IISER IAT 2026 Answer Key (Provisional) English
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IISER IAT 2026 Answer Key (Provisional) English – Text
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Page 1
FOR IISER IAT EXAM PREPARATION
IISER IAT 2026
Answer Key
(Provisional) · English
EXAM YEAR TYPE SUBJECT
IISER IAT 2026 Answer Key (Provisional) English
Notes · Sample Papers · Previous Year Papers · Mock Tests
IISER IAT 2026
Answer Key
(Provisional) · English
EXAM YEAR TYPE SUBJECT
IISER IAT 2026 Answer Key (Provisional) English
Notes · Sample Papers · Previous Year Papers · Mock Tests
Page 2
m
m .co
c. o
e m
em l a s
s a (Provisional) g
English Answer Key for IAT 2026
07-06-2026
om
m
Important Note: This document serves as the (provisional) answer
. c
c. o
key. For all the multiple-choice questions listed below, option (a) is the
s e m
e m a l
s g
correct answer.
l a a
ag
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
m .
.co s e m
e m l a
l a s ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 62
m .co
c. o
e m
em l a s
s a (Provisional) g
English Answer Key for IAT 2026
07-06-2026
om
m
Important Note: This document serves as the (provisional) answer
. c
c. o
key. For all the multiple-choice questions listed below, option (a) is the
s e m
e m a l
s g
correct answer.
l a a
ag
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
m .
.co s e m
e m l a
l a s ag
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 62
Page 3
Biology
1. Question 1
Which of the following processes result in development of a proton gradient
across the thylakoid membrane during photosynthesis?
i. Release of protons into the lumen of the thylakoid by plastoquinone
ii. Consumption of protons in the stroma during the reduction of NADP+
iii. Release of protons into the lumen of the thylakoid by ATP synthase
iv. Release of protons into the lumen of the thylakoid by water splitting
reaction
i, ii and iv
(a)
ii, iii and iv
(b)
i, iii and iv
(c)
i, ii and iii
(d)
1
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1. Question 1
Which of the following processes result in development of a proton gradient
across the thylakoid membrane during photosynthesis?
i. Release of protons into the lumen of the thylakoid by plastoquinone
ii. Consumption of protons in the stroma during the reduction of NADP+
iii. Release of protons into the lumen of the thylakoid by ATP synthase
iv. Release of protons into the lumen of the thylakoid by water splitting
reaction
i, ii and iv
(a)
ii, iii and iv
(b)
i, iii and iv
(c)
i, ii and iii
(d)
1
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Page 4
co m .
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2. Question 2
m
Which one of the following choices matches the organs in column I with
co
their vascular system arrangement described in column II?
.c om e m .
e m l a s
l a s a g
ag
P - (i); Q - (ii); R - (iii); S - (iv)
(a)
o m
c
P - (ii); Q - (i); R - (iv); S - (iii)
.
(b)
e m
s
P - (iii); Q - (iv); R - (i); S - (ii)
P - (iv); Q - (iii); R l-a
(c)
ag
(ii); S - (i)
(d)
m
m c. o
c. o s e m
s em la
gla ag
a
2
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c. o s e m
m a
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g lPage 3 of 62
. s e
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2. Question 2
m
Which one of the following choices matches the organs in column I with
co
their vascular system arrangement described in column II?
.c om e m .
e m l a s
l a s a g
ag
P - (i); Q - (ii); R - (iii); S - (iv)
(a)
o m
c
P - (ii); Q - (i); R - (iv); S - (iii)
.
(b)
e m
s
P - (iii); Q - (iv); R - (i); S - (ii)
P - (iv); Q - (iii); R l-a
(c)
ag
(ii); S - (i)
(d)
m
m c. o
c. o s e m
s em la
gla ag
a
2
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c. o s e m
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g lPage 3 of 62
Page 5
3. Question 3
The graphs below depict the number of individuals of two organisms, named
P and Q, when grown independently, and together. Based on these growth
patterns, which one of the following statements is correct?
Q is a predator of P
(a)
P and Q exhibit mutualism
(b)
P is a parasite of Q
(c)
Q is a commensal of P
(d)
3
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The graphs below depict the number of individuals of two organisms, named
P and Q, when grown independently, and together. Based on these growth
patterns, which one of the following statements is correct?
Q is a predator of P
(a)
P and Q exhibit mutualism
(b)
P is a parasite of Q
(c)
Q is a commensal of P
(d)
3
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 62
Page 6
co m .
. s e
em l a
as a g
4. Question 4
m
The pBR322 cloning vector has genes coding for tetracycline and ampicillin
co
resistance. A foreign DNA to be cloned is inserted into the tetracycline
om .
resistance gene and the recombinant plasmid is then transformed into E.
.c
coli cells. Which one of the following choices is the most likely outcome of
e m
m
e
this cloning reaction?
l a s
l a s a g
ag
The cells with the recombinant plasmid can grow in the presence of
ampicillin but not tetracycline
(a)
The cells with the recombinant plasmid can grow in the presence of both
ampicillin and tetracycline
(b)
The cells with the non-recombinant plasmid can grow in the presence of
ampicillin but not tetracycline
(c)
m
The cells with the non-recombinant plasmid can grow in the presence of
co
tetracycline but not ampicillin
.
(d)
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
4
m . c
c. o s e m
m a
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g lPage 5 of 62
. s e
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4. Question 4
m
The pBR322 cloning vector has genes coding for tetracycline and ampicillin
co
resistance. A foreign DNA to be cloned is inserted into the tetracycline
om .
resistance gene and the recombinant plasmid is then transformed into E.
.c
coli cells. Which one of the following choices is the most likely outcome of
e m
m
e
this cloning reaction?
l a s
l a s a g
ag
The cells with the recombinant plasmid can grow in the presence of
ampicillin but not tetracycline
(a)
The cells with the recombinant plasmid can grow in the presence of both
ampicillin and tetracycline
(b)
The cells with the non-recombinant plasmid can grow in the presence of
ampicillin but not tetracycline
(c)
m
The cells with the non-recombinant plasmid can grow in the presence of
co
tetracycline but not ampicillin
.
(d)
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
4
m . c
c. o s e m
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
g lPage 5 of 62
Page 7
5. Question 5
For which one of the following enzyme activity plots, will the Km of the
enzyme for substrate ‘S’ be 20? [S] indicates substrate concentration.
(a)
(b)
5
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For which one of the following enzyme activity plots, will the Km of the
enzyme for substrate ‘S’ be 20? [S] indicates substrate concentration.
(a)
(b)
5
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Page 8
co m .
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.c e m
e m l a s
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(c)
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s em
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a
(d)
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c. o s e m
s em la
gla ag
a
6
m . c
c. o s e m
m a
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For more Question Papers, Sample Papers, Notes & Syllabus visit
g lPage 7 of 62
. s e
em l a
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m
om . co
.c e m
e m l a s
l a s a g
ag
(c)
m
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s em
g l a
a
(d)
m
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c. o s e m
s em la
gla ag
a
6
m . c
c. o s e m
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
g lPage 7 of 62
Page 9
6. Question 6
Which one of the following correctly describes the mode of action of Follicle
Stimulating Hormone (FSH) and estrogen?
