WB JEE 2023

Paper was held on
Sun, Apr 30, 2023 4:30 AM

## Chemistry

Which of the following statements is incorrect?

View Question
The calculated spin-only magnetic moment values in BM for $$\mathrm{[FeCl_4]^-}$$ and $$\mathrm{[Fe(CN)_6]^{3-}}$$ are

View Question
$$\mathrm{BrF_3}$$ self ionises as following

View Question
4f$$^2$$ electronic configuration is found in

View Question
The correct order of C = O bond length in ethyl propanoate (I), ethyl propenoate (II) and ethenyl propanoate (III) is

View Question
Select the molecule in which all the atoms may lie on a single plane is

View Question
The IUPAC name of

View Question
The relationship between the pair of compounds shown above are respectively,

View Question
The correct stability order of the following carbocations is
(I) $$\mathrm{{H_2}\mathop C\limits^ \oplus - CH = CH - C

View Question
The correct order of boiling points of N-ethylethanamine (I), ethoxyethane (II) and butan-2-ol (III) is

View Question
Structure of M is,

View Question
The correct order of acidity of above compounds is

View Question
If all the nucleophilic substitution reactions at saturated carbon atoms in the above sequence of reactions follow SN2

View Question
The correct option for the above reaction is

View Question
Arrange the following in order of increasing mass
I. 1 mole of N$$_2$$
II. 0.5 mole of O$$_3$$
III. $$3.011\times10^{23}

View Question
Two base balls (masses : m$$_1$$ = 100 g, and m$$_2$$ = 50 g) are thrown. Both of them move with uniform velocity, but t

View Question
What is the edge length of the unit cell of a body centred cubic crystal of an element whose atomic radius is 75 pm?

View Question
The root mean square (rms) speed of X$$_2$$ gas is x m/s at a given temperature. When the temperature is doubled, the X$

View Question
Which of the following would give a linear plot?
(k is the rate constant of an elementary reaction and T is temp. in abs

View Question
The equivalent conductance of NaCl, HCl and CH$$_3$$COONa at infinite dilution are 126.45, 426.16 and 91 ohm$$^{-1}$$cm$

View Question
For the reaction A + B $$\to$$ C, we have the following data:
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{

View Question
If in case of a radio isotope the value of half-life (T$$_{1/2}$$) and decay constant ($$\lambda$$) are identical in mag

View Question
Suppose a gaseous mixture of He, Ne, Ar and Kr is treated with photons of the frequency appropriate to ionize Ar. What i

View Question
A solution containing 4g of polymer in 4.0 litre solution at 27$$^\circ$$C shows an osmotic pressure of 3.0 $$\times$$ 1

View Question
The equivalent weight of KIO$$_3$$ in the given reaction is (M = molecular mass):
$$\mathrm{2Cr{(OH)_3} + 4O{H^ - } + KI

View Question
At STP, the dissociation reaction of water is $$\mathrm{H_2O\rightleftharpoons H^+~(aq.)+OH^-~(aq.)}$$, and the pH of wa

View Question
Na$$_2$$CO$$_3$$ is prepared by Solvay process but K$$_2$$CO$$_3$$ cannot be prepared by the same because

View Question
The molecular shapes of SF$$_4$$, CF$$_4$$ and XeF$$_4$$ are

View Question
The species in which nitrogen atom is in a state of sp hybridisation is

View Question
The correct statement about the magnetic properties of $${\left[ {Fe{{(CN)}_6}} \right]^{3 - }}$$ and $${\left[ {Fe{F_6}

View Question
Nickel combines with a uninegative monodentate ligand (X$$^-$$) to form a paramagnetic complex [NiX$$_4$$]$$^{2-}$$. The

View Question
'$$\underline{\underline L} $$' in the above sequence of reaction is/are (where L $$\ne$$ M $$\ne$$ N)

View Question
'$$\underline G $$' in the above sequence of reactions is

View Question
Case - 1 : An ideal gas of molecular weight M at temperature T.
Case - 2 : Another ideal gas of molecular weight 2M at t

View Question
63 g of a compound (Mol. Wt. = 126) was dissolved in 500 g distilled water. The density of the resultant solution as 1.1

View Question
An electron in the 5d orbital can be represented by the following (n, l, m) values

View Question
The conversion(s) that can be carried out by bromine in carbon tetrachloride solvent is/are

View Question
The correct set(s) of reactions to synthesize benzoic acid starting from benzene is/are

View Question
Which statement(s) is/are applicable above critical temperature?

