IISER AT 2024 Question Paper
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Page 1
Entrance Exam
2024
QUESTION
PAPER
2024
QUESTION
PAPER
Page 2
Biology
1. Question 1
What will be the sequence of RNA synthesized using the following DNA
template strand?
5Õ -GTCTAGGCTTCTC-3Õ
5Õ -GAGAAGCCUAGAC-3Õ
(a)
5Õ -GUCUAGGCUUCUC-3Õ
(b)
5Õ -CAGAUCCGAAGAG-3Õ
(c)
5Õ -CUCUUCGGAUCUG-3Õ
(d)
1
1. Question 1
What will be the sequence of RNA synthesized using the following DNA
template strand?
5Õ -GTCTAGGCTTCTC-3Õ
5Õ -GAGAAGCCUAGAC-3Õ
(a)
5Õ -GUCUAGGCUUCUC-3Õ
(b)
5Õ -CAGAUCCGAAGAG-3Õ
(c)
5Õ -CUCUUCGGAUCUG-3Õ
(d)
1
Page 3
2. Question 2
The following pedigree diagram shows the inheritance of a rare genetic
disorder (filled shapes depict affected individuals).
Which of the following is the most likely pattern of inheritance of the
disorder?
X-linked dominant
(a)
X-linked recessive
(b)
Autosomal recessive
(c)
Autosomal dominant
(d)
2
The following pedigree diagram shows the inheritance of a rare genetic
disorder (filled shapes depict affected individuals).
Which of the following is the most likely pattern of inheritance of the
disorder?
X-linked dominant
(a)
X-linked recessive
(b)
Autosomal recessive
(c)
Autosomal dominant
(d)
2
Page 4
3. Question 3
Match the list of conditions (Column I) with the list of affected physiological
processes (Column II).
Which of the following combinations is correct?
P - (ii); Q - (iv); R - (iii); S - (i)
(a)
P - (iii); Q - (iv); R - (i); S - (ii)
(b)
P - (iv); Q - (iii); R - (i); S - (ii)
(c)
P - (ii); Q - (i); R - (iv); S - (iii)
(d)
3
Match the list of conditions (Column I) with the list of affected physiological
processes (Column II).
Which of the following combinations is correct?
P - (ii); Q - (iv); R - (iii); S - (i)
(a)
P - (iii); Q - (iv); R - (i); S - (ii)
(b)
P - (iv); Q - (iii); R - (i); S - (ii)
(c)
P - (ii); Q - (i); R - (iv); S - (iii)
(d)
3
Page 5
4. Question 4
Which of the following proteins plays a direct role in muscle contraction?
Troponin
(a)
Insulin
(b)
Myoglobin
(c)
Trypsin
(d)
4
Which of the following proteins plays a direct role in muscle contraction?
Troponin
(a)
Insulin
(b)
Myoglobin
(c)
Trypsin
(d)
4
Page 6
5. Question 5
Which of the following is NOT derived from the epidermal cell layer in
plants?
Casparian strip from rice root
(a)
Trichomes from maize leaf
(b)
Subsidiary cells from rice leaf
(c)
Bulliform cells from grass
(d)
5
Which of the following is NOT derived from the epidermal cell layer in
plants?
Casparian strip from rice root
(a)
Trichomes from maize leaf
(b)
Subsidiary cells from rice leaf
(c)
Bulliform cells from grass
(d)
5
Page 7
6. Question 6
Which of the following statements about meiosis in sexually reproducing
plants is INCORRECT?
The end products of meiosis II are haploid gametes.
(a)
The four products of meiosis are genetically different.
(b)
Meiotic recombination takes place in both males and females.
(c)
In most flowering plants, only one of the four products of meiosis survives
in females.
(d)
6
Which of the following statements about meiosis in sexually reproducing
plants is INCORRECT?
The end products of meiosis II are haploid gametes.
(a)
The four products of meiosis are genetically different.
(b)
Meiotic recombination takes place in both males and females.
(c)
In most flowering plants, only one of the four products of meiosis survives
in females.
(d)
6
Page 8
7. Question 7
Which of the following graphs represents the correct relationship between
light intensity (X-axis) and the rate of photosynthesis (Y-axis)?
(a)
(b)
(c)
7
Which of the following graphs represents the correct relationship between
light intensity (X-axis) and the rate of photosynthesis (Y-axis)?
(a)
(b)
(c)
7
Page 9
(d)
8
8
Page 10
8. Question 8
Match the enzymes in Column I with the cellular compartments in Column
II.
Which of the following combinations is correct?
P - (ii); Q - (iii); R - (i); S - (iv)
(a)
P - (iv); Q - (i); R - (iii); S - (ii)
(b)
P - (iii); Q - (ii); R - (i); S - (v)
(c)
P - (iii); Q - (i); R - (iv); S - (ii)
(d)
9
Match the enzymes in Column I with the cellular compartments in Column
II.
Which of the following combinations is correct?
P - (ii); Q - (iii); R - (i); S - (iv)
(a)
P - (iv); Q - (i); R - (iii); S - (ii)
(b)
P - (iii); Q - (ii); R - (i); S - (v)
(c)
P - (iii); Q - (i); R - (iv); S - (ii)
(d)
9
Page 11
9. Question 9
Two species of a flowering plant, P (2n = 20 chromosomes) and Q (2n = 30
chromosomes) are reciprocally crossed with each other as male or female as
shown below to produce F1 seeds.
Which of the following seed tissues from both the F1 seeds (R and S) will
have the same chromosome numbers?
Embryo
(a)
Endosperm
(b)
Embryo and seed coat
(c)
Embryo and endosperm
(d)
10
Two species of a flowering plant, P (2n = 20 chromosomes) and Q (2n = 30
chromosomes) are reciprocally crossed with each other as male or female as
shown below to produce F1 seeds.