FSH interacts with membrane-bound receptor and generates cyclic AMP,
while estrogen interacts with intracellular receptor and regulates gene
expression
(a)
FSH interacts with intracellular receptor and generates cyclic AMP, while
estrogen interacts with membrane-bound receptor and regulates cellular
metabolism
(b)
Both FSH and estrogen regulate gene expression via intracellular receptors
(c)
Both FSH and estrogen regulate cellular metabolism via membrane-bound
receptors
(d)
7
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Which one of the following correctly describes the mode of action of Follicle
Stimulating Hormone (FSH) and estrogen?
FSH interacts with membrane-bound receptor and generates cyclic AMP,
while estrogen interacts with intracellular receptor and regulates gene
expression
(a)
FSH interacts with intracellular receptor and generates cyclic AMP, while
estrogen interacts with membrane-bound receptor and regulates cellular
metabolism
(b)
Both FSH and estrogen regulate gene expression via intracellular receptors
(c)
Both FSH and estrogen regulate cellular metabolism via membrane-bound
receptors
(d)
7
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Page 10
co m .
. s e
em l a
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7. Question 7
m
If cell wall was used as the only criterion for classifying organisms, then
co
Mycoplasma would have belonged to which one of the following groups?
o m m .
(a) .c s e
m
Animals
se(b) Plants g l a
g la a
a (c)
Fungi
Protists
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
8
m . c
c. o s e m
m a
se
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g lPage 9 of 62
. s e
em l a
as a g
7. Question 7
m
If cell wall was used as the only criterion for classifying organisms, then
co
Mycoplasma would have belonged to which one of the following groups?
o m m .
(a) .c s e
m
Animals
se(b) Plants g l a
g la a
a (c)
Fungi
Protists
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
8
m . c
c. o s e m
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
g lPage 9 of 62
Page 11
8. Question 8
Which one of the following is the correct sequence of the coding strand of
the given gene?
5’ GTGCTGTAACGGCTTCAC 3’
(a)
5’ CACTTCGGCAATGTCGTG 3’
(b)
5’ GTGAAGCCGTTACAGCAC 3’
(c)
5’ CACGACATTGCCGAAGTG 3’
(d)
9
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Which one of the following is the correct sequence of the coding strand of
the given gene?
5’ GTGCTGTAACGGCTTCAC 3’
(a)
5’ CACTTCGGCAATGTCGTG 3’
(b)
5’ GTGAAGCCGTTACAGCAC 3’
(c)
5’ CACGACATTGCCGAAGTG 3’
(d)
9
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Page 12
co m .
. s e
em l a
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9. Question 9
m
Which one of the following correctly describes the sequence of events leading
co
to muscle contraction following acetylcholine release at the neuromuscular
om .
junction?
.cIncrease of Ca in sarcoplasm, unmasking of active sites for myosin, ‘Z’ se m
s e(a)m lines pulled inwards g l a
++
g la a
a Increase of Ca
pulled inwards
++
in sarcoplasm, masking of active sites for myosin, ‘Z’ lines
(b)
Increase of Ca++ in sarcoplasm, unmasking of active sites for myosin, ‘Z’
lines pulled outwards
(c)
Decrease of Ca++ in sarcoplasm, masking of active sites for myosin, ‘Z’ lines
pulled inwards
m
(d)
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
10
m . c
c. o s e m
m a
se
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g l
Page 11 of 62
. s e
em l a
as a g
9. Question 9
m
Which one of the following correctly describes the sequence of events leading
co
to muscle contraction following acetylcholine release at the neuromuscular
om .
junction?
.cIncrease of Ca in sarcoplasm, unmasking of active sites for myosin, ‘Z’ se m
s e(a)m lines pulled inwards g l a
++
g la a
a Increase of Ca
pulled inwards
++
in sarcoplasm, masking of active sites for myosin, ‘Z’ lines
(b)
Increase of Ca++ in sarcoplasm, unmasking of active sites for myosin, ‘Z’
lines pulled outwards
(c)
Decrease of Ca++ in sarcoplasm, masking of active sites for myosin, ‘Z’ lines
pulled inwards
m
(d)
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
10
m . c
c. o s e m
m a
se
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g l
Page 11 of 62
Page 13
10. Question 10
In which one of the following cases, will an anti-Rh antibody treatment
prevent erythroblastosis foetalis?
Anti-Rh antibody to the Rh-negative mother after delivery of the first
Rh-positive child
(a)
Anti-Rh antibody to the Rh-positive mother after delivery of the first
Rh-negative child
(b)
Anti-Rh antibody to the Rh-negative mother after delivery of the first
Rh-negative child
(c)
Anti-Rh antibody to the Rh-positive mother after delivery of the first
Rh-positive child
(d)
11
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In which one of the following cases, will an anti-Rh antibody treatment
prevent erythroblastosis foetalis?
Anti-Rh antibody to the Rh-negative mother after delivery of the first
Rh-positive child
(a)
Anti-Rh antibody to the Rh-positive mother after delivery of the first
Rh-negative child
(b)
Anti-Rh antibody to the Rh-negative mother after delivery of the first
Rh-negative child
(c)
Anti-Rh antibody to the Rh-positive mother after delivery of the first
Rh-positive child
(d)
11
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Page 14
co m .
. s e
em l a
as a g
11. Question 11
m
Which of the following schematics correctly depict a lac operon that can be
co
negatively regulated?
.c om e m .
e m l a s
l a s a g
ag
i and iii
(a)
m
co
i and ii
(b)
.
em
ii and iv
(c)
l a s
g
iii and iv
(d)
a
m
m c. o
c. o s e m
s em la
gla ag
a
12
m . c
c. o s e m
m a
se
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g l
Page 13 of 62
. s e
em l a
as a g
11. Question 11
m
Which of the following schematics correctly depict a lac operon that can be
co
negatively regulated?
.c om e m .
e m l a s
l a s a g
ag
i and iii
(a)
m
co
i and ii
(b)
.
em
ii and iv
(c)
l a s
g
iii and iv
(d)
a
m
m c. o
c. o s e m
s em la
gla ag
a
12
m . c
c. o s e m
m a
se
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g l
Page 13 of 62
Page 15
12. Question 12
For which one of the following parents, their children will NOT have the
same blood group phenotype as either of the parents?
Father: AB; Mother: O
(a)
Father: A; Mother: O
(b)
Father: AB; Mother: A
(c)
Father: O; Mother: B
(d)
13
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For which one of the following parents, their children will NOT have the
same blood group phenotype as either of the parents?
Father: AB; Mother: O
(a)
Father: A; Mother: O
(b)
Father: AB; Mother: A
(c)
Father: O; Mother: B
(d)
13
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Page 16
co m .
