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Page 1

FOR NEST EXAM PREPARATION

NEST 2026
Question Paper
EXAM YEAR TYPE DETAILS

NEST 2026 Question Paper Answers

Notes · Sample Papers · Previous Year Papers · Mock Tests

Page 2

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NEST 2026 - Final Answer Keys

Revised After Closure of Objections
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Correct answers are option A* in all the questions.

Please note: The sequence of questions and options were di↵erent in the
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examinations.

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NEST - 2026

Biology

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1. Mendel’s law of independent assortment implies that
A. alleles segregate independent of one another during gamete forma-
tion.
B. alleles segregate independent of their location on the chromosome during ga-
mete formation.
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C. traits are encoded by independent genes.
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D. traits areoalways
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2. Bacteria have cell wall made of a polymer of N-acetylglucosamine and N-acetylmuramic
acid connected by -1,4 glycosidic bonds. Lysozyme, an enzyme, cleaves the glycosidic
bond and disrupts the cell wall structure.
In an experiment, Gram-positive and Gram-negative bacteria, which di↵er in terms of
cell envelope and peptidoglycan thickness, are treated with lysozyme and subsequently
placed in a hypotonic solution. The correct statement about the e↵ect of the treatment
is:
A. Gram-positive bacteria are lysed, but not Gram-negative bacteria.
B. Both Gram-positive and Gram-negative bacteria are lysed.
C. Only Gram-negative bacteria are lysed.
D. Neither Gram-positive nor Gram-negative bacteria are lysed.

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3. The fate of a cell in which pyruvate dehydrogenase is completely inhibited will be:
A. Glycolysis continues with NAD+ regeneration via lactate fermenta-
tion, yielding 2 ATP per glucose molecule.
B. Pyruvate accumulates and enters the Krebs cycle via an alternative pathway,
yielding 32 ATP per glucose molecule.
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C. Glycolysis stops due to NAD+ depletion, and no ATP is produced.
D. Pyruvate oism .
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fermentation.
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4. Two spherical unicellular organisms, X and Y, have the same cytoplasmic composition,
metabolic pathways, and live in identical nutrient-rich aerobic conditions. The diameters
of X and Y are, respectively, 10 and 20 µm. When nutrients are not limiting, the ratio
of total oxygen consumption per hour per cell of organisms Y to X is:
A. 8:1
B. 1:2
C. 2:1
D. 4:1

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5. In an experiment, bacteria were grown for 500 generations in a medium containing 14 N
(light isotope), then transferred to a medium with 15 N (heavy isotope) for one generation,
and finally transferred back to the 14 N medium for one more generation.
Assuming all cells divide synchronously and replication is semi-conservative, the ratio of
N15 N to 14 N14 N double-stranded DNA at the end of the experiment is:
14

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A. 1:1
B. 1:2
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C. 1:3
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D. 1:4
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6. In the roots of plants, casparian strip made of suberin forms a ring around the cells of
the endodermis. It e↵ectively blocks the entry of water and mineral ions into the stele
via the apoplast. A defect in the casparian strip leads to
A. increased solute leakage and reduced root hydraulic conductivity.
B. decreased solute leakage and increased root hydraulic conductivity.
C. increased solute leakage and increased root hydraulic conductivity.
D. decreased solute leakage and reduced root hydraulic conductivity.

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7. The ability of phloem to distribute sugar depends on the companion cell and sieve
element working as a complex. Consider the following statements with regard to possible
e↵ects of reduction in companion cell plasmodesmata.

(i) Sugar loading into sieve tubes reduces due to collapse in osmotic pressure gradient.
(ii) Water moves from companion cells into the xylem to maintain osmotic balance.
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(iii) The sieve tubes collapse structurally due to loss of turgor pressure.
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(iv) Reverse loading

s emcondition, the correct statements are:
Under the given
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A.la(i) and (iii) a
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C. (iii) and (iv)
D. (ii) and (iv)

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8. Carbonic anhydrase catalyzes the following reaction in red blood cells.

CO2 + H2 O )* H2 CO3 )* HCO3 – + H+

This reaction acts as a bu↵ering system in blood. Consequence of failure of the enzyme
to catalyze the reverse reaction is:
A. Blood becomes acidic and the affinity of haemoglobin for O2 de-
creases.
B. The pCO2 increases and the affinity of haemoglobin for CO2 increases.
C. The pO2 of the blood decreases and the affinity of haemoglobin for O2 increases.
D. Blood becomes acidic and the formation of carbamino-haemoglobin decreases.

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9. Events occurring during signal propagation in a chemical synapse are given below.

P: Postsynaptic membrane potential changes.
Q: Synaptic vesicle fuses with the presynaptic membrane.
R: Action potential depolarizes the presynaptic terminal.

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S: Neurotransmitter binds to receptors on the postsynaptic membrane.

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T: Neurotransmitter is released into the synaptic cleft.
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The correct sequence of occurrence of these events is:
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A. R, Q, T, S, P
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C. R, T, Q, P, S
D. Q, R, P, S, T

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10. In a population of 1000 moths, 450 moths were brown-colored with homozygous genotype
and 350 albino moths that were homozygous for the recessive allele. Assuming random
mating within the population, the frequency of heterozygotes in the next generation
would be:
A. 0.495
B. 0.200
C. 0.800
D. 0.505

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11. In a haplodiploid ant species, sons are haploid and produced from unfertilized eggs, while
daughters are diploid and produced from fertilized eggs. A single queen establishes a
colony after mating with three di↵erent unrelated males. The queen uses the sperm from
all three males equally to produce her female o↵spring. The average genetic relatedness
between two randomly selected female o↵spring in this colony will be:
A. 0.417
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B. 0.500
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C. 0.750
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D. 0.333
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12. In the axon of a giant squid neuron,

(i) The resting membrane potential is -70 mV.
(ii) At the equilibrium potential of Na+ (ENa+ = +55 mV) there is no net movement
of Na+ ions across the membrane.

In an experiment, when the axon is stimulated, the voltage-gated Na+ channels open.
The membrane potential peaks at +30 mV, where the resistance of the axonal membrane
for Na+ flow is 1 ⇥ 106 ⌦.
The net Na+ current (INa+ ) across the membrane and the direction of ionic movement
at the peak is:
A. INa+ = 25 nA; direction = into the cell
B. INa+ = 100 nA; direction = out of the cell
C. INa+ = 25 nA; direction = out of the cell
D. INa+ = 100 nA; direction = into the cell

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13. Consider a mitochondrion in which the F0 subunit of ATP synthase is mutated, such
that it can still passively conduct protons but is mechanically uncoupled from the F1
subunit. If such a mitochondrion is provided with succinate, ADP, and Pi in aerobic
conditions, the correct outcome based on chemiosmotic theory is:
A. Continuous oxygen consumption and no ATP synthesis.

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B. No oxygen consumption and no ATP synthesis.

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C. Rapid initial oxygen consumption that plateaus at a low rate and normal ATP
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D. Continuous oxygen consumption and normal ATP synthesis.
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14. Three di↵erent bacterial strains (P, Q, and R) when grown independently in a culture
medium showed typical growth curves. Equal number of cells from all three actively
growing cultures are mixed and grown together for 10 days. The number of bacteria (N)
are counted each day and plotted.

Assuming nutrients are not limiting, the correct explanation for the observed trend is:
A. Q is an antibiotic producer, P is antibiotic sensitive, and R is an-
tibiotic sensitive but evolves resistance during the course of the ex-
periment.
B. Q is an antibiotic producer, P is antibiotic sensitive, and R is antibiotic resis-
tant.
C. R is an antibiotic producer, P is antibiotic sensitive, and Q is antibiotic resis-
tant.
D. P is an antibiotic producer, Q is antibiotic resistant, and R is antibiotic sen-
sitive but evolves resistance during the course of the experiment.

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15. There is a di↵erence between the predicted and observed global carbon budget. The
possible reason is:
A. Higher CO2 levels stimulate plant growth and productivity, leading
to more carbon being sequestered in plant tissues and root systems.
B. Higher CO2 levels lead to increased soil respiration rates, releasing more carbon
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C. Oceans are absorbing more carbon due to increased temperature, resulting in
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D. The thinning of the stratospheric ozone layer allows higher levels of ultraviolet
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16. The fundamental niche of a species is the full range of environmental conditions and
resources a species can potentially occupy in the absence of limitations. The realized
niche is the actual, smaller subset of the fundamental niche that the species occupies
due to biotic limitations.
The distribution of populations of Species 1 and Species 2 over various levels towards
the shore of an aquatic habitat is shown in the figure.

Species 1 Species 2

Zone M
Water depth

Zone N

Zone O

Key: Fundamental Niche Realized Niche

Consider the following statements based on the distribution.

(i) Competition for resources between Species 1 and Species 2 is mainly in the zones
M and N.
(ii) Species 2 is a stronger competitor as compared to Species 1.
(iii) In absence of Species 2, Species 1 could prevail in zone O.
(iv) Species 2 probably has predators who thrive in zone O.

The correct statement(s) is(are):
A. (ii) and (iv)
B. (i) only
C. (ii) only
D. (i) and (iii)

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17. Desert ants are known to use landmarks (reference points), pedometers (memorising
step counts), and optic flow (rate of passing objects across its eye to estimate navigation
speed) to navigate across deserts. A desert ant is trained to walk 100 m from its nest to
a feeder in an artificial arena as depicted in the schematic. The arena had a single tall
landmark placed at 40 m from the nest.

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At the feeder, certain manipulations were performed before allowing the ant to return
to its nest with the food.

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Manipulation 1: Stilts were attached to its legs, which doubled the step length.
Manipulation 2: The optic flow of the arena was doubled.
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While the ant uses the landmark exclusively for long-distance (>55 m) navigation, it
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switches to optic flow and pedometer simultaneously and exclusively for short-distance
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navigation. Due to the manipulations, the distance from the feeder where the ant will
search its nest is:
A. 110 m
B. 100 m
C. 120 m
D. 160 m

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18. The table shows the presence (+) / absence (-) of features 1 – 5 for animals P – U.

P Q R S T U
1 – – – – – +
2 – – – – + +
3 – – – + + +
4 – – + + + +
5 – + + + + +

Based on the table, the correct statement is:
A. If Q and R represent lamprey and fish respectively, then feature 4
could be jaws.
B. Feature 5 is the most recently evolved trait.
C. If S, T and U are respectively amphibian, reptile and mammal, then feature
3 could be amniotic egg.
D. If S, T and U respectively are salamander, turtle and leopard, then features
1 and 2 could respectively represent hair and four legs.

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19. The trophic relationships between species in a habitat can be represented in the form of
a food web matrix where, rows represent consumers/ predators, and columns represent
resources/prey. If the organism of a species in the row eats the organism of a particular
species in the column, then a ‘1’ is placed in the intersection. Otherwise a ‘0’ is placed
in the intersection. Such a matrix for species M – Q is given below.

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Resources/Prey
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P
1
0
1 0 0
1 1 0
0
0
Q 1 0 0 0 0

Based on the matrix, the correct statement is:
A. Species P is both a secondary and tertiary consumer.

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B. Scarcity of species M can directly a↵ect primary consumers O and P.
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C. There are two producer species in .this ecosystem.
D. Species N is an omnivore. se
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20. A researcher wants to insert a linear DNA fragment into a plasmid DNA. The linear
DNA fragment has two MfeI restriction sites at its ends. The plasmid DNA has only
one EcoRI restriction site. The plasmid was digested with EcoRI and the DNA frag-
ment was digested with MfeI. The recognition sequences of the restriction enzymes on
one strand are given.

