JEE Main 2026 Question Paper with Solutions

Initially a satellite of 100 kg is in a circular orbit of radius $1.5R_E$. This satellite can be moved to a circular orbit of radius $3R_E$ by supplying $\alpha \times 10^6$ J of energy. The value of $\alpha$ is __________. (Take Radius of Earth $R_E = 6 \times 10^6$ m and $g = 10$ m/s$^2$)

A 4 kg mass moves under the influence of a force $F = (4t^2 - 3t^2)$ N where $t$ is the time in second. If mass starts from origin at $t = 0$, the velocity and position after $t = 2$ s will be:

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of $120$ cm at $30^\circ$C. The coefficient of linear expansion of aluminium and steel are $24 \times 10^{-6}/^\circ$C and $1.2 \times 10^{-5}/^\circ$C, respectively. The length of this composite rod when its temperature is raised to $100^\circ$C, is ______ cm.

Two strings $A, B$ having linear densities $\mu_A = 2 \times 10^{-4}$ kg/m and $\mu_B = 4 \times 10^{-4}$ kg/m and lengths $L_A = 2.5$ m and $L_B = 1.5$ m respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively creating a tension of $500$ N in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1/t_2$ is:

The r.m.s. speed of oxygen molecules at $47^\circ$C is equal to that of the hydrogen molecules kept at \_\_\_\_\_\_ $^\circ$C. (Mass of oxygen molecule/mass of hydrogen molecule $= 32/2$)

Given below are two statements: Statement I: The number of species among $SF_4$, $NH_4^+$, $NiCl_4^{2-}$, $XeF_4$, $PtCl_4^{2-}$, $SeF_4$ and $Ni(CN)_4^{2-}$ that have tetrahedral geometry is 3. Statement II: In the set $[NO_2, BeH_2, BF_3, AlCl_3]$, all the molecules have incomplete octet around central atom. In the light of the above statements, choose the correct answer from the options given below:

An organic compound (P) on treatment with aqueous ammonia under hot condition forms compound (Q) which on heating with $Br_2$ and KOH forms compound (R) having molecular formula $C_6H_7N$. Names of P, Q and R respectively are:

Which of the following represents the correct trend for the mentioned property? A. F > P > S > B - First Ionization Energy B. Cl > F > S > P - Electron Affinity C. K > Al > Mg > B - Metallic character D. K2O>Na2O>MgO>Al2O3K2​O>Na2​O>MgO>Al2​O3​ - Basic character

Given below are two statements: Statement I: The number of pairs among $[SiO_2, CO_2]$, $[SnO, SnO_2]$, $[PbO, PbO_2]$ and $[GeO, GeO_2]$, which contain oxides that are both amphoteric is 2. Statement II: $BF_3$ is an electron deficient molecule, can act as a Lewis acid, forms adduct with $NH_3$ and has a trigonal planar geometry. In the light of the above statements, choose the correct answer from the options given below:

$14.0$ g of calcium metal is allowed to react with excess HCl at $1.0$ atm pressure and $273$ K. Which of the following statements is incorrect? [Given: Molar mass in g mol$^{-1}$ of Ca - 40, Cl - 35.5, H - 1]

Let $O$ be the vertex of the parabola $x^2 = 4y$ and $Q$ be any point on it. Let the locus of the point $P$, which divides the line segment $OQ$ internally in the ratio $2:3$ be the conic $C$. Then the equation of the chord of $C$, which is bisected at the point $(1,2)$, is:

Let the foci of a hyperbola coincide with the foci of the ellipse $\dfrac{x^2}{36} + \dfrac{y^2}{16} = 1$. If the eccentricity of the hyperbola is $5$, then the length of its latus rectum is:

The value of $\csc 10^\circ - \sqrt{3} \sec 10^\circ$ is equal to:

The number of relations, defined on the set $\{a, b, c, d\}$, which are both reflexive and symmetric, is equal to:

Let $A = \{2, 3, 5, 7, 9\}$. Let $R$ be the relation on $A$ defined by $xRy$ if and only if $2x \le 3y$. Let $l$ be the number of elements in $R$, and $m$ be the minimum number of elements required to be added in $R$ to make it a symmetric relation. Then $l + m$ is equal to:

If an alpha particle with energy $7.7$ MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is ______ m. (Atomic number of gold $= 79$ and $1/(4\pi\varepsilon_0) = 9 \times 10^9$ in SI units)

The electric field in a plane electromagnetic wave is given by $E_y = 69 \sin[0.6 \times 10^3 x - 1.8 \times 10^{11} t]$ V/m. The expression for magnetic field associated with this electromagnetic wave is _______ T.

