WB JEE 2017

Paper was held on
Sun, Apr 23, 2017 11:00 AM

## Chemistry

For same mass of two different ideal gases of molecular weights M1 and M2, Plots of log V vs log p at a given constant t

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Which of the following has the dimension if [$$M{L^0}{T^{ - 2}}$$] ?

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If the given four electronic configurations.(i) n = 4, l = 1(ii) n = 4, l = 0(iii) n = 3, l = 2(iv) n = 3, l = 1are arra

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Which of the following sets of quantum numbers represents the 19th electron of Cr(Z = 24) ?

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0.126 g of an acid is needed to completely neutralise 20 mL 0.1 (N) NaOH solution. The equivalent weight of the acid is

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In a flask, the weight ratio of CH4(g) and SO2(g) at 298 K and 1 bar is 1 : 2. The ratio of the number of molecules of S

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C6H5F18 is a F18 radio-isotope labelled organic compound. F18 decays by positron emission. The product resulting on deca

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Dissolving NaCN in de-ionised water will result in a solution having

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Among Me3N, C5H5N and MeCN (Me = methyl group) the electronegativity of N is in the order

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The shape of $$XeF_5^ - $$ will be

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The ground state magnetic property of B2 and C2 molecules will be

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The number of unpaired electrons in $${[NiC{l_4}]^{2 - }}$$, $$Ni{(CO)_4}$$ and $${[Cu{(N{H_3})_4}]^{2 + }}$$ respective

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Which of the following atoms should have the highest 1st electron affinity?

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PbCl2 is insoluble in cold water. Addition of HCl increases its solubility due to

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Of the following compounds, which one of the strongest Bronsted acid in a aqueous solution?

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The correct basicity order of the following lanthanide ions is

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When BaCl2 is added to an aqueous salt solution, a white precipitate is obtained. The anion among CO$$_3^{2 - }$$, SO$$_

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In the IUPAC system, PhCH2CH2CO2H is named as

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The isomerisation of 1-butyne to 2-butyne can be achieved by treatment with

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The correct order of acid strengths of benzoic acid (X), peroxybenzoic acid (Y) and p-nitrobenzoic acid (Z) is

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The yield of acetanilide in the reaction (100% conversion) of 2 moles of aniline with 1 mole of acetic anhydride is

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The structure of the product P of the following reaction is

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ADP and ATP differ in the number of

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The compound that would produce a nauseating smell/odour with a hot mixture of chloroform and ethanolic potassium hydrox

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For the reaction belowthe structure of the product Q is

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You are supplied with 500 mL each of 2N HCl and 5N HCl. What is the maximum volume of 3M HCl that you can prepare using

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Which one of the following corresponds to a photon of highest energy?

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Assuming the compounds to be completely dissociated in aqueous solution, identify the pair of the solutions that can be

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How many faradays are required to reduce 1 mol of $$C{r_2}O_7^{2 - }$$ to Cr3+ in acid medium?

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Equilibrium constants for the following reactions at 1200 K are given2H2O(g) $$\rightleftharpoons$$ 2H2(g) + O2(g), K1 =

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In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius (r) of potassi

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Which of the following solutions will turn violet when a drop of lime juice is added to it?

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The reaction sequence given below given product R.The structure of the product R is

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Reduction of the lactol S with sodium borohydride gives

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What will be the normality of the salt solution obtained by neutralising x mL y (N) HCl with y mL x(N) NaOH, and finally

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During electrolysis of molten NaCl, some water was added. What will happen?

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The role of fluorspar, which is added in small quantities in the electrolytic reduction of alumina dissolved in fused cr

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The reduction of benzene diazonium chloride to phenyl hydrazine can be accomplished by

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The major product(s) obtained form the following reaction of 1 mole of hexadeuteriobenzene is/are

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The conversion of CH3 $$-$$ CH2 $$-$$ COOH to can be accomplished by

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## Mathematics

The number of all numbers having 5 digits, with distinct digits is

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The greatest integer which divides $$(p + 1)(p + 2)(p + 3)...(p + q)$$ for all $$p \in N$$ and fixed $$q \in N$$ is

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Let $${(1 + x + {x^2})^9} = {a_0} + {a_1}x + {a_2}{x^2} + ... + {a_{18}}{x^{18}}$$. Then,

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The linear system of equations$$\left. \matrix{
8x - 3y - 5z = 0 \hfill \cr
5x - 8y + 3z = 0 \hfill \cr
3x + 5y

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Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 o

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Let $$A = \left( {\matrix{
{x + 2} & {3x} \cr
3 & {x + 2} \cr
} } \right),\,B = \left( {\matrix{

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The value of det A, where $$A\, = \left( {\matrix{
1 & {\cos \theta } & 0 \cr
{ - \cos \theta } & 1

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Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z)

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On the set R of real numbers we define xPy if and only if xy $$ \ge $$ 0. Then, the relation P is

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

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Mean of n observations x1, x2, ...., xn is $$\overline x $$. If an observation xq is replaced by xq' then the new mean i

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The probability that a non-leap year selected at random will have 53 Sunday is