. s e
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13. Question 13
m
Which one of the following molecules can be used for RNA interference?
om . co
.c e m
m
e l a s
a s
l (a) a g
ag
(b)
m
(c)
. co
s em
g l a
(d) a
m
m c. o
c. o s e m
s em la
gla ag
a
14
m . c
c. o s e m
m a
se
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g l
Page 15 of 62
. s e
em l a
as a g
13. Question 13
m
Which one of the following molecules can be used for RNA interference?
om . co
.c e m
m
e l a s
a s
l (a) a g
ag
(b)
m
(c)
. co
s em
g l a
(d) a
m
m c. o
c. o s e m
s em la
gla ag
a
14
m . c
c. o s e m
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
g l
Page 15 of 62
Page 17
14. Question 14
The following pedigree diagram shows the inheritance of a rare genetic
disorder in a family (filled shapes depict affected individuals). Which one
of the following is the most likely pattern of inheritance of the disorder?
X-linked dominant
(a)
X-linked recessive
(b)
Y-linked
(c)
Mitochondrial
(d)
15
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The following pedigree diagram shows the inheritance of a rare genetic
disorder in a family (filled shapes depict affected individuals). Which one
of the following is the most likely pattern of inheritance of the disorder?
X-linked dominant
(a)
X-linked recessive
(b)
Y-linked
(c)
Mitochondrial
(d)
15
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Page 18
co m .
. s e
em l a
as a g
15. Question 15
m
A female child is born with all the primary oocytes required during her
co
lifetime. At which one of the following stages of cell division are these
om .
oocytes found at birth?
.cProphase I e m
m
e l a s
a s(a)
l (b) Metaphase I a g
ag
Anaphase I
(c)
Telophase I
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
16
m . c
c. o s e m
m a
se
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g l
Page 17 of 62
. s e
em l a
as a g
15. Question 15
m
A female child is born with all the primary oocytes required during her
co
lifetime. At which one of the following stages of cell division are these
om .
oocytes found at birth?
.cProphase I e m
m
e l a s
a s(a)
l (b) Metaphase I a g
ag
Anaphase I
(c)
Telophase I
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
16
m . c
c. o s e m
m a
se
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Page 17 of 62
Page 19
Chemistry
1. Question 1
Which one of the following octahedral complexes has the highest spin-only
magnetic moment?
[Cr(H2 O)4 (OH)2 ]
(a)
[V(H2 O)4 I2 ]+
(b)
[Fe(NH3 )4 (CN)2 ]+
(c)
[Co(NH3 )4 Cl2 ]
(d)
1
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 18 of 62
1. Question 1
Which one of the following octahedral complexes has the highest spin-only
magnetic moment?
[Cr(H2 O)4 (OH)2 ]
(a)
[V(H2 O)4 I2 ]+
(b)
[Fe(NH3 )4 (CN)2 ]+
(c)
[Co(NH3 )4 Cl2 ]
(d)
1
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 18 of 62
Page 20
co m .
. s e
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as a g
2. Question 2
m
What are the numbers of protons (H+ ) and electrons (e− ), respectively,
co
required for the reduction of [Cr2 O7 ]2− to Cr3+ under an aqueous acidic
om m .
condition?
.c14, 6 s e
m a
se(a)
la (b) 6, 14 a g l
ag
7, 3
(c)
7, 6
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
2
m . c
c. o s e m
m a
se
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g l
Page 19 of 62
. s e
em l a
as a g
2. Question 2
m
What are the numbers of protons (H+ ) and electrons (e− ), respectively,
co
required for the reduction of [Cr2 O7 ]2− to Cr3+ under an aqueous acidic
om m .
condition?
.c14, 6 s e
m a
se(a)
la (b) 6, 14 a g l
ag
7, 3
(c)
7, 6
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
2
m . c
c. o s e m
m a
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
g l
Page 19 of 62
Page 21
3. Question 3
Which one of the following molecules shows an increase in bond order after
loss of an electron from the highest occupied molecular orbital?
F2
(a)
N2
(b)
C2
(c)
B2
(d)
3
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 20 of 62
Which one of the following molecules shows an increase in bond order after
loss of an electron from the highest occupied molecular orbital?
F2
(a)
N2
(b)
C2
(c)
B2
(d)
3
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Page 22
co m .
. s e
em l a
as a g
4. Question 4
m
Metal-ligand π-bond formation in Mn2 (CO)10 and [MnO4 ]− requires
co
electron-pair donation between metal and ligand orbitals. Which one of
om m .
the following represents the direction of electron-pair donation?
.cMn (CO) : metal orbital → ligand orbital s e
m
e(a) [MnO ] : ligand orbital → metal orbital l a
a s g
2 10
l a
−
g
4
a Mn (CO) : ligand orbital → metal orbital
2 10
[MnO ] : ligand orbital → metal orbital
−
4
(b)
Mn2 (CO)10 : metal orbital → ligand orbital
[MnO4 ]− : metal orbital → ligand orbital
(c)
Mn2 (CO)10 : ligand orbital → metal orbital
[MnO4 ]− : metal orbital → ligand orbital
m
(d)
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
4
m . c
c. o s e m
m a
se
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. s e
em l a
as a g
4. Question 4
m
Metal-ligand π-bond formation in Mn2 (CO)10 and [MnO4 ]− requires
co
electron-pair donation between metal and ligand orbitals. Which one of
om m .
the following represents the direction of electron-pair donation?
.cMn (CO) : metal orbital → ligand orbital s e
m
e(a) [MnO ] : ligand orbital → metal orbital l a
a s g
2 10
l a
−
g
4
a Mn (CO) : ligand orbital → metal orbital
2 10
[MnO ] : ligand orbital → metal orbital
−
4
(b)
Mn2 (CO)10 : metal orbital → ligand orbital
[MnO4 ]− : metal orbital → ligand orbital
(c)
Mn2 (CO)10 : ligand orbital → metal orbital
[MnO4 ]− : metal orbital → ligand orbital
m
(d)
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
4
m . c
c. o s e m
m a
se
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Page 23
5. Question 5
What is the order of bond energy between C=S & C=Te, and between Cl–Cl
& F–F?
C=S > C=Te and Cl–Cl > F–F
(a)
C=Te > C=S and Cl–Cl > F–F
(b)
C=Te > C=S and F–F > Cl–Cl
(c)
C=S > C=Te and F–F > Cl–Cl
(d)
5
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What is the order of bond energy between C=S & C=Te, and between Cl–Cl
& F–F?
C=S > C=Te and Cl–Cl > F–F
(a)
C=Te > C=S and Cl–Cl > F–F
(b)
C=Te > C=S and F–F > Cl–Cl
(c)
C=S > C=Te and F–F > Cl–Cl
(d)
5
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Page 24
co m .
. s e
em l a
as a g
6. Question 6
m
Which one is an INCORRECT statement with regard to the following
co
reaction?
.c om e m .
e m l a s
l a s a g
ag The reaction rate decreases upon changing the solvent from ethyl alcohol to
1:1 mixture of ethyl alcohol and water.
