WB JEE 2022

Paper was held on
Sat, Apr 30, 2022 4:30 AM

## Chemistry

A sample of MgCO3 is dissolved in dil. HCl and the solution is neutralized with ammonia and buffered with NH4Cl / NH4OH.

View Question XeF2, NO2, HCN, ClO2, CO2.
Identify the non-linear molecule-pair from the above mentioned molecules.

View Question The number of atoms in body centred and face centred cubic unit cell respectively are

View Question The number of unpaired electron in Mn2+ ion is

View Question The average speed of H2 at T1K is equal to that of O2 at T2K. The ratio T1 : T2 is

View Question Sodium nitroprusside is :

View Question Choose the correct statement for the [Ni(CN)4]2$$-$$ complex ion (Atomic no. of Ni = 28)

View Question The boiling point of the water is higher than liquid HF. The reason is that

View Question The metal-pair that can produce nascent hydrogen in alkaline medium is :

View Question The correct bond order of B-F bond in BF3 molecule is :

View Question Which of the following is radioactive?

View Question The correct order of acidity of the following hydra acids is

View Question To a solution of colourless sodium salt, a solution of lead nitrate was added to have a white precipitate which dissolve

View Question Oxidation states of Cr in K2Cr2O7 and CrO5 are respectively

View Question The correct order of relative stability for the given free radicals is :

View Question
Hybridisation of the negative carbons in (1) and (2) are

View Question
The correct relationship between molecules I and II is

View Question The enol form in which ethyle-3-oxobutanoate exists is

View Question How many monobriminated product(s) (including stereoisomers) would form in the free radical bromination of n-butane?

View Question What is the correct order of acidity of salicylic acid, 4-hydroxybenzoic acid, and 2, 6-dihydroxybenzoic acid ?

View Question How much solid oxalic acid (Molecular weight 126) has to be weighed to prepare 100 ml. exactly 0.1 (N) oxalic acid solut

View Question The major product of the following reaction is
$${F_3}C - CH = C{H_2} + HBr \to $$

View Question The correct order of relative stability of the given conformers of n-butane is

View Question $${C_6}{H_6}(liq) + {{15} \over 2}{O_2}(g) \to 6C{O_2}(g) + 3{H_2}O(liq)$$
Benzene burns in oxygen according to the abov

View Question Avogadro's law is valid for

View Question A metal (M) forms two oxides. The ratio M:O (by weight) in the two oxides are 25:4 and 25:6. The minimum value of atomic

View Question The de-Broglie wavelength ($$\lambda$$) for electron (e), proton (p) and He2+ ion ($$\alpha$$) are in the following orde

View Question 1 mL of water has 25 drops. Let N0 be the Avogadro number. What is the number of molecules present in 1 drop of water ?

View Question In Bohr model of atom, radius of hydrogen atom in ground state is r1 and radius of He+ ion in ground state is r2. Which

View Question Which one of the following is the correct set of four quantum numbers (n, 1, m, s) ?

View Question Let (Crms)H2 is the r.m.s. speed of H2 at 150 K. At what temperature, the most probable speed of helium [Cmp)He] will be

View Question The correct pair of electron affinity order is

View Question The product of the following reaction is :

View Question The product of the following hydrogenation reaction is:

View Question Pick the correct statement.

View Question During the preparation of NH3 in Haber's process, the promoter(s) used is/are -

View Question The correct statement(s) about B2H6 is /are :

View Question Which of the following would produce enantiomeric products when reacted with methyl magnesium iodide?

View Question
The above conversion can be carried out by,

View Question Which of the statements are incorrect?

View Question ## Mathematics

The values of a, b, c for which the function $$f(x) = \left\{ \matrix{
{{\sin (a + 1)x + \sin x} \over x},x 0 \hfill

View Question Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is

View Question Let $$f(x) = {a_0} + {a_1}|x| + {a_2}|x{|^2} + {a_3}|x{|^3}$$, where $${a_0},{a_1},{a_2},{a_3}$$ are real constants. The

View Question If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then

View Question $$\mathop {\lim }\limits_{x \to 0} \left( {{1 \over x}\ln \sqrt {{{1 + x} \over {1 - x}}} } \right)$$ is

View Question Let f : [a, b] $$\to$$ R be continuous in [a, b], differentiable in (a, b) and f(a) = 0 = f(b). Then

View Question $$I = \int {\cos (\ln x)dx} $$. Then I =

View Question Let f be derivable in [0, 1], then

View Question Let $$\int {{{{x^{{1 \over 2}}}} \over {\sqrt {1 - {x^3}} }}dx = {2 \over 3}g(f(x)) + c} $$ ; then
(c denotes constant o

