WB JEE 2026 | WB JEE Year Wise Previous Years Questions

Chemistry

1. The major products U and V in the following reaction are 2. Among $\mathrm{N}_2 \mathrm{O}, \mathrm{ClF}_2^{-}, \mathrm{SO}_2$ and $\mathrm{I}_3^{+}$, the species having the linear 3. In the following sequence of reactions, what is the end product ' $Z$ '? 4. A compound $(\mathrm{X})$ when treated with $\mathrm{CuSO}_4$ solution yields a brown precipitate．On adding hypo solutio 5. Three engines $\mathrm{A}, \mathrm{B}$ and C take steam at $130^{\circ} \mathrm{C}$ and reject it at $20^{\circ} \mathrm 6. In a conductance experiment, aqueous $\mathrm{AgNO}_3$ solution is added to aqueous KCl solution gradually and simultane 7. Indicate the major product of the following reaction: 8. The van't Hoff Factor (i) for a dilute aqueous solution of $\mathrm{Na}_2 \mathrm{SO}_4$ is 9. Which of the following is the structure of pyrosulphuric acid? 10. Peroxide ion is 11. How many isomers can a compound with molecular formula $\mathrm{C}_3 \mathrm{H}_5 \mathrm{Br}$ have？ 12. Which one of the following cations gives a chocolate brown precipitate upon addition of aqueous solution of $\mathrm{K}_ 13. A compound contains two types of atoms $A$ and $B$ ．Its crystal structure is a cubic lattice with＇$A$＇ atoms at the corn 14. The plot of radial probability density（ $4 \pi r^2 R^2$ ）against $r$ for an electron in $n p$ orbital of a many electron 15. A buffer solution contains 100 ml of $0.01(\mathrm{M}) \mathrm{CH}_3 \mathrm{COOH}$ and 200 ml of $0.02(\mathrm{M}) \mat 16. The correct order of conductivity of $0.001(\mathrm{M})$ separate aqueous solutions of $\left[\mathrm{Pt}\left(\mathrm{N 17. Borazole is prepared by heating the product isolated by reacting 18. The increasing order of basicity of the following compounds is 19. The products $\mathbf{X}$ and $\mathbf{Y}$ in the following reaction sequence are 20. The van der Waal's equation : $\left(P+\frac{a}{4 V^2}\right)\left(V-\frac{b}{2}\right)=\frac{R T}{2}$ is valid for 21. Which one of the following does not lose water even in conc. $\mathrm{H}_2 \mathrm{SO}_4$ ? 22. The major product in the following reaction is 23. Rank the following anions in order of decreasing nucleophilicity in a polar protic solvent (most → least nucleophilic). 24. In which of the following species, $\mathrm{sp}^3 \mathrm{~d}^2$ hybridisation is not associated? 25. For the reaction $A \rightarrow B$ ，variation of concentration is plotted against time as shown below． Which of the fol 26. In a first order reaction，the concentration of reactant decreases from 400 moles lit $^{-1}$ to 50 moles lit ${ }^{-1}$ 27. In the following reaction sequence, the product Y is $$ \mathrm{Br}\left(\mathrm{CH}_2\right)_{12}-\mathrm{C} \equiv \m 28. The mass of an electron is $9 \cdot 1 \times 10^{-31} \mathrm{~kg}$ ．If its K ．E．is $3 \cdot 0 \times 10^{-25} \mathrm{~ 29. The calculated magnetic moment for low spin $[\operatorname{Ru}(E D T A)]^{-}$is 30. Glucose is added to 1 litre of water to such an extent that $\Delta T_f / K_f$ equals to $\frac{1}{1000}$ ．The weight of 31. A $5.0 \mathrm{~cm}^3$ solution of $\mathrm{H}_2 \mathrm{O}_2$ liberates 1.27 g of iodine from an acidified KI solution. 32. An organic compound undergoes first order decomposition．The time taken for its decomposition to $\frac{1}{8}$ th and $\f 33. For the metal complex $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ ，coordination num 34. $$ \mathrm{RO}-\mathrm{CH}_2-\mathrm{C} \equiv \mathrm{CH} \xrightarrow{\mathrm{X}} \xrightarrow{\mathrm{Y}} \mathrm{RO} 35. 36. Which of the following statement(s) is/are correct about the given compound? 37. 1 mole of an ideal gas undergoes the following processes： Process $A \rightarrow$ Isothermal expansion at 400 K from vol 38. Which of the following statement（s）is／are correct？ 39. Which of the following have tetrahedral structures？ 40. Which of the following plot(s) is/are correct representation(s) of Boyle's Law?