EcoRI site: 50 -G # AATTC-30

MfeI site: 50 -C # AATTG-30
(arrow indicates enzyme cut sites)
Based on this information, the DNA fragments generated by EcoRI and MfeI
A. can ligate to each other, but the resultant product can neither be
digested by EcoRI nor MfeI.
B. cannot ligate to each other because the overhangs generated are from two
di↵erent enzymes.
C. can ligate to each other, and the resultant product can be digested by EcoRI
but not MfeI.
D. can ligate to each other, and the resultant product can be digested by MfeI
but not EcoRI.

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NEST - 2026

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जीव �व mान-�हं
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1. मडे ल के तं वग�करण के �नयम का ता य� है �क

A. यु क �नमा� ण के दौरान एलील एक- सरे से तं प से अलग हो जाते ह।
B. यु क �नमा� ण के दौरान एलील गु णसू पर अपने ान से तं प से अलग होते ह।
C. ल ण तं जीन ारा कूटब �कए जाते ह।
D. ल ण हमे शा अलग-अलग गु णसू ारा कूटब होते ह।

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2. जीवाणु के को�शका की �भ� एन-ए�सटाइल ू कोसामाइन और एन-ए�सटाइलमु र�मक ए�सड से बनी को�शका
होती है जो -1,4 ाइको�स�डक बॉ से जु ड़ी होती है । लाइसोजाइम नामक एक एंजाइम, ाइको�स�डक
बं धन को तोड़ता है और को�शका �भ� सं रचना को बा�धत करता है ।
एक योग म, ाम-पॉ�ज�टव और ाम-ने गे �टव जीवाणु , जो को�शका के आवरण और पे ��डो ाइकन की
सघनता के मामले म �भ होते ह, को लाइसोजाइम के साथ उपचा�रत �कया जाता है और बाद म एक हाइपोटो�नक
घोल म रखा जाता है । उपचार के भाव के बारे म सही कथन है ः
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c. o जीवाणु लयन ह गे ह, ले �कन ाम-ने गे �टव जीवाणु नह ।
A. ाम-पॉ�ज�टव
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B. दोनem l a
a s ाम-पॉ�ज�टव और ाम-ने गे �टव जीवाणु लयन ह।
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gC.l केवल ाम-ने गे �टव जीवाणु लयन होते ह।
a D. न तो ाम-पॉ�ज�टव और न ही ाम-ने गे �टव जीवाणु लयन होते ह।

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3. एक को�शका �जसम पाय वे ट �डहाइ ोजने ज पू री तरह से बा�धत होता है , उसका प�रणाम होगाः

A. ाइकोलाइ�सस लै े ट �क न के मा म से NAD+ पु नज� नन के साथ जारी रहे गा, �जससे �त
ू कोज अणु 2 ATP ा होगा।
B. पाय वे ट जमा होता है और एक वै क��क माग� के मा म से े च (Krebs cycle) म वे श
करता है , �जससे �त ू कोज अणु 32 ATP ा होगा।
C. ाइकोलाइ�सस NAD+ की कमी के कारण क जाता है , और कोई ATP उ नह होगा।
D. पाय वे ट को ए�सटाइल को. ए. (Acetyl CoA) म प�रव�त� त �कया जाता है , �जससे �क न के
मा म से �त ू कोज अणु 8 ATP ा होगा।

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4. दो गोलाकार एकको�शकीय जीव, X और Y, म समान को�शका सं रचना, चयापचय माग� होते ह, और समान
पोषक त से भरपू र एरो�बक � �तय म रहते ह। X और Y का ास मशः 10 और 20 माइ ोन है । जब
पोषक त सी�मत नह होते ह, तो जीव की �त को�शका �त घं टे कुल ऑ ीजन खपत का अनु पात Y से X है ः

A. 8:1

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C. 2:1
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D. 4:1
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5. एक योग म, जीवाणु को 500 पी�ढ़य के �लए एक ऐसे मा म म �वक�सत �कया गया था �जसम 14 N (ह ा
आइसोटोप) था, �फर एक पीढ़ी के �लए 15 N (भारी आइसोटोप) के साथ एक मा म म ानां त�रत �कया गया,
और अंत म एक और पीढ़ी के �लए 14 N मा म म वापस ानां त�रत �कया गया।
यह मानते ए �क सभी को�शकाएं समका�लक प से �वभा�जत होती ह और �तकृ�त अध� - �ढ़वादी होती है ,
योग के अंत म दोहरे- े े ड डीएनए 14 N15 N से 14 N14 N का अनु पात है ः

A. 1:1
B. 1:2
C. 1:3
D. 1:4

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6. पौध की जड़ म, सु बे �रन से बनी कै े �रयन प ी एंडोड�म� स की को�शका के चार ओर एक वलय बनाती है ।
यह भावी प से एपो ा के मा म से ीले म पानी और ख�नज आयन के वे श को अव करती है ।
कै े �रयन प ी के एक दोष की वजह से
A. �वलय के �रसाव म वृ � होगी और जड़ की हाइ ो�लक चालकता म कमी होगी।
B. �वलय के �रसाव म कमी होगी और जड़ की हाइ ो�लक चालकता म वृ � होगी।
m
C. �वलय के �रसाव म वृ �
m
होगी और जड़ की हाइ ो�लक चालकता म वृ � होगी।
. co
c. o म कमी होगी और जड़ की हाइ ो�लक चालकता म कमी होगी।
D. �वलय के �रसाव
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7. ोएम की शक�रा �वत�रत करने की मता सहको�शकाएँ और चालनी त पर �नभ� र करती है जो एक स�म
के प म काम करती है । सहको�शका के ा ोडे ाटा म कमी के सं भा�वत भाव के सं बं ध म �न �ल�खत
कथन पर �वचार कर।

(i) ऑ ो�टक े शर े �डएंट म �गरावट के कारण चालनी न�लका म शक�रा की लो�डं ग कम हो जाती है ।
(ii) परासरण सं तु लन बनाए रखने के �लए पानी सहको�शका से जाइले म म चला जाता है ।
(iii) टग� र दबाव के ास के कारण चालनी नलीयाँ सं रचना क प से ढह जाती ह।
(iv) दबाव ु म के कारण ोएम म शक�रा की �रवस� लो�डं ग तु रंत शु हो जाती है ।

दी गई � �त के तहत, सही कथन है ः

A. (i) और (iii)
B. (i) और (ii)
C. (iii) और (iv)
D. (ii) और (iv)

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8. काब� �नक एनहाइ े स लाल र को�शका म �न �ल�खत अ�भ� या को उ े �रत करता है ।

CO2 + H2 O ) * H2 CO3 ) * HCO3 – + H+

यह अ�भ� या र म एक बफ�रंग णाली के प म काय� करती है । �वपरीत अ�भ� या को उ े �रत करने म
एंजाइम की �वफलता का प�रणाम है ः
m
A. र अ ीयoहो mजाता है और O के �लए हीमो ो�बन की आ ीयता कम हो जाती है । . co
.c 2

B. pCOmबढ़ जाता है और CO के �लए हीमो ो�बन की आ ीयता बढ़ जाती है । s em
C. a
e
र s का pO कम हो जाता है और O के �लए हीमो ो�बन की आ ीयता बढ़ जाती है ।
2 2

g la
g l र अ ीय हो जाता है और काबा� �मनो-हीमो ो�बन का �नमा� ण कम हो जाता है ।
2 2
a
a D.

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Page 33

9. रासाय�नक �सनै म सं केत सार के दौरान होने वाली घटनाएं नीचे दी गई ह।

P: पो �सनै ��क �झ ी �वभव प�रवत� न।
Q: �सनै ��क पु �टका ी�सनै ��क �झ ी के साथ सं लयन करती है ।
R: ए न पोट�शयल ी�सनै ��क ट�म� नल को �व ु वीकृत करता है ।
S: ू रो ां समीटर पो �सनै ��क �झ ी पर ाही से जु ड़ता है ।
T: ू रो ां समीटर �सनै ��क े म छोड़ �दया जाता है ।

इन घटना की घटना का सही अनु म है ः

A. R, Q, T, S, P
B. Q, R, T, S, P
C. R, T, Q, P, S
D. Q, R, P, S, T

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10. 1000 कीट की आबादी म, 450 कीट सम पी जीनोटाइप के साथ भू रे रंग के थे और 350 रंजकहीन कीट
जो अ भावी एलील के �लए सम पी थे । जनसं ा के भीतर या � क सं भोग को मानते ए, अगली पीढ़ी म
�वषमयु की आवृ � होगीः
A. 0.495
B. 0.200
m
C. 0.800
om . co
D. 0.505
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Page 35

11. एक है ो�ड ॉइड च टी जा�त म, बे टे है ोइड होते ह और अ�नषे �चत अंड से उ होते ह, जब�क बे �टयां
� गु �णत (diploid) होती ह और �नषे �चत अंड से उ होती ह। एक एकल रानी तीन अलग-अलग असं बं �धत
पु ष के साथ सं भोग करने के बाद एक उप�नवे श ा�पत करती है । रानी अपनी मादा सं तान पै दा करने के �लए
तीन पु ष के शु ाणु का समान प से उपयोग करती है । इस उप�नवे श म या � क प से चु नी गई दो
मादा सं तान के बीच औसत आनु वं �शक सं बं ध होगाः
A. 0.417
B. 0.500
C. 0.750
D. 0.333

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12. एक �वशाल ��ड तं � का को�शका के अ त ु म,

(i) �व ाम �झ ी मता-70 mV है ।
(ii) Na+ (ENa+ = +55 mV) की सं तु लन मता पर �झ ी के आरपार Na+ आयन की कोई �नवल ग�त
नह होती है ।

m
co
एक योग म, जब अ त ु को उ े �जत �कया जाता है , तो �व ु त् �नयं � त Na+ चै नल खु लते ह। �झ ी मता

. c om
+30 mV पर चरम पर है , जहाँ Na+ वाह के �लए अ तं तु �झ ी का �तरोध 1 ⇥ 106 ⌦ है ।
e m .
�झ
m
ी के आरपार �नवल Na+ current (INa+ ) और चरम पर आय�नक ग�त की �दशा है ः
e l as
a s
A. INa+ = 25 nA; �दशा = क म
l = 100 nA; �दशा = क से बाहर ag
g
a C. I = 25 nA; �दशा = क से बाहर
B. INa+

Na+

D. INa+ = 100 nA; �दशा = क म

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13. एक माइटोकॉ�� यन पर �वचार कर �जसम ATP �सं थे स (synthase) की F0 उप-इकाई उ �रव�त� त होती है ,
जै से �क यह अभी भी �न��य प से ोटॉन का सं चालन कर सकता है ले �कन यां � क प से F1 उपइकाई
से अलग होता है । य�द इस तरह के माइटोकॉ�� यन को एरो�बक � �तय म स� ने ट (succinate), एडीपी
(ADP) और Pi दान �कया जाता है , तो रसायन परासरणी (chemiosmotic) �स ां त पर आधा�रत सही प�रणाम
है ः
A. लगातार ऑ ीजन की खपत और कोई ATP सं े षण नह ।
B. ऑ ीजन की खपत नह और कोई ATP सं े षण नह ।
C. ारं�भक ऑ ीजन की ती खपत जो कम दर पर � र हो जाती ह और सामा ATP सं े षण।
D. लगातार ऑ ीजन की खपत और सामा ATP सं े षण।

