For a particle executing S.H.M. the displacement
x is given by x = A cos wt. Identify the graph
which represents the variation of potential
energy (P.E.) as a function of time t and
displacement x.
      
(a) I, III (b) II, IV
(c) II, III (d) I, IV
21. A radioactive sample contains 10
–3
 kg each of
two nuclear species A and B with half-life 4 days
and 8 days respectively . The ratio of the amounts
of A and B after a period of 16 days is
(a) 1 : 2 (b) 4 : 1
(c) 1 : 4 (d) 2 : 1
22. A string of 7 m length has a mass of 0.035 kg. If
tension in the string is 60.5 N, then speed of a
wave on the string is
(a) 77 m/s (b) 102 m/s
(c) 110 m/s (d) 165 m/s
23. The following circut represents
Y
B
A
(a) OR gate (b) AND gate
(c) NAND gate (d) None of these
24. A straight section PQ of a circuit lies along the
X-axis from 
2
a
x =- to 
2
a
x = and carries a
steady current i. The magnetic field due to the
section PQ at a point X = + a will be
(a) proportional to a
(b) proportional to a
2
(c) proportional to 1/a
(d) zero
25. A source producing sound of frequency 170 Hz
is approaching a stationary observer with a
velocity 17 ms
–1
. The apparent change in the
wavelength of sound heard by the observer is
(speed of sound in air = 340 ms
–1
)
(a) 0.1 m (b) 0.2 m
(c) 0.4 m (d) 0.5 m
PART - II (CHEMISTRY)
26. Consider the following reactions:
NaCl + K
2
Cr
2
O
7 
+ H
2
SO
4
 (Conc.)
® (A) + Side products
(A) + NaOH ® (B) + Side products
(B) + H
2
SO
4
 (dilute) + H
2
O
2
 
® (C) + Side products
The sum of the total number of atoms in one
molecule each of (A), (B) and (C) is __ __ ___ _.
(a) 18 (b) 1 5
(c) 21 (d) 2 0
27. Xenon hexafluoride on partial hydrolysis
produces compounds 'X' and 'Y'. Compounds
'X', 'Y' and the oxidation state of Xe are
respectively :
(a) XeOF
4
(+6) and XeO
3
(+6)
(b) XeO
2
(+4) and XeO
3
(+6)
(c) XeOF
4
(+6) and XeO
2
F
2
(+6)
(d) XeO
2
F
2
(+6) and XeO
2
(+4)
28. The edge length of unit cell of a metal having
molecular weight 75 g/mol is 5Å which
crystallizes in cubic lattice. If the density is 2g/
cc then find the radius of metal atom.
(N
A 
= 6 × 10
23
). Give the answer in pm.
(a) 217 pm (b) 210 pm
(c) 220 pm (d) 205 pm
29. Consider the following statements:
I. Increase in concentration of reactant
increases the rate of a zero order reaction.
II. Rate constant k is equal to collision
frequency A if E
a
 = 0.
III. Rate constant k is equal to collision
frequency A if E
a
 = ¥.
IV . In k vs T is a straight line.
V . In k vs 1/T is a straight line.
Correct statements are
(a) I and IV (b) II and V
(c) III and IV (d) II and III
Page 4


SOLVED PAPER
VITEEE
2021
(memory based)
GENERAL INSTRUCTIONS
• This question paper contains total 80 questions divided into four parts :
Part I : Physics Q. No - 1 to 25
Part II : Chemistry Q. No - 26 to 50
Part III : Mathematics Q. No - 51 to 75
Part IV : English & Logical reasoning Q. No - 76 to 80
• All questions are multiple choice questions with four options, only one of them is correct.
• For each correct response, the candidate will get 1 mark.
• There is no negative marking for the wrong answer.
• The test is of 1½ hours duration.
(a) r
2
 + r
2 (b)
21
12
rr
rr
-
(c)
12
21
rr
rr -
(d)
22
12
rr +
5. A charge q is moving with a velocity v parallel to
a magnetic field B. Force on the charge due to
magnetic field is
(a) q v B (b) q B/v
(c) zero (d) B v/q
6. Two spheres A and B of masses m and 2m and
radii 2R and R  respectively are placed in contact
as shown. The COM of the system lies
A
B
2R R
(a) inside A
(b) inside B
(c) at the point of contact
(d) None of these
PART - I (PHYSICS)
1. The distance of the centres of moon and earth is
D. The mass of earth is 81 times the mass of the
moon. At what distance from the centre of the
earth, the gravitational force will be zero?