(a)
The reaction rate does not change upon increasing the concentration of
hydroxide ion.
(b)
The rate determining step is the dissociation of tert-butylbromide.
(c)
m
co
The reaction rate is proportional to the concentration of tert-butylbromide.
(d)
.
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
6
m . c
c. o s e m
m a
se
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. s e
em l a
as a g
6. Question 6
m
Which one is an INCORRECT statement with regard to the following
co
reaction?
.c om e m .
e m l a s
l a s a g
ag The reaction rate decreases upon changing the solvent from ethyl alcohol to
1:1 mixture of ethyl alcohol and water.
(a)
The reaction rate does not change upon increasing the concentration of
hydroxide ion.
(b)
The rate determining step is the dissociation of tert-butylbromide.
(c)
m
co
The reaction rate is proportional to the concentration of tert-butylbromide.
(d)
.
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
6
m . c
c. o s e m
m a
se
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Page 25
7. Question 7
Which one of the following molecules is chiral?
(a)
(b)
(c)
(d)
7
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Which one of the following molecules is chiral?
(a)
(b)
(c)
(d)
7
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Page 26
co m .
. s e
em l a
as a g
8. Question 8
m
Consider the following silica-gel based thin-layer chromatogram of
co
compounds A and B. Which one of the following statements is correct?
.c om e m .
e m l a s
l a s a g
ag
B is more polar than A; A has Rf = 0.75.
(a)
m
B is more polar than A; A has Rf = 0.25.
co
(b)
.
em
A is more polar than B; B has Rf = 0.33.
s
(c)
g l a
B is less polar than A; B has Rf = 0.75.
a
(d)
m
m c. o
c. o s e m
s em la
gla ag
a
8
m . c
c. o s e m
m a
se
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. s e
em l a
as a g
8. Question 8
m
Consider the following silica-gel based thin-layer chromatogram of
co
compounds A and B. Which one of the following statements is correct?
.c om e m .
e m l a s
l a s a g
ag
B is more polar than A; A has Rf = 0.75.
(a)
m
B is more polar than A; A has Rf = 0.25.
co
(b)
.
em
A is more polar than B; B has Rf = 0.33.
s
(c)
g l a
B is less polar than A; B has Rf = 0.75.
a
(d)
m
m c. o
c. o s e m
s em la
gla ag
a
8
m . c
c. o s e m
m a
se
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Page 27
9. Question 9
What are X and P in the following reaction sequence?
(a)
(b)
(c)
(d)
9
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What are X and P in the following reaction sequence?
(a)
(b)
(c)
(d)
9
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Page 28
co m .
. s e
em l a
as a g
10. Question 10
m
What is the order of pKb for the following molecules in an aqueous medium?
om . co
.c e m
me l a s
l a s a g
ag P<R<Q<S
(a)
P<Q<R<S
(b)
S<P<R<Q
(c)
S<P<Q<R
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
10
m . c
c. o s e m
m a
se
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. s e
em l a
as a g
10. Question 10
m
What is the order of pKb for the following molecules in an aqueous medium?
om . co
.c e m
me l a s
l a s a g
ag P<R<Q<S
(a)
P<Q<R<S
(b)
S<P<R<Q
(c)
S<P<Q<R
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
10
m . c
c. o s e m
m a
se
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Page 29
11. Question 11
100 mL of 1.0 M aqueous NaOH solution was diluted to 1.0 L by adding
water. Half of this solution was discarded. A new 100 mL of 0.5 M aqueous
NaOH solution was added to the remaining solution. What is the concen-
tration of the final aqueous NaOH solution?
0.17 M
(a)
0.10 M
(b)
0.50 M
(c)
0.33 M
(d)
11
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100 mL of 1.0 M aqueous NaOH solution was diluted to 1.0 L by adding
water. Half of this solution was discarded. A new 100 mL of 0.5 M aqueous
NaOH solution was added to the remaining solution. What is the concen-
tration of the final aqueous NaOH solution?
0.17 M
(a)
0.10 M
(b)
0.50 M
(c)
0.33 M
(d)
11
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Page 30
co m .
. s e
em l a
as a g
12. Question 12
m
An ideal gas goes through a reversible isothermal expansion (solid line)
co
followed by a reversible adiabatic expansion (dashed line). Which of the
om .
following diagram(s) closely depict(s) the entire process?
.c e m
e m l a s
l a s a g
ag
m
. co
(i) and (iii) only
s em
l a
(a)
(b)
(i) only
a g
(ii) and (iv) only
(c)
(i), (ii), and (iii) only
(d)
m
m c. o
c. o s e m
s em la
gla ag
a
12
m . c
c. o s e m
m a
se
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. s e
em l a
as a g
12. Question 12
m
An ideal gas goes through a reversible isothermal expansion (solid line)
co
followed by a reversible adiabatic expansion (dashed line). Which of the
om .
following diagram(s) closely depict(s) the entire process?
.c e m
e m l a s
l a s a g
ag
m
. co
(i) and (iii) only
s em
l a
(a)
(b)
(i) only
a g
(ii) and (iv) only
(c)
(i), (ii), and (iii) only
(d)
m
m c. o
c. o s e m
s em la
gla ag
a
12
m . c
c. o s e m
m a
se
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Page 31
13. Question 13
What is the ratio of the velocity of an electron in the fourth orbit of Be3+
to the velocity of the electron in the second orbit of He+ ?
1:1
(a)
1:2
(b)
3:2
(c)
6:1
(d)
13
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What is the ratio of the velocity of an electron in the fourth orbit of Be3+
to the velocity of the electron in the second orbit of He+ ?
1:1
(a)
1:2
(b)
3:2
(c)
6:1
(d)
13
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Page 32
co m .
. s e
em l a
as a g
14. Question 14
m
For two pure volatile liquids X and Y, attractive intermolecular interactions
co
of both X-X and Y-Y are weaker than those of X-Y. The total vapour
om .
pressure of an equimolar solution of X and Y is ptotal . The vapour pressure
.c
of pure X and pure Y are p0X and p0Y , respectively. Which one of the
e m
m
e
following relations is correct?
l a s
a s
l (a) p a g
ag
0 0
total < (pX + pY )/2
0 0
p total = (pX + pY )/2
(b)
ptotal = p0X + p0Y
(c)
ptotal > (p0X + p0Y )/2
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
14
m . c
c. o s e m
m a
se
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. s e
em l a
as a g
14. Question 14
m
For two pure volatile liquids X and Y, attractive intermolecular interactions
co
of both X-X and Y-Y are weaker than those of X-Y. The total vapour
om .
pressure of an equimolar solution of X and Y is ptotal . The vapour pressure
.c
of pure X and pure Y are p0X and p0Y , respectively. Which one of the
e m
m
e
following relations is correct?