Which of the following seed tissues from both the F1 seeds (R and S) will
have the same chromosome numbers?
Embryo
(a)
Endosperm
(b)
Embryo and seed coat
(c)
Embryo and endosperm
(d)
10
Page 12
10. Question 10
Which of the following is routinely performed to detect typhoid?
Widal test
(a)
ELISA
(b)
Gel electrophoresis
(c)
RT-PCR
(d)
11
Which of the following is routinely performed to detect typhoid?
Widal test
(a)
ELISA
(b)
Gel electrophoresis
(c)
RT-PCR
(d)
11
Page 13
11. Question 11
Which of the following plasmid vectors can be used for cloning of a gene, with
restriction enzymes BamHI and EcoRI, and ampicillin-containing nutrient
agar for selection?
[Ori and AmpR represent origin of replication and gene for ampicillin
resistance, respectively.]
(a)
(b)
12
Which of the following plasmid vectors can be used for cloning of a gene, with
restriction enzymes BamHI and EcoRI, and ampicillin-containing nutrient
agar for selection?
[Ori and AmpR represent origin of replication and gene for ampicillin
resistance, respectively.]
(a)
(b)
12
Page 14
(c)
(d)
13
(d)
13
Page 15
12. Question 12
Polymerase chain reaction (PCR) is used to amplify a gene of interest
(GOI). If, after 30 cycles of PCR, 1 billion copies of GOI are produced,
approximately how many copies of GOI were present at the end of the 20th
cycle?
1 million
(a)
0.66 billion
(b)
10 million
(c)
0.1 billion
(d)
14
Polymerase chain reaction (PCR) is used to amplify a gene of interest
(GOI). If, after 30 cycles of PCR, 1 billion copies of GOI are produced,
approximately how many copies of GOI were present at the end of the 20th
cycle?
1 million
(a)
0.66 billion
(b)
10 million
(c)
0.1 billion
(d)
14
Page 16
13. Question 13
A population with N = 400 individuals increases in numbers till it reaches an
asymptote at K = 500 individuals, K being the carrying capacity. Assuming
the intrinsic rate of natural increase (r) to be 0.01, what would be the
population growth rate (dN/dt)?
0.8
(a)
0.05
(b)
1
(c)
0.4
(d)
15
A population with N = 400 individuals increases in numbers till it reaches an
asymptote at K = 500 individuals, K being the carrying capacity. Assuming
the intrinsic rate of natural increase (r) to be 0.01, what would be the
population growth rate (dN/dt)?
0.8
(a)
0.05
(b)
1
(c)
0.4
(d)
15
Page 17
14. Question 14
Which one of the following statements is correct?
Hemichordata is not considered as a chordate sub-phylum, and possesses a
proto-notochord called stomochord.
(a)
Hemichordata is a sub-phylum under Chordata and possesses a
proto-notochord called stomochord.
(b)
Hemichordata is a sub-phylum under Chordata and possesses a proper
notochord and gill slits like chordates.
(c)
Hemichordata is not considered as a chordate sub-phylum because it
possesses a water vascular system.
(d)
16
Which one of the following statements is correct?
Hemichordata is not considered as a chordate sub-phylum, and possesses a
proto-notochord called stomochord.
(a)
Hemichordata is a sub-phylum under Chordata and possesses a
proto-notochord called stomochord.
(b)
Hemichordata is a sub-phylum under Chordata and possesses a proper
notochord and gill slits like chordates.
(c)
Hemichordata is not considered as a chordate sub-phylum because it
possesses a water vascular system.
(d)
16
Page 18
15. Question 15
Which of the following statements is correct about the oxygen (O2 )
dissociation curves (A and C) relative to curve B?
Curve A represents favourable O2 association with haemoglobin at low [H+ ].
(a)
Curve C represents favourable O2 association with haemoglobin at low
pCO2 .
(b)
Curve A represents favourable O2 association with haemoglobin at low pH.
(c)
Curve C represents favourable O2 association with haemoglobin at high
pO2 .
(d)
17
Which of the following statements is correct about the oxygen (O2 )
dissociation curves (A and C) relative to curve B?
Curve A represents favourable O2 association with haemoglobin at low [H+ ].
(a)
Curve C represents favourable O2 association with haemoglobin at low
pCO2 .
(b)
Curve A represents favourable O2 association with haemoglobin at low pH.
(c)
Curve C represents favourable O2 association with haemoglobin at high
pO2 .
(d)
17
Page 19
Chemistry
1. Question 1
If an element with Z = 120 is discovered, then which group of elements will
it belong to?
Alkaline earth metals
(a)
Alkali metals
(b)
Halogens
(c)
Noble gases
(d)
1
1. Question 1
If an element with Z = 120 is discovered, then which group of elements will
it belong to?
Alkaline earth metals
(a)
Alkali metals
(b)
Halogens
(c)
Noble gases
(d)
1
Page 20
2. Question 2
Which one of the following statements is correct about N2 , CO, and NO+ ?
These are isoelectronic and have identical bond order.
(a)
These are isoelectronic and have different bond orders.
(b)
These are not isoelectronic but have identical bond order.
(c)
These are neither isoelectronic nor have identical bond order.
(d)
2
Which one of the following statements is correct about N2 , CO, and NO+ ?
These are isoelectronic and have identical bond order.
(a)
These are isoelectronic and have different bond orders.
(b)
These are not isoelectronic but have identical bond order.
(c)
These are neither isoelectronic nor have identical bond order.
(d)
2
Page 21
3. Question 3
Which of the following complexes exhibit(s) magnetic moment close to 2
Bohr Magneton?