Mathematics

1. Given $P(x)=x^4+a x^3+b x^2+c x+d$ such that $x=0$ is the only real root of $P^{\prime}(x)=0$. If $P(-1) 2. If $\alpha, \beta$ are the roots of the equation $x^2-p x+q=0$ and $\alpha>0, \beta>0$, then $\alpha^{\frac{1}{4}}+\beta 3. If $\sum\limits_{r=1}^{\infty} \tan ^{-1}\left(\frac{1}{2 r^2}\right)=a$, then $\tan a$ is equal to 4. Consider a function $f(x)$ which has exactly two roots at $x=a$. If $\mathop {\lim }\limits_{x \to a}\left(\frac{\lambda 5. A vector given by $\vec{P}=f(t) \hat{i}+g(t)+\hat{k}$ moves in such a way that it is always parallel to the vector $\vec 6. The expression $\sum_{k=1}^{32}(3 K+2)\left\{\sum_{r=1}^{10}\left(\sin \frac{2 r \pi}{11}-i \cos \frac{2 r \pi}{11}\righ 7. $\theta$ elimination from the equation $x^2+y^2=\frac{x \cos 3 \theta+y \sin 3 \theta}{\cos ^3 \theta}=\frac{y \cos 3 \t 8. If $t_n$ denotes the $n^{\text {th }}$ term of an A.P. and $t_p=\frac{1}{q}, t_q=\frac{1}{p}$, then which one of the fol 9. Consider the sequence of numbers $(1,2,3, \ldots \ldots, 13)$. A person choose three numbers at random from the sequence 10. If $f(x)=\frac{1+x}{1-x}$ and $A$ is a matrix such that $A^3=0$, then $f(A)=$ 11. Which of the following statements is always true? 12. If $0 13. On the set $\mathbb{R}$ of real numbers the relation $\rho$, defined by $\mathrm{x} \rho \mathrm{y}(\mathrm{x}, \mathrm{ 14. If $\int \frac{\operatorname{cosec}^2 x-2010}{\cos ^{2010} x} d x=-\frac{f(x)}{(g(x))^{2010}}+c$, where $f\left(\frac{\p 15. If the locus of mid point of any normal chord of the parabola $y^2=4 x$ is $x-\lambda=\frac{\mu}{y^2}+\frac{y^2}{v}$, wh 16. The true set of values of ' $K$ ' for which $\sin ^{-1}\left(\frac{1}{1+\sin ^2 x}\right)=\frac{K \pi}{6}$ may have a so 17. A mapping is selected at random from all mappings $f: A \rightarrow A$, where set $A=\{1,2,3 \ldots, n\}$. If the probab 18. Let $A=[a, \infty)$ denotes the domain, then $f:(a, \infty) \rightarrow B$, which is defined by $f(x)=2 x^3-3 x^2+6$ wil 19. If $a=\mathop {\lim }\limits_{n \to \infty } \cos ^{2 n} x,(x=n \pi)$ and $b=\mathop {\lim }\limits_{n \to \infty } \co 20. The position vectors of two adjacent sides $\overrightarrow{O A}$ and $\overrightarrow{O B}$ of a rectangle $O A C B$ ar 21. The point of intersection of $\vec{r} \times \vec{a}=\vec{b} \times \vec{a}$ and $\vec{r} \times \vec{b}=\vec{a} \times 22. Let $a_1, a_2, a_3 \ldots$ are in G.P. such that $n>m, a_n>a_m$ and $a_1+a_n=66, a_2 \cdot a_{n-1}=128$. If $\sum_{r=1}^ 23. The minimum length of intercept on any tangent to the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ cut by the circle $x^2+y^2 24. Intercepts of the plane $\vec{r} \cdot \vec{n}=d(\neq 0)$ on the coordinate axes respectively are 25. The general solution of the equation $\sin ^{100} \mathrm{x}-\cos ^{100} \mathrm{x}=1$ is 26. If $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}, \vec{c}=\hat{i}+2 \hat{j}-\hat{k}$, then the value 27. Number