l a s
a s
l (a) p a g
ag
0 0
total < (pX + pY )/2
0 0
p total = (pX + pY )/2
(b)
ptotal = p0X + p0Y
(c)
ptotal > (p0X + p0Y )/2
(d)
m
. co
s em
g l a
a
m
m c. o
c. o s e m
s em la
gla ag
a
14
m . c
c. o s e m
m a
se
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Page 33
15. Question 15
The rate constant of a reaction at 600 K with an activation energy of
191.47 kJ mol−1 is 5.0 × 10−5 s−1 . What is the temperature at which
the half-life of the reaction becomes 152 s? [Consider pre-exponential fac-
tor and activation energy to be independent of temperature. R = 8.314 J
K−1 mol−1 ]
680 K
(a)
640 K
(b)
760 K
(c)
720 K
(d)
15
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The rate constant of a reaction at 600 K with an activation energy of
191.47 kJ mol−1 is 5.0 × 10−5 s−1 . What is the temperature at which
the half-life of the reaction becomes 152 s? [Consider pre-exponential fac-
tor and activation energy to be independent of temperature. R = 8.314 J
K−1 mol−1 ]
680 K
(a)
640 K
(b)
760 K
(c)
720 K
(d)
15
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Page 34
m
m .co
c. o
e m
em l a s
s a g
Mathematics
1. Question 1
Let p(x) be a quadratic polynomial such that p(1) = p(−1) = 0. What is
m
the coefficient of x in p(x)?
m .co
co m
(a) 0
m . s e
a
1
e
(b)
a s g l
l a
(c) −1
(d) g
a2
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
1
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 62
m .co
c. o
e m
em l a s
s a g
Mathematics
1. Question 1
Let p(x) be a quadratic polynomial such that p(1) = p(−1) = 0. What is
m
the coefficient of x in p(x)?
m .co
co m
(a) 0
m . s e
a
1
e
(b)
a s g l
l a
(c) −1
(d) g
a2
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
1
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 62
Page 35
2. Question 2
Consider the following sets of points in the complex plane
{ ( ) ( ) }
2nπ 2nπ
A = cos + i sin : n ∈ Z and
5 5
{ ( ) ( ) }
2n 2n
B = cos + i sin : n∈Z .
5 5
Which of the following statements is TRUE?
(a) A is finite but B is infinite.
(b) A is finite and B is also finite.
(c) A is infinite but B is finite.
(d) A is infinite and B is also infinite.
2
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Consider the following sets of points in the complex plane
{ ( ) ( ) }
2nπ 2nπ
A = cos + i sin : n ∈ Z and
5 5
{ ( ) ( ) }
2n 2n
B = cos + i sin : n∈Z .
5 5
Which of the following statements is TRUE?
(a) A is finite but B is infinite.
(b) A is finite and B is also finite.
(c) A is infinite but B is finite.
(d) A is infinite and B is also infinite.
2
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Page 36
m
m .co
c. o
e m
em l a s
s a g
3. Question 3
Consider the points A(4î + ĵ + 3k̂), B(2ĵ) and C(−4î + 3ĵ − 3k̂). Which of
the following statements is TRUE?
m
(a) A, B and C are collinear.
m .co
co
−−→ −−→ −→
(b)
m
AB + 3BC is perpendicular to AC.
m . s e
a
−−→ −−→
e l
(c) AB × BC = î + ĵ + k̂.
l a s
−−→ −−→ −→
a g
ag
(d) AB, BC and CA are mutually perpendicular.
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
3
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 35 of 62
m .co
c. o
e m
em l a s
s a g
3. Question 3
Consider the points A(4î + ĵ + 3k̂), B(2ĵ) and C(−4î + 3ĵ − 3k̂). Which of
the following statements is TRUE?
m
(a) A, B and C are collinear.
m .co
co
−−→ −−→ −→
(b)
m
AB + 3BC is perpendicular to AC.
m . s e
a
−−→ −−→
e l
(c) AB × BC = î + ĵ + k̂.
l a s
−−→ −−→ −→
a g
ag
(d) AB, BC and CA are mutually perpendicular.
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
3
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 35 of 62
Page 37
4. Question 4
Let l1 be the line joining (1, 1, 1) and (3, 1, 3) and let l2 be the line joining
(0, 2, −1) and (2, 0, 3). What is the angle between l1 and l2 ?
(a) 30o
(b) 60o
(c) 45o
(d) 90o
4
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Let l1 be the line joining (1, 1, 1) and (3, 1, 3) and let l2 be the line joining
(0, 2, −1) and (2, 0, 3). What is the angle between l1 and l2 ?
(a) 30o
(b) 60o
(c) 45o
(d) 90o
4
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Page 38
m
m .co
c. o
e m
em l a s
s a g
5. Question 5
Let r, l be two integers such that r ≥ l ≥ 3. What is the total number of
functions
f : {1, 2, . . . , r} → {1, 2, . . . , r}
m
such that f (1), f (2), . . . , f (l) are all distinct?
o m .co
c m
(a) rr−l+1 (r − 1)(r − 2) · · · (r − l + 1)
(b) r (r − 1)(r. − 2) · · · (r − l + 1) s e
e m l a
s
r−l
(c) r(r a
l a g
g
− 1)(r − 2) · · · (r − l + 1)
(d) a r
r
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
5
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 37 of 62
m .co
c. o
e m
em l a s
s a g
5. Question 5
Let r, l be two integers such that r ≥ l ≥ 3. What is the total number of
functions
f : {1, 2, . . . , r} → {1, 2, . . . , r}
m
such that f (1), f (2), . . . , f (l) are all distinct?
o m .co
c m
(a) rr−l+1 (r − 1)(r − 2) · · · (r − l + 1)
(b) r (r − 1)(r. − 2) · · · (r − l + 1) s e
e m l a
s
r−l
(c) r(r a
l a g
g
− 1)(r − 2) · · · (r − l + 1)
(d) a r
r
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
5
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 37 of 62
Page 39
6. Question 6
Let C be the set of all the circles in a plane. If
R = {(C1 , C2 ) ∈ C × C | C1 and C2 intersect},
then which of the following statements is TRUE?
(a) R is reflexive and symmetric but not transitive.
(b) R is reflexive and transitive but not symmetric.
(c) R is symmetric and transitive but not reflexive.
(d) R is not a relation.
6
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Let C be the set of all the circles in a plane. If
R = {(C1 , C2 ) ∈ C × C | C1 and C2 intersect},
then which of the following statements is TRUE?
(a) R is reflexive and symmetric but not transitive.
(b) R is reflexive and transitive but not symmetric.
(c) R is symmetric and transitive but not reflexive.
(d) R is not a relation.
6
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Page 40
m
m .co
c. o
e m
em l a s
s a g
7. Question 7
∫ 2
What is the value of min{1 − x, 1 − x3 } dx?
−1
m
(a)
co
−1
m .
co
0
m
(b)
m . s e
a
(c) 1
se g l
l a a
(d) 2
ag
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
7
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 39 of 62
m .co
c. o
e m
em l a s
s a g
7. Question 7
∫ 2
What is the value of min{1 − x, 1 − x3 } dx?