[Fe(H2 O)6 ](NO3 )2 , K2 [MnCl4 ], K4 [Mn(CN)6 ], and [Ni(CO)4 ]
Only K4 [Mn(CN)6 ]
(a)
K2 [MnCl4 ] and K4 [Mn(CN)6 ]
(b)
[Fe(H2 O)6 ](NO3 )2 and K2 [MnCl4 ]
(c)
K4 [Mn(CN)6 ] and [Ni(CO)4 ]
(d)
3
Which of the following complexes exhibit(s) magnetic moment close to 2
Bohr Magneton?
[Fe(H2 O)6 ](NO3 )2 , K2 [MnCl4 ], K4 [Mn(CN)6 ], and [Ni(CO)4 ]
Only K4 [Mn(CN)6 ]
(a)
K2 [MnCl4 ] and K4 [Mn(CN)6 ]
(b)
[Fe(H2 O)6 ](NO3 )2 and K2 [MnCl4 ]
(c)
K4 [Mn(CN)6 ] and [Ni(CO)4 ]
(d)
3
Page 22
4. Question 4
According to the VSEPR theory, what are the most stable shapes of XeF4
and SF4 , respectively?
Square planar and see-saw
(a)
Both see-saw
(b)
See-saw and square planar
(c)
Both square planar
(d)
4
According to the VSEPR theory, what are the most stable shapes of XeF4
and SF4 , respectively?
Square planar and see-saw
(a)
Both see-saw
(b)
See-saw and square planar
(c)
Both square planar
(d)
4
Page 23
5. Question 5
The following complex ions absorb in the ultraviolet-visible region of light.
Which one of these shows violet colour?
[CoCl(NH3 )5 ]2+ , [Co(H2 O)(NH3 )5 ]3+ , [Co(NH3 )6 ]3+ , and [Co(CN)6 ]3≠
[CoCl(NH3 )5 ]2+
(a)
[Co(H2 O)(NH3 )5 ]3+
(b)
[Co(NH3 )6 ]3+
(c)
[Co(CN)6 ]3≠
(d)
5
The following complex ions absorb in the ultraviolet-visible region of light.
Which one of these shows violet colour?
[CoCl(NH3 )5 ]2+ , [Co(H2 O)(NH3 )5 ]3+ , [Co(NH3 )6 ]3+ , and [Co(CN)6 ]3≠
[CoCl(NH3 )5 ]2+
(a)
[Co(H2 O)(NH3 )5 ]3+
(b)
[Co(NH3 )6 ]3+
(c)
[Co(CN)6 ]3≠
(d)
5
Page 24
6. Question 6
What is the relationship between the structures depicted below?
Conformational isomers
(a)
Structural isomers
(b)
Enantiomers
(c)
Positional isomers
(d)
6
What is the relationship between the structures depicted below?
Conformational isomers
(a)
Structural isomers
(b)
Enantiomers
(c)
Positional isomers
(d)
6
Page 25
7. Question 7
What is the correct order of acidity for the following compounds?
P>N>Q>M
(a)
P>Q>N>M
(b)
N>P>M>Q
(c)
N>P>Q>M
(d)
7
What is the correct order of acidity for the following compounds?
P>N>Q>M
(a)
P>Q>N>M
(b)
N>P>M>Q
(c)
N>P>Q>M
(d)
7
Page 26
8. Question 8
What are the products N and Q in the following reaction sequences?
(a)
(b)
(c)
(d)
8
What are the products N and Q in the following reaction sequences?
(a)
(b)
(c)
(d)
8
Page 27
9. Question 9
What are X and Z in the following sequence of reactions?
(a)
(b)
(c)
(d)
9
What are X and Z in the following sequence of reactions?
(a)
(b)
(c)
(d)
9
Page 28
10. Question 10
What are the correct structural descriptions for M and N?
M is –-D-(+)-glucopyranose and N is —-D-(≠)-fructofuranose
(a)
M is —-D-(+)-glucopyranose and N is —-D-(≠)-fructofuranose
(b)
M is –-D-(+)-glucopyranose and N is –-D-(≠)-fructofuranose
(c)
M is –-D-(+)-glucofuranose and N is —-D-(≠)-fructopyranose
(d)
10
What are the correct structural descriptions for M and N?
M is –-D-(+)-glucopyranose and N is —-D-(≠)-fructofuranose
(a)
M is —-D-(+)-glucopyranose and N is —-D-(≠)-fructofuranose
(b)
M is –-D-(+)-glucopyranose and N is –-D-(≠)-fructofuranose
(c)
M is –-D-(+)-glucofuranose and N is —-D-(≠)-fructopyranose
(d)
10
Page 29
11. Question 11
Consider an exothermic reaction:
2A(s) ≠æ B(s) + C(g) + D(g)
The correct statement about the reaction is
spontaneous at all temperatures.
(a)
spontaneous only at very high temperatures.
(b)
spontaneous only at very low temperatures.
(c)
non-spontaneous at all temperatures.
(d)
11
Consider an exothermic reaction:
2A(s) ≠æ B(s) + C(g) + D(g)
The correct statement about the reaction is
spontaneous at all temperatures.
(a)
spontaneous only at very high temperatures.
(b)
spontaneous only at very low temperatures.
(c)
non-spontaneous at all temperatures.
(d)
11
Page 30
12. Question 12
The minimum energy needed to remove an electron from a metal
corresponds to a wavelength of 500 nm. What is the total kinetic energy
of all the photoelectrons ejected per second when the entire radiation from
a 100 Watt bulb with a wavelength of 300 nm falls on the surface of the
metal?
Planck’s constant = 6.6 ◊ 10≠34 J s; speed of light = 3 ◊ 108 m s≠1
40 J
(a)
2.6 ◊ 10≠19 J
(b)
1.6 ◊ 10≠19 J
(c)
80 J
(d)
12
The minimum energy needed to remove an electron from a metal
corresponds to a wavelength of 500 nm. What is the total kinetic energy
of all the photoelectrons ejected per second when the entire radiation from
a 100 Watt bulb with a wavelength of 300 nm falls on the surface of the
metal?