of elements in the range set of $f(x)=\left[\frac{x}{15}\right]\left[-\frac{15}{x}\right]$, for all $x \in(0,90$ 28. Let 10 Bags $B_1, B_2, \ldots, B_{10}$ which contains $21,22, \ldots, 30$ different articles respectively. Then the tota 29. Let domain and range of $f(x)$ and $g(x)$ is $[0, \infty)$. If $f(x)$ is an increasing function, $g(x)$ is a decreasing 30. Consider the following ellipse : $\frac{x^2}{f\left(K^2+2 K+5\right)}+\frac{y^2}{f(K+11)}=1$, where $f(x)$ is a positive 31. The solution of the differential equation $2 x^2 y \frac{d y}{d x}=\tan \left(x^2 y^2\right)-2 x y^2$, given $y(1)=\sqrt 32. $$ \int \frac{\left(\sqrt[3]{x+\sqrt{2-x^2}}\right)\left(\sqrt[6]{1-x \sqrt{2-x^2}}\right)}{\sqrt[3]{1-x^2}} d x ;(x \in 33. Consider the function $y=f(x)$ defined implicitly by the equation $y^3-3 y+x=0$ on the interval $(-\infty,-2) \cup(2, \i 34. The total number of polynomials of the form $x^3+a x^2+b x+c$ which is divisible by $x^2+1$, where $a, b, c \in\{1,2,3, 35. The term independent of $x$ in the expansion of $\left(\frac{x+1}{x^{\frac{2}{3}}-x^{\frac{1}{3}}+1}-\frac{x-1}{x-x^{\fr 36. For a real number $y$, consider $(y)$ denotes the greatest integer less than or equal to $y$. If $f(x)=\frac{\tan (\pi[x 37. If $\int_0^1\left(\sum_{r=1}^{2013} \frac{x}{x^2+r^2}\right)\left(\prod_{r=1}^{2013}\left(x^2+r^2\right)\right) d x=\fra 38. The least positive value of ' $a$ ' for which the equation $\int_0^x\left(t^2-8 t+13\right) d t=x \sin \frac{a}{x}$ has 39. Let all the points on the curve $x^2+y^2-10 x=0$ are reflected about the line $y=x+3$. If the locus of the reflected poi 40. The equation $|x+1|^{\log _{(x+1)}\left(3+2 x-x^2\right)}=(x-3)|x|$ has 41. If the domain of $f(x)$ is $(0,1)$, then the domain of $y=f\left(e^x\right)+f(\ln |x|)$ is 42. The number of 3-digit numbers we of the form $x y z$ with $x 43. Suppose $A$ is denoted the set of all numbers between 1 and 700 which are divisible by 3 and let $B$ is denoted the set 44. Let us define the power of a matrix $A$ as the maximum $m \in Z^{+}$such that $A^m=I$. For two matrices $A$ and $B$ if $ 45. If for two real numbers $\mathrm{a}, \mathrm{b}$ with $|\mathrm{a}| \leq 1$ and $|\mathrm{b}| \leq 1$, $\frac{1}{3}+\fra 46. Let $\operatorname{det} A=\left|\begin{array}{ccc}\mathrm{l} & \mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q} & \mat 47. Let $f:(0,1) \rightarrow(0,1)$ be a differentiable function such that $f^{\prime}(x) \neq 0 \forall x \in(0,1)$ and $f\l 48. If ' $a$ ' is an integer lying in $[-5,30]$, then the probability that the graph of $y=x^2+2(a+4) x-5 a+64$ lies above t 49. Consider a square $A B C D$ of diagonal length 2a. The square is folded along the diagonal $A C$ so that the plane of $\ 50. If $\int \frac{\left(1-x^2\right)}{\sqrt{x} \sqrt{\left(1+x^2\right)^3}}=\alpha \frac{x^\beta}{\left(1+x^2\right)^\gamma 51. Let $\vec{a}=(x, y, z)$ be the vector with $|\vec{a}|=2 \sqrt{3}$, which makes equal