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14. तीन अलग-अलग जीवाणु उपभे द (P, Q, और R) जब एक सं वध� न मा म म तं प से �वक�सत �कये जाते
ह तो �व�श �वकास व �दखाई दे ते ह। स� य प से बढ़ने वाले तीन सं वध� न से समान सं ा म को�शका
को �मलाया जाता है और 10 �दन के �लए एक साथ �वक�सत जाता है । जीवाणु की सं ा (N) को े क �दन
�गना जाता है (days in culture) और ॉट �कया जाता है ।

m
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ag

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यह मानते ए �क पोषक त
g l a
सी�मत नह ह, दे खी गई वृ � के �लए सहीा ा है ः

a
A. Q एक एंटीबायो�टक उ ादक है , P एंटीबायो�टक सं वे दनशील है , और R एंटीबायो�टक सं वे दनशील
है ले �कन योग के दौरान �तरोध �वक�सत करता है ।
B. Q एक एंटीबायो�टक उ ादक है , P एंटीबायो�टक सं वे दनशील है , और R एंटीबायो�टक �तरोधी
है ।
C. R एक एंटीबायो�टक उ ादक है , P एंटीबायो�टक सं वे दनशील है , और Q एंटीबायो�टक �तरोधी
है ।
D. P एक एंटीबायो�टक उ ादक है , Q एंटीबायो�टक �तरोधी है , और R एंटीबायो�टक सं वे दनशील
m
m है ले �कन योग के दौरान �तरोध �वक�सत करता है ।
.co
m .co s e m
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15. अनु मा�नत और पाए गए वै � क काब� न बजट के बीच अंतर है । सं भा�वत कारण है ः
A. उ CO2 र पौध के �वकास और उ ादकता को उ ी�पत करते ह, �जससे पौध के ऊतक और
जड़ णा�लय म अ�धक काब� न पृ थक हो जाता है ।
B. उ CO2 र �म ी के सन दर म वृ � करता ह, �जससे वातावरण म अ�धक काब� न उ �ज� त
होता है ।
C. तापमान म वृ � के कारण महासागर अ�धक काब� न को अवशो�षत कर रहा ह, �जसके प�रणाम प
अ ीकरण बढ़ रहा है ।
D. समतापमं डलीय ओजोन परत के पतले होने के कारण उ र पराबगनी �व�करण सीधे CO2 अणु
को तोड़ते है ।

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16. एक जा�त (species) का मौ�लक ान (fundamental niche) सं भा�वत प से पया� वरणीय � �तय और
उन सं साधन की पू री ृं खला है , जो एक जा�त सीमा के अभाव म क ा कर सकती है । वा �वक ान
(realized niche), मौ�लक ान का एक छोटा उपसमु य है जो जा�त जै �वक सीमा के कारण क ा
करती है ।
जल की गहराई (Water Depth) के सं बं ध म जलीय आवास के तट की ओर �व�भ े (zone) पर जा�तय
1 और जा�तय 2 की आबादी का �वतरण �च म �दखाया गया है ।
m
om . co
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e m
Species 2
l as
l as ag
ag Zone M
Water depth

Zone N

om
Zone O

. c
e m
l as
Key: ag Niche
Fundamental Realized Niche

�वतरण के आधार पर �न �ल�खत कथन पर �वचार कर।

(i) जा�तय 1 और जा�तय 2 के बीच सं साधन के �लए �त धा� मु प से M और N े म है ।
(ii) जा�तयां 2 जा�तय 1 की तु लना म एक मजबू त �तयोगी है ।
(iii) जा�तय 2 की अनु प� �त म, जा�तयां 1 े O म बल हो सकती है ।
m
m (iv) जा�तय 2 के परभ ी सं भवतः े O म पनपते ह।
c. o सही कथन है ( ह): m.co
m s e
s e g la
g la A. (ii) और (iv) a
a B. केवल (i)
C. केवल (ii)
D. (i) और (iii)

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17. रे�ग ान च �टय को रे�ग ान म ने �वगे ट करने के �लए लडमाक� (सं दभ� �बं / landmark), पे डोमीटर (कदम
की �गनती को याद रखना), और ऑ��क वाह (ने �वगे शन ग�त का अनु मान लगाने के �लए अपनी आंख के सामने
से गु जरती ई व ु को पार करने की दर) का उपयोग करने के �लए जाना जाता है । एक रे�ग ानी च टी को
एक कृ� म े म अपने घ सले (nest) से फीडर (feeder) तक 100 मीटर चलने के �लए �श� त �कया जाता
है जै सा �क योजनाब म दशा� या गया है । अखाड़े म घ सले से 40 मीटर की री पर एक लं बा ल�च था।

फीडर म, च टी को भोजन के साथ अपने घ सले म लौटने की अनु म�त दे ने से पहले कुछ हे रफेर �कए गए थे ।
हे रफेर 1: इसके पै र पर � जोड़े गए थे , �जससे कदम की लं बाई दोगु नी हो गई।
हे रफेर 2: अखाड़े का ऑ��क वाह दोगु ना �कया गया था।
जब�क च टी �वशे ष प से लं बी री (>55 m) ने �वगे शन के �लए लडमाक� का उपयोग करती है , यह एक साथ
और �वशे ष प से कम री के ने �वगे शन के �लए ऑ��क ो और पे डोमीटर पर � च करती है । हे रफेर के
कारण, फीडर से री जहां च टी अपने घ सले की खोज करेगीः
A. 110 m
B. 100 m
C. 120 m
D. 160 m

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18. ता�लका जानवर (P – U) के �वशे षता (1-5) की उप� �त (+)/अनु प� �त (-) �दखाती है ।

P Q R S T U
1 – – – – – +
2 – – – – + +
3 – – – + + +
m
om
4 – – + + + +
. co
. c 5 – + + + + +
e m
e m l as
l as
ता�लका के आधार पर, सही कथन है ः
ag
g
aA. य�द Q और R मशः लै े और मछली का �त�न�ध करते ह, तो ीचर 4 जबड़े हो सकते ह।
B. �वशे षता 5 सबसे हाल ही म �वक�सत ई है ।
C. य�द S, T और U मशः उभयचर, सरीसृ प और नधारी ह, तो �वशे षता 3 उ ीय (amniotic)
अंडा हो सकता है ।
D. य�द S, T और U मशः सै लामडर, कछुआ और त आ ह, तो �वशे षता 1 और 2 मशः बाल और
चार पै र का �त�न�ध कर सकते ह।

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o
Page 19
e m
em as
s
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19. एक आवास म जा�तय के बीच पोषण सं बं ध को एक खा जाल आ ू ह (food web matrix) के प म दशा� या
जा सकता है , जहां पं � याँ उपभो ा /�शका�रय का �त�न�ध करती ह, और कॉलम सं साधन /�शकार का
�त�न�ध करते ह। य�द पं � म �कसी जा�त का जीव कॉलम म �कसी �वशे ष जा�त के जीव को खाता है , तो
’1’ को �त े दन म रखा जाता है । अ था एक ’0’ �त े दन म रखा जाता है । जा�त M-Q के �लए ऐसा आ ू ह
(मै � ) नीचे �दया गया है ।

सं साधन / �शकार
M N O P Q
M 0 0 0 0 0
N 1 0 0 0 0
उपभो ा /परभ ी O 1 1 0 0 0
P 0 1 1 0 0
Q 1 0 0 0 0

आ ू ह (मै � ) के आधार पर, सही कथन है ः
A. जा�त P � तीयक और तृ तीयक उपभो ा दोन है ।
B. जा�त M की कमी, ाथ�मक उपभो ा O और P को सीधे भा�वत कर सकती है ।
C. इस पा�र� �तकी तं म दो उ ादक जा�तयाँ ह।
D. जा�त N एक सव� भ ी है ।

Page 20

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m .co s e m NEST 2026 Question Paper

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20. एक शोधकता� ा� ड डीएनए (DNA) म एक डीएनए खं ड (�जसके सं रचना म दो खु ले छोर ह) डालना चाहता
है । डीएनए खं ड के दोन छोर पर M f eI �तबं धन ल ह। ा� ड डीएनए म केवल एक EcoRI �तबं धन
ल है । ा� ड डीएनए को EcoRI के साथ �वखं �डत �कया गया था और डीएनए खं ड को M f eI के साथ
�वखं �डत �कया गया था। �तबं ध एंजाइम के एक लड़ी (one strand) पर पहचान अनु म नीचे �दए गए ह।

EcoRI site: 50 -G # AATTC-30
o m
M f eI site: 5 -C # m
o . c
c AATTG-3
m
0 0

m . s e
s e
(तीर एंजाइम काटने का ान इं �गत करता है )
g l a
g l
इस जानकारी a क
े आधार पर, EcoRI और M f eI ारा उ डीएनए खं ड।
a �डत
a A. एक सरे से जु
�कया जा सकता है ।
ड़ सकते ह, ले �कन प�रणामी उ ाद को न तो EcoRI और न ही M f eI ारा �वखं

B. एक- सरे से जु ड़ नह सकते �क उ ओवरहग �सरे दो अलग एंजाइम से बने ह।
C. एक सरे से जु ड़ सकते ह, और प�रणामी उ ाद को EcoRI ारा �वखं �डत �कया जा सकता है , ले �कन
M f eI ारा नह ।
D. एक सरे से जु ड़ सकते ह, और प�रणामी उ ाद को M f eI ारा �वखं �डत �कया जा सकता है ले �कन
EcoRI ारा नह ।
m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o
Page 21
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em as
s
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NEST - 2026

Chemistry

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Page 46

.
m .co s e m NEST 2026 Question Paper

s e l a
a ag
1. The reaction that produces butanoic acid as a product is

A.

m
om . co
. c e m
B.
e m l as
l as ag
g
a C.

D.

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 2
. c
. c e m
m as
se
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Page 47

2. The compound that produces aromatic species upon deprotonation of the indicated
hydrogen is:

A.

B.

C.

D.

Page 3

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m .co s e m NEST 2026 Question Paper

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a ag
3. Two students (P and Q) independently made three measurements (denoted by I,
II, and III) of the same property. The expected correct value is 9.0. The observed
values by the students are provided in the given table.

Student I II III Average
P 8.9 9.1 9.0 9.0
m
co
Q 8.0 9.0 10.0 9.0

. c om e m .
Based on the given data, the correct statement is:
em l as
l as
A. Both P and Q are equally accurate but P is more precise than
ag
g Q.
a B. P is more accurate but less precise than Q.
C. P is less accurate but more precise than Q.
D. Both P and Q are equally precise but P is more accurate than Q.

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 4
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Page 49

4. Species that are both isoelectronic and isostructural are:
A. NH+
4 and BH4

B. O3 and NO+
2

C. N2 O and NO2
D. NH2 and BH4

Page 5

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Page 50

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m .co s e m NEST 2026 Question Paper

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a ag
5. Two galvanic cells, Cell I and Cell II, operate at the same temperature and involve
two di↵erent redox systems. It is observed that at a particular value of the reaction
quotient QI = QII = Q0 , the ratio of EMF of the two cells (EI /QII ) as well as
the ratio of change of Gibbs free energy for the two cells ( GI / GII ) are both 1/3.
Assuming standard cell reactions written in the spontaneous direction and reversible
operation, the pair of cells can satisfy these conditions is
m
om
A. Cell I: Zn(s)|Zn2+ (aq)||Ag+ (aq)|Ag(s)
. co
c
Cell II: Zn(s)|Zn2+ (aq)||Cu2+ (aq)|Cu(s)
. e m
m
eCell I: Ag (aq)|Ag(s)||Fe (aq)|Fe (aq) l as
as
B. +

l Cell II: Al(s)|Al (aq)||Ag (aq)|Ag(s)
2+ 3+

ag
ag 3+ +

C. Cell I: Zn(s)|Zn2+ (aq)||Cu2+ (aq)|Cu(s)
Cell II: Al(s)|Al3+ (aq)||Ag+ (aq)|Ag(s)

D. Cell I: Fe2+ (aq)|Fe3+ (aq)||Cu2+ (aq)|Cu+ (aq)
Cell II: Cu(s)|Cu2+ (aq)||Ag+ (aq)|Ag(s)

m
m .co
s e
Question Droppedl a
ag

m
m .co
m .co s e m
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g la a
a

om
Page 6
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Page 51

6. Consider the following compound.

The compound undergoes reaction with two equivalents of diisobutyl aluminium
hydride followed by acid hydrolysis to provide P as the major product. The structure
of P is:

A.

