WB JEE 2024

Paper was held on
Sun, Apr 28, 2024 4:30 AM

## Chemistry

In the following sequence of reaction compound 'M' is

View Question Identify the ion having $$4 f^6$$ electronic configuration.

View Question Metallic conductors and semiconductors are heated separately. What are the changes with respect to conductivity?

View Question The equivalent weight of $$\mathrm{Na}_2 \mathrm{S}_2 \mathrm{O}_3(\mathrm{Gram}$$ molecular weight $$=\mathrm{M})$$ in

View Question The reactivity order of the following molecules towards $$\mathrm{S}_{\mathrm{N}} 1$$ reaction is
$$\begin{array}{ccc}
\

View Question Toluene reacts with mixed acid at $$25^{\circ} \mathrm{C}$$ to produce

View Question
The product 'P' in the above reaction is

View Question The decreasing order of reactivity of the following alkenes towards $$\mathrm{HBr}$$ addition is

View Question Ozonolysis of $$\underline{o}$$-xylene produces

View Question The compounds A and B are respectively

View Question The compound that does not give positive test for nitrogen in Lassaigne's test is

View Question The correct acidity order of phenol (I), 4-hydroxybenzaldehyde (II) and 3-hydroxybenzaldehyde (III) is

View Question The major product of the following reaction is :

View Question Which of the following statements is correct for a spontaneous polymerization reaction ?

View Question At 25$$^\circ$$C, the ionic product of water is 10$$^{-14}$$. The free energy change for the self-ionization of water in

View Question Consider an electron moving in the first Bohr orbit of a $$\mathrm{He}^{+}$$ ion with a velocity $$v_1$$. If it is allow

View Question The compressibility factor for a van der Waal gas at high pressure is

View Question For a spontaneous process, the incorrect statement is

View Question Identify the incorrect statement among the following :

View Question Which of the following statements is true about equilibrium constant and rate constant of a single step chemical reactio

View Question After the emission of a $$\beta$$-particle followed by an $$\alpha$$-particle from $${ }_{83}^{214} \mathrm{Bi}$$, the n

View Question Which hydrogen like species will have the same radius as that of $$1^{\text {st }}$$ Bohr orbit of hydrogen atom?

View Question For a first order reaction with rate constant $$\mathrm{k}$$, the slope of the plot of $$\log$$ (reactant concentration)

View Question Equal volumes of aqueous solution of $$0.1(\mathrm{M}) \mathrm{HCl}$$ and $$0.2(\mathrm{M}) \mathrm{H}_2 \mathrm{SO}_4$$

View Question The correct order of boiling point of the given aqueous solutions is

View Question Correct solubility order of $$\mathrm{AgF}, \mathrm{AgCl}, \mathrm{AgBr}, \mathrm{AgI}$$ in water is

View Question What will be the change in acidity if
(i) $$\mathrm{CuSO}_4$$ is added in saturated $$(\mathrm{NH}_4)_2 \mathrm{SO}_4$$

View Question Which of the following contains maximum number of lone pairs on the central atom?

View Question Number of moles of ions produced by complete dissociation of one mole of Mohr's salt in water is

View Question Which of the following species exhibits both LMCT and paramagnetism?

View Question How many $$\mathrm{P}-\mathrm{O}-\mathrm{P}$$ linkages are there in $$\mathrm{P}_4 \mathrm{O}_{10}$$

View Question
$$\mathrm{Q}$$ and $$\mathrm{R}$$ in the above reaction sequences are respectively

View Question $$\mathrm{pH}$$ of $$10^{-8}(\mathrm{M}) \mathrm{~HCl}$$ solution is

View Question The specific conductance $$(\mathrm{k})$$ of $$0.02(\mathrm{M})$$ aqueous acetic acid solution at $$298 \mathrm{~K}$$ is

View Question The number(s) of $$-\mathrm{OH}$$ group(s) present in $$\mathrm{H}_3 \mathrm{PO}_3$$ and $$\mathrm{H}_3 \mathrm{PO}_4$$

View Question Which of the following statements about the $$\mathrm{S}_{\mathrm{N}} 2$$ reaction mechanism is/are true?