Planck’s constant = 6.6 ◊ 10≠34 J s; speed of light = 3 ◊ 108 m s≠1
40 J
(a)
2.6 ◊ 10≠19 J
(b)
1.6 ◊ 10≠19 J
(c)
80 J
(d)
12
Page 31
13. Question 13
For a reaction R ≠æ P with a rate constant of 3 ◊ 10≠3 mol L≠1 s≠1 , which
one of the following plots is correct?
(Given [R]0 is the initial concentration of R and [R] is the concentration of
R at time t)
(a)
(b)
13
For a reaction R ≠æ P with a rate constant of 3 ◊ 10≠3 mol L≠1 s≠1 , which
one of the following plots is correct?
(Given [R]0 is the initial concentration of R and [R] is the concentration of
R at time t)
(a)
(b)
13
Page 32
(c)
(d)
14
(d)
14
Page 33
14. Question 14
Which one of the following plots correctly describes the variation of osmotic
pressure ( ) of a fixed amount of a solute against the volume (V) of the
solution at a fixed temperature?
(a)
(b)
(c)
(d)
15
Which one of the following plots correctly describes the variation of osmotic
pressure ( ) of a fixed amount of a solute against the volume (V) of the
solution at a fixed temperature?
(a)
(b)
(c)
(d)
15
Page 34
15. Question 15
Consider the following data for KCl solution at a particular temperature:
What is the value of the limiting molar conductivity?
150.1 S cm2 mol≠1
(a)
149.2 S cm2 mol≠1
(b)
151.1 S cm2 mol≠1
(c)
152.1 S cm2 mol≠1
(d)
16
Consider the following data for KCl solution at a particular temperature:
What is the value of the limiting molar conductivity?
150.1 S cm2 mol≠1
(a)
149.2 S cm2 mol≠1
(b)
151.1 S cm2 mol≠1
(c)
152.1 S cm2 mol≠1
(d)
16
Page 35
Mathematics
1. Question 1
Consider the following lines in the XY -plane:
L1 : 5x ≠ 2y = 1,
L2 : the line passing through (0, 1) and (100, 101),
L3 : the line passing through (1, 11) and parallel to the vector ≠ ‚i + 2‚
j.
Let A = (L1 fl L2 ) fi (L2 fl L3 ) fi (L3 fl L1 ). What is the total number of
elements of A ?
3
(a)
0
(b)
1
(c)
2
(d)
1
1. Question 1
Consider the following lines in the XY -plane:
L1 : 5x ≠ 2y = 1,
L2 : the line passing through (0, 1) and (100, 101),
L3 : the line passing through (1, 11) and parallel to the vector ≠ ‚i + 2‚
j.
Let A = (L1 fl L2 ) fi (L2 fl L3 ) fi (L3 fl L1 ). What is the total number of
elements of A ?
3
(a)
0
(b)
1
(c)
2
(d)
1
Page 36
2. Question 2
Let A be the set of points in the XY -plane which are equidistant from
P (≠1, 0) and Q(1, 0). Let B be the set of points in the XY -plane which are
equidistant from A and Q. If (5, y) is a point in B, then what is the value
of y 2 ?
9
(a)
1
(b)
4
(c)
16
(d)
2
Let A be the set of points in the XY -plane which are equidistant from
P (≠1, 0) and Q(1, 0). Let B be the set of points in the XY -plane which are
equidistant from A and Q. If (5, y) is a point in B, then what is the value
of y 2 ?
9
(a)
1
(b)
4
(c)
16
(d)
2
Page 37
3. Question 3
Consider the lines L1 and L2 given below:
L1 : x = 2 + ⁄, y = 3 + 2⁄, z = 4 + 3⁄;
L2 : x = 4 + ⁄, y = 4, z = 4 + ⁄.
If (2, 3, 4) is the point of L1 that is closest to L2 , then which point of L2 is
closest to L1 ?
(3, 4, 3)
(a)
(3, 4, 4)
(b)
(5, 4, 5)
(c)
(4, 4, 4)
(d)
3
Consider the lines L1 and L2 given below:
L1 : x = 2 + ⁄, y = 3 + 2⁄, z = 4 + 3⁄;
L2 : x = 4 + ⁄, y = 4, z = 4 + ⁄.
If (2, 3, 4) is the point of L1 that is closest to L2 , then which point of L2 is
closest to L1 ?
(3, 4, 3)
(a)
(3, 4, 4)
(b)
(5, 4, 5)
(c)
(4, 4, 4)
(d)
3
Page 38
4. Question 4
Let a1 , a2 , a3 , . . . be a sequence of real numbers. Let sn = a1 + a2 + · · · + an .
If 2sn = n(c + an ) for some real number c and for all n = 1, 2, 3, . . ., then
which one of the following statements is Correct?
a1 , a2 , a3 , . . . is an Arithmetic Progression.
(a)
a1 , 2a2 , 3a3 , . . . is an Arithmetic Progression.
(b)
a1 , a2 , a3 , . . . is a Geometric Progression.
(c)
a1 , 2a2 , 3a3 , . . . is a Geometric Progression.
(d)
4
Let a1 , a2 , a3 , . . . be a sequence of real numbers. Let sn = a1 + a2 + · · · + an .
If 2sn = n(c + an ) for some real number c and for all n = 1, 2, 3, . . ., then
which one of the following statements is Correct?
a1 , a2 , a3 , . . . is an Arithmetic Progression.
(a)
a1 , 2a2 , 3a3 , . . . is an Arithmetic Progression.
(b)
a1 , a2 , a3 , . . . is a Geometric Progression.
(c)
a1 , 2a2 , 3a3 , . . . is a Geometric Progression.
