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.

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

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

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The number of unpaired electron in Mn2+ ion is

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

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Sodium nitroprusside is :

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

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

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

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

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Which of the following is radioactive?

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The correct order of acidity of the following hydra acids is

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

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Oxidation states of Cr in K2Cr2O7 and CrO5 are respectively

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

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

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The correct relationship between molecules I and II is

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

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

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

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

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

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

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

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Avogadro's law is valid for

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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

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

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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 ?

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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

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

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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

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The correct pair of electron affinity order is

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The product of the following reaction is :

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The product of the following hydrogenation reaction is:

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Pick the correct statement.

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

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

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

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The above conversion can be carried out by,

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Which of the statements are incorrect?

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## 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

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

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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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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

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

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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

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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

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

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

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

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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)

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

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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

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

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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 $$

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

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

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

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

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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

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

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

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

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

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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

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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

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

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

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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

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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}

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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

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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

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

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

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

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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^

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

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

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

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

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

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

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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

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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

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

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

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

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

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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

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

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

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

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

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

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

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

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

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

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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

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The line y = x + 5 touches

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## Physics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

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

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

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

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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

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

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

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

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

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

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

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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)

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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

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

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

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

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

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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

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

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

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

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

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

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

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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

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