Chemistry
1. The number of lone pair of electrons and the hybridization of Xenon ( Xe ) in $\mathrm{XeOF}_2$ are 2. In the following reaction, the major product $(\mathrm{H})$ is
3. Increasing order of the nucleophilic substitution of following compounds
4. Which of the following hydrocarbons reacts easily with $\mathrm{MeMgBr}$ to give methane? 5. Adiabatic free expansion of ideal gas must be 6. An optically active alkene having molecular formula $\mathrm{C}_8 \mathrm{H}_{16}$ gives acetone as one of the products 7. $360 \mathrm{~cm}^3$ of a hydrocarbon diffuses in 30 minutes, while under the same conditions $360 \mathrm{~cm}^3$ of $\ 8. The number of terminal and bridging hydrogens in $\mathrm{B}_2 \mathrm{H}_6$ are respectively 9. The major product (F) in the following reaction is
10. For a chemical reaction, half-life period $\left(t_{\frac{1}{2}}\right)$ is 10 minutes. How much reactant will be left a 11. Equal volume of two solutions $A$ and $B$ of a strong acid having $\mathrm{pH}=6.0$ and $\mathrm{pH}=4.0$ respectively a 12. $P$ and $Q$ combines to form two compounds $\mathrm{PQ}_2$ and $\mathrm{PQ}_3$. If $1 \mathrm{~g} ~\mathrm{PQ}{ }_2$ is 13. Identify the major product (G) in the following reaction
14. Increasing order of solubility of AgCl in (i) $\mathrm{H}_2 \mathrm{O}$, (ii) 1 M NaCl (aq.), (iii) 1 M CaCl 2 (aq.) and 15. Arrange the following compounds in order of their increasing acid strength
16. Which of the following hydrogen bonds is likely to be the weakest? 17. How many oxygen atoms are present in 0.36 g of a drop of water at STP? 18. The molar conductances of $\mathrm{Ba}(\mathrm{OH})_2, \mathrm{BaCl}_2$ and $\mathrm{NH}_4 \mathrm{Cl}$ at infinite dilu 19. The common stable oxidation states of Eu and Gd are respectively 20. Which one among the following compounds will most readily be dehydrated under acidic condition? 21. $$\begin{aligned}
&{ }_5 \mathrm{~B}^{10}+{ }_2 \mathrm{He}^4 \rightarrow \mathrm{X}+{ }_0 \mathrm{n}^1\\
&\text { In th 22. An LPG (Liquified Petroleum Gas) cylinder weighs 15.0 kg when empty. When full, it weighs 30.0 kg and shows a pressure o 23. What is the four-electron reduced form of $\mathrm{O}_2$ ? 24. Kjeldahl's method cannot be used for the estimation of nitrogen in which compound? 25. Which of the following compounds is most reactive in $\mathrm{S}_{\mathrm{N}} 1$ reaction? 26. The coagulating power of electrolytes having ions $\mathrm{Na}^{+}, \mathrm{Al}^{3+}$ and $\mathrm{Ba}^{2+}$ for $\mathr 27. If three elements $A, B, C$ crystalise in a cubic solid lattice with $B$ atoms at the cubic centres, $C$ aton at the cen 28. Which of the following oxides is paramagnetic? 29. How many electrons are needed to reduce $\mathrm{N}_2$ to $\mathrm{NH}_3 ?$ 30. The bond order of $\mathrm{HeH}^{+}$is 31. An egg takes 4.0 minutes to boil at sea level where the boiling point of water is $T_1 K$, where as it takes 8.0 minutes 32. As per the following equation, 0.217 g of HgO (molecular mass $=217 \mathrm{~g} \mathrm{~mol}^{-1}$ ) reacts with excess 33.
The major product 'P' and 'Q' in the above reactions are 34. Consider the following gas phase dissociation, $\mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g 35. Compound given below will produce effervescence when mixed with aqueous sodium bicarbonate solution 36. Which of the following statement(s) is/are correct about the given compound?
