WB JEE 2018

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

## Chemistry

Cl2O7 is the anhydride of

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

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

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

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

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

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Identify 'M' in the following sequence of reactions

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Methoxybenzene on treatment with HI produces

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

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

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

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Which of the following electronic configuration is not possible?

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

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Which of the following has the strongest H-bond?

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

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

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

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How many moles of electrons will weigh one kilogram?

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

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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

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

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

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

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

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Which one of the following is a condensation polymer?

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

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

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

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At room temperature, the reaction between water and fluorine produces

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Which of the following is least thermally stable?

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

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

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

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

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

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

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The major products obtained in the following reaction is/are

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Which statements are correct for the peroxide ion?

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Among the following, the extensive variables are

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White phosphorus P4 has the following characteristics

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## Mathematics

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

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

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

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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

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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) -

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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

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

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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

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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,

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

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

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

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

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

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

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

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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

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

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

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

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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

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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

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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}

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

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

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

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

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

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

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

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

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

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

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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

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

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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

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

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

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

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

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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 =

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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

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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

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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 =

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

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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

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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

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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

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

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

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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

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

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

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

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

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

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

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

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

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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

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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

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

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

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

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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

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

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

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

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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

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

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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=

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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

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

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

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

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## Physics

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

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

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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

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

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

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

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

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

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

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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

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

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

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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

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

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

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

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

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

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

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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

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

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

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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

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

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

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

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

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

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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

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

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

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

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

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

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

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

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

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

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

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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

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