WB JEE 2018

Paper was held on
Sun, Apr 22, 2018 11:00 AM

## Chemistry

Cl2O7 is the anhydride of

View Question The main reason that SiCl4 is easily hydrolysed as compared to CCl4 is that

View Question Silver chloride dissolves in excess of ammonium hydroxide solution. The cation present in the resulting solution is

View Question The ease of hydrolysis in the compounds CH3COCl(I), CH3 $$-$$ CO $$-$$ O $$-$$ COCH3 (II), CH3COOC2H5 (III) and CH3CONH2

View Question CH3 $$-$$ C $$ \equiv $$ C MgBr can be prepared by the reaction of

View Question The number of alkene (s) which can produce 2-butanol by the successive treatment of (i) B2H6 in tetrahydrofuran solvent

View Question Identify 'M' in the following sequence of reactions

View Question Methoxybenzene on treatment with HI produces

View Question $$\mathop {{C_4}{H_{10}}O}\limits_{(N)} \mathop {\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{{H_2}S{O_4}}^{{K_2}C

View Question The correct order of reactivity for the addition reaction of the following carbonyl compounds with ethylmagnesium iodide

View Question If aniline is treated with conc. H2SO4 and heated at 200$$^\circ$$C, the product is

View Question Which of the following electronic configuration is not possible?

View Question The number of unpaired electrons in Ni (atomic number = 28) are

View Question Which of the following has the strongest H-bond?

View Question The half-life of C14 is 5760 years. For a 200 mg sample of C14, the time taken to change to 25 mg is

View Question Ferric ion forms a Prussian blue precipitate due to the formation of

View Question The nucleus $$_{29}^{64}$$Cu accepts an orbital electron to yield,

View Question How many moles of electrons will weigh one kilogram?

View Question Equal weights of ethane and hydrogen are mixed in an empty container at 25$$^\circ$$C. The fraction of total pressure ex

View Question The heat of neutralisation of a strong base and a strong acid is 13.7 kcal. The heat released when 0.6 mole HCl solution

View Question A compound formed by elements X and Y crystallises in the cubic structure, where X atoms are at the corners of a cube an

View Question What amount of electricity can deposit 1 mole of Al metal at cathode when passed through molten AlCl3 ?

View Question Given the standard half-cell potentials (E$$^\circ$$) of the following as$$\matrix{
{Zn \to Z{n^{2 + }} + 2{e^ - };}

View Question The following equilibrium constants are given$${N_2} + 3{H_2}$$ $$\rightleftharpoons$$ $$2N{H_3}$$; $${K_1}$$$${N_2} + {

View Question Which one of the following is a condensation polymer?

View Question Which of the following is present in maximum amount in 'acid rain'?

View Question Which of the set of oxides are arranged in the proper order of basic, amphoteric, acidic?

View Question Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?

View Question At room temperature, the reaction between water and fluorine produces

View Question Which of the following is least thermally stable?

View Question $$[P]\buildrel {B{r_2}} \over
\longrightarrow {C_2}{H_4}B{r_2}\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{N{H_3}

View Question The number of possible organobromine compounds which can be obtained in the allylic bromination of 1-butene with N-bromo

View Question A metal M (specific heat 0.16) forms a metal chloride with 65% chlorine present in it. The formula of the metal chloride

View Question During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute tem

View Question $$[X] + Dil.\,{H_2}S{O_4} \to [Y]:$$ Colourless, suffocating gas$$[Y] + {K_2}C{r_2}{O_7} + {H_2}S{O_4} \to $$ Green colo

View Question The possible product(s) to be obtained from the reaction of cyclobutyl amine with HNO2 is/are

View Question The major products obtained in the following reaction is/are

View Question Which statements are correct for the peroxide ion?

View Question Among the following, the extensive variables are

View Question White phosphorus P4 has the following characteristics

View Question ## Mathematics

The approximate value of sin31$$^\circ$$ is

View Question Let $${f_1}(x) = {e^x}$$, $${f_2}(x) = {e^{{f_1}(x)}}$$, ......, $${f_{n + 1}}(x) = {e^{{f_n}(x)}}$$ for all n $$ \ge $$

View Question The domain of definition of $$f(x) = \sqrt {{{1 - |x|} \over {2 - |x|}}} $$ is

View Question Let f : [a, b] $$ \to $$ R be differentiable on [a, b] and k $$ \in $$ R. Let f(a) = 0 = f(b). Also let J(x) = f'(x) + k