−1
m
(a)
co
−1
m .
co
0
m
(b)
m . s e
a
(c) 1
se g l
l a a
(d) 2
ag
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
7
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 39 of 62
Page 41
8. Question 8
Consider the data of scores obtained by students in an examination. If the
score of every student is increased by 2 marks, then which of the following
statements is TRUE?
(a) The mean deviation about the mean does not change.
(b) The mean deviation about the mean is increased by 2.
(c) The mean deviation about the median is increased by 2.
(d) The variance is increased by 2.
8
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Consider the data of scores obtained by students in an examination. If the
score of every student is increased by 2 marks, then which of the following
statements is TRUE?
(a) The mean deviation about the mean does not change.
(b) The mean deviation about the mean is increased by 2.
(c) The mean deviation about the median is increased by 2.
(d) The variance is increased by 2.
8
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9. Question 9
Consider the function f : R → R defined by f (x) = sin2 (7x) − sin2 (5x).
Which of the following statements is NOT TRUE?
( )
3π
m
(a) , 2π .
co
f is increasing on
2
m .
co m
( π)
. e
(b) f (x) > 0, for all x ∈ 0, .
s
48
em l a
s
( π)
a g
(c) f x+ + f (x) = 0, for all x ∈ R.
l a
2
(d) g
a
(π)
f =0
12
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
9
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 41 of 62
m .co
c. o
e m
em l a s
s a g
9. Question 9
Consider the function f : R → R defined by f (x) = sin2 (7x) − sin2 (5x).
Which of the following statements is NOT TRUE?
( )
3π
m
(a) , 2π .
co
f is increasing on
2
m .
co m
( π)
. e
(b) f (x) > 0, for all x ∈ 0, .
s
48
em l a
s
( π)
a g
(c) f x+ + f (x) = 0, for all x ∈ R.
l a
2
(d) g
a
(π)
f =0
12
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
9
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 41 of 62
Page 43
10. Question 10
For real numbers a and b, consider the function f : R → R given by
−ax − b if x < −1,
f (x) = 5x + 1 if − 1 ≤ x ≤ 1,
2
a x + 3b if x > 1.
How many pairs (a, b) are there for which f is continuous at every point of
R?
(a) 0
(b) 1
(c) 2
(d) infinitely many
10
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For real numbers a and b, consider the function f : R → R given by
−ax − b if x < −1,
f (x) = 5x + 1 if − 1 ≤ x ≤ 1,
2
a x + 3b if x > 1.
How many pairs (a, b) are there for which f is continuous at every point of
R?
(a) 0
(b) 1
(c) 2
(d) infinitely many
10
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Page 44
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11. Question 11
For a 2 × 2 matrix A, whose elements are real numbers, denote by Am the
product AA · · · A}, where m is a positive integer. Define x0 = 0, x1 = 1,
| {z
m times
xn = xn−1 + xn−2 , for all n ≥ 2 and
m
co
m .
xn+1 xn
An = , for all n ≥ 1.
co m
xn xn−1
m . s e
e a
Which of the following statements is TRUE for all m ≥ 3?
a s g l
g l
1 = A1 + Am−2
a
m−1
(a) Am
(b) a det(A ) = −1
1
m
[ ] [ ]
1 0 0 0
(c) Am m−1
1 − A1 + =
0 1 0 0
[ ] [ ]
1 0 0 0
(d) Am − Am−1 − =
0 1 0 0
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
11
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 43 of 62
m .co
c. o
e m
em l a s
s a g
11. Question 11
For a 2 × 2 matrix A, whose elements are real numbers, denote by Am the
product AA · · · A}, where m is a positive integer. Define x0 = 0, x1 = 1,
| {z
m times
xn = xn−1 + xn−2 , for all n ≥ 2 and
m
co
m .
xn+1 xn
An = , for all n ≥ 1.
co m
xn xn−1
m . s e
e a
Which of the following statements is TRUE for all m ≥ 3?
a s g l
g l
1 = A1 + Am−2
a
m−1
(a) Am
(b) a det(A ) = −1
1
m
[ ] [ ]
1 0 0 0
(c) Am m−1
1 − A1 + =
0 1 0 0
[ ] [ ]
1 0 0 0
(d) Am − Am−1 − =
0 1 0 0
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
11
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 43 of 62
Page 45
12. Question 12
Let a1 , a2 , a3 , . . . be a geometric progression of positive integers such that
a1 = 3 and an+2 − 2an = an+1 for all positive integers n. What is the value
of a1 + a2 + a3 + a4 + a5 ?
(a) 93
(b) 120
(c) 255
(d) 99
12
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Let a1 , a2 , a3 , . . . be a geometric progression of positive integers such that
a1 = 3 and an+2 − 2an = an+1 for all positive integers n. What is the value
of a1 + a2 + a3 + a4 + a5 ?
(a) 93
(b) 120
(c) 255
(d) 99
12
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Page 46
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13. Question 13
Let n = 2026 . What is the remainder when 49n + 41n + 10n is divided by
100?
(a) 2
m
(b) 1
m .co
(c) 90
.co s em
e m l a
a s g
(d) 49
l a
ag
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
13
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 45 of 62
m .co
c. o
e m
em l a s
s a g
13. Question 13
Let n = 2026 . What is the remainder when 49n + 41n + 10n is divided by
100?
(a) 2
m
(b) 1
m .co
(c) 90
.co s em
e m l a
a s g
(d) 49
l a
ag
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
13
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 45 of 62
Page 47
14. Question 14
Suppose there are two boxes B1 and B2 , each having 3 red and 4 black
balls. One ball is drawn at random from B1 . If it is red, 4 red balls are put
into B2 , otherwise 3 black balls are put into B2 . Then one ball is randomly
drawn from B2 . If this ball is red, what is the conditional probability that
the ball drawn from B1 was also red?
(a) 35
57
(b) 99
257
(c) 3
7
(d) 33
53
14
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Suppose there are two boxes B1 and B2 , each having 3 red and 4 black
balls. One ball is drawn at random from B1 . If it is red, 4 red balls are put
into B2 , otherwise 3 black balls are put into B2 . Then one ball is randomly
drawn from B2 . If this ball is red, what is the conditional probability that
the ball drawn from B1 was also red?
(a) 35
57
(b) 99
257
(c) 3
7
(d) 33
53
14
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Page 48
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15. Question 15
Let f : R → R be the function given by
f (x) = |x − 2| + 3|x − 1| + ||x − 2| − 1| .
m
What is the number of points where f is NOT differentiable?
m .co
.co m
(a) 2
m s e
e l a
(b) 1
l a s a g
(d) g
(c) 0
a3
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
15
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 47 of 62
m .co
c. o
e m
em l a s
s a g
15. Question 15
Let f : R → R be the function given by
f (x) = |x − 2| + 3|x − 1| + ||x − 2| − 1| .
m
What is the number of points where f is NOT differentiable?
m .co
.co m
(a) 2
m s e
e l a
(b) 1
l a s a g
(d) g
(c) 0
a3
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
15
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 47 of 62
Page 49
Physics
1. Question 1
A sphere and a cube of equal masses on a horizontal frictionless floor, are
confined between two vertical walls, as shown in the figure. The cube is
attached to the wall by a massless spring. At the equilibrium position of
the spring, the sphere just touches the cube. The cube is moved towards
the left by a small amount ℓ from its equilibrium position, compressing the
spring and is released at t = 0. The system keeps returning to its initial
configuration as that of t = 0 with a time period T . If all the collisions are
elastic, which of the following statements is correct?