B.

C.

D.

Page 7

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m .co s e m NEST 2026 Question Paper

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7. tert-Butylbenzene reacts with 1-chloro-2-methylpropane in the presence of anhy-
drous AlCl3 . The major product in this reaction is:

A.
m
om . co
. c e m
B.e m l as
l as ag
ag
C.

m
m .co
D.
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 8
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. c e m
m as
se
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Page 53

8. Consider the following compound.

The compound reacts with SOCl2 to produce P. P reacts with dimethyl cadmium
to produce Q. Q upon reaction with ethyl magnesium bromide (3 equiv) followed
by water workup produces R. The structure of R is:

A.

B.

C.

D.

Page 9

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m .co s e m NEST 2026 Question Paper

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9. Acetylene is passed through red hot iron tube at 873 K to produce P. P reacts with
chlorine gas in the presence of anhydrous AlCl3 to produce Q. Q reacts with benzyl
chloride and sodium to produce R as the major product. The structure of R is:

A.
m
om . co
. c e m
e m l as
as
l B. ag
ag

C.

m
D.
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 10
. c
. c e m
m as
se
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10. 1,2-dimethylbenzene on treatment with chromic oxide in acetic anhydride at 273-
283 K followed by hydrolysis produces P. P on heating with concentrated NaOH
followed by hydrolysis provides Q. The functional groups present in the product Q
are:
A. One carboxylic acid and one alcohol
B. Two aldehydes
C. One aldehyde and one carboxylic acid
D. Two carboxylic acids

Page 11

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m .co s e m NEST 2026 Question Paper

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11. The increasing order of acidic strength for the aqua complexes [V(H2 O)6 ]2+ , [Fe(H2 O)6 ]2+ ,
[Fe(H2 O)6 ]3+ , and [Co(H2 O)6 ]3+ is:
A. [V(H2 O)6 ]2+ < [Fe(H2 O)6 ]2+ < [Fe(H2 O)6 ]3+ < [Co(H2 O)6 ]3+
B. [Fe(H2 O)6 ]2+ < [Fe(H2 O)6 ]3+ < [V(H2 O)6 ]2+ < [Co(H2 O)6 ]3+
C. [Co(H2 O)6 ]3+ < [Fe(H2 O)6 ]3+ < [Fe(H2 O)6 ]2+ < [V(H2 O)6 ]2+
m
om
D. [Fe(H2 O)6 ]2+ < [Fe(H2 O)6 ]3+ < [Co(H2 O)6 ]3+ < [V(H2 O)6 ]2+
. co
. c e m
e m l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 12
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. c e m
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Page 57

12. Consider the following table of three lanthanoid ions X, Y, and Z and their prop-
erties.

Lanthanoid Ions Properties
X Diamagnetism
Y Reducing agent in solution
Z Empty 4f orbitals

Atomic numbers of Ce, Eu, and Lu are 58, 63, and 71, respectively. Given these
atomic numbers, the lanthanoid ions X, Y, and Z, respectively, are:
A. Lu3+ , Eu2+ , and Ce4+
B. Lu3+ , Ce4+ , and Eu2+
C. Eu2+ , Ce4+ , and Lu3+
D. Eu2+ , Lu3+ , and Ce4+

Page 13

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m .co s e m NEST 2026 Question Paper

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13. Consider the following complex ions:

[Ni(CN)4 ]2 , [Fe(CN)6 ]3 , [Cu(H2 O)6 ]2+ , and [Co(CN)6 ]3 .

The complex ions that are expected to show diamagnetic behavior at room tem-
perature are:
m
m
A. [Ni(CN)4 ]2 and [Co(CN)6 ]3
. co
c. o ] and [Cu(H O) ]
B. [Ni(CN) 4
2
2 6
2+

s e m
C. m a
s e[Co(CN) ] and [Fe(CN) ]
6
3
6
3

g l
g laD. [Cu(H O) ] and [Co(CN) ]
2+ 3
a
a
2 6 6

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
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14. Consider the following species:

(i) ClO
(ii) ClO2
(iii) ClO3
(iv) ClO4

Among them, the species that undergoes(undergo) disproportionation reactions is(are):
A. (i), (ii), and (iii) only
B. (iv) only
C. (i) and (ii) only
D. (iii) and (iv) only

Page 15

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m .co s e m NEST 2026 Question Paper

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15. X, Y, and Z are three volatile liquids, which when mixed make an ideal solution. At
a given temperature T0 , the constituents X, Y, and Z have pure vapour pressures
in the ratio 3:2:1. A mixture prepared with mole-fractions of X, Y, and Z in the
ratio 1:2:3 starts to boil at temperature T0 at 1.5 atm pressure. At temperature T0 ,
the partial vapour pressure (in atm) of Y is:
3
m
co
A.

om .
5
B.
9
. c e m
e m10
l as
l asC.
1
ag
ag D.
6
9
20

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 16
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Page 61

16. Consider a reversible thermodynamic process involving one mole of ideal gas repre-
sented by a line on the P V diagram connecting two states X (4 bar, 1 L, T1 ) and
Y (1 bar, 2 L, T2 ) as shown in the figure:

During the process the change in temperature (in K) as a function of volume (in L)
is best represented as:

A.

B.

Page 17

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m .co s e m NEST 2026 Question Paper

s e l a
a ag

m
om . co
. c e m
e m l as
l as
C.
ag
ag

m
D.
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 18
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. c e m
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Page 63

17. PQ2 is a sparingly soluble salt with solubility product Ksp = 4 ⇥ 10 12 in aqueous
medium at some given temperature. It is observed that upon addition of a highly
soluble salt RQ at the same temperature, the solubility of PQ2 drops by a factor
of 100. The concentration (in millimoles per litre) of added RQ in the solution is
closest to:
A. 2
B. 0.2
C. 20
D. 0.02

Page 19

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m .co s e m NEST 2026 Question Paper

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18. Consider the following chemical reactions performed at identical temperature and
volume:

Experiment I: X(g) ↵ 2Y(g)
Experiment II: X(g) ↵ Z(g)

m
om
The partial pressure of the reactant and product are denoted, respectively, by
. co
c
preactant and pproduct during the course of the reactions. Assuming ideal gas be-
. e m
m
haviour, the correct plot of preactant versus pproduct for Experiments I and II is:
e l as
l as ag
ag

A.
m
m .co
s e
l a
ag

B.

m
m .co
m .co s e m
s e g la
g la a
a
C.

om
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Page 65

D.

Page 21

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m .co s e m NEST 2026 Question Paper

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19. If velocity of an electron in the first Bohr orbit is denoted by v0 , then the velocity
(v) of the electron in other orbits (as a function of principle quantum number ‘n’)
is represented as

m
om . co
. c e m
e m l as
l as ag
ag
A.

m
m .co
s e
l a
ag
B.

m
m .co
m .co s e m
s e g la
g la C. a
a

om
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Page 67

D.

Page 23

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m .co s e m NEST 2026 Question Paper

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20. Consider two reactions.

I. A zero order reaction: X! P1 .
II. A first order reaction: Y! P2 .

Both reactions begin simultaneously with the same initial concentration ‘C’, that is
m
co
X0 = Y0 = C. It is observed that the concentrations of the reactants fall to one-third

. c om
of their initial values at the same time, provided the rate constants satisfy a certain
e m .
ratio. If k0 and k1 denote, respectively, the zero and first order rate constants then
em l as
s
the ratio k0 /k1 necessary for this condition to be satisfied is

l a 2C ag
ag A.
3ln3
C
B.
ln3
C
C.
ln2
3C
D.
2ln2

m
m .co
s e
l a
ag

m
m .co
m .co s e m
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Page 69

NEST - 2026

रसायन �व ान

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m .co s e m NEST 2026 Question Paper

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1. अ�भ� या जो उ ाद के प म बू टेनॉइक (butanoic) अ उ करती है , वह ह:
(’dry ether’ का �हं दी अथ� ’�नज� ल ईथर’ ह।)

A.
m
om . co
. c e m
e m l as
l as ag
ag
B.

m
C.
m .co
s e
l a
ag
D.

m
m .co
m .co s e m
s e g la
g la a
a

om
Page 2
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. c e m
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Page 71

2. यौ�गक जो दशा� ए गए हाइ ोजन के �ड ोटोने शन पर ऐरोमै �टक जा�त उ करता है , वह ह:

A.

B.

C.

D.

Page 3

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m .co s e m NEST 2026 Question Paper

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3. दो छा (P और Q) ने तं प से एक ही गु ण के तीन माप ( मशः I, II, and III) �कए। अपे � त सही
मान 9 है । छा ारा दे खे गए मान �न �ल�खत ता�लका म �दए गए ह।

Student I II III Average
P 8.9 9.1 9.0 9.0
Q 8.0 9.0 10.0 9.0
m
om
�दए गए आंकड़ के आधार पर, सही कथन है ः . co
. c e m
m
A. दोन P और Q समान प से यथाथ� परक ह, पर ु Q की तु लना म P अ�धक प�रशु
eP अ�धक यथाथ� परक है , पर ु Q की तु लना म कम प�रशु है ।
है ।
l as
as
B.
l C. P कम यथाथ� परक है , पर ु Q की तु लना म अ�धक प�रशु है । ag
ag
D. दोन P और Q समान प से प�रशु ह, पर ु Q की तु लना म P अ�धक यथाथ� परक है ।

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
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Page 73

4. जा�तयाँ जो सम-इले ो�नक और सम-सं रचना क दोन ह, वे ह:
A. NH+
4 and BH4

B. O3 and NO+
2

C. N2 O and NO2
D. NH2 and BH4

Page 5

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5. दो गै े �नक से ल, से ल I और से ल II, समान तापमान पर काय� कर रहा ह और इसम दो अलग अलग रेडॉ
तं शा�मल ह। यह दे खा गया है �क �त� या भागफल के एक �वशे ष मान QI = QII = Q0 पर , दो से ल के
�व ु तवाहक बल (emf) का अनु पात (EI /EII ) एवं �ग मु ऊजा� के प�रवत� न का अनु पात ( GI / GII )
1/3 ह। तः ू त� �दशा और �तवत� सं चालन म �लखी गई मानक से ल �त� या की जोड़ी जो इन
प�र� �तय (conditions) को पू रा कर सकती ह, वे ह:
A. Cell I: Zn(s)|Zn2+ (aq)||Ag+ (aq)|Ag(s)
m
om
Cell II: Zn(s)|Zn2+ (aq)||Cu2+ (aq)|Cu(s)
. co
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m I:II:AgAl(s)|Al
eCell
B. Cell (aq)|Ag(s)||Fe (aq)|Fe (aq)
+ 2+ 3+
l as
l as (aq)||Ag (aq)|Ag(s)
3+ +
ag
ag C. Cell I: Zn(s)|Zn (aq)||Cu (aq)|Cu(s)
2+ 2+

Cell II: Al(s)|Al (aq)||Ag (aq)|Ag(s)
3+ +

D. Cell I: Fe2+ (aq)|Fe3+ (aq)||Cu2+ (aq)|Cu+ (aq)
Cell II: Cu(s)|Cu2+ (aq)||Ag+ (aq)|Ag(s)

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6. �न �ल�खत यौ�गक पर �वचार कर।

यौ�गक डाइआइसो ू �टल ए ू मी�नयम हाइ ाइड के दो समक के साथ �त� या से गु जरता है । �जसके
प ात् अ ीय अपघटन के होने पर मु ख उ ाद के प म P दान करता है । P की सं रचना इस कार है ः

A.