View Question Let $$f(x) = 3{x^{10}} - 7{x^8} + 5{x^6} - 21{x^3} + 3{x^2} - 7$$. Then $$\mathop {\lim }\limits_{h \to 0} {{f(1 - h) -

View Question Let f : [a, b] $$ \to $$ R be such that f is differentiable in (a, b), f is continuous at x = a and x = b and moreover f

View Question Let f : R $$ \to $$ R be a twice continuously differentiable function such that f(0) = f(1) = f'(0) = 0. Then

View Question If $$\int {{e^{\sin x}}} .\left[ {{{x{{\cos }^3}x - \sin x} \over {{{\cos }^2}x}}} \right]dx = {e^{\sin x}}f(x) + c$$, w

View Question If $$\int {f(x)} \sin x\cos xdx = {1 \over {2({b^2} - {a^2})}}\log (f(x)) + c$$, where c is the constant of integration,

View Question If $$M = \int\limits_0^{\pi /2} {{{\cos x} \over {x + 2}}dx} $$, $$N = \int\limits_0^{\pi /4} {{{\sin x\cos x} \over {{{

View Question The value of the integral $$I = \int_{1/2014}^{2014} {{{{{\tan }^{ - 1}}x} \over x}} dx$$ is

View Question Let $$I = \int\limits_{\pi /4}^{\pi /3} {{{\sin x} \over x}} dx$$. Then

View Question The value of $$I = \int_{\pi /2}^{5\pi /2} {{{{e^{{{\tan }^{ - 1}}(\sin x)}}} \over {{e^{{{\tan }^{ - 1}}(\sin x)}} + {e

View Question The value of $$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\left\{ {{{\sec }^2}{\pi \over {4n}} + {{\sec }^2}{{2\

View Question The differential equation representing the family of curves $${y^2} = 2d(x + \sqrt d )$$, where d is a parameter, is of

View Question Let y(x) be a solution of $$(1 + {x^2}){{dy} \over {dx}} + 2xy - 4{x^2} = 0$$. Then y(1) is equal to

View Question The law of motion of a body moving along a straight line is x = $${1 \over 2}$$ vt. x being its distance from a fixed po

View Question Number of common tangents of y = x2 and y = $$-$$x2 + 4x $$-$$ 4 is

View Question Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b $$ \in $$ R

View Question If $$x + {\log _{10}}(1 + {2^x}) = x{\log _{10}}5 + {\log _{10}}6$$, then the value of x is

View Question If $${Z_r} = \sin {{2\pi r} \over {11}} - i\cos {{2\pi r} \over {11}}$$, then $$\sum\limits_{r = 0}^{10} {{Z_r}} $$ is e

View Question If z1 and z2 be two non-zero complex numbers such that $${{{z_1}} \over {{z_2}}} + {{{z_2}} \over {{z_1}}} = 1$$, then t

View Question If $${b_1}{b_2} = 2({c_1} + {c_2})$$ and b1, b2, c1, c2 are all real numbers, then at least one of the equations $${x^2}

View Question The number of selection of n objects from 2n objects of which n are identical and the rest are different, is

View Question If (2 $$ \le $$ r $$ \le $$ n), then $${}^n{C_r}$$ + 2 . $${}^n{C_{r + 1}}$$ + $${}^n{C_{r + 2}}$$ is equal to

View Question The number (101)100 $$-$$ 1 is divisible by

View Question If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)n may also have the

View Question If $$\left| {\matrix{
{ - 1} & 7 & 0 \cr
2 & 1 & { - 3} \cr
3 & 4 & 1 \cr
} } \

View Question If $${a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}$$, then the value of $$\left| {\matrix{
{{a_1}} & {{a_2}} &

View Question If $${S_r} = \left| {\matrix{
{2r} & x & {n(n + 1)} \cr
{6{r^2} - 1} & y & {{n^2}(2n + 3)} \cr

View Question If the following three linear equations have a non-trivial solution, thenx + 4ay + az = 0x + 3by + bz = 0x + 2cy + cz =

View Question On R, a relation $$\rho $$ is defined by x$$\rho $$y if and only if x $$-$$ y is zero or irrational. Then,

View Question On the set R of real numbers, the relation $$\rho $$ is defined by x$$\rho $$y, (x, y) $$ \in $$ R.