(d)
4
Page 39
5. Question 5
Let f : R æ R be a strictly decreasing function with |f (t)| < fi/2 for all
t œ R. Let g : [0, fi] æ R be a function defined by g(t) = sin(f (t)). Which
one of the following statements is Correct ?
g is decreasing on [0, fi].
(a)
g is increasing on [0, fi].
(b)
g is increasing on (0, fi/2) and decreasing on (fi/2, fi).
(c)
g is decreasing on (0, fi/2) and increasing on (fi/2, fi).
(d)
5
Let f : R æ R be a strictly decreasing function with |f (t)| < fi/2 for all
t œ R. Let g : [0, fi] æ R be a function defined by g(t) = sin(f (t)). Which
one of the following statements is Correct ?
g is decreasing on [0, fi].
(a)
g is increasing on [0, fi].
(b)
g is increasing on (0, fi/2) and decreasing on (fi/2, fi).
(c)
g is decreasing on (0, fi/2) and increasing on (fi/2, fi).
(d)
5
Page 40
6. Question 6
Let f, g : R æ R be functions. If g is continuous, then which one of the
following cases implies that f is continuous ?
g(x) = (f (x))3
(a)
g(x) = |f (x)|
(b)
g(x) = (f (x))2
(c)
g(x) = sin(f (x))
(d)
6
Let f, g : R æ R be functions. If g is continuous, then which one of the
following cases implies that f is continuous ?
g(x) = (f (x))3
(a)
g(x) = |f (x)|
(b)
g(x) = (f (x))2
(c)
g(x) = sin(f (x))
(d)
6
Page 41
7. Question 7
What is the largest area of a rectangle, whose sides are parallel to the
coordinate axes, that can be inscribed under the graph of the curve
y = 1 ≠ x2
and above the X-axis ?
4
Ô
3 3
(a)
2
Ô
3 3
(b)
4
3
(c)
1
3
(d)
7
What is the largest area of a rectangle, whose sides are parallel to the
coordinate axes, that can be inscribed under the graph of the curve
y = 1 ≠ x2
and above the X-axis ?
4
Ô
3 3
(a)
2
Ô
3 3
(b)
4
3
(c)
1
3
(d)
7
Page 42
8. Question 8
Let M be the set of all 3◊3 matrices with real entries. Consider the relation
R on M given by R = {(A, B) œ M ◊ M : det(A ≠ B) is an integer}. Which
one of the following statements is Correct ?
R is reflexive and symmetric, but not transitive.
(a)
R is reflexive, but neither symmetric nor transitive.
(b)
R is an equivalence relation.
(c)
R is symmetric and transitive, but not reflexive.
(d)
8
Let M be the set of all 3◊3 matrices with real entries. Consider the relation
R on M given by R = {(A, B) œ M ◊ M : det(A ≠ B) is an integer}. Which
one of the following statements is Correct ?
R is reflexive and symmetric, but not transitive.
(a)
R is reflexive, but neither symmetric nor transitive.
(b)
R is an equivalence relation.
(c)
R is symmetric and transitive, but not reflexive.
(d)
8
Page 43
9. Question 9
What is the value of 23 C0 + 23 C2 + 23 C4 + · · · + 23 C22 ?
222
(a)
222 ≠ 1
(b)
223 + 1
(c)
223
(d)
9
What is the value of 23 C0 + 23 C2 + 23 C4 + · · · + 23 C22 ?
222
(a)
222 ≠ 1
(b)
223 + 1
(c)
223
(d)
9
Page 44
10. Question 10
Let f : Q æ Q be a function such that f (x + y) = f (x) + f (y) for all
x, y œ Q, and f (1) = 10. Which one of the following statements is Correct ?
f is bijective.
(a)
f is injective but not surjective.
(b)
f is surjective but not injective.
(c)
f is neither injective nor surjective.
(d)
10
Let f : Q æ Q be a function such that f (x + y) = f (x) + f (y) for all
x, y œ Q, and f (1) = 10. Which one of the following statements is Correct ?
f is bijective.
(a)
f is injective but not surjective.
(b)
f is surjective but not injective.
(c)
f is neither injective nor surjective.
(d)
10
Page 45
11. Question 11
Let
⁄ efi/2
! "
I= sin2 (log(x)) + sin(log(x2 )) dx.
e≠fi/2
What is the value of I ?
efi/2 ≠ e≠fi/2
(a)
0
(b)
fiefi/2
2
(c)
efi ≠ 1
(d)
11
Let
⁄ efi/2
! "
I= sin2 (log(x)) + sin(log(x2 )) dx.
e≠fi/2
What is the value of I ?
efi/2 ≠ e≠fi/2
(a)
0
(b)
fiefi/2
2
(c)
efi ≠ 1
(d)
11
Page 46
12. Question 12
Consider the following subset of the XY -plane:
) *
S = (|z ≠ iz|, |z|2 ) : z is a complex number .
Which one of the following statements is Correct ?
S is a parabola.
(a)
S is a circle.
(b)
S is an ellipse but not a circle.
(c)
S is a hyperbola.
(d)
12
Consider the following subset of the XY -plane:
) *
S = (|z ≠ iz|, |z|2 ) : z is a complex number .
Which one of the following statements is Correct ?
S is a parabola.
(a)
S is a circle.
(b)
S is an ellipse but not a circle.
(c)
S is a hyperbola.
(d)
12
Page 47
13. Question 13
A ship sets off on a voyage with three engines, labelled A, B, and C, which
work independently. The ship can complete the voyage only if at least two
of these engines keep working. The probability that engine A breaks down
is 1/4, that engine B breaks down is 1/4, and that engine C breaks down is
1/2. What is the probability that the ship can complete the voyage ?
3
4
(a)
1
2
(b)
1
32
(c)
1
4
(d)
13
A ship sets off on a voyage with three engines, labelled A, B, and C, which
work independently. The ship can complete the voyage only if at least two
of these engines keep working. The probability that engine A breaks down
is 1/4, that engine B breaks down is 1/4, and that engine C breaks down is
1/2. What is the probability that the ship can complete the voyage ?