B.

C.

D.

Page 7

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7. तृ तीयक- ू �टलबजीन (tert-Butylbenzene) �नज� ल AlCl3 की उप� �त म 1- ोरो-2-�मथाइल ोपे न
के साथ �त� या करता है । इस अ�भ� या म मु ख उ ाद है ः

A.
m
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B.
ag
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C.

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8. �न �ल�खत यौ�गक पर �वचार कर।

यौ�गक, SOCl2 के साथ अ�भ� या करके P का उ ादन करता है । P डाइ �मथाइल कैड�मयम के साथ
अ�भ� या करके Q का उ ादन करता है । Q ए�थल मै गनी�शयम ोमाइड (3 समतु तु ां क) और उसके
उपरां त जल के साथ अ�भ� या कर R का उ ादन करता है । R की सं रचना इस कार है ः

A.

B.

C.

D.

Page 9

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9. ऐसी�टलीन को 873 K पर लाल त लोह न�लका के मा म से पा�रत �कया जाता है ता�क P का उ ादन
�कया जा सके। P �नज� ल AlCl3 की उप� �त म ोरीन गै स के साथ अ�भ� या कर Q का उ ादन करता
है । Q ब�जल ोराइड एवं सो�डयम के साथ अ�भ� या कर के मु ख प से R का उ ादन करता है । R
की सं रचना इस कार है ः

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C.

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10. 1,2-डाइ�मथाइलबजीन ए�स�टक एनहाइ ाइड की उप� �त म ो�मक ऑ ाइड के साथ, 273-283 K
तापमान पर अ�भ� या करके तथा जल अपघटन के प ात् P का उ ादन करता है । P को सा NaOH
के साथ गरम करके तथा जल अपघटन के प ात Q की ा� होती है । उ ाद Q म उप� त काया� क
समू ह ह:
A. एक काब�� लक ए�सड और एक अ ोहल
B. दो ए��हाइड
C. एक ए��हाइड और एक काब�� लक ए�सड
D. दो काब�� लक ए�सड

Page 11

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11. ए ा स�म ो, [V(H2 O)6 ]2+ , [Fe(H2 O)6 ]2+ , [Fe(H2 O)6 ]3+ , और [Co(H2 O)6 ]3+ के �लए अ ीय
श� का बढ़ता म है ः
A. [V(H2 O)6 ]2+ < [Fe(H2 O)6 ]2+ < [Fe(H2 O)6 ]3+ < [Co(H2 O)6 ]3+
B. [Fe(H2 O)6 ]2+ < [Fe(H2 O)6 ]3+ < [V(H2 O)6 ]2+ < [Co(H2 O)6 ]3+
C. [Co(H2 O)6 ]3+ < [Fe(H2 O)6 ]3+ < [Fe(H2 O)6 ]2+ < [V(H2 O)6 ]2+
m
D. [Fe(H2 O)6 ]2+ < [Fe(H2 O)6 ]3+ < [Co(H2 O)6 ]3+ < [V(H2 O)6 ]2+
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12. तीन लथे नोइड आयन X, Y, और Z और उनके गु ण की �न �ल�खत ता�लका पर �वचार कर।

लथे नोइड आयन गु ण
X �तचु क
Y �वलयन म अपचायक
Z �र 4f क� काएँ

Ce, Eu, और Lu के परमाणु मां क (atomic numbers) मशः 58, 63, और 71 ह। इन परमाणु मां क
को दे खते ए, लथे नोइड आयन मशः X, Y, और Z, ह:
A. Lu3+ , Eu2+ , and Ce4+
B. Lu3+ , Ce4+ , and Eu2+
C. Eu2+ , Ce4+ , and Lu3+
D. Eu2+ , Lu3+ , and Ce4+

Page 13

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13. �न �ल�खत स�म आयन पर �वचार करः

[Ni(CN)4 ]2 , [Fe(CN)6 ]3 , [Cu(H2 O)6 ]2+ , और [Co(CN)6 ]3 .

वो स�म आयन �जनसे कमरे के तापमान पर �तचु कीय वहार द�श� त करने की अपे ा की जाती है ,
वे ह:
m
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A. [Ni(CN)4 ]2 और [Co(CN)6 ]3
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B. [Ni(CN) 2 2+

s e m
m ] और [Fe(CN) ]
4 2 6

C.e[Co(CN)
s
3 3

g l a
laD. [Cu(H O) ] और [Co(CN) ]
6 6

g
2+ 3
a
a
2 6 6

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14. �न �ल�खत जा�तय पर �वचार की�जएः

(i) ClO
(ii) ClO2
(iii) ClO3
(iv) ClO4

उनम से , जो जा�त(याँ ) असमानु पाती अ�भ� या से गु जरती ह, वे ह:
A. केवल (i), (ii), और (iii)
B. केवल (iv)
C. केवल (i) और (ii)
D. केवल (iii) और (iv)

Page 15

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15. X, Y, और Z तीन वा शील तरल पदाथ� ह, �ज �मलाने पर एक आदश� �वलयन बनाते है । एक �न� त
तापमान T0 पर, घटक X, Y, और Z म शु वा दबाव 3:2:1 के अनु पात म होता है । X, Y, और Z के मोल-
अंश के अनु पात 1:2:3 से बनाया गया एक �म ण, जो की दबाव 1.5 atm और तापमान T0 पर उबलने
लगता है । T0 तापमान पर Y का आं�शक वा दबाव (atm म) है ः
3
A.
5
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B.
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9
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16. एक �तवत� ऊ ाग�तकीय � या पर �वचार कर �जसम दो अव ा X (4 bar, 1 L, T1 ) और Y (1
bar, 2 L, T2 ) को जोड़ने वाली P V आरेख पर एक रेखा ारा दशा� ए गए आदश� गै स के एक मोल को
शा�मल �कया गया है जै सा �क �च म �दखाया गया है ः

इस � या के दौरान आयतन के फलन (L म) के प म तापमान (K म) म प�रवत� न को सबसे उ म प
से �जस कार दशा� या जा सकता है , वह है :

A.

B.

Page 17

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Page 87

17. �कसी �न� त तापमान पर ज�लया मा म म PQ2 एक अ �वले य लवण है , �जसका �वलयता गु णनफल
Ksp = 4 ⇥ 10 12 ह। यह दे खा गया है �क उसी तापमान पर अ �धक घु लनशील नमक RQ �मलाने पर,
PQ2 की घु लनशीलता 100 के कारक से कम हो जाती है । घोल म जोड़े गए RQ की सां ता (�मलीमोल �त
लीटर म) इसके सबसे �नकट है ः
A. 2
B. 0.2
C. 20
D. 0.02

Page 19

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18. समान तापमान और आयतन पर की जाने वाली �न �ल�खत रासाय�नक �त� या पर �वचार कर:

योग I (Experiment I): X(g) ↵ 2Y(g)
योग II (Experiment II): X(g) ↵ Z(g)

अ�भकारक और उ ाद के आं�शक दबाव को �त� या के दौरान मशः preactant और pproduct ारा
m
�न �पत �कया गया है । आदश� गै स वहार को मानते ए, योग I और II के �लए preactant बनाम
om . co
c
pproduct का सही आले ख है ः
. e m
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ag

A.

m
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B.

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m .co s e m
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D.

Page 21

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19. य�द पहली बोहर क ा म एक इले ॉन के वे ग को v0 से �न �पत �कया गया है , तो अ क ा म
इले ॉन के वे ग (v) को (मु ां टम सं ा ’n’ के फलन के प म) �जस कार दशा� या जा सकता है ,
वह है :

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A.

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B.

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D.

Page 23

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20. दो अ�भ� या पर �वचार कर।

I. एक शू को�ट अ�भ� या: X! P1 .
II. थम को�ट अ�भ� या: Y! P2 .

दोन �त� याएँ एक ही ारं�भक सां ता ‘C’ के साथ एक साथ शु होती ह, अथा� त् X0 = Y0 = C ।
m
यह दे खा गया है �क अ�भकारक की सां ता एक ही समय म उनके ारं�भक मू
om
के एक �तहाई तक �गर
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जाती है , बशत� दर � रां क एक �न� त अनु पात को पू रा कर। य�द k0 और k1 मशः शू और थम को�ट
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वे ग � रां क �न �पत करते ह, तो इस शत� को पू रा करने के �लए आव क अनु पात k0 /k1 है :
l as
l as A.
2C
ag
ag 3ln3
C
B.
ln3
C
C.
ln2
3C
D.
2ln2

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Page 93

Solution

Mathematics 2026

Notations

• N : The set of all natural numbers

• Z : The set of all integers

• Q : The set of all rational numbers

• R : The set of all real numbers

• R+ : The set of all positive real numbers i.e., {x 2 R | x > 0}

• C : The set of all complex numbers

• For x 2 R,
|x| : The absolute value of x

• For z 2 C,
|z| : The modulus of z

• For a set
( A,
The number of distinct elements of the set A if A is finite
|A| :=
1 (or, infinity) if A is infinite

• For a line segment AB,
|AB| : The length of the line segment AB

• For a 2 R+ ,
log a := loge a i.e., the natural logarithm of a
p
• i : The imaginary number 1

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1. A possible solution of the system of equations

x2 8xy + 16y 2 = 0

m
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(log10 x)2 + 2(log10 x)(log10 y) + (log10 y)2 = 4
is
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1
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A. x = , y =
1
l as
l as 5 20
B. x = 100, y = 25 ag
g
a x = 40, y = 10
C.
4 1
D. x = , y=
25 16

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2. The parabola y = x2 + 16 intersects the x-axis at points A and B. Further, the
parabola intersects the line y = 7 at points M and N. Then the area of the quadrilateral
with vertices A, B, M and N is
A. 49
B. 42
C. 56
D. 35

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2
3. The domain of the real function f (x) = sin 1 (log2 ( x2 )) is
A. [ 2, 1] [ [1, 2]
B. [ 2, 1]
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4. Let f : R ! R be a twice di↵erentiable function such that f 00 (x) = f (x).
Let h : R ! R be a di↵erentiable function such that h0 (x) = f (x)2 + (f 0 (x))2 for all
x 2 R. If h(0) = 1 and h( 31 ) = 53 , then the value of h(100) is
A. 201
B. 101
C. 100
D. 202

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bx2 + 15x + 15 + b
5. Suppose lim = L, where b and L are real numbers. Then
x! 2 x2 + x 2
A. b = 3 and L = 1
B. b = 3 and L = 1
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C. b = 3 and L = 1
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D. b =
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3 and L = 1
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6. If x 2 (0, 1) and sin 1 x sin 1 41 = ⇡3 , then x equals
p
A. 81 (1 + 3 5)
p
B. 61 (1 + 2 5)
p
C. 61 (1 + 4 3)
p
D. 51 (2 + 3 2)

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7. Let S = {(x, y) | x, y 2 N, 1  x  15, 1  y  20} be a set. Let R be the equivalence
relation on S defined by

(x, y) R (x0 , y 0 ) if and only if x + y = x0 + y 0 .
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Then the number of equivalence classes of R on S is
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B. 35
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C.l 15
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aD. 20

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g la a
a

m . c
c. o s e m
s em
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Page 99 of 175

Page 101

8. For a complex number z = x + iy, where x, y 2 R, denote ẑ = y + ix.
The locus of z satisfying |z + ẑ| = |z ẑ| in the complex plane is
A. union of the real axis and the imaginary axis
B. the real axis
C. a circle
D. the straight line y = x