View Question The value of $$\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{\sin x}}} \over {{{(\cos x)}^{\sin x}} + {{(\sin x)}^{\cos

View Question Let $$\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x

View Question Let $$f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt} $$. Then $$f'\left( {{\pi \over 4}} \right)$$ equals

View Question If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to

View Question A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes

View Question The solution of $$\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}$$ is $$f(x) + {e^{ - \sin y}} = C$$ (C

View Question The point of contact of the tangent to the parabola y2 = 9x which passes through the point (4, 10) and makes an angle $$

View Question Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then

View Question If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \wide

View Question If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation

View Question Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is

View Question A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k

View Question If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the

View Question Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then

View Question The number of zeros at the end of $$\left| \!{\underline {\,
{100} \,}} \right. $$ is

View Question If $$|z - 25i| \le 15$$, then Maximum arg(z) $$-$$ Minimum arg(z) is equal to
(arg z is the principal value of argument

View Question If z = x $$-$$ iy and $${z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)$$, then $${{\left( {{x \over p} + {y \over q}} \right)

View Question If a, b are odd integers, then the roots of the equation $$2a{x^2} + (2a + b)x + b = 0$$, $$a \ne 0$$ are

View Question There are n white and n black balls marked 1, 2, 3, ...... n. The number of ways in which we can arrange these balls in

View Question Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then

View Question A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P $$

View Question Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{
1 & 2 & 4 \cr
2 &

View Question If $$\Delta (x) = \left| {\matrix{
{x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr
{x - 1} & {{x^2}} & {{{(x + 1)}^3}}

View Question If $$p = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \right]$$ is the adjoint

View Question If $$A = \left( {\matrix{
1 & 1 \cr
0 & i \cr
} } \right)$$ and $${A^{2018}} = \left( {\matrix{
a & b \c

View Question Let S, T, U be three non-void sets and f : S $$\to$$ T, g : T $$\to$$ U and composed mapping g . f : S $$\to$$ U be defi

View Question For the mapping $$f:R - \{ 1\} \to R - \{ 2\} $$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is c

View Question A, B, C are mutually exclusive events such that $$P(A) = {{3x + 1} \over 3}$$, $$P(B) = {{1 - x} \over 4}$$ and $$P(C) =

View Question A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability

View Question If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0

View Question If the algebraic sum of the distances from the points (2, 0), (0, 2) and (1, 1) to a variable straight line be zero, the

View Question The side AB of $$\Delta$$ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical ang

View Question If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is

View Question A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the po

View Question Two circles $${S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0$$ and $${S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0$$ have a

View Question Let $$P(3\sec \theta ,2\tan \theta )$$ and $$Q(3\sec \phi ,2\tan \phi )$$ be two points on $${{{x^2}} \over 9} - {{{y^2}

View Question Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)2 = 2(x $$-$$ 4). Then the locus of mid-point of PQ i

View Question AB is a chord of a parabola y2 = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The

View Question AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right

View Question The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y $$-$$ z + 4 = 0 and parallel

View Question The line $$x - 2y + 4z + 4 = 0$$, $$x + y + z - 8 = 0$$ intersect the plane $$x - y + 2z + 1 = 0$$ at the point

View Question If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} $$, $${I_2} = \int\limits_0^1 {{e^{ - {x^

View Question $$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + 1} \over {x + 1}} - ax - b} \right),(a,b \in R)$$ = 0. Then

View Question If the transformation $$z = \log \tan {x \over 2}$$ reduces the differential equation $${{{d^2}y} \over {d{x^2}}} + \cot

View Question From the point ($$-$$1, $$-$$6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is

View Question If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$,

View Question The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is

View Question A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the ori

View Question Let the tangent and normal at any point P(at2, 2at), (a > 0), on the parabola y2 = 4ax meet the axis of the parabola at

View Question The value of a for which the sum of the squares of the roots of the equation $${x^2} - (a - 2)x - a - 1 = 0$$ assumes th

View Question If x satisfies the inequality $${\log _{25}}{x^2} + {({\log _5}x)^2}

View Question The solution of $$\det (A - \lambda {I_2}) = 0$$ be 4 and 8 and $$A = \left( {\matrix{
2 & 2 \cr
x & y \cr
}

View Question If P1P2 and P3P4 are two focal chords of the parabola y2 = 4ax then the chords P1P3 and P2P4 intersect on the

View Question $$f:X \to R,X = \{ x|0

View Question Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x

View Question PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OP

View Question From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon ab

View Question Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then

View Question Let z1 and z2 be two non-zero complex numbers. Then

View Question Let $$\Delta = \left| {\matrix{
{\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr
{\cos

View Question Let R and S be two equivalence relations on a non-void set A. Then

View Question Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on

View Question Consider the equation $$y - {y_1} = m(x - {x_1})$$. If m and x1 are fixed and different lines are drawn for different va