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The equation $$\sin x(\sin x + \cos x) = k$$ has real solutions, where k is a real number. Then,

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The possible values of x, which satisfy the trigonometric equation $${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \rig

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Transforming to parallel axes through a point (p, q), the equation $$2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0$$ becomes

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Let A(2, $$-$$3) and B($$-$$ 2, 1) be two angular points of $$\Delta$$ABC. If the centroid of the triangle moves on the

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The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-

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Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines

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The common chord of the circles $${x^2} + {y^2} - 4x - 4y = 0$$ and $$2{x^2} + 2{y^2} = 32$$ subtends at the origin an

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The locus of the mid-points of the chords of the circle $${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$

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Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1

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B is an extremity of the minor axis of an ellipse whose foci are S and S'. If $$\angle SBS'$$ is a right angle, then the

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The axis of the parabola $${x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0$$ is

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The line segment joining the foci of the hyperbola $${x^2} - {y^2} + 1 = 0$$ is one of the diameters of a circle. The eq

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The equation of the plane through (1, 2, $$-$$3) and (2, $$-$$2, 1) and parallel to X-axis is

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Three lines are drawn from the origin O with direction cosines proportional to (1, $$-$$1, 1), (2, $$-$$3, 0) and (1, 0,

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Consider the non-constant differentiable function f one one variable which obeys the relation $${{f(x)} \over {f(y)}} =

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If $$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to

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Let, $$F(x) = {e^x},G(x) = {e^{ - x}}$$ and $$H(x) = G(F(x))$$, where x is a real variable. Then, $${{dH} \over {dx}}$$

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If f'' (0) = k, k $$ \ne $$ 0, then the value of $$\mathop {\lim }\limits_{x \to 0} {{2f(x) - 3f(2x) + f(4x)} \over {{x^

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If $$y = {e^{m{{\sin }^{ - 1}}x}}$$ then $$(1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} - $$ky = 0, where k

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The chord of the curve $$y = {x^2} + 2ax + b$$, joining the points where x = $$\alpha$$ and x = $$\beta$$, is parallel t

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Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has

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Let $$f(x) = \left\{ {\matrix{
{{{{x^p}} \over {{{(\sin x)}^q}}},} & {if\,0 < x \le {\pi \over 2}} \cr
{

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$$\mathop {\lim }\limits_{x \to 0} {(\sin x)^{2\tan x}}$$ is equal to

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$$\int {\cos (\log x)dx} $$ = F(x) + C, where C is an arbitrary constant. Here, F(x) is equal to

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$$\int {{{{x^2} - 1} \over {{x^4} + 3{x^2} + 1}}dx} $$ (x > 0) is

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Let I = $$\left| {\int {_{10}^{19}{{\sin x} \over {1 + {x^8}}}dx} } \right|$$. Then,

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Let $${I_1} = \int_0^n {[x]} \,dx$$ and $${I_2} = \int_0^n {\{ x\} } \,dx$$, where [x] and {x} are integral and fraction

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The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ..

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The value of the integral $$\int_0^1 {{e^{{x^2}}}} dx$$

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$$\int_0^{100} {{e^{x - [x]}}} dx$$ is equal to

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Solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2}$$ ('a' belong a constant) is

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The integrating factor of the first order differential equation $${x^2}({x^2} - 1){{dy} \over {dx}} + x({x^2} + 1)y = {x

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In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of

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If $$({\log _5}x)({\log _x}3x)({\log _{3x}}y) = {\log _x}{x^3}$$, then y equals

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The expression $${{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}$$ equals

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Let z = x + iy, where x and y are real. The points (x, y) in the X-Y plane for which $${{{z + i} \over {z - i}}}$$ is pu

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If p, q are odd integers, then the roots of the equation $$2p{x^2} + (2p + q)x + q = 0$$ are

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Out of 7 consonants and 4 vowels, words are formed each having 3 consonants and 2 vowels. The number of such words that

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Let $$A = \left( {\matrix{
1 & 1 & 1 \cr
0 & 1 & 1 \cr
0 & 0 & 1 \cr
} } \right

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Let a, b, c be such that b(a + c) $$ \ne $$ 0. If $$\left| {\matrix{
a & {a + 1} & {a - 1} \cr
{ - b} &a

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On set A = {1, 2, 3}, relations R and S are given byR = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},S = {(1, 1), (2, 2), (3

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If one of the diameters of the curve x2 + y2 $$-$$ 4x $$-$$ 6y + 9 = 0 is a chord of a circle with centre (1, 1), the ra

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Let A($$-$$ 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $$\angle MBA$$ = 2$$\angle

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If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to

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Let for all x > 0, $$f(x) = \mathop {\lim }\limits_{n \to \infty } n({x^{1/n}} - 1)$$, then

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Let $$I = \int_0^{100\pi } {\sqrt {(1 - \cos 2x)} } \,dx$$, then

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The area of the figure bounded by the parabolas x = $$-$$ 2y2 and x = 1 $$-$$ 3y2 is

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Tangents are drawn to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ at the ends of both latusrectum. The ar

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The value of K in order that f(x) = sin x $$-$$ cos x $$-$$ kx + 5 decreases for all positive real values of x is given