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Page 102

.
m .co s e m NEST 2026 Question Paper

s e l a
a ag

9. Let m and p be real numbers such that the polynomial f (x) = x2 + mx + p has two
distinct negative rational roots. Then the polynomial g(x) = x2 (m2 2p)x + p2 has
distinct
A. positive rational roots
m
om
B. positive irrational roots
. co
. c e m
C. negative rational roots
em l as
as
D. negative irrational roots
l ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 101 of 175

Page 103

10. Amar, Akbar, and Anthony write a test independently.
3
The probability that Amar passes the test and Akbar fails the test is .
20
1
The probability that Akbar passes the test and Anthony fails the test is .
4
2
The probability that Amar and Anthony both pass the test is .
5
Then the probability that at least one of Amar, Akbar and Anthony fails the test is
7
A.
10
3
B.
10
3
C.
5
4
D.
5

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Page 104

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m .co s e m NEST 2026 Question Paper

s e l a
a ag

11. The probability that the sum of two integers m and n, where m, n 2 {1, 2, . . . , 50},
chosen randomly and independently, being divisible by 3 is
A. 0.3336

m
co
B. 0.3332
C. 0.3333
. c om e m .
m
D. 0.3338
e l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 103 of 175

Page 105

12. Let a variable line L meet x-axis and y-axis at points A and B, respectively. Suppose
the distance of the line L from the origin is 3 units. Then the equation of the locus of
the point C that divides the line segment AB internally in the ratio 2 : 1 is
4 1
A. 2 + 2 = 1
x y
1 4
B. 2 + 2 = 1
x y
C. x2 + 4y 2 = 9
D. 4x2 + y 2 = 9

Answer stands corrected as ‘B’

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Page 106

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m .co s e m NEST 2026 Question Paper

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a ag

13. In a building, an elevator starts from the ground floor (that is, 0th floor) with 10
passengers and stops at every floor until the 15th floor which is the topmost floor. No
new passengers enter the elevator on any floor from the 1st through the 15th floor. If
all the passengers got o↵ the elevator then the probability that at most one passenger
m
co
got o↵ at each floor is

A.
15!
. c om e m .
m
5! ⇥ 1510
e l as
l
B.as10!
ag
ag 1510
15!
C.
1015
15!
D.
5! ⇥ 1015

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 105 of 175

Page 107

14. Let S be the set of real values of k for which the system of equations

kx + y + z = k
x + ky + z = k
x + y + kz = k

has no solution. Then |S| is
A. 1
B. 2
C. 0
D. 1

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Page 108

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m .co s e m NEST 2026 Question Paper

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a ag

Z⇡
sin x x cos x
15. dx equals
x(x + sin x)
⇡
2

m
✓ ◆
2
co
A. log 1 +
om .
⇡
⇣
. c
⇡⌘
e m
em
B. log 1 +
2
l as
l as
C. 1 +
2
ag
ag ⇡
⇡
D. 1 +
2

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 107 of 175

Page 109

1
16. The number of solutions of the equation | sin(⇡x)| = 50 (x2 + 1) in R is
A. 28
B. 26
C. 14
D. 13

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Page 110

.
m .co s e m NEST 2026 Question Paper

s e l a
a ag

17. Let f : R ! R be a function defined by f (x) = x5 + x3 and let g(x) = f 1 (x) be the
a
inverse of f. If g 00 ( 2) = where a and b are positive coprime integers, then the value
b
of a is
m
co
A. 13
B. 26
. c om e m .
C. 39
e m l as
l as
D. 256
ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 109 of 175

Page 111

18. Let S1 and S2 be two circles drawn inside a unit square ABCD, touching each other
externally. Further, the circle S1 touches the sides AD and DC; and the circle S2
touches the sides AB and BC. If the area of S2 is twice the area of S1 , then the radius
of S1 is
p
A. 3 2 4
p
B. 3 2 2
p
C. 2 2
3
D. p 2
2

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Page 112

.
m .co s e m NEST 2026 Question Paper

s e l a
a ag

19. Let f : R ! R be a function defined by
8 ✓ 1/x
e 1/x
◆
<x e if x 6= 0
f (x) = e1/x + e 1/x
m
co
0 if x = 0.
:

Then
. c om e m .
e m l as
a s
A. there exists a constant C such that |f (x)|  C for all x 2 R.
B.l f is monotonically increasing in the interval ( 1, 1). ag
g
a C. f is di↵erentiable at x = 0.
D. f is not continuous at x = 0.

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 111 of 175

Page 113


1 1 1 1
20. lim p 1 + p + p + · · · + p
n!1 n 2 3 n
A. equals 2
B. equals 1
C. equals 0
D. does not exist

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Page 114

.
m .co s e m NEST 2026 Question Paper

s e l a
a ag

ग�णत 2026

m
co
Notations
m .
conatural numbers
• N : The set of.all
s e m
• Z : The s emof all integers g l a
la
set

• Qa:gThe set of all rational numbers
a
• R : The set of all real numbers

• R+ : The set of all positive real numbers i.e., {x 2 R | x > 0}

• C : The set of all complex numbers

• For x 2 R,
|x| : The absolute value of x
m
• For z 2 C,
m .co
|z| : The modulus of z
s e
l a
• For a set
( A,
agelements of the set A if A is finite
The number of distinct
|A| :=
1 (or, infinity) if A is infinite

• For a line segment AB,
|AB| : The length of the line segment AB

• For a 2 R+ ,
log a := loge a i.e., the natural logarithm of a
m
.co
p
m • i : The imaginary number 1

m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 113 of 175

Page 115

1. �न �ल�खत समीकरण की णाली

x2 8xy + 16y 2 = 0

(log10 x)2 + 2(log10 x)(log10 y) + (log10 y)2 = 4
का एक सं भा�वत समाधान होगा
1 1
A. x = , y =
5 20
B. x = 100, y = 25
C. x = 40, y = 10
4 1
D. x = , y =
25 16

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Page 116

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m .co s e m NEST 2026 Question Paper

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a ag

2. परवलय y = x2 + 16, x-अ को �बं A और B पर �त े द करता है तथा रेखा y = 7 को �बं M
और N पर �त े द करता है । तब शीष� A, B, M और N वाले चतु भु� ज का े फल होगा
A. 49
B. 42 m
C. 56
om . co
. c e m
D. 35
e m l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 115 of 175

Page 117

✓ ✓ 2 ◆◆
x
3. वा �वक फलन f (x) = sin 1
log2 का ा (domain) है
2
A. [ 2, 1] [ [1, 2]
B. [ 2, 1]
C. [1, 2]
D. [ 2, 2]

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Page 118

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m .co s e m NEST 2026 Question Paper

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a ag

4. मान ली�जए �क f : R ! R एक � -अवकलनीय फलन है , जहाँ f 00 (x) = f (x)।
मान ली�जए h : R ! R एक अवकलनीय फलन है , जहाँ सभी x 2 R के �लए

h0 (x) = f (x)2 + (f 0 (x))2 .
m
om
य�द h(0) = 1 और h( 31 ) = 53 है , तो h(100) का मान होगा
. co
. c e m
A. 201
e m l as
s
B. 101
a ag
C.l 100
g
a D. 202

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 117 of 175

Page 119

bx2 + 15x + 15 + b
5. मान ली�जए �क lim = L, जहाँ b और L वा �वक सं ाएँ ह। तब
x! 2 x2 + x 2
A. b = 3 और L = 1
B. b = 3 और L = 1
C. b = 3 और L = 1
D. b = 3 और L = 1

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Page 120

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m .co s e m NEST 2026 Question Paper

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a ag

6. य�द x 2 (0, 1) और sin 1 x sin 1 41 = ⇡3 , तो x का मान होगा
p
A. 18 (1 + 3 5)
p
B. 61 (1 + 2 5)
m
co
p

om .
C. 61 (1 + 4 3)

. c
p
D. 51 (2 + 3 2)
e m
e m l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 121

7. मान ली�जए �क S = {(x, y) | x, y 2 N, 1  x  15, 1  y  20} एक समु ह। मान ली�जए S पर
R एक तु ता सं बं ध (equivalence relation) है जो इस कार प�रभा�षत है �क

(x, y) R (x0 , y 0 ) य�द और केवल य�द x + y = x0 + y 0 .

तब S पर R के तु ता वग� (equivalence class) की सं ा होगी
A. 34
B. 35
C. 15
D. 20

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Page 122

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m .co s e m NEST 2026 Question Paper

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a ag

8. �कसी भी स�� सं ा z = x + iy के �लए, जहाँ x, y 2 R, ẑ = y + ix को दशा� ता है ।
स�� तल म समीकरण |z + ẑ| = |z ẑ| को सं तु करने वाले z का ान (locus) है
A. वा �वक अ और का �नक अ का स��लन
m
co
B. वा �वक अ
C. एक वृ
. c om e m .
m
D. सीधी रेखा y = x
e l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 121 of 175

Page 123

9. मान ली�जए �क m और p ऐसी वा �वक सं ाएँ ह जो �क ब पद f (x) = x2 + mx + p के दो �भ
ऋणा क (negative) प�रमे य मू ल ह। तब ब पद g(x) = x2 (m2 2p)x + p2 के दो �भ
A. धना क प�रमे य मू ल ह गे
B. धना क अप�रमे य मू ल ह गे
C. ऋणा क प�रमे य मू ल ह गे
D. ऋणा क अप�रमे य मू ल ह गे

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Page 124

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m .co s e m NEST 2026 Question Paper

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a ag

10. अमर, अकबर और एंथनी तं प से एक परी ा �लखते ह। परी ा म अमर के उ ीण� होने और अकबर
3
के अनु ीण� होने की ा�यकता (probability) है , अकबर के उ ीण� होने और एंथनी के अनु ीण� होने की
20
1 2
ा�यकता है , और अमर और एंथनी दोन के उ ीण� होने की ा�यकता है । तब अमर, अकबर और एंथनी म
m
co
4 5

om .
से कम से कम एक के अनु ीण� होने की ा�यकता है
7
. c e m
A.
e
10 m l as
l
B.as 3
ag
ag 10
3
C.
5
4
D.
5

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 125

11. दो पू णा� क m और n, जहाँ m, n 2 {1, 2, . . . , 50}, या � क और तं प से चु ने जाते ह। तब उनके
योग के 3 से �वभा होने की ा�यकता (probability) है
A. 0.3336
B. 0.3332
C. 0.3333
D. 0.3338

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Page 126

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m .co s e m NEST 2026 Question Paper

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a ag

12. मान ली�जए �क एक चर रेखा (variable line) L x-अ को �ब ु A पर तथा y-अ को �ब ु B पर �त े �दत
करती है । मान ली�जए �क रेखा L की मू ल �ब ु से री 3 इकाई है । तब �बं C, जो रेखाख AB को आतं �रक
प से 2:1 के अनु पात म �वभा�जत करता है , के ान (locus) का समीकरण होगा
4 1
m
co
A. 2 + 2 = 1
om .
x y
1
.
4 c e m
B. 2 + 2 = 1
x
e my
l as
as
l 4x + y = 9
C. x2 + 4y 2 = 9
ag
agD. 2 2

सं शो�धत करने के बाद अब सही उ र `B’ माना जाएगा।

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 127

13. एक इमारत म, एक उ ा�हनी (lift) भू तल (0वी मं �जल) से 10 या� य के साथ �नकलती है और 15वी (सबसे
उपरी) मं �जल तक हर मं �जल पर कती है । �कसी भी मं �जल पर कोई नया या ी उ ा�हनी म वे श नह करता है ।
य�द सभी या ी उ ा�हनी से उतर जाते ह तो े क मं �जल पर अ�धकतम एक ही या ी के उतरने की ा�यकता
(probability) है
15!
A.
5! ⇥ 1510
10!
B.
1510
15!
C.
1015
15!
D.
5! ⇥ 1015