View Question Let p(x) be a polynomial with real co-efficient, p(0) = 1 and p'(x) > 0 for all x $$\in$$ R. Then

View Question Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of t

View Question The line y = x + 5 touches

View Question ## Physics

Two infinite line-charges parallel to each other are moving with a constant velocity v in the same direction as shown i

View Question The electric potential for an electric field directed parallel to X-axis is shown in the figure. Choose the correct plot

View Question An electron revolves around the nucleus in a circular path with angular momentum $$\overrightarrow L $$. A uniform magne

View Question A straight wire is placed in a magnetic field that varies with distance x from origin as $$\overrightarrow B = {B_0}\le

View Question In a closed circuit there is only a coil of inductance L and resistance 100 $$\Omega$$. The coil is situated in a unifor

View Question When an AC source of emf E with frequency $$\omega$$ = 100 Hz is connected across a circuit, the phase difference betwee

View Question
A battery of emf E and internal resistance r is connected with an external resistance R as shown in the figure. The bat

View Question If the kinetic energies of an electron, an alpha particle and a proton having same de-Broglie wavelength are $${\varepsi

View Question In a Young's double slit experiment, the intensity of light at a point on the screen where the path difference between t

View Question In Young's double slit experiment with a monochromatic light, maximum intensity is 4 times the minimum intensity in the

View Question The human eye has an approximate angular resolution of $$\theta$$ = 5.8 $$\times$$ 10$$-$$4 rad and typical photo printe

View Question Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of $${h \over {2\pi }}$$

View Question A Zener diode having break down voltage Vz = 6V is used in a voltage regulator circuit as shown in the figure. The minim

View Question The expression $$\overline A (A + B) + (B + AA)(A + \overline B )$$ simplifies to

View Question Given : The percentage error in the measurements of A, B, C and D are respectively, 4%, 2%, 3% and 1%. The relative erro

View Question The Entropy (S) of a black hole can be written as $$S = \beta {k_B}A$$, where kB is the Boltzmann constant and A is the

View Question The kinetic energy (Ek) of a particle moving along X-axis varies with its position (X) as shown in the figure. The force

View Question
A particle is moving in an elliptical orbit as shown in figure. If $$\overrightarrow p $$, $$\overrightarrow L $$ and $

View Question A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency

View Question A body of mass m is thrown with velocity u from the origin of a co-ordinate axes at an angle $$\theta$$ with the horizon

View Question Three particles, each of mass 'm' grams situated at the vertices of an equilateral $$\Delta$$ABC of side 'a' cm (as show

View Question A body of mass m is thrown vertically upward with speed $$\sqrt3$$ ve, where ve is the escape velocity of a body from ea

View Question If a string, suspended from the ceiling is given a downward force F1, its length becomes L1. Its length is L2, if the do

View Question 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

View Question Certain amount of an ideal gas is taken from its initial state 1 to final state 4 through the paths 1 $$\to$$ 2 $$\to$$

View Question Consider a thermodynamic process where integral energy $$U = A{P^2}V$$ (A = constant). If the process is performed adiab

View Question One mole of a diatomic ideal gas undergoes a process shown in P-V diagram. The total heat given to the gas (ln 2 = 0.7)

View Question Two charges, each equal to $$-$$q are kept at ($$-$$a, 0) and (a, 0). A charge q is placed at the origin. If q is given

View Question
A neutral conducting solid sphere of radius R has two spherical cavities of radius a and b as shown in the figure. Cent

View Question Consider two concentric conducting sphere of radii R and 2R respectively. The inner sphere is given a charge +Q. The oth

View Question A horizontal semi-circular wire of radius r is connected to a battery through two similar springs X and Y to an electric

View Question Find the equivalent capacitance between A and B of the following arrangement :

View Question A golf ball of mass 50 gm placed on a tee, is struck by a golf-club. The speed of the golf ball as it leaves the tee is

View Question Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities +$$\sigm

View Question One mole of an ideal monoatomic gas expands along the polytrope PV3 = constant from V1 to V2 at a constant pressure P1.

View Question
As shown in figure, a rectangular loop of length 'a' and width 'b' and made of a conducting material of uniform cross-s

View Question A sample of hydrogen atom in its ground state is radiated with photons of 10.2 eV energies. The radiation from the sampl

View Question A particle is moving in x-y plane according to $$\overrightarrow r = b\cos \omega t\widehat i + b\sin \omega t\widehat

View Question
Two wires A and B of same length are made of same material. Load (F) vs. elongation (x) graph for these two wires is

View Question
A hemisphere of radius R is placed in a uniform electric field E so that its axis is parallel to the field. Which of th

View Question