3
4
(a)
1
2
(b)
1
32
(c)
1
4
(d)
13
Page 48
14. Question 14
Consider the differential equation
dy 1
cos(y)+ sin(y) = x, (x > 0);
dx x
fi Ô
given that y = at x = 3. Which one of the following is the value of y
Ú 2
3
at x = ?
2
fi
6
(a)
fi
3
(b)
fi
2
(c)
fi
4
(d)
14
Consider the differential equation
dy 1
cos(y)+ sin(y) = x, (x > 0);
dx x
fi Ô
given that y = at x = 3. Which one of the following is the value of y
Ú 2
3
at x = ?
2
fi
6
(a)
fi
3
(b)
fi
2
(c)
fi
4
(d)
14
Page 49
15. Question 15
In the given figure, the angles \BAQ =
fi
\CP Q = \CBQ = ; and the lengths QA = 3
2
unit, AB = 4 unit, and BC = 1 unit. What is
the length of P Q ?
2.2 unit
(a)
2 unit
(b)
Ô
2 unit
(c)
Ô
3≠ 2 unit
(d)
15
In the given figure, the angles \BAQ =
fi
\CP Q = \CBQ = ; and the lengths QA = 3
2
unit, AB = 4 unit, and BC = 1 unit. What is
the length of P Q ?
2.2 unit
(a)
2 unit
(b)
Ô
2 unit
(c)
Ô
3≠ 2 unit
(d)
15
Page 50
Physics
1. Question 1
On a circular track, two cyclists, Abhijit and Vani, start moving in opposite
directions from a point. Abhijit moves with a constant speed. Vani starts
with a constant acceleration from rest. They meet again on the track with
the same speed. Which of the following is correct?
Abhijit travelled double the distance travelled by Vani.
(a)
Abhijit travelled half the distance travelled by Vani.
(b)
Abhijit travelled the same distance travelled by Vani.
(c)
Abhijit travelled 4/3 of the distance travelled by Vani.
(d)
1
1. Question 1
On a circular track, two cyclists, Abhijit and Vani, start moving in opposite
directions from a point. Abhijit moves with a constant speed. Vani starts
with a constant acceleration from rest. They meet again on the track with
the same speed. Which of the following is correct?
Abhijit travelled double the distance travelled by Vani.
(a)
Abhijit travelled half the distance travelled by Vani.
(b)
Abhijit travelled the same distance travelled by Vani.
(c)
Abhijit travelled 4/3 of the distance travelled by Vani.
(d)
1
Page 51
2. Question 2
Consider a simple pendulum undergoing simple harmonic motion with a
time period T , and a fixed amplitude ◊0 of angular oscillation. Its angular
momentum about the point of suspension exhibits an oscillatory behavior
with an amplitude A. Which of the following relations between A and T is
correct?
A Ã T3
(a)
A Ã T2
(b)
AÃT
(c)
A Ã T4
(d)
2
Consider a simple pendulum undergoing simple harmonic motion with a
time period T , and a fixed amplitude ◊0 of angular oscillation. Its angular
momentum about the point of suspension exhibits an oscillatory behavior
with an amplitude A. Which of the following relations between A and T is
correct?
A Ã T3
(a)
A Ã T2
(b)
AÃT
(c)
A Ã T4
(d)
2
Page 52
3. Question 3
An inextensible cord of negligible mass passes over the rim of a solid disc
of mass M and radius R. The disc is free to rotate about an axis passing
through the centre perpendicular to the plane of the screen, as shown in
the figure. Two blocks of masses M and M/2 are attached to the two free
ends of the cord. Assume that there is no slipping of the cord on the disc.
The acceleration due to gravity is g. What is the value of the angular
acceleration of the disc?
g
4R
(a)
g
2R
(b)
g
R
(c)
g
3R
(d)
3
An inextensible cord of negligible mass passes over the rim of a solid disc
of mass M and radius R. The disc is free to rotate about an axis passing
through the centre perpendicular to the plane of the screen, as shown in
the figure. Two blocks of masses M and M/2 are attached to the two free
ends of the cord. Assume that there is no slipping of the cord on the disc.
The acceleration due to gravity is g. What is the value of the angular
acceleration of the disc?
g
4R
(a)
g
2R
(b)
g
R
(c)
g
3R
(d)
3
Page 53
4. Question 4
A solid bob of a material having density twice that of water is suspended
with a massless and inextensible string of length L. The whole set-up is
placed inside a water-filled tank. The bob is imparted a horizontal velocity
V0 at the lowest point A, while the other end of the string is fixed, such that
the bob completes a semi-circular trajectory in the vertical plane. The string
becomes slack only when the bob reaches the topmost point C. Assume that
the effects of viscosity and water currents are negligible. The acceleration
due to gravity is g. What is the expression for V0 ?
C
B
L
V0
A
Ú
5
gL
2
(a)
Ô
5gL
(b)
Ô
2gL
(c)
Ú
3
gL
2
(d)
4
A solid bob of a material having density twice that of water is suspended
with a massless and inextensible string of length L. The whole set-up is
placed inside a water-filled tank. The bob is imparted a horizontal velocity
V0 at the lowest point A, while the other end of the string is fixed, such that
the bob completes a semi-circular trajectory in the vertical plane. The string
becomes slack only when the bob reaches the topmost point C. Assume that
the effects of viscosity and water currents are negligible. The acceleration
due to gravity is g. What is the expression for V0 ?
C
B
L
V0
A
Ú
5
gL
2
(a)
Ô
5gL
(b)
Ô
2gL
(c)
Ú
3
gL
2
(d)
4
Page 54
5. Question 5
Consider a solid sphere of radius R floating in a pond with half of the sphere
submerged. The sphere is pushed vertically downwards at the topmost point
and released, such that it executes a simple harmonic motion. Acceleration
due to gravity is g. What is the time period of oscillation?