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Page 128

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m .co s e m NEST 2026 Question Paper

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a ag

14. मान ली�जए �क S उन वा �वक सं ा k का समु य है , �जनके �लए �न समीकरण

kx + y + z = k
x + ky + z = k
m
om
x + y + kz = k
. co
. c e m
की णाली (system) का कोई समाधान नह है । तब |S| का मान होगा
em l as
A. 1
a s ag
gB.l 2
a C. 0
D. 1

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 129

Z⇡
sin x x cos x
15. dx का मान होगा
x(x + sin x)
⇡
2
✓ ◆
2
A. log 1 +
⇡
⇣ ⇡⌘
B. log 1 +
2
2
C. 1 +
⇡
⇡
D. 1 +
2

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Page 130

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m .co s e m NEST 2026 Question Paper

s e l a
a ag

16. समीकरण | sin(⇡x)| = 50
1
(x2 + 1) के R म समाधान की सं ा है
A. 28
B. 26
m
co
C. 14
D. 13
. c om e m .
e m l as
l as ag
ag

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 131

17. मान ली�जए �क f : R ! R एक फलन है , जो f (x) = x5 + x3 ारा प�रभा�षत है , और मान ली�जए �क
a
g(x) = f 1 (x) (फलन f का ु म फलन g है )। य�द g 00 ( 2) = , जहाँ a और b धना क सहअभा
b
(coprime) पू णा� क ह तो a का मान होगा
A. 13
B. 26
C. 39
D. 256

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Page 132

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m .co s e m NEST 2026 Question Paper

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a ag

18. मान ली�जए �क एक इकाई वग� (unit square) ABCD म S1 और S2 दो वृ बनाए गए ह जो एक सरे को
बाहर से श� करते ह। इसके अलावा, वृ S1 भु जा AD और DC को श� करता है तथा वृ S2 भु जा
AB और BC को श� करता है । य�द S2 का े फल S1 के े फल का दोगु ना है , तो S1 की � ा (radius)
होगी
m
co
p
om .
A. 3 2 4
.
p
c e m
B. 3 2 2
e mp
l as
l as
C. 2 2
ag
ag D. p
3
2
2

m
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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Page 133

19. मान ली�जए �क f : R ! R एक फलन है �जसकी प�रभाषा है :
8 ✓ 1/x
e 1/x
◆
<x e if x 6= 0
f (x) = e1/x + e 1/x
0 if x = 0.
:

तब
A. एक ऐसा � रां क C अ� म है की सभी वा �वक सं ा x के �लए |f (x)|  C.
B. अंतराल ( 1, 1) म f एक�द बढ़ता आ (monotonically increasing) फलन है |
C. फलन f , x = 0 पर अवकलनीय है |
D. फलन f , x = 0 पर सं तत नह है |

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.
m .co s e m NEST 2026 Question Paper

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
1 1 1 1
20. lim p 1 + p + p + · · · + p का मान
n!1 n 2 3 n
A. 2 के बराबर है |
B. 1 के बराबर है | m
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C. 0 के बराबर है | . co
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gl a
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Page 135

NEST 2026 PHYSICS

Some Useful Constants

Acceleration due to gravity on Earth g 10.00 m·s 2
Boltzmann constant kB 1.38 ⇥ 10 23 J·K 1
Current Mass of the Sun Ms 2.00 ⇥ 1030 kg
Current Radius of the Sun Rs 7.00 ⇥ 108 m
Magnitude of the electron charge e 1.60 ⇥ 10 19 C
Mass of the electron me 9.11 ⇥ 10 31 kg
Mass of the proton mp 1.67 ⇥ 10 27 kg
Atomic Mass Unit u 931.50 MeV/c2
Permeability of free space µ0 1.26 ⇥ 10 6 H·m 1
Permittivity of free space ✏0 8.85 ⇥ 10 12 F·m 1
Planck’s constant h 6.63 ⇥ 10 34 J·s
Avogadro Constant NA 6.02 ⇥ 1023 mol 1
Speed of light in vacuum c 3.00 ⇥ 108 m·s 1
Stefan-Boltzmann constant 5.67 ⇥ 10 8 W·m 2 · K 4
Universal Gas constant R 8.31 J·K 1 · mol 1
3
Universal Gravitational constant G 6.67 ⇥ 10 11 kg 1 ·m · s 2
Wien’s constant b 2.90 ⇥ 10 3 m·K

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Page 136

m
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m . c s em
se g la
a is 7.3 ⇥ 10 5 rad·s 1.
1. The angular speed of the Earth’s rotation
Take the radius of the Earth at the equator to be 6400 km. Then
the ratio (ac/g) of the magnitude of the centripetal acceleration ac
at a point on the equator to g, is of the order
A. 10 3
m
B. 10 5m
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.
C.m10 0
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s e 1 l a
g a
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D. ag
a

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Page 137

2. An electromagnetic wave travels from vacuum into a non-magnetic
dielectric medium with permittivity ✏ = 4✏0. If the ratio (E0/B0)
of the electric field amplitude E0 to the magnetic field amplitude B0
in vacuum is equal to the speed of light c, then the corresponding
ratio in the given medium is
A. c/2
B. c
p
C. c/ 2
D. c/4

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Page 138

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a
3. Among the following, the waves responsible for energy transfer in
vacuum are
A. infrared waves.
B. sound waves.
C. SONAR waves.
m
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D. seismic
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Page 139

4. Let A be the mass number, Z be the atomic number and N be the
neutron number of a nucleus. Then the statement which is always
true, is
A. A2 NZ
B. A 2N
C. A 2Z
D. AN Z2

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Page 140

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m . c s em
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5. Two wave pulses, one rectangular anda other triangular, approach
each other as shown in the figure below.

m
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em at the point P at time t. The diagram0 best grepre-
They overlap
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senting
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Page 141

6. Ice on land mass melting into ocean, due to global warming, is
estimated to be around 1.3 ⇥ 1015 kg per year. The density of
sea water is 1025 kg · m 3. Assuming that the melting rate of
ice remains constant and the e↵ective surface area covered by the
oceans is 3.6 ⇥ 1014 m2, the estimated average rise in sea level (in
m) in the next 75 years will be closest to
A. 0.25
B. 0.45
C. 0.15
D. 0.50

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Page 142

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m . c s em
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a wall thickness is placed
7. A spherical glass bottle having negligible
in air. When the bottle is completely filled with water, its focal
length is f . If the water is replaced by another transparent liquid
of higher refractive index, then the focal length changes to f 0. Then
the correct option is
m
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A. f 0 < f
m
B. f.0co> f e m
e m0 l as
l asC. f = f = 1
ag
ag D. f 0 = f , but finite

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Page 143

8. Physicist Luis Alvarez and his collaborators hypothesised that the
extinction of dinosaurs was due to the impact of an asteroid with
the Earth. They estimated the mass and the radius of the asteroid
to be about 2 ⇥1015 kg and 10 km respectively. Take the mass
of the Earth to be 6 ⇥1024 kg. The gravitational acceleration (in
SI units) of the Earth due to the asteroid just before the impact
would be of the order
A. 10 9
B. 101
C. 10 1
D. 10 5

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a
9. An infinitely long straight wire with uniform line charge density
lies at a perpendicular distance d from a point O. The total electric
flux through the surface of a sphere of radius R > d centred at O,
is
2
p
A. ✏0 R2 d2
p
o m
B. 2✏0 m
o
Rd . c
2. cp e m
C. m
e 0 R 2 + d2
l as
a s ✏
a g
a gl D. 0

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Page 145

10. A sphere made of a material with density 12 kg·m 3 and weighing
100 N in vacuum is immersed in a container of gas. Its weight in
gas is 85 N. The density of the gas in kg·m 3 is closest to
A. 1.80
B. 0.01
C. 80.00
D. 0.55

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Page 146

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11. One mole of a monatomic ideal gas aundergoes a transformation
from an initial state with temperature 290 K and volume 30 litres
to a final state with temperature 310 K and volume 16 litres. On
the pressure–volume (P V ) diagram, this process is represented
by a straight line path. The magnitude of the work done (in joules)
during this process is close to m
c. o
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A. 1690
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B.
g la C. 877
a
D. 1375

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Page 147

12. The electron in the hydrogen atom is in the third excited state. Its
potential energy (in eV) is
A. 1.70
B. -1.51
C. -0.85
D. -3.02

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a it starts rolling (without
13. A sphere is given an initial push so that
slipping) up an inclined plane. During its climb
A. the direction of the force of friction on the
sphere is up the incline.
B. the direction of the net force on the sphere is up the
o m
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C.mthe
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D. the work done by the force of friction on the sphere
ag negative.

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Page 149

14. All the capacitors in a given circuit are initially fully charged with
all switches open. At a later time t, all the switches are simul-
taneously closed. The current flowing through the circuit at that
instant is given by

A. 4V0/RL
B. V0/R0
C. 3V0/R0
D. V0/RL

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Page 150

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15. An incandescent lamp of wattage W ais filled with argon gas and
has a tungsten filament. The collision frequency of evaporated
tungsten atoms with the argon atoms is found to be proportional
to W ↵ . The most reasonable value of ↵ is
1
A.
8
o m
1 m
B. co . c
4. e m
m
e1 l as
as
l 2C. ag
g
a D. 0

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Page 151

16. Two protons are separated by a distance of 1 nanometer. The
magnitudes of gravitational, electromagnetic and strong nuclear
forces between them are denoted by FG, FE and FS respectively.
Select the correct option.
A. FE > FG > FS
B. FE > FS > FG
C. FS > FG > FE
D. FS > FE > FG

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Page 152

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a and sent into two vacuum
17. A laser beam of wavelength 1 µm is split
cavities of equal length L as shown in the figure. A detector can
register an interference signal only if the phase di↵erence between
the returning beams is at least 5 ⇥ 10 11 rad. A certain physical
e↵ect changes the length of cavity 2 by an amount L such that
L/L ' 10 21. The minimum cavity length (in km) needed for
o m
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measuring this
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A. 4
B. 1
C. 2
D. 16
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Page 153

18. The critical electric field required to produce electron-positron pairs
depends on the physical constants h, c, me and e. Use dimensional
analysis and assume that the dimensionless coefficient is of order
one. The magnitude of the critical electric field, in SI units, is of
the order
A. 1018
B. 1021
C. 1024
D. 1015

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19. A parallel plate capacitor with circulara plates of radius R is being
charged as shown in the figure. Let B(r) be the induced magnetic
field at a distance r from the central axis between the plates. As-
B(2d)
suming d ⌧ R, the ratio , while charging, is
B(d)
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A. 2
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1
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B.
l a
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2
1
C.
4
D. 1

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Page 155

20. Two point bodies of masses m and 3m are connected by a mass-
less spring of spring constant k = m!02 and kept on a frictionless
horizontal surface. The spring is extended by a small distance l
over its natural length at time t = 0 and then released so that the
masses execute simple harmonic motion. The maximum speed of
the particle with mass m is given by
p
3!0l
A.
2
2!0l
B. p
3
!0l
C. p
3
3!0l
D.
4