37. $X$ is an extensive property and $x$ is an intensive property of a thermodynamic system. Which of the following statemen 38. Which pair of ions among the following can be separated by precipitation method? 39. The compound(s) showing optical activity is/are 40. Identify 'P' and 'Q' in the following reaction
Mathematics
1. If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x>1\end{array}, x \in \mathbb{R}\right.$, is everywhe 2. Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1 3. The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has 4. Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is 5. If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then 6. The expression $2^{4 n}-15 n-1$, where $n \in \mathbb{N}$ (the set of natural numbers) is divisible by 7. If $z_1, z_2$ are complex numbers such that $\frac{2 z_1}{3 z_2}$ is a purely imaginary number, then the value of $\left 8. The value of the integral $\int\limits_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is 9. The line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at the points $P$ and $Q$. If the co-ordinates of the point $X$ 10. Let $f(x)=|1-2 x|$, then 11. If ' $f$ ' is the inverse function of ' $g$ ' and $g^{\prime}(x)=\frac{1}{1+x^n}$, then the value of $f^{\prime}(x)$ is 12. If the matrix $\left(\begin{array}{ccc}0 & a & a \\ 2 b & b & -b \\ c & -c & c\end{array}\right)$ is orthogonal, then th 13. Let $A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]$. If $|A|^2 14. A function $f: \mathbb{R} \rightarrow \mathbb{R}$, satisfies $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)+f(0)}{3}$ for 15. Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2 16. If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E / F)-P(F / E)$ equals 17. The set of points of discontinuity of the function $f(x)=x-[x], x \in \mathbb{R}$ is 18. For what value of ' $a$ ', the sum of the squares of the roots of the equation $x^2-(a-2) x-a+1=0$ will have the least v 19. $\int_\limits{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x$ is equal to 20. If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then the vectors $\vec{a}+2 \vec{ 21. Let $\omega(\neq 1)$ be a cubic root of unity. Then the minimum value of the set $\left\{\mid a+b \omega+c \omega^2\righ 22. $\int\limits_0^{1 \cdot 5}\left[x^2\right] d x$ is equal to 23. If the sum of ' $n$ ' terms of an A.P. is $3 n^2+5 n$ and its $m$ th term is 164 , then the value of $m$ is 24. If $x=\int\limits_0^y \frac{1}{\sqrt{1+9 t^2}} d t$ and $\frac{d^2 y}{d x^2}=a y$, then $a$ is equal to 25. If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is 26. If ' $\theta$ ' is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7,|\vec{b}|=1$ and $|\vec{ 27. Consider three points $P(\cos \alpha, \sin \beta), Q(\sin \alpha, \cos \beta)$ and $R(0,0)$, where $0 28. An $n \times n$ matrix is formed using 0, 1 and $-$1 as its elements. The number of such matrices which are skew symmetr 29. Suppose $\alpha, \beta, \gamma$ are the roots of the equation $x^3+q x+r=0($ with $r \neq 0)$ and they are in A.P. Then 30. Let $f_n(x)=\tan \frac{x}{2}(1+\sec x)(1+\sec 2 x) \ldots\left(1+\sec 2^n x\right)$, then 31. The value of the expression ${ }^{47} C_4+\sum\limits_{j=1}^5{ }^{52-j} C_3$ is 32. If $\operatorname{adj} B=A,|P|=|Q|=1$, then $\operatorname{adj}\left(Q^{-1} B P^{-1}\right)=$ 33. Let $\vec{a}, \vec{b}$ and $\vec{c}$ be vectors of equal magnitude such that the angle between $\vec{a}$ and $\vec{b}$ i 34. Let $f(x)$ be a second degree polynomial. If $f(1)=f(-1)$ and $p, q, r$ are in A.P., then $f^{\prime}(p), f^{\prime}(q), 35. The line parallel to the $x$-axis passing through the intersection of the lines $a x+2 b y+3 b=0$ and $b x-2 a y-3 a=0$ 36. A function $f$ is defined by $f(x)=2+(x-1)^{2 / 3}$ on $[0,2]$. Which of the following statements is incorrect? 