(a)
2
D
(b)
2
3
D
(c)
4
3
D
(d)
9
10
D
2. T wo wires A and B are of the same material. Their
lengths are in the ratio of 1 : 2 and the diameter
are in the ratio 2 : 1. If they are pulled by the
same force, then increase in length will be in the
ratio of
(a) 2 : 1 (b) 1 : 4
(c) 1 : 8 (d) 8 : 1
3. If x = at + bt
2
, where x is the distance travelled
by the body in kilometers while t is the time in
seconds, then the unit of b is
(a) km/s (b) kms
(c) km/s
2
(d) kms
2
4. A soap bubble of radius r
1
 is placed on another
soap bubble of radius r
2
 (r
1
 < r
2
). The radius R
of the soapy film separating the two bubbles is
7. Identify the correct statement.
(a) Static friction depends on the area of
contact
(b) Kinetic friction depends on the area of
contact
(c) Coefficient of kinetic friction is more than
the coefficient of static friction
(d) Coefficient of kinetic friction is less than
the coefficient of static friction
8. The distance travelled by a particle starting from
rest and moving with an acceleration 
2
4
ms
3
-
, in
the third second is:
(a) 6 m (b) 4 m
(c)
10
m
3
(d)
19
m
3
9. Photoelectric work function of a metal is 1eV.
Light of wavelength l = 3000 Å falls on it. The
photo electrons come out with a maximum
velocity of :
(a) 10 metres/sec (b) 10
2
 metres/sec
(c) 10
4
 metres/sec (d) 10
6
 metres/sec
10. The coefficient of apparent expansion of mercury
in a glass vessel is 153 × 10
–6
/ºC and in a steel
vessel is 144 × 10
–6
/ºC. If  a for steel is 12 × 10
–
6
/ºC , then that of glass is
(a) 9 × 10
–6
/ºC (b) 6 × 10
–6
/ºC
(c) 36 × 10
–6
/ºC (d) 27 × 10
–6
/ºC
11. A step-up transformer operates on a 230 V line
and supplies a load of 2 ampere. The ratio of
the primary and secondary windings is 1 : 25.
The current in the primary is
(a) 15 A (b) 50 A
(c) 25 A (d) 12.5 A
12. Two bodies of same mass are projected with the
same velocity at an angle 30° and 60°
respectively . The ratio of their horizontal ranges
will be
(a) 1 : 1 (b) 1 : 2
(c) 1 : 3 (d) 2 : 2
13. Two point charges +3µC and +8µC repel each
other with a force of 40N. If a charge of –5µC is
added to each of them, then the force between
them will become
(a) –10N (b) +10N
(c) +20N (d) –20N
14. A sphere rolls down on an inclined plane of
inclination q. What is the acceleration as the
sphere reaches the bottom?
(a)
5
sin
7
g q (b)
3
sin
5
g q
(c)
2
sin
7
g q (d)
2
sin
5
g q
15. A given ray of light suffers minimum deviation
in an equilateral prism P . Additional prisms Q
and R of identical shape and of same material as
that of P are now combined as shown in figure.
The ray will now suffer
Q
P R
(a) greater deviation
(b) no deviation
(c) same deviation as before
(d) total internal reflection
16. The current in the W 1 resistor shown in the
circuit is
6V
W 1
W 4
W 4
(a)
3
2
 AA (b) 3 A
(c) 6 A (d) 2 A
17. The root mean square velocity of hydrogen
molecules at 300 K is 1930 metre/sec. Then the
r.m.s velocity of oxygen molecules at 1200 K will
be
(a) 482.5 metre/sec (b) 965 metre/sec
(c) 1930 metre/sec (d) 3860 metre/sec
18. Lenz’s law gives
(a) the magnitude of the induced e.m.f.