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NEST 2026 भौ�तक �व ान
Some Useful Constants

m
m .co
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Acceleration due to gravity on Earth
m
g 10.00 m·s 2
s e m
s e
Boltzmann constant 1.38 ⇥ 10 23 J·K 1
l a
ag
kB

g l a
Current Mass of the Sun Ms 2.00 ⇥ 1030 kg
a
Current Radius of the Sun
Magnitude of the electron charge
Rs
e
7.00 ⇥ 108 m
1.60 ⇥ 10 19 C
Mass of the electron me 9.11 ⇥ 10 31 kg
Mass of the proton mp 1.67 ⇥ 10 27 kg
Atomic Mass Unit u 931.50 MeV/c2
Permeability of free space µ0 1.26 ⇥ 10 6 H·m 1
Permittivity of free space ✏0 8.85 ⇥ 10 12 F·m 1
Planck’s constant h 6.63 ⇥ 10 34 J·s
m
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Avogadro Constant NA 6.02 ⇥ 1023 mol 1
Speed of light in vacuum c 3.00 ⇥ 108 m·s 1
Stefan-Boltzmann constant
e m 5.67 ⇥ 10 8 W·m 2 · K 4
Universal Gas constant
l as R 8.31 J·K 1 · mol 1

ag
3
Universal Gravitational constant G 6.67 ⇥ 10 11 kg 1 ·m · s 2
Wien’s constant b 2.90 ⇥ 10 3 m·K
ln 2 ⇡ 0.69
ln 3 ⇡ 1.10
ln 10 ⇡ 2.30
ln 11 ⇡ 2.40
⇡ ⇡ 3.14
Base of the Napierian logarithm e ⇡ 2.72
m
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Page 157

1. पृ ी के घू ण� न की कोणीय ग�त 7.3 ⇥10 5
rad·s 1 है । भू म रेखा पर पृ ी की � ा को 6400 km ल।
�फर भू म रेखा के एक �बं पर अ�भक रण ac से g के अनु पात (ac /g) का प�रमाण लगभग है
A. 10 3
B. 10 5
C. 100
D. 10 1

Page 2

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2. एक �व ु त चु कीय तरंग �नवा� त से परावै ु तां क ✏ = 4✏0 वाले अचु कीय, परावै ु त मा म म गमन करती
है । य�द �नवा� त म, �व ु त े आयाम E0 और चुं बकीय े आयाम B0 , का अनु पात (E0 /B0 ) काश की ग�त
c के बराबर है , तो �दए गए मा म म सं बं �धत अनु पात है
A. c/2
B. c
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C. c/ 2
m
D. c/4
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Page 159

3. �न �ल�खत म, �नवा� त म ऊजा� के प�रवहन के �लए �ज े दार तरंग ह
A. अवर तरंग
B. �न तरंग
C. सोनार (SONAR) तरंग
D. भू कंपीय तरंग

Page 4

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Page 160

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4. मान ली�जए �क एक ना�भक की मान सं ा A है , परमाणु सं ा Z है और ू ॉन सं ा N है । तब जो
कथन सदै व स होता है , वह है
A. A2 NZ
B. A 2N
C. A 2Z
m
D. AN m .co
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Z2
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Page 161

5. दो तरंग ं द, एक आयताकार और सरी � कोणीय, एक सरे से सं पक� करती ह जै सा �क नीचे �दए गए �च
म �दखाया गया है ।

ये समय t पर �बं P पर अ�त ापन (overlap) करती ह। समय t0 > t म तरंग ं दो के प को दशा� ने वाला
�वक है

A.

B.

C.

D.

र �कया गया

Page 6

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6. ोबल वा�म� ग के कारण �त वष� लगभग 1.3 ⇥ 1015 kg भू � त बफ� �पघल कर महासागर जाती है । समु ी
जल का घन 1025 kg · m 3 है । यह मानते ए �क बफ� की �पघलने की दर � र रहती है और महासागर
ारा आव�रत �कया गया भावी सतह े 3.6 ⇥ 1014 m2 है , अगले 75 वष� म समु के र म अनु मा�नत
औसत वृ �� (m म) इसके सबसे करीब होगी
A. 0.25
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B. 0.45
m
C. 0.15
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D. 0.50
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Page 163

7. एक गोलाकार कां च की बोतल, �जसकी दीवार की मोटाई न के बराबर है , को हवा म रखा जाता है । जब बोतल
पू री तरह से पानी से भर जाती है , तो इसकी फोकस री f होती है । य�द पानी को उ अपवत� नां क वाले एक
अ पारदश� व से �त ा�पत �कया जाता है , तो फोकस री f 0 हो जाती है । तब सही �वक है
A. f 0 < f
B. f 0 > f
C. f 0 = f = 1
D. f 0 = f , ले �कन प�र�मत

Page 8

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8. भौ�तक �व ानी लु इस अ ारेज़ और उनके सहयो�गय ने प�रक ना दी �क डायनासोर का �वलु होना पृ ी
के साथ एक ु ह के सं घात (impact) के कारण था। उ ने ु ह का मान और � ा मशः लगभग
2 ⇥10 kg और 10 km होने का अनु मान लगाया। पृ ी के
15
मान को 6 ⇥10 kg ल। सं घात से ठीक
24

पहले ु ह के कारण पृ ी का गु ीय रण (SI इकाइय म) लगभग होगा
A. 10 9
m
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B. 101
m
C. 10 1
m .co s e m
e
D. 10
s
5
l a
g l a ag
a

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m .co s e m
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Page 165

9. एक अनं त लबाई और एकसमान रै�खक आवे श घन का सीधा तार एक �बं O से d की लं बवत री पर
� त है । �बं O पर क� त और � ा R > d वाले गोलीय पृ से गु ज़रने वाला वै ु त ल (electric
flux) होगा
p
A. 2✏0 R2 d2
p
B. 2✏0 Rd
p
C. 2✏0 R2 + d2
D. 0

Page 10

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10. घन 12 kg·m 3 के पदाथ� से बना एक गोला, �जसका वजन �नवा� त म 100 N है , गै स के एक पा म डूबा आ
है । गै स म इसका वजन 85 N है । गै स के घन (kg·m 3 म) का मान सबसे करीब है
A. 1.80
B. 0.01
C. 80.00
m
D. 0.55
m .co
m .co s e m
s e l a
g l a ag
a

m
m .co
s e
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ag

m
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m .co s e m
s e g la
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a

om
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Page 167

11. एक एकपरमाणु क आदश� गै स की एक मोल की मा ा तापमान 290 K और आयतन 30 लीटर की ारं�भक
अव ा से तापमान 310 K और आयतन 16 लीटर की अं�तम अव ा म प�रव�त� त हो जाती है । P V आरेख
पर इस � या को एक सीधी रेखा पथ ारा दशा� या जाता है । इस � या के दौरान �कए गए काय� का प�रमाण
(जू ल म) लगभग है
A. 1690
B. 1939
C. 877
D. 1375

Page 12

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Page 168

m
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12. हाइ ोजन परमाणु म इले ॉन तीसरी उ े �जत अव ा म है । इसकी � �तज ऊजा� (eV म) है
A. 1.70
B. -1.51
C. -0.85
D. -3.02 m
m .co
m .co s e m
s e l a
g l a ag
a

m
m .co
s e
l a
ag

m
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Page 13
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Page 169

13. एक गोले को एक ारं�भक ध ा �दया जाता है ता�क यह एक नत-तल पर उपर की तरफ़ लु ढ़कना (�फसलने
के �बना) शु कर दे । चढ़ाई के दौरान
A. गोले पर घष� ण बल की �दशा ढलान के ऊपर है ।
B. गोले पर ने ट बल की �दशा ढलान के ऊपर है ।
C. गोले पर ने ट बल आघू ण� (net torque) शू है ।
D. गोले पर घष� ण बल ारा �कया गया काय� ऋणा क है ।

Page 14

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Page 170

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14. �दए गए प�रपथ म सभी सं धा�र शु म पू री तरह से आवे �शत (charged) ह और सभी ��च खु ली अव ा म
है । बाद के समय (t म), सभी ��च एक साथ बं द हो जाते ह। उस समय प�रपथ से बहने वाली धारा का मान है

m
m .co
m .co s e m
s e l a
g l a ag
a
A. 4V0 /RL
B. V0 /R0
C. 3V0 /R0
D. V0 /RL

m
m .co
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ag

m
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m .co s e m
s e g la
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Page 15
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Page 171

15. वॉटेज W का एक तापदी (incandescent) लै आग� न गै स से भरा है और इसम एक टंग न �फलामट
है । आग� न परमाणु के साथ वा� त टंग न परमाणु के सं घ की दर W ↵ के समानु पाती पाई जाती है । ↵
का सबसे उ�चत मान है
1
A.
8
1
B.
4
1
C.
2
D. 0

Page 16

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Page 172

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16. दो ोटॉन 1 नै नोमीटर की री पर � त ह। उनके बीच गु ाकष� ण, �व ु त चु कीय और बल ना�भकीय
बल के प�रमाण को मशः FG , FE औरFS ारा दशा� या जाता है । सही �वक चु न
A. FE > FG > FS
B. FE > FS > FG
C. FS > FG > FE
m
D. FS > FE > FGm .co
m .co s e m
s e l a
g l a ag
a

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m
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m .co s e m
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Page 173

17. 1 µm तरंग दै � की एक ले जर �करण को �वभा�जत �कया जाता है और समान लं बाई L की दो �नवा� त गु हा
(cavities) म भे जा जाता है जै सा �क �च म �दखाया गया है । एक �डटे र एक �तकरण (interference)
सं केत को केवल तभी पं जीकृत कर सकता है जब लौटने वाली �करण के बीच कलां तर (phase difference)
कम से कम 5 ⇥ 10 11 rad हो। एक भौ�तक भाव गु हा 2 की लं बाई को L से बदल दे ता है , जहाँ L/L '
10 21 है । इस भौ�तक भाव को मापने के �लए आव क ू नतम गु हा लं बाई (km म) लगभग है

A. 4
B. 1
C. 2
D. 16

Page 18

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Page 174

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18. इले ॉन-पॉ�ज़ ॉन जोड़े का उ ादन करने के �लए आव क ां �तक �व ु त े (critical electric field)
भौ�तक �नयतां क h, c, me और e पर �नभ� र करता है । �वमीय �व े षण का उपयोग कर और मान ल �क
�वमाहीन गु णां क का प�रमाण लगभग एक है । SI इकाइय म ां �तक �व ु त े का प�रमाण लगभग है
A. 1018
B. 1021
m
C. 1024
m .co
D. 1015
m .co s e m
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a

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Page 175

19. � ा R की वृ ाकार े ट वाले साथ एक समानां तर े ट सं धा�र को चाज� �कया जा रहा है जै सा �क �च
म �दखाया गया है । मान ली�जए �क B(r) े ट के बीच क ीय अ से r की री पर े �रत चुं बकीय े है ।
B(2d)
d ⌧ R मानते ए, चाज� करते समय अनु पात का मान है
B(d)

R

I 2d
d

A. 2
1
B.
2
1
C.
4
D. 1

Page 20

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20. मान m और 3m के दो �बं �नकाय ि�ं ग � रां क k = m!02 के मान र�हत ि�ं ग ारा जु ड़े ए ह और
एक घष� ण र�हत ै �तज सतह पर रखे गए ह। ि�ं ग को t = 0 समय पर अपनी ाकृ�तक लं बाई से एक छोटी
री l तक बढ़ाया जाता है और �फर छोड़ �दया जाता है ता�क दोन मान सरल आवत� ग�त को �न ा�दत
कर सके। मान m वाले कण की अ�धकतम ग�त है
p
3!0 l
A.
m
.co
2
m
.co
2!0 l
B. p
e m
e m
3
l as
l as !0 l
C. p
ag
ag 3
3!0 l
D.
4

m
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Page 21
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Document Details

Board / Org	Default
Exam	NEET MDS
Type	Question Paper
Pages	176
Updated	08 Jul 2026

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