View Question
Which of the following mixtures act(s) as buffer solution?

View Question
## Mathematics

$$\mathop {\lim }\limits_{x \to \infty } \left\{ {x - \root n \of {(x - {a_1})(x - {a_2})\,...\,(x - {a_n})} } \right\}$

View Question
Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{
1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr
{e^

View Question
Let $$f:[1,3] \to R$$ be continuous and be derivable in (1, 3) and $$f'(x) = {[f(x)]^2} + 4\forall x \in (1,3)$$. Then

View Question
f(x) is a differentiable function and given $$f'(2) = 6$$ and $$f'(1) = 4$$, then $$L = \mathop {\lim }\limits_{h \to 0}

View Question
Let $${\cos ^{ - 1}}\left( {{y \over b}} \right) = {\log _e}{\left( {{x \over n}} \right)^n}$$, then $$A{y_2} + B{y_1} +

View Question
If $$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then $$f(x)$$ is

View Question
If $$\int {{{dx} \over {(x + 1)(x - 2)(x - 3)}} = {1 \over k}{{\log }_e}\left\{ {{{|x - 3{|^3}|x + 1|} \over {{{(x - 2)}

View Question
the expression $${{\int\limits_0^n {[x]dx} } \over {\int\limits_0^n {\{ x\} dx} }}$$, where $$[x]$$ and $$\{ x\} $$ are

View Question
The value $$\int\limits_0^{1/2} {{{dx} \over {\sqrt {1 - {x^{2n}}} }}} $$ is $$(n \in N)$$

View Question
If $${I_n} = \int\limits_0^{{\pi \over 2}} {{{\cos }^n}x\cos nxdx} $$, then I$$_1$$, I$$_2$$, I$$_3$$ ... are in

View Question
If $$y = {x \over {{{\log }_e}|cx|}}$$ is the solution of the differential equation $${{dy} \over {dx}} = {y \over x} +

View Question
The function $$y = {e^{kx}}$$ satisfies $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \o

View Question
Given $${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$. Changing the independent variable x

View Question
Let $$f(x) = \left\{ {\matrix{
{x + 1,} & { - 1 \le x \le 0} \cr
{ - x,} & {0

View Question
A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t

View Question
If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to th

View Question
A, B are fixed points with coordinates (0, a) and (0, b) (a > 0, b > 0). P is variable point (x, 0) referred to rectangu

View Question
The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le

View Question
The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\w

View Question
If the vertices of a square are $${z_1},{z_2},{z_3}$$ and $${z_4}$$ taken in the anti-clockwise order, then $${z_3} = $$

View Question
If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of th

View Question
If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals

View Question
Reflection of the line $$\overline a z + a\overline z = 0$$ in the real axis is given by

View Question
If one root of $${x^2} + px - {q^2} = 0,p$$ and $$q$$ are real, be less than 2 and other be greater than 2, then

View Question
The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels

View Question
n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one o

View Question
Let $$P(n) = {3^{2n + 1}} + {2^{n + 2}}$$ where $$n \in N$$. Then

View Question
Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the element

View Question
Let A and B are orthogonal matrices and det A + det B = 0. Then

View Question
Let $$A = \left( {\matrix{
2 & 0 & 3 \cr
4 & 7 & {11} \cr
5 & 4 & 8 \cr
} } \right)$$. Then

View Question
If the matrix Mr is given by $${M_r} = \left( {\matrix{
r & {r - 1} \cr
{r - 1} & r \cr
} } \right)$$ for r

View Question
Let $$\alpha,\beta$$ be the roots of the equation $$a{x^2} + bx + c = 0,a,b,c$$ real and $${s_n} = {\alpha ^n} + {\beta

View Question
Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:

View Question
Let X be a nonvoid set. If $$\rho_1$$ and $$\rho_2$$ be the transitive relations on X, then
($$\circ$$ denotes the compo

View Question
Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability t

View Question
Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b

View Question
If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is
(Here $$n \i

View Question
The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents

View Question
Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpen

View Question
If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at

View Question
The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x

View Question
ABC is an isosceles triangle with an inscribed circle with centre O. Let P be the midpoint of BC. If AB = AC = 15 and BC

View Question
Let O be the vertex, Q be any point on the parabola x$$^2$$ = 8y. If the point P divides the line segment OQ internally

View Question
The tangent at point $$(a\cos \theta ,b\sin \theta ),0

View Question
Let $$A(2\sec \theta ,3\tan \theta )$$ and $$B(2\sec \phi ,3\tan \phi )$$ where $$\theta + \phi = {\pi \over 2}$$ be

View Question
If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$,

View Question
If the distance between the plane $$\alpha x - 2y + z = k$$ and the plane containing the lines $${{x - 1} \over 2} = {{y

View Question
The angle between a normal to the plane $$2x - y + 2z - 1 = 0$$ and the X-axis is

View Question
Let $$f(x) = [{x^2}]\sin \pi x,x > 0$$. Then

View Question
If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x

View Question
$$\int\limits_0^{2\pi } {\theta {{\sin }^6}\theta \cos \theta d\theta } $$ is equal to

View Question
If $$x = \sin \theta $$ and $$y = \sin k\theta $$, then $$(1 - {x^2}){y_2} - x{y_1} - \alpha y = 0$$, for $$\alpha=$$

View Question
In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

View Question
The average ordinate of $$y = \sin x$$ over $$[0,\pi ]$$ is

View Question
The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point

View Question
If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overr

View Question
Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$

View Question
Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no r

View Question
Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} +

View Question
Let $$A = \left( {\matrix{
0 & 0 & 1 \cr
1 & 0 & 0 \cr
0 & 0 & 0 \cr
} } \right),B = \left( {\matrix{

View Question
Let $$\rho$$ be a relation defined on set of natural numbers N, as $$\rho = \{ (x,y) \in N \times N:2x + y = 4\} $$. Th

View Question
From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 1

View Question
The locus of points (x, y) in the plane satisfying $${\sin ^2}x + {\sin ^2}y = 1$$ consists of

View Question
The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {\left( {{1 \over {2\,.\,3}} + {1 \over {{2^2}\,.\,3}}} \ri

View Question
The family of curves $$y = {e^{a\sin x}}$$, where 'a' is arbitrary constant, is represented by the differential equation

View Question
Let f be a non-negative function defined on $$\left[ {0,{\pi \over 2}} \right]$$. If $$\int\limits_0^x {(f'(t) - \sin 2

View Question
A balloon starting from rest is ascending from ground with uniform acceleration of 4 ft/sec$$^2$$. At the end of 5 sec,

View Question
If $$f(x) = 3\root 3 \of {{x^2}} - {x^2}$$, then

View Question
If z$$_1$$ and z$$_2$$ are two complex numbers satisfying the equation $$\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}}

View Question
A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible

View Question
If R and R$$^1$$ are equivalence relations on a set A, then so are the relations

View Question
Let f be a strictly decreasing function defined on R such that $$f(x) > 0,\forall x \in R$$. Let $${{{x^2}} \over {f({a^

View Question
A rectangle ABCD has its side parallel to the line y = 2x and vertices A, B, D are on lines y = 1, x = 1 and x = $$-$$1

View Question
Let $$f(x) = {x^m}$$, m being a non-negative integer. The value of m so that the equality $$f'(a + b) = f'(a) + f'(b)$$

View Question
Which of the following statements are true?

View Question
## Physics

A ray of monochromatic light is incident on the plane surface of separation between two media $$\mathrm{X}$$ and $$\math

View Question
Three identical convex lenses each of focal length $$\mathrm{f}$$ are placed in a straight line separated by a distance

View Question
X-rays of wavelength $$\lambda$$ gets reflected from parallel planes of atoms in a crystal with spacing d between two p

View Question
If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of n

View Question
In the given circuit, find the voltage drop $$\mathrm{V_L}$$ in the load resistance $$\mathrm{R_L}$$.