(b) the direction of the induced current
(c) both the magnitude and direction of the
induced current
(d) the magnitude of the induced current
3
19. A parallel plate capacitor with air between the
plates has a capacitance of 8 pF. Calculate the
capacitance if the distance between the plates is
reduced by half and the space between them is
filled with a substance of dielectric constant. (k
= 6)
(a) 72 pF (b) 81 pF
(c) 84 pF (d) 96 pF
20. For a particle executing S.H.M. the displacement
x is given by x = A cos wt. Identify the graph
which represents the variation of potential
energy (P.E.) as a function of time t and
displacement x.
      
(a) I, III (b) II, IV
(c) II, III (d) I, IV
21. A radioactive sample contains 10
–3
 kg each of
two nuclear species A and B with half-life 4 days
and 8 days respectively . The ratio of the amounts
of A and B after a period of 16 days is
(a) 1 : 2 (b) 4 : 1
(c) 1 : 4 (d) 2 : 1
22. A string of 7 m length has a mass of 0.035 kg. If
tension in the string is 60.5 N, then speed of a
wave on the string is
(a) 77 m/s (b) 102 m/s
(c) 110 m/s (d) 165 m/s
23. The following circut represents
Y
B
A
(a) OR gate (b) AND gate
(c) NAND gate (d) None of these
24. A straight section PQ of a circuit lies along the
X-axis from 
2
a
x =- to 
2
a
x = and carries a
steady current i. The magnetic field due to the
section PQ at a point X = + a will be
(a) proportional to a
(b) proportional to a
2
(c) proportional to 1/a
(d) zero
25. A source producing sound of frequency 170 Hz
is approaching a stationary observer with a
velocity 17 ms
–1
. The apparent change in the
wavelength of sound heard by the observer is
(speed of sound in air = 340 ms
–1
)
(a) 0.1 m (b) 0.2 m
(c) 0.4 m (d) 0.5 m
PART - II (CHEMISTRY)
26. Consider the following reactions:
NaCl + K
2
Cr
2
O
7 
+ H
2
SO
4
 (Conc.)
® (A) + Side products
(A) + NaOH ® (B) + Side products
(B) + H
2
SO
4
 (dilute) + H
2
O
2
 
® (C) + Side products
The sum of the total number of atoms in one
molecule each of (A), (B) and (C) is __ __ ___ _.
(a) 18 (b) 1 5
(c) 21 (d) 2 0
27. Xenon hexafluoride on partial hydrolysis
produces compounds 'X' and 'Y'. Compounds
'X', 'Y' and the oxidation state of Xe are
respectively :
(a) XeOF
4
(+6) and XeO
3
(+6)
(b) XeO
2
(+4) and XeO
3
(+6)
(c) XeOF
4
(+6) and XeO
2
F
2
(+6)
(d) XeO
2
F
2
(+6) and XeO
2
(+4)
28. The edge length of unit cell of a metal having
molecular weight 75 g/mol is 5Å which
crystallizes in cubic lattice. If the density is 2g/
cc then find the radius of metal atom.
(N
A 
= 6 × 10
23
). Give the answer in pm.
(a) 217 pm (b) 210 pm
(c) 220 pm (d) 205 pm
29. Consider the following statements:
I. Increase in concentration of reactant
increases the rate of a zero order reaction.
II. Rate constant k is equal to collision
frequency A if E
a
 = 0.
III. Rate constant k is equal to collision
frequency A if E
a
 = ¥.
IV . In k vs T is a straight line.
V . In k vs 1/T is a straight line.
Correct statements are
(a) I and IV (b) II and V
(c) III and IV (d) II and III
30. To deposit 0.634 g of copper by electrolysis of
aqueous cupric sulphate solution, the amount
of electricity required (in coulombs) is
(a) 1930 (b) 3960
(c) 4825 (d) 9650
31. In the following skew conformation of ethane,
H¢ – C – C – H¢¢  dihedral angle is :
(a) 58
o
(b) 149
o
(c) 151
o
(d) 120
o
32. What is the product of following reaction?
Hex-3-ynal 
4
+
3 23
(i) NaBH
(ii) PBr , (iii) Mg/ether,  (iv) CO /H O
? ¾¾¾¾¾¾¾¾¾¾¾¾¾¾ ®
(a) COOH
(b)
COOH
(c) COOH
(d)
COOH
33. In the following sequence of reactions,
2
P I Mg HCHO
32
ether
CH CH OH A B
+
¾¾¾ ® ¾¾¾ ® ¾¾¾¾ ®
2
HO
CD ¾¾¾®
the compound D is
(a) propanal (b) butanal
(c) n-butyl alcohol (d) n-propyl alcohol.
