Let [ . ] denotes greatest integer function. Then the value of ∫_0^3 ( e^x+e^-x [x]! )dx is :

(1)/(2) (e^2+e^3-(1)/(e^2)-(1)/(e^3) )

JEE Main 2026 April 02, Shift 1 Question Paper with Solutions

All 75 questions from the JEE Main 2026 (April 02, Shift 1) shift — Physics (25), Chemistry (25) and Mathematics (25) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics PYQs 2026 Chemistry PYQs 2026 Mathematics PYQs 2026

Chemistry25 questions

Q51Single correctSome Basic Concepts in Chemistry

The mass of iron converted into

Fe_{3} O_{4}

by the action of 18g of steam is (Given :Molar mass of

H_{2} O

and Fe are 1,16 and 56 g

mol^{- 1}

respectively) Assume iron is present in excess.

(A)

2.1 gm

(B)

4.2 gm

(C)

21 gm

(D)

42 gm

Q52Single correctAtomic Structure

What is the energy (in J ato

m^{- 1}

) required for the following process?

Li_{(g)}^{2 +} \to Li_{(g)}^{3 +} + e^{-}

(Take the ionization energy for the H atom in the ground state as

2.18 \times 1 0^{- 18}

J ato

m^{- 1}

)

(A)

8.72 \times 1 0^{- 18}

(B)

1.962 \times 1 0^{- 18}

(C)

1.962 \times 1 0^{- 17}

(D)

6.542 \times 1 0^{- 17}

Q53Single correctChemical Bonding and Molecular Structure

Given below are two statements

Statement-I : The correct sequence of bond length in the following species is

O_{2}^{\oplus} < O_{2} < O_{2}^{-} < O_{2}^{2 -}

Statement-II : The correct sequence of number of unpaired electrons in the following species is

O_{2} > O_{2}^{-} > O_{2}^{-} > O_{2}^{2 -}

In the light of the above statements choose the correct answers from the options given below

(A)

Both Statement-I and Statement-II are true

(B)

Both Statement-I and Statement-II are false

(C)

Statement-I is true but Statement-II is false

(D)

Statement-I is false but Statement-II is true

Q54Single correctChemical Thermodynamics

Consider the following data i)

2 A l_{(s)} + 6 HCl_{(a q)} \to A l_{2} C l_{6 (a q)} + 3 H_{2 (g)} + 1200 k J / mol

ii)

H_{2 (g)} + C l_{2 (g)} \to 2 HCl_{(g)} + 164 k J / mol

iii)

HCl_{(g)} + a q \to HCl_{(a q)} + 83 k J / mol

iv)

A l_{2} C l_{6 (s)} + a q \to A l_{2} C l_{6 (a q)} + 663 k J / mol

The enthalpy of formation of anhydrous solid

A l_{2} C l_{6}

is :

(A)

- 648 k J mol^{- 1}

(B)

- 1350 k J mol^{- 1}

(C)

- 2002 k J mol^{- 1}

(D)

- 1527 k J mol^{- 1}

Q55Single correctSolutions

19.5 g of fluoro acetic acid (molar mass

= 78

mol^{- 1}

) is dissolved in 500g of water at 298K. The depression in the freezing point of water was

1^{0} C

. What is

k_{a}

of fluoro acetic acid? (For water,

K_{f} = 1.86

K kg

mol^{- 1}

). Assume molarity and molality to have same values.

(A)

1 0^{- 6}

(B)

4 \times 1 0^{- 4}

(C)

3 \times 1 0^{- 5}

(D)

3 \times 1 0^{- 3}

Q56Single correctEquilibrium

The solubility product constants of

A g_{2} CrO_{4}

and AgBr are

32 x

and

4 y

respectively at 298K. The value of

(\frac{m o l a r i t y o f A g _{2} C r O _{4}}{m o l a r i t y o f A g B r})

can be expressed as :

(A)

\frac{2 3 x}{y}

(B)

Option 2 expression rendered as a small image in the PDF; appears to contain a graphical/mathematical figure rather than plain text

(C)

\frac{x}{y}

(D)

\frac{3 x}{y}

Q57Single correctRedox Reactions and Electrochemistry

An electrochemical cell is constructed using half cells in the direction of spontaneous change

F e (O H)_{2} (s) + 2 e^{-} \to F e (s) + 2 O H^{-} (a q) E^{0} = - 0.88 V

AgBr (s) + e^{-} \to A g (s) + B r^{-} (a q) E^{0} = 0.07 V

Which of the following option is correct

(A)

Overall reaction

F e (s) + 2 O H^{-} (a q) + 2 AgBr (s) ⇌ F e (O H)_{2} (s) + 2 A g (s) + 2 B r^{-} (a q)

(B)

E_{ce ll}^{0} = - 0.95 V

(C)

Fe is reduced in the electrochemical cell

(D)

E_{ce ll}^{0}

is an extensive property

Q58Single correctChemical Kinetics

t_{100%}

is the time required for the 100% completion of the reaction while

t_{1/2}

is the time required for the 50% of the reaction to be completed which of the following option correctly represents relation between

t_{100%}

and

t_{1/2}

for zero and first order reactions respectively?