View Question Which of the following represent(s) the enantiomer of Y ?

View Question Identify the correct statement(s) :

View Question Which of the following ion/ions is/are diamagnetic ?

View Question Which of the following statement/statements is/are correct ?

View Question ## Mathematics

All values of a for which the inequality $$\frac{1}{\sqrt{a}} \int_\limits1^a\left(\frac{3}{2} \sqrt{x}+1-\frac{1}{\sqrt

View Question For any integer $$\mathrm{n}, \int_\limits0^\pi \mathrm{e}^{\cos ^2 x} \cdot \cos ^3(2 n+1) x \mathrm{~d} x$$ has the va

View Question Let $$\mathrm{f}$$ be a differential function with $$\lim _\limits{x \rightarrow \infty} \mathrm{f}(x)=0$$. If $$\mathrm

View Question If $$x y^{\prime}+y-e^x=0, y(a)=b$$, then $$\lim _\limits{x \rightarrow 1} y(x)$$ is

View Question The area bounded by the curves $$x=4-y^2$$ and the Y-axis is

View Question $$f(x)=\cos x-1+\frac{x^2}{2!}, x \in \mathbb{R}$$ Then $$\mathrm{f}(x)$$ is

View Question Let $$\mathrm{y}=\mathrm{f}(x)$$ be any curve on the $$\mathrm{X}-\mathrm{Y}$$ plane & $$\mathrm{P}$$ be a point on the

View Question If a particle moves in a straight line according to the law $$x=a \sin (\sqrt{\lambda} t+b)$$, then the particle will co

View Question A unit vector in XY-plane making an angle $$45^{\circ}$$ with $$\hat{i}+\hat{j}$$ and an angle $$60^{\circ}$$ with $$3 \

View Question Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be given by $$\mathrm{f}(x)=\left|x^2-1\right|$$, then

View Question Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If $$a_n$

View Question If for the series $$a_1, a_2, a_3$$, ...... etc, $$\mathrm{a}_{\mathrm{r}}-\mathrm{a}_{\mathrm{r}+\mathrm{i}}$$ bears a

View Question If $$z_1$$ and $$z_2$$ be two roots of the equation $$z^2+a z+b=0, a^2

View Question If $$\cos \theta+i \sin \theta, \theta \in \mathbb{R}$$, is a root of the equation
$$a_0 x^n+a_1 x^{n-1}+\ldots .+a_{n-1

View Question If $$\left(x^2 \log _x 27\right) \cdot \log _9 x=x+4$$ then the value of $$x$$ is

View Question If $$\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$$ and $$\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}$

View Question Let $$\mathrm{N}$$ be the number of quadratic equations with coefficients from $$\{0,1,2, \ldots, 9\}$$ such that 0 is a

View Question If $$a, b, c$$ are distinct odd natural numbers, then the number of rational roots of the equation $$a x^2+b x+c=0$$

View Question The numbers $$1,2,3, \ldots \ldots, \mathrm{m}$$ are arranged in random order. The number of ways this can be done, so t

View Question If $$A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)$$ and $$\theta=\

View Question If $$\left(1+x+x^2+x^3\right)^5=\sum_\limits{k=0}^{15} a_k x^k$$ then $$\sum_\limits{k=0}^7(-1)^{\mathbf{k}} \cdot a_{2

View Question The coefficient of $$a^{10} b^7 c^3$$ in the expansion of $$(b c+c a+a b)^{10}$$ is

View Question $$
\text { If }\left|\begin{array}{lll}
x^k & x^{k+2} & x^{k+3} \\
y^k & y^{k+2} & y^{k+3} \\
z^k & z^{k+2} & z^{k+3}
\e

View Question If $$\left[\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right] \cdot A \cdot\left[\begin{array}{cc}-3 & 2 \\ 5 & -3\end{ar

View Question $$
\text { Let } f(x)=\left|\begin{array}{ccc}
\cos x & x & 1 \\
2 \sin x & x^3 & 2 x \\
\tan x & x & 1
\end{array}\righ