34. Which of the following reactions can produce
aniline as main product?
(a)C
6
H
5
NO
2
 + Zn/KOH
(b) C
6
H
5
NO
2
 + Zn/NH
4
Cl
(c)C
6
H
5
NO
2
 + LiAlH
4
(d) C
6
H
5
NO
2
 + Zn/HCl
35. Secondary structure of protein refers to
(a) mainly denatured proteins and structure of
prosthetic groups
(b) three -dimensional structure, especially the
bond between amino acid residues that are
distinct from each other in the polypeptide
chain
(c) linear sequence of amino acid residues in
the polypetide chain
(d) regular folding patterns of continous
portions of the polypeptide chain
36. The increasing order for the values of e/m
(charge/mass) is
(a) e, p, n, a (b) n, p, e, a
(c) n, p, a, e (d) n, a, p, e
37. In which of the following pairs both the ions are
coloured in aqueous solutions ?
(a) Sc
3+
, Ti
3+
(b) Sc
3+
, Co
2+
(c) Ni
2+
, Cu
+
(d) Ni
2+
, Ti
3+
38. The total number of possible isomers for square-
planar [Pt(Cl)(NO
2
)(NO
3
)(SCN)]
2–
 is:
(a) 16 (b) 1 2
(c)8 (d) 2 4
39. For the reaction,
2SO
2
(g) + O
2
(g) 
???
???
2 SO
3
(g),
DH = – 57.2 kJ mol
–1
 and K
c
 = 1.7×10
16
Which of the following statement is
INCORRECT ?
(a) The equilibrium constant is large
suggestive of reaction going to completion
and so no catalyst is required.
(b) The equilibrium will shift in forward
direction as the pressure increases.
(c) The equilibrium constant decreases as the
temperature increases.
(d) The addition of inert gas at constant
volume will not affect the equilibrium
constant.
40. The half-life of a reaction is inversely
proportional to the square of the initial
concentration of the reactant. Then the order of
the reaction is
(a)0 (b) 1
(c)2 (d) 3
Page 5


SOLVED PAPER
VITEEE
2021
(memory based)
GENERAL INSTRUCTIONS
• This question paper contains total 80 questions divided into four parts :
Part I : Physics Q. No - 1 to 25
Part II : Chemistry Q. No - 26 to 50
Part III : Mathematics Q. No - 51 to 75
Part IV : English & Logical reasoning Q. No - 76 to 80
• All questions are multiple choice questions with four options, only one of them is correct.
• For each correct response, the candidate will get 1 mark.
• There is no negative marking for the wrong answer.
• The test is of 1½ hours duration.
(a) r
2
 + r
2 (b)
21
12
rr
rr
-
(c)
12
21
rr
rr -
(d)
22
12
rr +
5. A charge q is moving with a velocity v parallel to
a magnetic field B. Force on the charge due to
magnetic field is
(a) q v B (b) q B/v
(c) zero (d) B v/q
6. Two spheres A and B of masses m and 2m and
radii 2R and R  respectively are placed in contact
as shown. The COM of the system lies
A
B
2R R
(a) inside A
(b) inside B
(c) at the point of contact
(d) None of these
PART - I (PHYSICS)
1. The distance of the centres of moon and earth is
D. The mass of earth is 81 times the mass of the
moon. At what distance from the centre of the
earth, the gravitational force will be zero?