Ú
2R
2fi
3g
(a)
Ú
R
2fi
g
(b)
Ú
3R
2fi
2g
(c)
Ú
2R
2fi
g
(d)
5
Consider a solid sphere of radius R floating in a pond with half of the sphere
submerged. The sphere is pushed vertically downwards at the topmost point
and released, such that it executes a simple harmonic motion. Acceleration
due to gravity is g. What is the time period of oscillation?
Ú
2R
2fi
3g
(a)
Ú
R
2fi
g
(b)
Ú
3R
2fi
2g
(c)
Ú
2R
2fi
g
(d)
5
Page 55
6. Question 6
One mole of an ideal gas of volume V and temperature T is allowed to
expand adiabatically to volume 2V while doing no external work. The
universal gas constant is R. What is the pressure of the gas after expansion?
RT
2V
(a)
RT
4V
(b)
RT
V
(c)
2RT
V
(d)
6
One mole of an ideal gas of volume V and temperature T is allowed to
expand adiabatically to volume 2V while doing no external work. The
universal gas constant is R. What is the pressure of the gas after expansion?
RT
2V
(a)
RT
4V
(b)
RT
V
(c)
2RT
V
(d)
6
Page 56
7. Question 7
Consider the motion of a particle along the x-axis. The position of the
particle varies with time t as x(t) = sin2 (Êt) cos3 (Êt), where Ê is a constant.
What is the time period of the motion?
2fi
Ê
(a)
2fi
3Ê
(b)
2fi
5Ê
(c)
2fi
15Ê
(d)
7
Consider the motion of a particle along the x-axis. The position of the
particle varies with time t as x(t) = sin2 (Êt) cos3 (Êt), where Ê is a constant.
What is the time period of the motion?
2fi
Ê
(a)
2fi
3Ê
(b)
2fi
5Ê
(c)
2fi
15Ê
(d)
7
Page 57
8. Question 8
Two identical boxes contain the same ideal gas. Let (n1 , ⁄1 , T1 ) and (n2 ,
⁄2 , T2 ) be the number density, mean free path and temperature of the gas
in the first and the second box, respectively. One of the boxes is emptied
into the other one. What will be the mean free path ⁄ and temperature T
of the gas now?
⁄1 ⁄ 2 n1 T1 + n2 T2
⁄= ,T =
⁄1 + ⁄2 n1 + n2
(a)
n1 ⁄1 + n2 ⁄2 n1 T1 + n2 T2
⁄= ,T =
n1 + n2 n1 + n2
(b)
n1 ⁄1 + n2 ⁄2 Ô
⁄= , T = T1 T2
n1 + n2
(c)
⁄1 ⁄ 2 Ô
⁄= , T = T 1 T2
⁄1 + ⁄2
(d)
8
Two identical boxes contain the same ideal gas. Let (n1 , ⁄1 , T1 ) and (n2 ,
⁄2 , T2 ) be the number density, mean free path and temperature of the gas
in the first and the second box, respectively. One of the boxes is emptied
into the other one. What will be the mean free path ⁄ and temperature T
of the gas now?
⁄1 ⁄ 2 n1 T1 + n2 T2
⁄= ,T =
⁄1 + ⁄2 n1 + n2
(a)
n1 ⁄1 + n2 ⁄2 n1 T1 + n2 T2
⁄= ,T =
n1 + n2 n1 + n2
(b)
n1 ⁄1 + n2 ⁄2 Ô
⁄= , T = T1 T2
n1 + n2
(c)
⁄1 ⁄ 2 Ô
⁄= , T = T 1 T2
⁄1 + ⁄2
(d)
8
Page 58
9. Question 9
Consider two point charges +q and +2q fixed on the x≠y plane at (≠¸/2, 0)
and (+¸/2, 0) respectively.
Ô
Another point charge ≠q having mass m is
released from rest at (0, 23 ¸) on the x ≠ y plane, as shown in the figure.
The permittivity of free space is ‘0 . What is the acceleration of the charge
≠q at the time of release?
y
Ô
(0, 3¸/2) ≠q
x
+q +2q
(≠¸/2, 0) (¸/2, 0)
q2 1 Ô 2
î ≠ 3 3 ĵ
8fi‘0 m¸2
(a)
q2 1 Ô 2
î ≠ 3 ĵ
8fi‘0 m¸2
(b)
q2 1 Ô 2
3 î ≠ 3 ĵ
8fi‘0 m¸2
(c)
q2 1 Ô 2
3 3 î ≠ ĵ
8fi‘0 m¸2
(d)
9
Consider two point charges +q and +2q fixed on the x≠y plane at (≠¸/2, 0)
and (+¸/2, 0) respectively.
Ô
Another point charge ≠q having mass m is
released from rest at (0, 23 ¸) on the x ≠ y plane, as shown in the figure.
The permittivity of free space is ‘0 . What is the acceleration of the charge
≠q at the time of release?
y
Ô
(0, 3¸/2) ≠q
x
+q +2q
(≠¸/2, 0) (¸/2, 0)
q2 1 Ô 2
î ≠ 3 3 ĵ
8fi‘0 m¸2
(a)
q2 1 Ô 2
î ≠ 3 ĵ
8fi‘0 m¸2
(b)
q2 1 Ô 2
3 î ≠ 3 ĵ
8fi‘0 m¸2
(c)
q2 1 Ô 2
3 3 î ≠ ĵ
8fi‘0 m¸2
(d)
9
Page 59
10. Question 10
Consider the circuit diagram as shown in the figure. The source has a
voltage V = V0 sin Êt. Both the resistors A and B have the same resistance.