If ℓ increases, T decreases.
(a)
If ℓ increases, T does not change.
(b)
If ℓ increases, T increases.
(c)
The sphere never moves.
(d)
1
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1. Question 1
A sphere and a cube of equal masses on a horizontal frictionless floor, are
confined between two vertical walls, as shown in the figure. The cube is
attached to the wall by a massless spring. At the equilibrium position of
the spring, the sphere just touches the cube. The cube is moved towards
the left by a small amount ℓ from its equilibrium position, compressing the
spring and is released at t = 0. The system keeps returning to its initial
configuration as that of t = 0 with a time period T . If all the collisions are
elastic, which of the following statements is correct?
If ℓ increases, T decreases.
(a)
If ℓ increases, T does not change.
(b)
If ℓ increases, T increases.
(c)
The sphere never moves.
(d)
1
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Page 50
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2. Question 2
A spherical concave mirror of focal length 10 cm and a double convex lens
of focal length 5 cm are arranged on the common principal axis as shown in
the figure. A small object is placed on the principal axis between the focal
points F1 and F2 of the mirror and the lens, respectively. If two real and
m
mutually inverted images are formed by the lens at the same location on
m .co
the principal axis, what is the distance of the object from the mirror on the
co m
principal axis?
m . s e
s e g l a
l a a
ag
F1 F2
50 cm
20 cm
(a)
m
co
30 cm
(b)
.
em
25 cm
s
(c)
(d)
12 cm
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
2
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 49 of 62
m .co
c. o
e m
em l a s
s a g
2. Question 2
A spherical concave mirror of focal length 10 cm and a double convex lens
of focal length 5 cm are arranged on the common principal axis as shown in
the figure. A small object is placed on the principal axis between the focal
points F1 and F2 of the mirror and the lens, respectively. If two real and
m
mutually inverted images are formed by the lens at the same location on
m .co
the principal axis, what is the distance of the object from the mirror on the
co m
principal axis?
m . s e
s e g l a
l a a
ag
F1 F2
50 cm
20 cm
(a)
m
co
30 cm
(b)
.
em
25 cm
s
(c)
(d)
12 cm
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
2
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 49 of 62
Page 51
3. Question 3
A simple pendulum of length L, mass m and electric charge q on its bob
is oscillating with a time period T under uniform gravity which is in the
−ẑ direction. Upon applying a uniform electric field |E|n̂ (where n̂ is a
unit vector in the plane of oscillation), the time period of the pendulum
decreases. Which of the following statements is NOT correct?
q is positive and n̂ = ẑ
(a)
q is positive and n̂ = −ẑ
(b)
q is negative and n̂ = ẑ
(c)
q is positive and n̂ · ẑ = − √12
(d)
3
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A simple pendulum of length L, mass m and electric charge q on its bob
is oscillating with a time period T under uniform gravity which is in the
−ẑ direction. Upon applying a uniform electric field |E|n̂ (where n̂ is a
unit vector in the plane of oscillation), the time period of the pendulum
decreases. Which of the following statements is NOT correct?
q is positive and n̂ = ẑ
(a)
q is positive and n̂ = −ẑ
(b)
q is negative and n̂ = ẑ
(c)
q is positive and n̂ · ẑ = − √12
(d)
3
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4. Question 4
A particle of mass m1 and electric charge q starts from rest under the
influence of a uniform external electric field E to travel a distance d in time
t1 . If the particle had mass m2 , it would take time t2 to travel the same
t1
distance. What is the ratio ?
m
co
t2
m .
.co em
r
s
m1
em l a
m2
s g
(a)
g
r
l a a
(b) a
m2
m1
m2
m1
(c)
m1
m2
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
4
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 51 of 62
m .co
c. o
e m
em l a s
s a g
4. Question 4
A particle of mass m1 and electric charge q starts from rest under the
influence of a uniform external electric field E to travel a distance d in time
t1 . If the particle had mass m2 , it would take time t2 to travel the same
t1
distance. What is the ratio ?
m
co
t2
m .
.co em
r
s
m1
em l a
m2
s g
(a)
g
r
l a a
(b) a
m2
m1
m2
m1
(c)
m1
m2
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
4
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 51 of 62
Page 53
5. Question 5
An exotic spherical jellyfish has a bulk modulus B. Close to the surface of
the sea (depth d=0), its radius is R. When it dives to a depth d (d ≫ R), its
radius is reduced by ∆R > 0. Given the density of the incompressible sea
water ρ, and the uniform acceleration due to gravity g such that ρgd ≪ B,
∆R
what is ?
R
1/3
1− 1− B
ρgd
(a)
2/3
1 − 1 − ρgd
B
(b)
2/3
1 + ρgd
B −1
(c)
1/3
1 + ρgd
B −1
(d)
5
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An exotic spherical jellyfish has a bulk modulus B. Close to the surface of
the sea (depth d=0), its radius is R. When it dives to a depth d (d ≫ R), its
radius is reduced by ∆R > 0. Given the density of the incompressible sea
water ρ, and the uniform acceleration due to gravity g such that ρgd ≪ B,
∆R
what is ?
R
1/3
1− 1− B
ρgd
(a)
2/3
1 − 1 − ρgd
B
(b)
2/3
1 + ρgd
B −1
(c)
1/3
1 + ρgd
B −1
(d)
5
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6. Question 6
A planet is revolving in a circular orbit with a time period T around the
center of a star solely under the gravity of the star. Suppose the distance
between the star and the planet is halved. The individual radii of the
star and the planet are also halved, keeping their uniform mass densities
m
unchanged. What will be the time period of the new orbit of the planet?
m .co
T
.co s em
m
(a)
s e g l a
a
2T
l a
(b)
agT2
(c)
T
4
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
6
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 53 of 62
m .co
c. o
e m
em l a s
s a g
6. Question 6
A planet is revolving in a circular orbit with a time period T around the
center of a star solely under the gravity of the star. Suppose the distance
between the star and the planet is halved. The individual radii of the
star and the planet are also halved, keeping their uniform mass densities
m
unchanged. What will be the time period of the new orbit of the planet?
m .co
T
.co s em
m
(a)
s e g l a
a
2T
l a
(b)
agT2
(c)
T
4
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
6
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 53 of 62
Page 55
7. Question 7
The position of a particle of mass 1 kg at time t is given by r = t î+ ĵ+2 t2 k̂,
where t is in seconds and the coefficients have the proper units for r to be
in metres. What is the component of the angular momentum (with respect
to the origin) in kg m2 s−1 along the vector (î + ĵ)?