(a)
2
D
(b)
2
3
D
(c)
4
3
D
(d)
9
10
D
2. T wo wires A and B are of the same material. Their
lengths are in the ratio of 1 : 2 and the diameter
are in the ratio 2 : 1. If they are pulled by the
same force, then increase in length will be in the
ratio of
(a) 2 : 1 (b) 1 : 4
(c) 1 : 8 (d) 8 : 1
3. If x = at + bt
2
, where x is the distance travelled
by the body in kilometers while t is the time in
seconds, then the unit of b is
(a) km/s (b) kms
(c) km/s
2
(d) kms
2
4. A soap bubble of radius r
1
 is placed on another
soap bubble of radius r
2
 (r
1
 < r
2
). The radius R
of the soapy film separating the two bubbles is
7. Identify the correct statement.
(a) Static friction depends on the area of
contact
(b) Kinetic friction depends on the area of
contact
(c) Coefficient of kinetic friction is more than
the coefficient of static friction
(d) Coefficient of kinetic friction is less than
the coefficient of static friction
8. The distance travelled by a particle starting from
rest and moving with an acceleration 
2
4
ms
3
-
, in
the third second is:
(a) 6 m (b) 4 m
(c)
10
m
3
(d)
19
m
3
9. Photoelectric work function of a metal is 1eV.
Light of wavelength l = 3000 Å falls on it. The
photo electrons come out with a maximum
velocity of :
(a) 10 metres/sec (b) 10
2
 metres/sec
(c) 10
4
 metres/sec (d) 10
6
 metres/sec
10. The coefficient of apparent expansion of mercury
in a glass vessel is 153 × 10
–6
/ºC and in a steel
vessel is 144 × 10
–6
/ºC. If  a for steel is 12 × 10
–
6
/ºC , then that of glass is
(a) 9 × 10
–6
/ºC (b) 6 × 10
–6
/ºC
(c) 36 × 10
–6
/ºC (d) 27 × 10
–6
/ºC
11. A step-up transformer operates on a 230 V line
and supplies a load of 2 ampere. The ratio of
the primary and secondary windings is 1 : 25.
The current in the primary is
(a) 15 A (b) 50 A
(c) 25 A (d) 12.5 A
12. Two bodies of same mass are projected with the
same velocity at an angle 30° and 60°
respectively . The ratio of their horizontal ranges
will be
(a) 1 : 1 (b) 1 : 2
(c) 1 : 3 (d) 2 : 2
13. Two point charges +3µC and +8µC repel each
other with a force of 40N. If a charge of –5µC is
added to each of them, then the force between
them will become
(a) –10N (b) +10N
(c) +20N (d) –20N
14. A sphere rolls down on an inclined plane of
inclination q. What is the acceleration as the
sphere reaches the bottom?
(a)
5
sin
7
g q (b)
3
sin
5
g q
(c)
2
sin
7
g q (d)
2
sin
5
g q
15. A given ray of light suffers minimum deviation
in an equilateral prism P . Additional prisms Q
and R of identical shape and of same material as
that of P are now combined as shown in figure.
The ray will now suffer
Q
P R
(a) greater deviation
(b) no deviation
(c) same deviation as before
(d) total internal reflection
16. The current in the W 1 resistor shown in the
circuit is
6V
W 1
W 4
W 4
(a)
3
2
 AA (b) 3 A
(c) 6 A (d) 2 A
17. The root mean square velocity of hydrogen
molecules at 300 K is 1930 metre/sec. Then the
r.m.s velocity of oxygen molecules at 1200 K will
be
(a) 482.5 metre/sec (b) 965 metre/sec
(c) 1930 metre/sec (d) 3860 metre/sec
18. Lenz’s law gives
(a) the magnitude of the induced e.m.f.
(b) the direction of the induced current
(c) both the magnitude and direction of the
induced current
(d) the magnitude of the induced current
3
19. A parallel plate capacitor with air between the
plates has a capacitance of 8 pF. Calculate the
capacitance if the distance between the plates is
reduced by half and the space between them is
filled with a substance of dielectric constant. (k
= 6)
(a) 72 pF (b) 81 pF
(c) 84 pF (d) 96 pF
20. For a particle executing S.H.M. the displacement
x is given by x = A cos wt. Identify the graph
which represents the variation of potential
energy (P.E.) as a function of time t and
displacement x.