The capacitor and the inductor have capacitance C and inductance L,
respectively. For some frequency Ê, and certain initial charge in the
capacitor, the current through the resistor A is in phase with the source.
What is the value of Ê?
A
B
V¶ sin Êt C
L
1
Ô
2LC
(a)
1
Ô
LC
(b)
1
Ô
2 LC
(c)
1
Ô
3LC
(d)
10
Consider the circuit diagram as shown in the figure. The source has a
voltage V = V0 sin Êt. Both the resistors A and B have the same resistance.
The capacitor and the inductor have capacitance C and inductance L,
respectively. For some frequency Ê, and certain initial charge in the
capacitor, the current through the resistor A is in phase with the source.
What is the value of Ê?
A
B
V¶ sin Êt C
L
1
Ô
2LC
(a)
1
Ô
LC
(b)
1
Ô
2 LC
(c)
1
Ô
3LC
(d)
10
Page 60
11. Question 11
A conducting wire carrying a steady current I is shaped as shown in the
figure below. All connected straight segments meet at right angles. What
is the magnetic moment of the current loop?
b
a
ĵ
î
I
a k̂
b
Iab (ĵ + k̂)
(a)
Iab (ĵ ≠ k̂)
(b)
Ô
2Iab (ĵ + k̂)
(c)
Iab (k̂ ≠ ĵ)
(d)
11
A conducting wire carrying a steady current I is shaped as shown in the
figure below. All connected straight segments meet at right angles. What
is the magnetic moment of the current loop?
b
a
ĵ
î
I
a k̂
b
Iab (ĵ + k̂)
(a)
Iab (ĵ ≠ k̂)
(b)
Ô
2Iab (ĵ + k̂)
(c)
Iab (k̂ ≠ ĵ)
(d)
11
Page 61
12. Question 12
Consider the circuit shown in the figure. The capacitors C1 and C2 have
capacitances 2 µF and 8 µF, respectively. The switch can connect point
X to either Y or Z. Initially XY is connected until the capacitor is fully
charged by the battery. Then the switch connects X and Z, and the final
charges on C1 and C2 are Q1 and Q2 , respectively. What is the value of
Q2
the ratio ?
Q1 + Q2
X
Y Z
C1
C2
4
5
(a)
1
5
(b)
1
4
(c)
1
2
(d)
12
Consider the circuit shown in the figure. The capacitors C1 and C2 have
capacitances 2 µF and 8 µF, respectively. The switch can connect point
X to either Y or Z. Initially XY is connected until the capacitor is fully
charged by the battery. Then the switch connects X and Z, and the final
charges on C1 and C2 are Q1 and Q2 , respectively. What is the value of
Q2
the ratio ?
Q1 + Q2
X
Y Z
C1
C2
4
5
(a)
1
5
(b)
1
4
(c)
1
2
(d)
12
Page 62
13. Question 13
Atomic masses of two oxygen isotopes 168 O and 188 O are 15.99491 u and
17.99916 u, respectively, where u is the atomic mass unit. Masses of proton
and neutron are given by 1.00727 u and 1.00866 u, respectively. The speed
of light is c. What is the difference between the binding energies of 188 O and
16 2
8 O nuclei in units of u c ?
0.01307
(a)
2.00425
(b)
0.99559
(c)
3.01291
(d)
13
Atomic masses of two oxygen isotopes 168 O and 188 O are 15.99491 u and
17.99916 u, respectively, where u is the atomic mass unit. Masses of proton
and neutron are given by 1.00727 u and 1.00866 u, respectively. The speed
of light is c. What is the difference between the binding energies of 188 O and
16 2
8 O nuclei in units of u c ?
0.01307
(a)
2.00425
(b)
0.99559
(c)
3.01291
(d)
13
Page 63
14. Question 14
Ô
The refractive indices (n) of two transparent slabs are 2 and 2/ 3. They are
attached
Ô together and placed in a third transparent medium of refractive
index 2, as shown in the figure. The thickness of the upper slab is 1 cm. A
monochromatic light ray is incident on the upper slab at 45o . What would
be the thickness in cm of the lower slab such that the lateral shift of the ray
after passing through both the slabs is zero?
45o Ô
incident ray n= 2
1 cm n=2
Ô
n = 2/ 3
Ô
n= 2
outgoing ray
Ô
1/ 3
(a)
Ô
1/ 2
(b)
1/2
(c)
Ô
3/2
(d)
14
Ô
The refractive indices (n) of two transparent slabs are 2 and 2/ 3. They are
attached
Ô together and placed in a third transparent medium of refractive
index 2, as shown in the figure. The thickness of the upper slab is 1 cm. A
monochromatic light ray is incident on the upper slab at 45o . What would
be the thickness in cm of the lower slab such that the lateral shift of the ray
after passing through both the slabs is zero?
45o Ô
incident ray n= 2
1 cm n=2
Ô
n = 2/ 3
Ô
n= 2
outgoing ray
Ô
1/ 3
(a)
Ô
1/ 2
(b)
1/2
(c)
Ô
3/2
(d)
14
Page 64
15. Question 15
Two monochromatic sources emit light at wavelengths ⁄ and ⁄/2. The
stopping potentials for a photosensitive material using these two sources
are found to be 1 V and 3 V , respectively. What is the work function of the
material ?
1 eV
(a)
2 eV
(b)
1.5 eV
(c)
1.25 eV
(d)
15
Two monochromatic sources emit light at wavelengths ⁄ and ⁄/2. The
stopping potentials for a photosensitive material using these two sources
are found to be 1 V and 3 V , respectively. What is the work function of the
material ?
1 eV
(a)
2 eV
(b)
1.5 eV
(c)
1.25 eV
(d)
15
Page 65
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Document Details
| Board / Org | Default |
| Exam | IISER Aptitude Test |
| Type | Question Paper |
| Pages | 65 |
| Updated | 22 Jul 2026 |