angles with the vector $\vec{b}=(y, 52. Let $A_1, A_2, \ldots, A_6$ are six sets, each with four elements and $B_1, B_2, \ldots ., B_n$ are $n$ sets, each with 53. A figure is bounded by the curves $y=x^2+1, y=0, x=0$ and $x=1$. The point at which a tangent should be drawn to the cur 54. The ends $A$, $B$ of a straight line segment of constant length $c$ slide upon the fixed rectangular axes $O X, O Y$ res 55. Let 1 lies between the roots of the equation $y^2-m y+1=0$ and $[x]$ denotes the greatest integer function. Then the val 56. Let $f(x)$ be a twice differentiable function in $[1,3]$ and $f(1)=f(3)$. Further if $\left|f^{\prime \prime}(x)\right| 57. The quantities $a_1, a_2, a_3, \ldots$ form an infinite decreasing G.P. If $a_1=1$, then the common ratio of the progres 58. If $f$ be a real valued function defined for all real numbers $x$ such that for some fixed $a>0$, it satisfies $f(x+a)=\ 59. Four natural numbers selected at random are multiplied together, then the probability that the digit in the unit's place 60. Let $f(x)$ be a real valued $f$ unction which is monotonic and differentiable. Then for any reals a and $b, \int_{f(a)}^ 61. Tangent at a point $P_1$ (other than $(0,0)$ ) on the curve $y=x^3$ meets the curve again at $P_2$. The tangent at $P_2$ 62. The equation $x^3+5 x^2+p x+q=0$ and $x^3+7 x^2+p x+r=0$ have two roots in common. If the third root of each equation is 63. Let $a, b, c$ be non-zero real numbers, such that $\int_0^r\left(1+\cos ^8 x\right)\left(a x^2+b x+c\right) d x=\int_0^{ 64. Let $Z_1, Z_2$ be the roots of the equation $Z^2+p Z+q=0$, where the coefficients $p$ and $q$ may be complex numbers and 65. Let $g(x)=a x+b$, where $a 66. If $\sum_{r=0}^{2 n} a_r(x-2)^r=\sum_{r=0}^{2 n} b_r(x-3)^r$ and $a_k=1 \forall k \geq 1$, then the value of $\frac{b_n} 67. If $f(x)$ is differentiable for all $x \in \mathbb{R}$ and satisfies the relation $x=\mathop {\lim }\limits_{n \to \inft 68. If a differentiable function satisfies $(x-y) f(x+y)-(x+y) f(x-y)=2\left(x^2 y-y^3\right) \forall x, y \in \mathbb{R}$ a 69. Let $f(x)>0$ for all $x \in \mathbb{R}$ and $f(x)$ is bounded. If $\mathop {\lim }\limits_{n \to \infty } \sum_{r-1}^n a 70. Consider the curve $x=1-3 t^2, y=t-3 t^3$. The tangent to the curve at the point $t$ is inclined at an angle $\phi$ to O 71. If $f(x)=x\left(1331 x^2-3630 x+3300\right)$, then for $a=\cos ^2\left(\tan ^{-1}\left(\sin \left(\cot ^{-1} 3\right)\ri 72. Let $\vec{r}=\sin x(\vec{a} \times \vec{b})+\cos y(\vec{b} \times \vec{c})+2(\vec{c} \times \vec{a})$ ，where $\vec{a}, \ 73. The parabola $y=4-x^2$ has vertex P. It intersects $x$-axis at A and B. If the parabola is translated from its initial p 74. If $A_1, A_2, A_3, \ldots, A_{1006}$ be independent events such that $P\left(A_l\right)=\frac{1}{2 i},(i=1,2, \ldots, 10 75. If $\left(4^{\sec ^2 \alpha}\right) x^2+2 x+\left(\beta^2-\beta+\frac{1}{2}\right)=0$ has real roots，then the value／valu