View Question In R, a relation p is defined as follows:
$$\forall a, b \in \mathbb{R}, a p$$ holds iff $$a^2-4 a b+3 b^2=0$$. Then

View Question Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined by $$\mathrm{f}(x)=\frac{\mathrm{e}^{|x|}-\m

View Question Let A be the set of even natural numbers that are

View Question Two smallest squares are chosen one by one on a chess board. The probability that they have a side in common is

View Question Two integers $$\mathrm{r}$$ and $$\mathrm{s}$$ are drawn one at a time without replacement from the set $$\{1,2, \ldots,

View Question A biased coin with probability $$\mathrm{p}(0

View Question The expression $$\cos ^2 \phi+\cos ^2(\theta+\phi)-2 \cos \theta \cos \phi \cos (\theta+\phi)$$ is

View Question If $$0

View Question The equation $$\mathrm{r} \cos \theta=2 \mathrm{a} \sin ^2 \theta$$ represents the curve

View Question If $$(1,5)$$ be the midpoint of the segment of a line between the line $$5 x-y-4=0$$ and $$3 x+4 y-4=0$$, then the equat

View Question In $$\triangle \mathrm{ABC}$$, co-ordinates of $$\mathrm{A}$$ are $$(1,2)$$ and the equation of the medians through $$\m

View Question A line of fixed length $$\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}$$ moves so that its ends are always on two f

View Question With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end o

View Question Chords $$\mathrm{AB}$$ & $$\mathrm{CD}$$ of a circle intersect at right angle at the point $$\mathrm{P}$$. If the length

View Question The plane $$2 x-y+3 z+5=0$$ is rotated through $$90^{\circ}$$ about its line of intersection with the plane $$x+y+z=1$$.

View Question If the relation between the direction ratios of two lines in $$\mathbb{R}^3$$ are given by
$$l+\mathrm{m}+\mathrm{n}=0,2

View Question $$\triangle \mathrm{OAB}$$ is an equilateral triangle inscribed in the parabola $$\mathrm{y}^2=4 \mathrm{a} x, \mathrm{a

View Question For every real number $$x \neq-1$$, let $$\mathrm{f}(x)=\frac{x}{x+1}$$.
Write $$\mathrm{f}_1(x)=\mathrm{f}(x)$$ & for $

View Question If $$\mathrm{U}_{\mathrm{n}}(\mathrm{n}=1,2)$$ denotes the $$\mathrm{n}^{\text {th }}$$ derivative $$(\mathrm{n}=1,2)$$

View Question The equation $$2^x+5^x=3^x+4^x$$ has

View Question Consider the function $$\mathrm{f}(x)=(x-2) \log _{\mathrm{e}} x$$. Then the equation $$x \log _{\mathrm{e}} x=2-x$$

View Question If $$\alpha, \beta$$ are the roots of the equation $$a x^2+b x+c=0$$ then $$\lim _\limits{x \rightarrow \beta} \frac{1-\

View Question If $$\mathrm{f}(x)=\frac{\mathrm{e}^x}{1+\mathrm{e}^x}, \mathrm{I}_1=\int_\limits{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\

View Question Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a differentiable function and $$f(1)=4$$. Then the value of $$\lim _\lim

View Question $$
\text { If } \int \frac{\log _e\left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \mathrm{~d} x=\mathrm{f}(\mathrm{g}(x))+\ma

View Question Let $$\mathrm{I}(\mathrm{R})=\int_\limits0^{\mathrm{R}} \mathrm{e}^{-\mathrm{R} \sin x} \mathrm{~d} x, \mathrm{R}>0$$. t

View Question Consider the function $$\mathrm{f}(x)=x(x-1)(x-2) \ldots(x-100)$$. Which one of the following is correct?