37. The number of reflexive relations on a set $A$ of $n$ elements is equal to 38. Let $f(x)$ be continuous on $[0,5]$ and differentiable in $(0,5)$. If $f(0)=0$ and $\left|f^{\prime}(x)\right| \leq \fra 39. $\lim\limits_{x \rightarrow 0} \frac{\tan \left(\left[-\pi^2\right] x^2\right)-x^2 \tan \left(\left[-\pi^2\right]\right) 40. If $\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi$, then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma( 41. If $\vec{\alpha}=3 \vec{i}-\vec{k},|\vec{\beta}|=\sqrt{5}$ and $\vec{\alpha} \cdot \vec{\beta}=3$, then the area of the 42. If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)$, then 43. If for a matrix $A,|A|=6$ and adj $A=\left[\begin{array}{ccc}1 & -2 & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]$, t 44. If $a, b, c$ are positive real numbers each distinct from unity, then the value of the determinant $\left|\begin{array}{ 45. The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is 46. The sum of the first four terms of an arithmetic progression is 56 . The sum of the last four terms is 112. If its first 47. The value of the integral $\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x$ is 48. If the sum of the squares of the roots of the equation $x^2-(a-2) x-(a+1)=0$ is least for an appropriate value of the va 49. If $\left(1+x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots+a_{12} x^{12}$, then the value of $a_2+a_4+a_6+\ldots+a_{12}$ is 50. Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors. Suppose $\vec{a} \cdot \vec{b}=\vec{a} \cdot \vec{c}=0$ and the angle b 51. The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is 52. If $\left|Z_1\right|=\left|Z_2\right|=\left|Z_3\right|=1$ and $Z_1+Z_2+Z_3=0$, then the area of the triangle whose verti 53. Let $f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\e 54. If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be 55. Let $f(x)=\max \{x+|x|, x-[x]\}$, where $[x]$ stands for the greatest integer not greater than $x$. Then $\int\limits_{- 56. If $a, b, c$ are in A.P. and if the equations $(b-c) x^2+(c-a) x+(a-b)=0$ and $2(c+a) x^2+(b+c) x=0$ have a common root, 57. Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origi 58. Let $f(x)=|x-\alpha|+|x-\beta|$, where $\alpha, \beta$ are the roots of the equation $x^2-3 x+2=0$. Then the number of p 59. The maximum number of common normals of $y^2=4 a x$ and $x^2=4 b y$ is equal to 60. The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is 61. The number of solutions of $\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x$ is 62. Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mat 63. Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin (1 / n)}{x^2}\right]^{3 n}$, then $ 64. If $\cos (\theta+\phi)=\frac{3}{5}$ and $\sin (\theta-\phi)=\frac{5}{13}, 0 65. If $f(x)$ and $g(x)$ are two polynomials such that $\phi(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+ 66. If the equation $\sin ^4 x-(p+2) \sin ^2 x-(p+3)=0$ has a solution, the $p$ must lie in the interval 67. If $0 \leq a, b \leq 3$ and the equation $x^2+4+3 \cos (a x+b)=2 x$ has real solutions, then the value of $(a+b)$ is 68. Let $f(x)=x^3, x \in[-1,1]$. Then which of the following are correct? 69. Three numbers are chosen at random without replacement from $\{1,2, \ldots 10\}$. The probability that the minimum of th 70. The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation
$$\frac{d p(t)}{d t}=0.5 71. If $P$ is a non-singular matrix of order $5 \times 5$ and the sum of the elements of each row is 1 , then the sum of the 72. The solution set of the equation $\left(x \in\left(0, \frac{\pi}{2}\right)\right) \tan (\pi \tan x)=\cot (\pi \cot x)$, 73. If $f(x)=\int_0^{\sin ^2 x} \sin ^{-1} \sqrt{t} d t$ and $g(x)=\int_0^{\cos ^2 x} \cos ^{-1} \sqrt{t} d t$, then the val 74. The value of $\int\limits_{-100}^{100} \frac{\left(x+x^3+x^5\right)}{\left(1+x^2+x^4+x^6\right)} d x$ is 75. Let $f:[0,1] \rightarrow \mathbb{R}$ and $g:[0,1] \rightarrow \mathbb{R}$ be defined as follows :
$\left.\begin{array}{r
Physics
1. The velocity-time graph for a body of mass 10 kg is shown in the figure. Work done on the body in the first two seconds 2. For a domestic AC supply of 220 V at 50 cycles per sec, the potential difference between the terminals of a two-pin elec 3. A radioactive nucleus decays as follows :
$$ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 4. A single slit diffraction pattern is obtained using a beam of red light. If red light is replaced by blue light then 5. The variation of density of a solid cylindrical rod of cross sectional area $\alpha$ and length $L$ is $\rho=\rho_0 \fra 6. A simple pendulum is taken at a place where its distance from the earth's surface is equal to the radius of the earth. C 7. Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field $ 8. The minimum force required to start pushing a body up a rough (having co-efficient of friction $\mu$ ) inclined plane is 9. Acceleration-time $(a-t)$ graph of a body is shown in the figurd. Corresponding velocity-time $(v-t)$ graph is