(A)

t_{100%} = (t_{1/2})^{2}

and

t_{100%} = (t_{1/2})^{- \infty}

(B)

t_{100%} = 2 \times t_{1/2} : t_{100%} = (t_{1/2})^{\infty}

(C)

t_{100%} = 2 \times t_{1/2} : t_{100%} = (2 t_{1/2})^{2}

(D)

t_{100%} = (t_{1/2})^{\infty} : t_{100%} = 2 t_{1/2}

Q59Single correctClassification of Elements and Periodicity

Given below are two statements

Statement – I : The first Ionization enthalpy of the elements

Na, Mg, Cl

and

Ar

follows the order

Na > Mg > Cl > Ar

Statement – II : Among

Ca, Al, Fe

and

B

, the third ionisation enthalpy is very high for

Ca

.

In the light of the above statements choose the correct answers from the options given below

(A)

Both Statement-I and Statement-II are true

(B)

Both Statement-I and Statement-II are false

(C)

Statement-I is true but Statement-II is false

(D)

Statement-I is false and Statement-II is true

Q60Single correctp-Block Elements

Given below are two statements :

Statement I : Oxidising power of halogens decreases in the order

F_{2} > C l_{2} > B r_{2} > I_{2}

which is the basis of “Layer test”

Statement II : “Layer test” to identify

B r_{2}

and

I_{2}

in aqueous solution involves the oxidation of bromide or iodide into

B r_{2}

I_{2}

respectively with

C l_{2}

, which is a type of displacement redox reaction.

In the light of the above statements choose the correct answers from the options given below

(A)

Both Statement-I and Statement-II are true

(B)

Both Statement-I and Statement-II are false

(C)

Statement-I is true but Statement-II is false

(D)

Statement-I is false but Statement-II is true

Q61Single correctd- and f- Block Elements

Which of the following sets includes all the species that will change the orange colour of

K_{2} C r_{2} O_{7}

in acidic medium?

(A)

F e^{2 +}, S n^{2 +}, I^{-}, S^{2 -}

(B)

S^{2 -}, F e^{3 +}, I^{-}, C_{2} O_{4}^{2 -}

(C)

F e^{2 +}, N O_{2}^{-}, S O_{2}, S n^{4 +}

(D)

F e^{3 +}, S O_{4}^{2 -}, S^{2 -}, S n^{4 +}

Q62Single correctCoordination Compounds

Match List – I with List – II

List– I (Chromium (III) Complexes, en = ethylene diamine)	List– II $Δ_{0} (c m^{- 1})$
A) $[C r (CN)_{6}]^{3 -}$	I) 15060
B) $[CrF_{6}]^{3 -}$	II) 17400
C) $[C r (H_{2} O)_{6}]^{3 +}$	III) 22300
D) $[C r (e n)_{3}]^{3 +}$	IV) 26600

Choose the correct answer from the options given below:

(A)

A - I, B - II, C - III, D - I V

(B)

A - II, B - III, C - I V, D - I

(C)

A - III, B - I V, C - I, D - II

(D)

A - I V, B - I, C - II, D - III

Q63Single correctPurification and Characterisation of Organic Compounds

Given below are two statements :

Statement-I : 1, 2, 3-trihydroxy propane can be separated from water by simple distillation.

Statement-II : An azeotropic mixture cannot be separated by fractional Distillation

In the light of the above statements choose the correct answers from the options given below

(A)

Both Statement-I and Statement-II are true

(B)

Both Statement-I and Statement-II are false

(C)

Statement-I is true but Statement-II is false

(D)

Statement-I is false but Statement-II is true

Q64Single correctOrganic Compounds Containing Halogens

Given below are two statements

Statement-1 : Benzyl chloride reacts faster in

S_{N}^{1}

mechanism than ethyl chloride

Statement-II : Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance.