View Question If f : R $$ \to $$ R be defined by f (x) = ex and g : R $$ \to $$ R be defined by g(x) = x2. The mapping gof : R $$ \to

View Question In order to get a head at least once with probability $$ \ge $$ 0.9, the minimum number of times a unbiased coin needs t

View Question A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabil

View Question If sin6$$\theta$$ + sin4$$\theta$$ + sin2$$\theta$$ = 0, then general value of $$\theta$$ is

View Question If $$0 \le A \le {\pi \over 4}$$, then $${\tan ^{ - 1}}\left( {{1 \over 2}\tan 2A} \right) + {\tan ^{ - 1}}(\cot A) + {

View Question Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 $$-

View Question The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x $$-$$ 6y + 9sin2$$\alpha$$ + 13cos2

View Question The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y =

View Question The angular points of a triangle are A($$-$$ 1, $$-$$ 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle

View Question If one of the diameter of the circle, given by the equation x2 + y2 + 4x + 6y $$-$$ 12 = 0, is a chord of a circle S, wh

View Question A chord AB is drawn from the point A(0, 3) on the circle x2 + 4x + (y $$-$$ 3)2 = 0, and is extended to M such that AM =

View Question Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of

View Question Let A, B the two distinct points on the parabola y2 = 4x. If the axis of the parabola touches a circle of radius r havin

View Question Let P(at2, 2at), Q, R(ar2, 2ar) be three points on a parabola y2 = 4ax. If PQ is the focal chord and PK, QR are parallel

View Question Let P be a point on the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and the line through P parallel to the Y-a

View Question A point P lies on a line through Q(1, $$-$$2, 3) and is parallel to the line $${x \over 1} = {y \over 4} = {z \over 5}$$

View Question The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, $$-$$11, 4) and (2, $$-$$

View Question A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate

View Question For 0 $$ \le $$ p $$ \le $$ 1 and for any positive a, b; let I(p) = (a + b)p, J(p) = ap + bp, then

View Question Let $$\overrightarrow \alpha $$ = $$\widehat i + \widehat j + \widehat k$$, $$\overrightarrow \beta $$ = $$\widehat i

View Question Let $$\overrightarrow \alpha $$, $${\overrightarrow \beta }$$, $${\overrightarrow \gamma }$$ be the three unit vector

View Question Let z1 and z2 be complex numbers such that z1 $$ \ne $$ z2 and |z1| = |z2|. If Re(z1) > 0 and Im(z2) < 0, then $${

View Question From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of

View Question The least positive integer n such that $${\left( {\matrix{
{\cos \pi /4} & {\sin \pi /4} \cr
{ - \sin {\pi

View Question Let $$\rho $$ be a relation defined on N, the set of natural numbers, as$$\rho $$ = {(x, y) $$ \in $$ N $$ \times $$ N :

View Question If the polynomial $$f(x) = \left| {\matrix{
{{{(1 + x)}^a}} & {{{(2 + x)}^b}} & 1 \cr
1 & {{{(1 + x)

View Question A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, $$-$$3). A variable line PQ is drawn perpendicular to AB cuttin

View Question Let A be the centre of the circle $${x^2} + {y^2} - 2x - 4y - 20 = 0$$. Let B(1, 7) and D(4, $$-$$2) be two points on th

View Question Let $$f(x) = \left\{ {\matrix{
{ - 2\sin x,} & {if\,x \le - {\pi \over 2}} \cr
{A\sin x + B,} & {if\,

View Question The normal to the curve $$y = {x^2} - x + 1$$, drawn at the points with the abscissa $${x_1} = 0$$, $${x_2} = - 1$$ and

View Question The equation x log x = 3 $$-$$ x

View Question Consider the parabola y2 = 4x. Let P and Q be points on the parabola where P(4, $$-$$ 4) and Q(9, 6). Let R be a point o

View Question Let $$I = \int\limits_0^I {{{{x^3}\cos 3x} \over {2 + {x^2}}}dx} $$, then

View Question A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in

View Question The area of the region lying above X-axis, and included between the circle x2 + y2 = 2ax and the parabola y2 = ax, a >

View Question If the equation $${x^2} - cx + d = 0$$ has roots equal to the fourth powers of the roots of $${x^2} + ax + b = 0$$, wher

View Question On the occasion of Dipawali festival each student of a class sends greeting cards to others. If there are 20 students in

View Question In a third order matrix A, aij denotes the element in the ith row and jth column. If aij = 0 for i = j= 1 for i > j=

View Question The area of the triangle formed by the intersection of a line parallel to X-axis and passing through P(h, k), with the l

View Question A hyperbola, having the transverse axis of length 2sin$$\theta$$ is confocal wit6h the ellipse 3x2 + 4y2 = 12. Its equat