10. One end of a stecl wire is fixed to the ceiling of an elevator moving up with an acceleration $2 \mathrm{~m} / \mathrm{s 11. Ruma reached the metro station and found that the escalator was not working. She walked up the stationary escalator with 12. A quantity $X$ is given by $\varepsilon_0 L \frac{\Delta V}{\Delta t}$, where $\varepsilon_0$ is the permittivity of fre 13. A diode is connected in parallel with a resistance as shown in Figure. The most probable current (I) - voltage (V) chara 14. The minimum wavelength of Lyman series lines is $P$, then the maximum wavelength of these lines is 15. An electron in Hydrogen atom jumps from the second Bohr orbit to the ground state and the difference between the energie 16. A ball falls from a height $h$ upon a fixed horizontal floor. The co-efficient of restitution for the collision between 17. Manufacturers supply a zener diode with zener voltage $\mathrm{V}_{\mathrm{z}}=5.6 \mathrm{~V}$ and maximum power dissip 18. A force $\vec{F}=a \hat{i}+b \hat{j}+c \hat{k}$ is acting on a body of mass $m$. The body was initially at rest at the o 19. Figure shows the graph of angle of deviation $\delta$ versus angle of incidence i for a light ray striking a prism. The 20. Two charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance $2 L_{\mathrm{p} p a t}$ 21. Which logic gate is represented by the following combinations of logic gates?
22. The number of undecayed nuclei $N$ in a sample of radioactive material as a function of time $(t)$ is shown in the figur 23. For an ideal gas, a cyclic process ABCA as shown in P-T diagram, when presented in P-V plot, would be
24. The resistance $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}$ where $\mathrm{V}=(25 \pm 0.4)$ Volt and $\mathrm{I}=(200 \pm 25. A particle of charge ' $q$ ' and mass ' $m$ ' moves in a circular orbit of radius ' $r$ ' with angular speed ' $\omega$ 26. The de-Broglie wavelength of a moving bus with speed $v$ is $\lambda$. Some passengers left the bus at a stoppage. Now w 27. The variation of displacement with time of a simple harmonic motion (SHM) for a particle of mass $m$ is represented by $ 28. What are the charges stored in the $1 \mu \mathrm{~F}$ and $2 \mu \mathrm{~F}$ capacitors in the circuit as shown in fig 29. Three different liquids are filled in a U-tube as shown in figure. Their densities are $\rho_1, \rho_2$ and $\rho_3$ res 30. A piece of granite floats at the interface of mercury and water contained in a beaker as in figure. If the densities of 31. $10^{20}$ photons of wavelength 660 nm are emitted per second from a lamp. The wattage of the lamp is (Planck's constant 32. The apparent coefficient of expansion of a liquid, when heated in a copper vessel is $C$ and when heated in silver vesse 33. The equation of a stationary wave along a stretched string is given by $y=5 \sin \frac{\pi x}{3} \cos 40 \pi t$.
Here $ 34. Temperature of a body $\theta$ is slightly more than the temperature of the surrounding $\theta_0$. Its rate of cooling 35. Let $\bar{V}, V_{m s}, V_p$ denotes the mean speed, root mean square speed and most probable speed of the molecules each 36. Let the binding energy per nucleon of nucleus is denoted by ' $E_{b n}$ ' and radius of the nucleus is denoted by ' $r$ 37. A wave disturbance in a medium is described by $y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)$ w 38. If the dimensions of length are expressed as $G^x C^y h^z$, where $G, C$ and $h$ are the universal gravitational constan 39. Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially $S_1$ is at rest a 40. Six vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}, \vec{e}$ and $\vec{f}$ have the magnitudes and directions indicated in
1
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is
A
2
B
3
C
4
D
5
2
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
The number of solutions of $\sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x$ is
A
0
B
1
C
2
D
4
3
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mathbb{R}$. Then $f(1)$ is equal to
A
$\frac{5}{2}$
B
$\frac{1}{2}$
C
$\frac{1}{\sqrt{2}}$
D
$3$
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Let $a_n$ denote the term independent of $x$ in the expansion of $\left[x+\frac{\sin (1 / n)}{x^2}\right]^{3 n}$, then $\lim \limits_{n \rightarrow \infty} \frac{\left(a_n\right) n!}{{ }^{3 n} P_n}$ equals
A
0
B
1
C
e
D
e/$\sqrt3$
Paper analysis
Total Questions
Chemistry
40
Mathematics
75
Physics
40
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