Physics

1. A body of density＇$\rho$＇is dropped slowly on the surface of a lake of depth $d$ ．If the density of the lake water be＇$\ 2. Beyond what distance，the ray optics is sufficiently valid when the aperture is 6 mm wide and the wavelength is $6000 \ma 3. A plano－convex lens fits exactly into a plano－concave lens．Their plane surfaces are parallel to each other．If lenses are 4. Consider a fuse wire of length $l$ and radius $r$ ．The time of heating $(t)$ for passing the maximum current will depend 5. Density and volume of a body are given as $(20 \pm 4) \mathrm{gm} / \mathrm{cm}^3$ and $(10 \pm 1) \mathrm{cm}^3$ respec 6. If a vector $\vec{v}=3 \hat{i}$ is rotated in the $x-z$ plane by an angle $\theta$ with respect to $x$－axis in the clock 7. A circular coil, carrying current, has radius $R$. The distance from the centre of the coil on the axis where the magnet 8. A square of side $L$ lies in the $x-y$ plane，where the magnetic field is given by $B=B_0(2 \hat{i}+3 \hat{j}+4 \hat{k})$ 9. A resistor of resistance＇$R$＇draws power＇$P$＇when connected to an AC source．If an inductance is now placed in series wit 10. A simple pendulum of length $l$ has a bob of mass $m$ ，with a charge $q$ ．On it a vertical sheet of charge， with surface 11. The equation of a transverse wave is $y=y_0 \sin 2 \pi\left(f t-\frac{x}{\lambda}\right)$ ．If the maximum particle veloc 12. A uniform but time varying magnetic field is present in a circular region of radius ' $R$ '. The magnetic field is perpe 13. From a tower of height $H$ ，a particle is thrown vertically upwards with a speed $u$ ．The time taken by the particle to 14. There is a ring of radius $r$ having linear charge density $\lambda$ and rotating with a uniform angular velocity $\omeg 15. Three vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $|\vec{a}|=1,|\vec{b}|=2$ and $|\vec{c}|=4$ along with $\ve 16. Two identical metal bars are heated in two different temperatures and allowed to cool in the same surroundings. Which on 17. The inputs to a digital circuit are as shown below. The output Y is 18. The velocity $v$ of a particle at time $t$ is given by $v=a t+\frac{b}{t+c}$, where $a, b$ and $c$ are constants. The di 19. A body initially at rest and sliding along a frictionless track from a height＇$h$＇（as shown in figure） just completes a 20. The I-V characteristics graph shown below is exhibited by 21. A person has a minimum distance of distinct vision of 50 cm ．The power of lenses required to read a book at a distance o 22. Three blocks of masses $m_1=2 \mathrm{~kg}, m_2=3 \mathrm{~kg}$ and $m_3=5 \mathrm{~kg}$ are placed on a horizontal fric 23. Which one of the following graphs represents the velocity-time $(v-t)$ graph of a small spherical body falling in a visc 24. A ray of light travelling in air is incident on one face of a parallel glass slab of thickness $t$ and refractive index 25. Radiation of wavelength $\lambda$ is incident on a photocell．The fastest emitted electron has speed $v$ . If the wavelen 26. Two spherical soap bubbles of radii $r_1$ and $r_2$ in vaccum coalesce under isothermal condition．The newly formed bubbl 27. A radioactive element ${ }_{92}^{242} \mathrm{X}$ emits two $\alpha$－particles，one electron and two positrons．The transf 28. The magnetic moment of an iron bar is $M$. It is now bent in such a way that it forms an arc section of a circle subtend 29. A uniform $\operatorname{rod} A B$ is suspended from a point $P$ ，at a variable distance $x$ ，from $A$ ，as shown in figu 30. A pipe $A$ is connected with other pipes $B$ and $C$ as shown in the figure．The areas of cross－section of $A, B$ and $C$ 31. A particle of mass $m$ is suspended from a point O by a string of length $R$ ．It is given a velocity $u=3 \sqrt{g R}$ at 32. The de-Broglie wavelength of an electron in 4th orbit is (where $r=$ radius of the 1st orbit) 33. An electromagnetic wave，whose wave normal makes an angle of $45^{\circ}$ with the vertical，is travelling in air and stri 34. The circuit has two oppositely connected ideal diodes in parallel as shown in the figure．What is the current flowing in 35. 2 moles of an ideal gas with $\frac{C_p}{C_v}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{C_p}{ 36. Which of the velocity-time $(v-t)$ graph(s) can possibly represent one-dimensional motion of a particle? 37. The moment of inertia of a thin disc about axes $a, b, c, d$ are $\mathbf{I}_1, \mathbf{I}_2, \mathbf{I}_3$ and $\mathbf 38. The displacement current flows through a capacitor when the voltage across its plates 39. Two points of monochromatic and coherent sources of light of wavelength $\lambda$ each, are placed as shown in figure. T 40. For Boolean variables $A$ and $B, A \oplus B=A \bar{B}+\bar{A} B$ ．Then，which of the following statements is / are corre

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

There is a ring of radius $r$ having linear charge density $\lambda$ and rotating with a uniform angular velocity $\omega$. The magnitude of the magnetic field produced by this ring at its own centre would be ( $\mu_0=$ permeability of air)

$\frac{\lambda \omega^2}{2-\mu_0}$

$\frac{\mu_0 \lambda^2 \omega}{\sqrt{2}}$

$\frac{\mu_0 \lambda \omega}{2}$

$\frac{\mu_0 \lambda}{2 \omega^2}$

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

Three vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $|\vec{a}|=1,|\vec{b}|=2$ and $|\vec{c}|=4$ along with $\vec{a}+\vec{b}+\vec{c}=0$ ．Then，the value of $4 \vec{a} \cdot \vec{b}+3 \vec{b} \cdot \vec{c}+3 \vec{c} \cdot \vec{a}$ will be

-26

-68 problem is wrong．

-34

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

Two identical metal bars are heated in two different temperatures and allowed to cool in the same surroundings. Which one of the following figures correctly shows their cooling curves?

WB JEE 2026 Physics - Heat and Thermodynamics Question 1 English Option 1