      
(a) I, III (b) II, IV
(c) II, III (d) I, IV
21. A radioactive sample contains 10
–3
 kg each of
two nuclear species A and B with half-life 4 days
and 8 days respectively . The ratio of the amounts
of A and B after a period of 16 days is
(a) 1 : 2 (b) 4 : 1
(c) 1 : 4 (d) 2 : 1
22. A string of 7 m length has a mass of 0.035 kg. If
tension in the string is 60.5 N, then speed of a
wave on the string is
(a) 77 m/s (b) 102 m/s
(c) 110 m/s (d) 165 m/s
23. The following circut represents
Y
B
A
(a) OR gate (b) AND gate
(c) NAND gate (d) None of these
24. A straight section PQ of a circuit lies along the
X-axis from 
2
a
x =- to 
2
a
x = and carries a
steady current i. The magnetic field due to the
section PQ at a point X = + a will be
(a) proportional to a
(b) proportional to a
2
(c) proportional to 1/a
(d) zero
25. A source producing sound of frequency 170 Hz
is approaching a stationary observer with a
velocity 17 ms
–1
. The apparent change in the
wavelength of sound heard by the observer is
(speed of sound in air = 340 ms
–1
)
(a) 0.1 m (b) 0.2 m
(c) 0.4 m (d) 0.5 m
PART - II (CHEMISTRY)
26. Consider the following reactions:
NaCl + K
2
Cr
2
O
7 
+ H
2
SO
4
 (Conc.)
® (A) + Side products
(A) + NaOH ® (B) + Side products
(B) + H
2
SO
4
 (dilute) + H
2
O
2
 
® (C) + Side products
The sum of the total number of atoms in one
molecule each of (A), (B) and (C) is __ __ ___ _.
(a) 18 (b) 1 5
(c) 21 (d) 2 0
27. Xenon hexafluoride on partial hydrolysis
produces compounds 'X' and 'Y'. Compounds
'X', 'Y' and the oxidation state of Xe are
respectively :
(a) XeOF
4
(+6) and XeO
3
(+6)
(b) XeO
2
(+4) and XeO
3
(+6)
(c) XeOF
4
(+6) and XeO
2
F
2
(+6)
(d) XeO
2
F
2
(+6) and XeO
2
(+4)
28. The edge length of unit cell of a metal having
molecular weight 75 g/mol is 5Å which
crystallizes in cubic lattice. If the density is 2g/
cc then find the radius of metal atom.
(N
A 
= 6 × 10
23
). Give the answer in pm.
(a) 217 pm (b) 210 pm
(c) 220 pm (d) 205 pm
29. Consider the following statements:
I. Increase in concentration of reactant
increases the rate of a zero order reaction.
II. Rate constant k is equal to collision
frequency A if E
a
 = 0.
III. Rate constant k is equal to collision
frequency A if E
a
 = ¥.
IV . In k vs T is a straight line.
V . In k vs 1/T is a straight line.
Correct statements are
(a) I and IV (b) II and V
(c) III and IV (d) II and III
30. To deposit 0.634 g of copper by electrolysis of
aqueous cupric sulphate solution, the amount
of electricity required (in coulombs) is
(a) 1930 (b) 3960
(c) 4825 (d) 9650
31. In the following skew conformation of ethane,
H¢ – C – C – H¢¢  dihedral angle is :
(a) 58
o
(b) 149
o
(c) 151
o
(d) 120
o
32. What is the product of following reaction?
Hex-3-ynal 
4
+
3 23
(i) NaBH
(ii) PBr , (iii) Mg/ether,  (iv) CO /H O
? ¾¾¾¾¾¾¾¾¾¾¾¾¾¾ ®
(a) COOH
(b)
COOH
(c) COOH
(d)
COOH
33. In the following sequence of reactions,
2
P I Mg HCHO
32
ether
CH CH OH A B
+
¾¾¾ ® ¾¾¾ ® ¾¾¾¾ ®
2
HO
CD ¾¾¾®
the compound D is
(a) propanal (b) butanal
(c) n-butyl alcohol (d) n-propyl alcohol.
34. Which of the following reactions can produce
aniline as main product?