View Question In a plane $$\vec{a}$$ and $$\vec{b}$$ are the position vectors of two points A and B respectively. A point $P$ with pos

View Question Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can p

View Question Let $$A=\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1\end{array}\right), B=\left(\begin{array}{l}2 \\ 1

View Question If $$\alpha_1, \alpha_2, \ldots, \alpha_n$$ are in A.P. with common difference $$\theta$$, then the sum of the series
$$

View Question For the real numbers $$x$$ & $$y$$, we write $$x$$ p y iff $$x-y+\sqrt{2}$$ is an irrational number. Then relation p is

View Question Let $$A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$$, then

View Question $$
\text { If } 1000!=3^n \times m \text { where } m \text { is an integer not divisible by } 3 \text {, then } n=
$$

View Question If $$A$$ and $$B$$ are acute angles such that $$\sin A=\sin ^2 B$$ and $$2 \cos ^2 A=3 \cos ^2 B$$, then $$(A, B)=$$

View Question If two circles which pass through the points $$(0, a)$$ and $$(0,-a)$$ and touch the line $$\mathrm{y}=\mathrm{m} x+\mat

View Question The locus of the midpoint of the system of parallel chords parallel to the line $$y=2 x$$ to the hyperbola $$9 x^2-4 y^2

View Question Angle between two diagonals of a cube will be

View Question $$
\text { If } y=\tan ^{-1}\left[\frac{\log _e\left(\frac{e}{x^2}\right)}{\log _e\left(e x^2\right)}\right]+\tan ^{-1}\

View Question $$\lim _\limits{n \rightarrow \infty} \frac{1}{n^{k+1}}[2^k+4^k+6^k+\ldots .+(2 n)^k]=$$

View Question The acceleration f $$\mathrm{ft} / \mathrm{sec}^2$$ of a particle after a time $$\mathrm{t}$$ sec starting from rest is

View Question Let $$\Gamma$$ be the curve $$\mathrm{y}=\mathrm{be}^{-x / a}$$ & $$\mathrm{L}$$ be the straight line $$\frac{x}{\mathrm

View Question If $$n$$ is a positive integer, the value of $$(2 n+1){ }^n C_0+(2 n-1){ }^n C_1+(2 n-3){ }^n C_2 +\ldots .+1 \cdot{ }^n

View Question If the quadratic equation $$a x^2+b x+c=0(a>0)$$ has two roots $$\alpha$$ and $$\beta$$ such that $$\alpha2$$, then

View Question If $$\mathrm{a}_{\mathrm{i}}, \mathrm{b}_{\mathrm{i}}, \mathrm{c}_{\mathrm{i}} \in \mathbb{R}(\mathrm{i}=1,2,3)$$ and $$

View Question The function $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$\mathrm{f}(x)=\mathrm{e}^x+\mathrm{e}^{-x}$$

View Question A square with each side equal to '$$a$$' above the $$x$$-axis and has one vertex at the origin. One of the sides passing

View Question If $$\mathrm{ABC}$$ is an isosceles triangle and the coordinates of the base points are $$B(1,3)$$ and $$C(-2,7)$$. The

View Question $$
\text { The points of extremum of } \int_\limits0^{x^2} \frac{t^2-5 t+4}{2+e^t} d t \text { are }
$$

View Question Choose the correct statement :

View Question ## Physics

Let $$\theta$$ be the angle between two vectors $$\vec{A}$$ and $$\vec{B}$$. If $$\hat{a}_{\perp}$$ is the unit vector p

View Question The Power $$(\mathrm{P})$$ radiated from an accelerated charged particle is given by $$\mathrm{P} \propto \frac{(q \math

View Question Two convex lens $$(\mathrm{L}_1$$ and $$\mathrm{L}_2)$$ of equal focal length $$\mathrm{f}$$ are placed at a distance $$

View Question Which of the following quantity has the dimension of length ?
(h is Planck's constant, m is the mass of electron and c i

View Question The speed distribution for a sample of $$\mathrm{N}$$ gas particles is shown below. $$\mathrm{P}(\mathrm{v})=0$$ for $$\

View Question The internal energy of a thermodynamic system is given by $$U=a s^{4 / 3} V^\alpha$$ where $$\mathrm{s}$$ is entropy, $$

View Question A particle of mass '$$m$$' moves in one dimension under the action of a conservative force whose potential energy has th