In the light of the above statements choose the correct answers from the options given below

(A)

Both Statement-I and Statement-II are true

(B)

Both Statement-I and Statement-II are false

(C)

Statement-I is true but Statement-II is false

(D)

Statement-I is false but Statement-II is true

Q65Single correctSome Basic Principles of Organic Chemistry

In IUPAC nomenclature, the correct order of decreasing priority of functional group is :

(A)

- CONH_{2}, ⟩ C = O, - CHO, - N H_{2}, - C \equiv C -

(B)

- CONH_{2}, - COOCH_{3}, - CHO, - N H_{2}, - O H

(C)

- CONH_{2}, - CHO, ⟩ C = O, - N H_{2}, - C \equiv C -

(D)

- CONH_{2}, - CHO, - CN, - N H_{2}, - C \equiv C -

Q66Single correctOrganic Compounds Containing Nitrogen

For the given molecule, "

x

", the preferred site for the attack of the electrophile is :

N-phenylbenzamide skeletal structure labelled x=. Two benzene rings linked by a -C(=O)-N(H)- amide group. Left (benzoyl) ring carries position labels r (meta) and p (ortho to the carbonyl). Right (anilide) ring carries position labels s (ortho to the N-H) and u (para to the N-H).

(A)

Predominantly at “r”

(B)

“r” and “u”

(C)

“p” and “s”

(D)

Predominantly at “u”

Q67Single correctPrinciples Related to Practical Chemistry

Match List - I with List - II

List-I (Mixture of compounds)	List-II (Reagent used to distinguish)
A. Diethyl amine + Ethyl amine	I. Bromine water
B. Acetaldehyde + Acetone	II. $CHCl_{3} + KOH, Δ$
C. Ethanol + Phenol	III. Neutral $FeCl_{3}$
D. Benzoic acid + Cinnamic acid	IV. Ammonical silver nitrate

Choose the correct answer from the options given below :

(A)

A - IV, B - II, C - I, D - III

(B)

A - IV, B - II, C - III, D - I

(C)

A - II, B - IV, C - I, D - III

(D)

A - II, B - IV, C - III, D - I

Q68Single correctOrganic Compounds Containing Nitrogen

Consider the three aromatic molecules (P, Q and R) whose structures have been given below:

The correct order regarding the reactivity of these compounds with

Ph-N^{+} \equiv NCl^{-}

under optimum but slightly acidic medium is :

Three substituted N,N-dimethylaniline structures arranged on the page. P: unsubstituted N,N-dimethylaniline (phenyl ring bonded to N with two methyl groups; lone pair shown on N). Q: 2-methyl-N,N-dimethylaniline (ortho-methyl on the ring; N still bears two methyl groups). R: 2,6-dimethyl-N,N-dimethylaniline (two ortho-methyl substituents flanking the N; N still bears two methyl groups). Lone pair on N shown in each structure.

(A)

P > Q > R

(B)

R > P > Q

(C)

R > Q > P

(D)

P > R > Q

Q69Single correctBiomolecules

Match List - I with List - II

List-I (Vitamin)	List-II (Name)
A. Vitamin $B_{1}$	I. Pyridoxine
B. Vitamin $B_{2}$	II. Ascorbic acid
C. Vitamin $B_{6}$	III. Thiamine
D. Vitamin C	IV. Riboflavin

Choose the correct answer from the options given below:

(A)

A - II, B - I, C - III, D - IV

(B)

A - IV, B - III, C - II, D - I

(C)

A - III, B - IV, C - I, D - II

(D)

A - I, B - III, C - II, D - IV

Q70Single correctPrinciples Related to Practical Chemistry

A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with

K_{2} CrO_{4}

To give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc.

HNO_{3}

and ammonium molybdate it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively.

(A)

Ca^{+ 2}

and

SO_{4}^{2 -}

(B)

Ba^{+ 2}

and

PO_{4}^{3 -}

(C)

Mn^{2 +}

and

PO_{4}^{3 -}

(D)

Ba^{2 +}

and

SO_{4}^{2 -}

Q71NumericalCoordination Compounds

5.33

g of

CrCl_{3} \cdot 6 H_{2} O

which is a 1:3 electrolyte, is dissolved in water and is passed through a cation exchanger. The Chloride ions in the eluted solution on treatment with

AgNO_{3}

results in

8.61

g of

AgCl

. The ratio of moles of complex reacted and moles of

AgCl

formed is ________

\times 1 0^{- 2}

. (Nearest integer)

[Molar mass in g

mol^{- 1}

Cr : 52, Ag : 108, Cl : 35.5, H : 1, O : 16]

Q72NumericalHydrocarbons

Consider the isomers of hydrocarbon with molecular formula

C_{5} H_{10}

. These isomers do not decolorise

KMnO_{4}

solutions. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is ________

SolutionAnswer: 14

Approach:

Isomers of

C_{5} H_{10}

that do not decolourise

KMnO_{4}

have no

π

-bond, so they are the saturated cycloalkanes only. Enumerate the five cycloalkane structural isomers and, for each, count the number of distinct H-environments; each environment yields one monochloro structural isomer on photochlorination.