View Question Let $$f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0$$, then assuming k as an integer,

View Question Consider the function $$y = {\log _a}(x + \sqrt {{x^2} + 1} ),a > 0,a \ne 1$$. The inverse of the function

View Question ## Physics

Four resistors, 100$$\Omega $$, 200$$\Omega $$, 300$$\Omega $$ and 400$$\Omega $$ are connected to form four sides of a

View Question What will be current through the 200$$\Omega $$ resistor in the given circuit, a long time after the switch K is made on

View Question A point source is placed at coordinates (0, 1) in xy-plane. A ray of light from the source is reflected on a plane mirro

View Question Two identical equiconvex lenses, each of focal length f are placed side by side in contact with each other with a layer

View Question There is a small air bubble at the centre of a solid glass sphere of radius r and refractive index $$\mu$$. What will be

View Question If Young's double slit experiment is done with white light, which of the following statements will be true?

View Question How the linear velocity v of an electron in the Bohr orbit is related to its quantum number n?

View Question If the half-life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on

View Question An electron accelerated through a potential of 10000 V from rest has a de-Broglie wave length $$\lambda$$. What should b

View Question In the circuit shown, inputs A and B are in states 1 and 0 respectively. What is the only possible stable state of the o

View Question What will be the current flowing through the 6k$$\Omega $$ resistor in the circuit shown, where the breakdown voltage of

View Question In case of a simple harmonic motion, if the velocity is plotted along the X-axis and the displacement (from the equilibr

View Question A block of mass m2 is placed on a horizontal table and another block of mass m1 is placed on top of it. An increasing ho

View Question In a triangle ABC, the sides AB and AC are represented by the vectors $$3\widehat i + \widehat j + \widehat k$$ and $$\w

View Question The velocity (v) of a particle (under a force F) depends on its distance (x) from the origin (with x > 0) $$v \propto

View Question The ratio of accelerations due to gravity g1 : g2 on the surfaces of two planets is 5 : 2 and the ratio of their respect

View Question A spherical liquid drop is placed on a horizontal plane. A small distance causes the volume of the drop to oscillate. Th

View Question The stress along the length of a rod (with rectangular cross-section) is 1% of the Young's modulus of its material. What

View Question What will be the approximate terminal velocity of a rain drop of diameter $${1.8 \times {{10}^{ - 3}}}$$ m, when density

View Question The water equivalent of a calorimeter is 10 g and it contains 50 g of water at 15$$^\circ$$C. Some amount of ice, initia

View Question One mole of a monoatomic ideal gas undergoes a quasistatic process, which is depicted by a straight line joining points

View Question For an ideal gas with initial pressure and volume pi and Vi respectively, a reversible isothermal expansion happens, whe

View Question A point charge $$-$$ q is carried from a point A to another point B on the axis of a charged ring of radius r carrying a

View Question Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length a as shown in the fi

View Question Four equal charges of value + Q are placed at any four vertices of a regular hexagon of side 'a'. By suitably choosing t

View Question A proton of mass m moving with a speed v (< < c, velocity of light in vacuum) completes a circular orbit in time T

View Question A uniform current is flowing along the length of an infinite, straight, thin, hollow cylinder of radius R. The magnetic

View Question A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a ma

View Question An alternating current is flowing through a series L-C-R circuit. It is found that the current reaches a value of 1 mA a

View Question An electric bulb, a capacitor, a battery and a switch are all in series in a circuit. How does the intensity of light va

View Question A light charged particle is revolving in a circle of radius r in electrostatic attraction of a static heavy particle wit

View Question As shown in the figure, a rectangular loop of conducting wire is moving away with a constant velocity v in a perpendicul

View Question A solid spherical ball and a hollow spherical ball of two different materials of densities $$\rho $$1 and $$\rho $$2 res

View Question The insulated plates of a charged parallel plate capacitor (with small separation between the plates) are approaching ea

View Question The bob of a pendulum of mass m, suspended by an inextensible string of length L as shown in the figure carries a small

View Question A non-zero current passes through the galvanometer G shown in the circuit when the key K is closed and its value does no

View Question A ray of light is incident on a right angled isosceles prism parallel to its base as shown in the figure. Refractive ind

View Question The intensity of a sound appears to an observer to be periodic. Which of the following can be the cause of it?

View Question Which of the following statement(s) is/are true?"Internal energy of an ideal gas .............."

View Question Two positive charges Q and 4Q are placed at points A and B respectively, where B is at a distance d units to the right o

View Question