View Question Longitudinal waves cannot

View Question A $$2 \mathrm{~V}$$ cell is connected across the points $$\mathrm{A}$$ and $$\mathrm{B}$$ as shown in the figure. Assume

View Question A charge Q is placed at the centre of a cube of sides a. The total flux of electric field through the six surfaces of th

View Question The elastic potential energy of a strained body is

View Question Which of the following statement(s) is/are truc in respect of nuclear binding energy ?
(i) The mass energy of a nucleus

View Question A satellite of mass $$\mathrm{m}$$ rotates round the earth in a circular orbit of radius R. If the angular momentum of t

View Question What force $$\mathrm{F}$$ is required to start moving this $$10 \mathrm{~kg}$$ block shown in the figure if it acts at a

View Question Light of wavelength $$6000 \mathop A\limits^o$$ is incident on a thin glass plate of r.i. 1.5 such that the angle of ref

View Question
Consider a circuit where a cell of emf $$E_0$$ and internal resistance $$\mathrm{r}$$ is connected across the terminal

View Question The equivalent capacitance of a combination of connected capacitors shown in the figure between the points $$\mathrm{P}$

View Question In a single-slit diffraction experiment, the slit is illuminated by light of two wavelengths $$\lambda_1$$ and $$\lambda

View Question The acceleration-time graph of a particle moving in a straight line is shown in the figure. If the initial velocity of t

View Question The position vector of a particle of mass $$\mathrm{m}$$ moving with a constant velocity $$\vec{v}$$ is given by $$\vec{

View Question
The position of the centre of mass of the uniform plate as shown in the figure is

View Question
In a series LCR circuit, the rms voltage across the resistor and the capacitor are $$30 \mathrm{~V}$$ and $$90 \mathrm{

View Question
A small ball of mass m is suspended from the ceiling of a floor by a string of length $$\mathrm{L}$$. The ball moves al

View Question If $$\hat{n}_1, \hat{n}_2$$ and $$\hat{\mathrm{t}}$$ represent, unit vectors along the incident ray, reflected ray and n

View Question A beam of light of wavelength $$\lambda$$ falls on a metal having work function $$\phi$$ placed in a magnetic field B. T

View Question A charged particle moving with a velocity $$\vec{v}=v_1 \hat{i}+v_2 \hat{j}$$ in a magnetic field $$\vec{B}$$ experience

View Question Two straight conducting plates form an angle $$\theta$$ where their ends are joined. A conducting bar in contact with th

View Question Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$\mathrm{q}$$ are placed along $$x$$ axis at $$x=-\mathrm{a}, 0$$

View Question A body floats with $$\frac{1}{n}$$ of its volume keeping outside of water. If the body has been taken to height $$\mathr

View Question A small sphere of mass m and radius r slides down the smooth surface of a large hemispherical bowl of radius R. If the s

View Question When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is 45 cm from the

View Question In the given network of AND and OR gates, output Q can be written as (assuming n even)

View Question Water is filled in a cylindrical vessel of height $$\mathrm{H}$$. A hole is made at height $$\mathrm{z}$$ from the botto

View Question A metal plate of area $$10^{-2} \mathrm{~m}^2$$ rests on a layer of castor oil, $$2 \times 10^{-3} \mathrm{~m}$$ thick,

View Question The following figure shows the variation of potential energy $$V(x)$$ of a particle with distance $$x$$. The particle ha

View Question Monochromatic light of wavelength $$\lambda=4770 \mathop A\limits^o $$ is incident separately on the surfaces of four di

View Question Consider the integral form of the Gauss' law in electrostatics
$$\oint {\overrightarrow E .d\overrightarrow S } = {Q \o

View Question
A uniform rod $$\mathrm{AB}$$ of length $$1 \mathrm{~m}$$ and mass $$4 \mathrm{~kg}$$ is sliding along two mutually per

View Question
The variation of impedance $$\mathrm{Z}$$ of a series $$\mathrm{L C R}$$ circuit with frequency of the source is shown

View Question The electric field of a plane electromagnetic wave in a medium is given by
$$
\overrightarrow{\mathrm{E}}(x, y, z, t)=\m

View Question