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
1
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
If $\sum\limits_{r=1}^{\infty} \tan ^{-1}\left(\frac{1}{2 r^2}\right)=a$, then $\tan a$ is equal to
A
1
B
0
C
$\sqrt{3}$
D
$\frac{\pi}{4}$
2
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
Consider a function $f(x)$ which has exactly two roots at $x=a$. If $\mathop {\lim }\limits_{x \to a}\left(\frac{\lambda f^{\prime}(x)}{f(x)}-\frac{1}{x-a}\right)=m(\neq 0)$, then the value of $\lambda$ ix
A
2
B
1
C
$\frac{1}{2}$
D
$\frac{1}{4}$
3
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
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 $\vec{Q}=-f^{\prime \prime}(t) \hat{i}+f^{\prime}(t) \hat{j}+\hat{k}$.
A
a linear function of time
B
a quadratic function of time
C
a cubic function of time
D
constant
4
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
The expression $\sum_{k=1}^{32}(3 K+2)\left\{\sum_{r=1}^{10}\left(\sin \frac{2 r \pi}{11}-i \cos \frac{2 r \pi}{11}\right)\right\}^k$ represents
A
$48(1+\mathrm{i})$
B
$-48(1-\mathrm{i})$
C
$-\frac{48}{11}(1-\mathrm{i})$
D
$48(1-\mathrm{i})$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 75
Physics 40
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