(a)C
6
H
5
NO
2
 + Zn/KOH
(b) C
6
H
5
NO
2
 + Zn/NH
4
Cl
(c)C
6
H
5
NO
2
 + LiAlH
4
(d) C
6
H
5
NO
2
 + Zn/HCl
35. Secondary structure of protein refers to
(a) mainly denatured proteins and structure of
prosthetic groups
(b) three -dimensional structure, especially the
bond between amino acid residues that are
distinct from each other in the polypeptide
chain
(c) linear sequence of amino acid residues in
the polypetide chain
(d) regular folding patterns of continous
portions of the polypeptide chain
36. The increasing order for the values of e/m
(charge/mass) is
(a) e, p, n, a (b) n, p, e, a
(c) n, p, a, e (d) n, a, p, e
37. In which of the following pairs both the ions are
coloured in aqueous solutions ?
(a) Sc
3+
, Ti
3+
(b) Sc
3+
, Co
2+
(c) Ni
2+
, Cu
+
(d) Ni
2+
, Ti
3+
38. The total number of possible isomers for square-
planar [Pt(Cl)(NO
2
)(NO
3
)(SCN)]
2–
 is:
(a) 16 (b) 1 2
(c)8 (d) 2 4
39. For the reaction,
2SO
2
(g) + O
2
(g) 
???
???
2 SO
3
(g),
DH = – 57.2 kJ mol
–1
 and K
c
 = 1.7×10
16
Which of the following statement is
INCORRECT ?
(a) The equilibrium constant is large
suggestive of reaction going to completion
and so no catalyst is required.
(b) The equilibrium will shift in forward
direction as the pressure increases.
(c) The equilibrium constant decreases as the
temperature increases.
(d) The addition of inert gas at constant
volume will not affect the equilibrium
constant.
40. The half-life of a reaction is inversely
proportional to the square of the initial
concentration of the reactant. Then the order of
the reaction is
(a)0 (b) 1
(c)2 (d) 3
5
41. A galvanic cell is set up from electrodes A and B
Electrode A : 
+ - 3 2
7 2
Cr / O Cr , 
red
o
E = + 1.33 V
Electrode B : 
+ + 2 3
Fe / Fe ,
red
o
E = 0.77 V
Which of the following statements is false ?
(a) Standard e.m.f of the cell is 0.56 V
(b) Current will flow from electrode A to B in
the external circuit
(c) A will act as cathode and have positive
polarity
(d) None of these
42. Keto-enol tautomerism is observed in :
(a) H C – C – CH – C – C H
5 6 2 65
|| ||
O O
(b) H C – C – CH
563
||
O
(c) H C – C – H
56
||
O
(d) Both (a) and (b)
43. In a set of reactions, ethylbenzene yield a product
D.
CH
23
CH
4
KMnO
KOH
¾¾¾¾®
2
3
Br
FeCl
B ¾¾ ¾®
25
C H OH
H
CD
+
¾¾ ¾ ¾®
Identify D :
(a)
CH
2 25
– CH – COOC H
Br
(b)
CH
2 25
COOC H
Br
Br
(c)
OCH CH
23
COOH
(d)
Br
COOC H
25
44. What will be the final product in the following
reaction sequence –
CH
3
CH
2
CN  
NH H /HO NaOBr
3 2
A BC
+
D
¾¾¾¾® ¾¾¾ ® ¾¾¾¾ ®
(a) CH
3
CH
2
CONH
2
(b) CH
3
CH
2
COBr
(c) CH
3
CH
2
NH
2
(d) CH
3
CH
2
CH
2
NH
2
45. In a set of reactions acetic acid yielded a product
D.
SOCl Benzene
2
3
AlCl
3
CH COOH (A) (B) ¾¾¾¾ ® ¾¾¾¾ ®
HCN HOH
(C) (D) ¾¾¾ ® ¾¾¾ ®
The structure of (D) would be –
(a)
CH – C – CH
23
COOH
OH
(b) 
C – CH
3
CN
OH
(c)
CH – C – CH
23
OH
CN
(d)   
C – COOH
OH
CH
3
46. In fructose, the possible optical isomers are
(a) 12 (b) 8
(c) 16 (d) 4
47. The position of both, an electron and a helium
atom is known within 1.0 nm. Further the
momentum of the electron is known within 5.0
× 10
–26
 kg ms
–1
. The minimum uncertainty in
the measurement of the momentum of the
helium atom is
(a) 50 kg ms
–1
(b) 80 kg ms
–1
(c) 8.0 × 10
–26
 kg ms
–1
(d) 5.0 × 10
–26
 k g ms
–1