A parallel plate capacitor has capacitance $C$ when there is vacuum within the parallel plates. A sheet having thickness $t = (1/3)$ of the separation between the plates and relative permittivity $K = 2$ is introduced between the plates. The new capacitance of the system is:

In a double slit experiment the distance between the slits is $0.1$ cm and the screen is placed at $50$ cm from the slits plane. When one slit is covered with a transparent sheet having thickness $t$ and refractive index $n = 1.5$, the central fringe shifts by $0.2$ cm. The value of $t$ is _______ cm.

A light wave described by $E = 60[\sin(3 \times 10^{15}t) + \sin(12 \times 10^{15}t)]$ (in SI units) falls on a metal surface of work function $2.8$ eV. The maximum kinetic energy of ejected photoelectron is (approximately) \_\_\_\_\_\_ eV. ($h = 6.6 \times 10^{-34}$ J$\cdot$s and $e = 1.6 \times 10^{-19}$ C)

Let the mean and variance of 7 observations $2,4,10,x,12,14,y$ $(x>y)$, be $8$ and $16$ respectively. Two numbers are chosen from $\{1,2,3,x-4,y,5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than $4$, is:

Let $(\alpha, \beta, \gamma)$ be the coordinates of the foot of the perpendicular drawn from the point $(5, 4, 2)$ on the line $\vec{r} = (-\hat{i} + 3\hat{j} + \hat{k}) + \lambda(2\hat{i} + 3\hat{j} - \hat{k})$. Then the length of the projection of the vector $\alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}$ on the vector $6\hat{i} + 2\hat{j} + 3\hat{k}$ is:

The area of the region, inside the ellipse $x^2 + 4y^2 = 4$ and outside the region bounded by the curves $y = |x| - 1$ and $y = 1 - |x|$, is:

If the domain of the function $f(x) = \cos^{-1}\left(\dfrac{2x-5}{11-3x}\right) + \sin^{-1}(2x^2 - 3x + 1)$ is the interval $[\alpha, \beta]$, then $\alpha + 2\beta$ is equal to:

Let $\vec{a} = -\hat{i} + 2\hat{j} + 2\hat{k}$, $\vec{b} = 8\hat{i} + 7\hat{j} - 3\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a} \times \vec{c} = \vec{b}$. If $\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = 4$, then $|\vec{a} + \vec{c}|^2$ is equal to:

Given below are two statements: Statement I: Among $[Cu(NH_3)_4]^{2+}$, $[Ni(en)_3]^{2+}$, $[Ni(NH_3)_6]^{2+}$ and $[Mn(H_2O)_6]^{2+}$, $[Mn(H_2O)_6]^{2+}$ has the maximum number of unpaired electrons. Statement II: The number of pairs among $[NiCl_4]^{2-}$, $[Ni(CO)_4]$, $[NiCl_4]^{2-}$, $[Ni(CN)_4]^{2-}$ and $[Ni(CO)_4]$, $[Ni(CN)_4]^{2-}$ that contain only diamagnetic species is two.

Identify the correct statements. A. Arginine and Tryptophan are essential amino acids. B. Histidine does not contain heterocyclic ring in its structure. C. Proline is a six membered cyclic ring amino acid. D. Glycine does not have chiral centre. E. Cysteine has characteristic feature of side chain as MeS � CH$_2$ � CH$_2$�.

Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation energy of second reaction by $20$ kJ mol$^{-1}$. If $k_1$ and $k_2$ are the rate constants of first and second reaction respectively at $300$ K, then $\ln(k_2/k_1)$ will be (nearest integer). Given: $R = 8.3$ J K$^{-1}$ mol$^{-1}$.

The correct statements are: A. Activation energy for enzyme catalysed hydrolysis of sucrose is lower than that of acid catalysed hydrolysis. B. During denaturation, secondary and tertiary structures of a protein are destroyed but primary structure remains intact. C. Nucleotides are joined together by glycosidic linkage between $C_1$ and $C_4$ carbons of the pentose sugar. D. Quaternary structure of proteins represents overall folding of the polypeptide chain.

Decomposition of A is a first order reaction at T(K) and is given by $A(g) \rightarrow B(g) + C(g)$. In a closed 1 L vessel, 1 bar $A(g)$ is allowed to decompose at T(K). After 100 minutes, the total pressure was 1.5 bar. What is the rate constant (in min$^{-1}$) of the reaction? ($\log 2 = 0.3$)