View Question
Consider the logic circuit with inputs A, B, C and output Y. How many combinations of A, B and C gives the output Y = 0

View Question
A particle of mass m is projected at a velocity u, making an angle $$\theta$$ with the horizontal (x-axis). If the angle

View Question
A body of mass 2 kg moves in a horizontal circular path of radius 5 m. At an instant, its speed is 2$$\sqrt5$$ m/s and i

View Question
In an experiment, the length of an object is measured to be 6.50 cm. This measured value can be written as 0.0650 m. The

View Question
A mouse of mass m jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius R. The fractiona

View Question
Acceleration due to gravity at a height H from the surface of a planet is the same as that at a depth of H below the sur

View Question
A uniform rope of length 4 m and mass 0.4 kg is held on a frictionless table in such a way that 0.6 m of the rope is han

View Question
The displacement of a plane progressive wave in a medium, travelling towards positive x-axis with velocity 4 m/s at t =

View Question
In a simple harmonic motion, let f be the acceleration and t be the time period. If x denotes the displacement, then |fT

View Question
As shown in the figure, a liquid is at same levels in two arms of a U-tube of uniform cross-section when at rest. If th

View Question
Six molecules of an ideal gas have velocities 1, 3, 5, 5, 6 and 5 m/s respectively. At any given temperature, if $$\math

View Question
As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice hav

View Question
A given quantity of gas is taken from A to C in two ways; a) directly from A $$\to$$ C along a straight line and b) in

View Question
Two substances A and B of same mass are heated at constant rate. The variation of temperature $$\theta$$ of the substan

View Question
Consider a positively charged infinite cylinder with uniform volume charge density $$\rho > 0$$. An electric dipole

View Question
A thin glass rod is bent in a semicircle of radius R. A charge is non-uniformly distributed along the rod with a linear

View Question
12 $$\mu$$C and 6 $$\mu$$C charges are given to the two conducting plates having same cross-sectional area and placed f

View Question
A wire carrying a steady current I is kept in the x-y plane along the curve $$y=A \sin \left(\frac{2 \pi}{\lambda} x\ri

View Question
The figure represents two equipotential lines in x-y plane for an electric field. The x-component E$$_x$$ of the electr

View Question
An electric dipole of dipole moment $$\vec{p}$$ is placed at the origin of the co-ordinate system along the $$\mathrm{z}

View Question
The electric field of a plane electromagnetic wave of wave number k and angular frequency $$\omega$$ is given $$\vec{E}=

View Question
A charged particle in a uniform magnetic field $$\vec{B}=B_{0} \hat{k}$$ starts moving from the origin with velocity $$v

View Question
In an experiment on a circuit as shown in the figure, the voltmeter shows 8 V reading. The resistance of the voltmeter

View Question
An interference pattern is obtained with two coherent sources of intensity ratio n : 1. The ratio $$\mathrm{{{{I_{\max }

View Question
A circular coil is placed near a current carrying conductor, both lying on the plane of the paper. The current is flowi

View Question
An amount of charge Q passes through a coil of resistance R. If the current in the coil decreases to zero at a uniform r

View Question
A modified gravitational potential is given by $$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{r}}+\frac{\mathrm{A}}{\mathrm{r}

View Question
There are n elastic balls placed on a smooth horizontal plane. The masses of the balls are $$\mathrm{m}, \frac{\mathrm{m

View Question
An earth's satellite near the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also

View Question
A bar magnet falls from rest under gravity through the centre of a horizontal ring of conducting wire as shown in figur

View Question
A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the regi

View Question
A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead alo

View Question
A cyclic process is shown in p-v diagram and T-S diagram. Which of the following statements is/are true?

View Question
The figure shows two identical parallel plate capacitors A and B of capacitances C connected to a battery. The key K is

View Question
A charged particle of charge q and mass m is placed at a distance 2R from the centre of a vertical cylindrical region of

View Question