Step 1:

C_{5} H_{10}

has DoU

= 1

. "Not decolorising

KMnO_{4}

" rules out alkenes, leaving only the cycloalkanes.

DoU = 1, no C=C \Rightarrow ring only

Step 2:The cycloalkane structural isomers of

C_{5} H_{10}

: (i) cyclopentane, (ii) methylcyclobutane, (iii) ethylcyclopropane, (iv) 1,1-dimethylcyclopropane, (v) 1,2-dimethylcyclopropane.

{C_{5} H_{10}}_{sat} = {cyclopentane, MeC_{4} H_{7}, EtC_{3} H_{5}, 1, 1 -Me_{2} C_{3} H_{4}, 1, 2 -Me_{2} C_{3} H_{4}}

Step 3:Cyclopentane: all 10 H atoms are equivalent (single environment), giving 1 monochloro product.

Cyclopentane : 1 H environment \Rightarrow 1

Step 4:Methylcyclobutane: the four ring carbons differ as C1 (CH-Me), C2 and C4 (equivalent

α

to C1), C3 (

β

); plus the C

H_{3}

group. This gives 4 distinct H-environments and thus 4 monochloro products.

Methylcyclobutane : {C1-H, C2/4-H, C3-H, CH_{3}} \Rightarrow 4

Step 5:Ethylcyclopropane: ring C1 (bearing Et), ring C2 and C3 (equivalent), and the ethyl group

-CH_{2} -CH_{3}

contributes two more (the

CH_{2}

and the

CH_{3}

). Four distinct H-environments, hence 4 monochloro products.

Ethylcyclopropane : {C1-H, C2/3-H, CH_{2}, CH_{3}} \Rightarrow 4

Step 6:1,1-dimethylcyclopropane: the two methyls on C1 are equivalent; ring C

H_{2}

groups (C2, C3) are equivalent. Two distinct H-environments give 2 monochloro products.

1, 1 -Dimethylcyclopropane : {CH_{3} (on C1), CH_{2} (C2/3)} \Rightarrow 2

Step 7:1,2-dimethylcyclopropane: equivalent ring methyls; equivalent ring C-H (on C1 and C2); the two H atoms on C3 are diastereotopic (cis and trans to the methyls) and give two different monochloro structural products. Total = 3 monochloro structural isomers.

1, 2 -Dimethylcyclopropane : {CH_{3}, C1/2-H, C3-H_{cis} vs C3-H_{trans}} \Rightarrow 3

Step 8:Sum the monochloro structural isomers across all five parent cycloalkanes.

1 + 4 + 4 + 2 + 3 = 14

Step 9:Cross-check by independent counting (replacement-of-each-distinct-H method) on each parent; the totals 1, 4, 4, 2, 3 are reproduced, summing to 14.

\sum n_{i} = 14

Step 10:Result.

Total monochloro structural isomers = 14

Final answer: 14

Q73NumericalHydrocarbons

One mole of an alkane (x) requires 8 moles oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is ________

Q74NumericalChemical Kinetics

For reaction

A \to P

, rate constant

k = 1.5 \times 1 0^{3} s^{- 1}

2 7^{\circ} C

. If activation energy for the above reaction is

60

kJ mo

l^{- 1}

, then the temperature

(in^{\circ} C)

at which rate constant,

k = 4.5 \times 1 0^{3} s^{- 1}

is ________. (Nearest integer)

Given :

lo g 2 = 0.30, lo g 3 = 0.48, R = 8.3 J K^{- 1} mol^{- 1}, ln 10 = 2.3

Q75NumericalChemical Thermodynamics

At the transition temperature T,

A = B

and

Δ G^{0} = 105 - 35 lo g T

where A and B are two states of substance X. The transition temperature in

^{\circ} C

when pressure is 1 atm is ________ (Nearest integer)

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JEE Main 2026 April 02, Shift 1 Question Paper with Solutions

Physics25 questions

Chemistry25 questions

Mathematics25 questions

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