√1 (4t − 2t2 )
2
(a)
√1 (4t + 6t2 )
2
(b)
4t − 2t2
(c)
4t + 6t2
(d)
7
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The position of a particle of mass 1 kg at time t is given by r = t î+ ĵ+2 t2 k̂,
where t is in seconds and the coefficients have the proper units for r to be
in metres. What is the component of the angular momentum (with respect
to the origin) in kg m2 s−1 along the vector (î + ĵ)?
√1 (4t − 2t2 )
2
(a)
√1 (4t + 6t2 )
2
(b)
4t − 2t2
(c)
4t + 6t2
(d)
7
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Page 56
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8. Question 8
A long solenoid of initial radius R0 is put in a region of uniform magnetic
field B with the axis of the solenoid aligned along the magnetic field. The
solenoid is a part of a closed circuit that has no initial current running
through it. If the radius of the solenoid starts increasing at a uniform rate,
m
how do the magnetic field strength Bin and the associated magnetic energy
m .co
Uin inside the solenoid change?
.co s em
e m a
Bin decreases, Uin decreases.
s l
(a)
l a a g
g
Bin increases, Uin decreases.
a B increases, U increases.
(b)
in in
(c)
Bin decreases, Uin increases.
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
8
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 55 of 62
m .co
c. o
e m
em l a s
s a g
8. Question 8
A long solenoid of initial radius R0 is put in a region of uniform magnetic
field B with the axis of the solenoid aligned along the magnetic field. The
solenoid is a part of a closed circuit that has no initial current running
through it. If the radius of the solenoid starts increasing at a uniform rate,
m
how do the magnetic field strength Bin and the associated magnetic energy
m .co
Uin inside the solenoid change?
.co s em
e m a
Bin decreases, Uin decreases.
s l
(a)
l a a g
g
Bin increases, Uin decreases.
a B increases, U increases.
(b)
in in
(c)
Bin decreases, Uin increases.
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
8
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 55 of 62
Page 57
9. Question 9
The acceleration of a point particle is given by the equation
d2 x x dx
=α 7 +β
dt2 |x| dt
where x denotes position and t denotes time. Which of the following
relations show the correct dimensions for α and β?
[α] = [M 0 L7 T −2 ]
[β] = [M 0 L0 T −1 ]
(a)
[α] = [M 1 L6 T −2 ]
[β] = [M 0 L0 T −3 ]
(b)
[α] = [M 0 L6 T −1 ]
[β] = [M 0 L1 T −2 ]
(c)
[α] = [M 0 L7 T −2 ]
[β] = [M 0 L0 T 0 ]
(d)
9
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The acceleration of a point particle is given by the equation
d2 x x dx
=α 7 +β
dt2 |x| dt
where x denotes position and t denotes time. Which of the following
relations show the correct dimensions for α and β?
[α] = [M 0 L7 T −2 ]
[β] = [M 0 L0 T −1 ]
(a)
[α] = [M 1 L6 T −2 ]
[β] = [M 0 L0 T −3 ]
(b)
[α] = [M 0 L6 T −1 ]
[β] = [M 0 L1 T −2 ]
(c)
[α] = [M 0 L7 T −2 ]
[β] = [M 0 L0 T 0 ]
(d)
9
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10. Question 10
Consider normal incidence of a monochromatic beam of photons of power
P on a flat surface. Of the incident beam, 10% gets absorbed, 10% gets
transmitted, and the rest is reflected by the flat surface. If c is the speed of
light, what is the force exerted on the flat surface by the beam?
m
m .co
co m
1.7 Pc
. e
(a)
em l a s
s g
1.8 Pc
l a a
(b)
(c) ag
1.6 P
c
0.9 Pc
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
10
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 57 of 62
m .co
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s a g
10. Question 10
Consider normal incidence of a monochromatic beam of photons of power
P on a flat surface. Of the incident beam, 10% gets absorbed, 10% gets
transmitted, and the rest is reflected by the flat surface. If c is the speed of
light, what is the force exerted on the flat surface by the beam?
m
m .co
co m
1.7 Pc
. e
(a)
em l a s
s g
1.8 Pc
l a a
(b)
(c) ag
1.6 P
c
0.9 Pc
(d)
m
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s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
10
m .
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e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 57 of 62
Page 59
11. Question 11
An experimental study of the photoelectric effect involves a metal of work
function ϕ0 . What is the smallest wavelength of the incident photon to
photoemit an electron of mass m which has the same de Broglie wavelength
as that of the incident photon? [Given h is the Planck’s constant, c is the
speed of light, and ϕ0 ≪ mc2 ]
r !−1
h 2ϕ0
1+ 1−
mc mc2
(a)
r !−1
h 2ϕ0
1− 1−
mc mc2
(b)
r !−1
h ϕ0
1− 1−
mc mc2
(c)
r !−1
h ϕ0
1+ 1−
mc mc2
(d)
11
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 58 of 62
An experimental study of the photoelectric effect involves a metal of work
function ϕ0 . What is the smallest wavelength of the incident photon to
photoemit an electron of mass m which has the same de Broglie wavelength
as that of the incident photon? [Given h is the Planck’s constant, c is the
speed of light, and ϕ0 ≪ mc2 ]
r !−1
h 2ϕ0
1+ 1−
mc mc2
(a)
r !−1
h 2ϕ0
1− 1−
mc mc2
(b)
r !−1
h ϕ0
1− 1−
mc mc2
(c)
r !−1
h ϕ0
1+ 1−
mc mc2
(d)
11
For more Question Papers, Sample Papers, Notes & Syllabus visit Page 58 of 62
Page 60
m
m .co
c. o
e m
em l a s
s a g
12. Question 12
The three numbers: (number of protons, number of neutrons, the radius)
r1
characterize a nucleus. What is the value of for two nuclei characterized
r2
by (1, 0, r1 ) and (4, 4, r2 )?
m
1
m .co
.co em
2
s
(a)
em l a
s g
2
8 la a
(b)
(c) g
a1
8
(d)
m
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s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
12
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 59 of 62
m .co
c. o
e m
em l a s
s a g
12. Question 12
The three numbers: (number of protons, number of neutrons, the radius)
r1
characterize a nucleus. What is the value of for two nuclei characterized
r2
by (1, 0, r1 ) and (4, 4, r2 )?
m
1
m .co
.co em
2
s
(a)
em l a
s g
2
8 la a
(b)
(c) g
a1
8
(d)
m
. co
s em
g l a
a
m
m .co
c. o se
m
s em g la
gla a
a
12
m .
.co s e m
e m la
l a s a g
ag For more Question Papers, Sample Papers, Notes & Syllabus visit Page 59 of 62
Document Details
| Board / Org | IISER |
| Exam | IISER AT |
| Type | Answer Key |
| Pages | 63 |
| Language | english |
| Updated | 23 Oct 2026 |