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For any vector x, where $$\widehat i$$, $$\widehat j$$, $$\widehat k$$ have their usual meanings the value of $${(x \tim

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If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

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Let $$\alpha$$ and $$\beta$$ be the roots of $${x^2} + x + 1 = 0$$. If n be a positive integer, then $$\alpha$$n + $$\be

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For real x, the greatest value of $${{{x^2} + 2x + 4} \over {2{x^2} + 4x + 9}}$$ is

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If a, b$$ \in $$ {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then

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If the tangent to $${y^2} = 4ax$$ at the point $$(a{t^2},2at)$$ where | t | > 1 is a normal to $${x^2} - {y^2} = {a^2

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The focus of the conic x2 $$-$$ 6x + 4y + 1 = 0 is

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Let f : R $$ \to $$ R be twice continuously differentiable. Let f(0) = f(1) = f'(0) = 0. Then,

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If f(x) = xn, being a non-negative integer, then the values of n for which f'($$\alpha$$ + $$\beta$$) = f'($$\alpha$$) +

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Let f be a non-constant continuous function for all x $$ \ge $$ 0. Let f satisfy the relation f(x) f(a $$-$$ x) = 1 for

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If the line ax + by + c = 0, ab $$ \ne $$ 0, is a tangent to the curve xy = 1 $$-$$ 2x, then

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Two particles move in the same straight line starting at the same moment from the same point in the same direction. The

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The complex number z satisfying the equation | z $$-$$ 1 | = | z + 1 | = 1 is

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On R, the set of real numbers, a relation $$\rho $$ is defined as 'a$$\rho $$b if and only if 1 + ab > 0'. Then,

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## Physics

The velocity of a particle executing a simple harmonic motion is 13 ms$$-$$1, when its distance from the equilibrium pos

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A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at freq

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A uniform capillary tube of length l and inner radius r with its upper end sealed is submerged vertically into water. Th

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A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01%. The

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Temperature of an ideal gas, initially at 27$$^\circ$$C, is raised by 6$$^\circ$$C. The rms velocity of the gas molecule

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2 moles of an ideal monoatomic gas is carried from a state (p0, V0) to state (2p0, 2V0) along a straight line path in a

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A solid rectangular sheet has two different coefficients of linear expansion $$\alpha$$1 and $$\alpha$$2 along its lengt

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A positive charge Q is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)

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Three capacitors of capacitance 1.0, 2.0 and 5.0 $$\mu$$F are connected in series to a 10 V source. The potential differ

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A charge of 0.8 coulomb is divided into two charges Q1 and Q2. These are kept at a separation of 30 cm. The force on Q1

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The magnetic field due to a current in a straight wire segment of length L at a point on its perpendicular bisector at

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The magnets of two suspended coil galvanometers are of the same strength so that they produce identical uniform magnetic

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A proton is moving with a uniform velocity of $${{{10}^6}}$$ ms$$-$$1 along the Y-axis, under the joint action of a magn

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When the frequency of the AC voltage applied to a series LCR circuit is gradually increased from a low value, the impeda

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Six wires, each of resistance r, are connected so as to form a tetrahedron. The equivalent resistance of the combination

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Consider the circuit shown in the figure.The value of the resistance X for which the thermal power generated in it is pr

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Consider the circuit shown in the figure where all the resistances are of magnitude 1 k$$\Omega$$. If the current in the

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The ratio of the diameter of the sun to the distance between the earth and the sun is approximately 0.009. The approxima

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Two monochromatic coherent light beams A and B have intensities L and $${{L \over 4}}$$, respectively. If these beams ar

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A point object is held above a thin equiconvex lens at its focus. The focal length is 0.1 m and the lens rests on a hori

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A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius R = 0.05 m and refrac

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The de-Broglie wavelength of an electron is $$0.4 \times {10^{ - 10}}$$ m when its kinetic energy is 1.0 keV. Its wavele

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When light of frequency v1 is incident on a metal with work function W (where hv1 > W), then photocurrent falls to ze

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Radon-222 has a half-life of 3.8 days. If one starts with 0.064 kg of radon-222 left after 19 days will be

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In the given circuit, the binary inputs at A and B are both 1 in one case and both 0 in the next case. The respective ou

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When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the c

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The dimension of the universal constant of gravitation, G is

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Two particles A and B (both initially at rest) start moving towards each other under a mutual force of attraction. At th

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Three vectors $$\overrightarrow A $$ = a$$\widehat i$$ + $$\widehat j$$ + $$\widehat k$$; $$\overrightarrow B $$ = $$\wi

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A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is

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A particle with charge Q coulomb, tied at the end of an inextensible string of length R metre, revolves in a vertical pl

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A bullet of mass 4.2 $$ \times $$ 10$$-$$2 kg, moving at a speed of 300 ms$$-$$1, gets stuck into a block with a mass 9

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A particle with charge e and mass m, moving along the X-axis with a uniform speed u, enters a region where a uniform ele

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A unit negative charge with mass M resides at the mid-point of the straight line of length 2a adjoining two fixed charge

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Consider the circuit given here. The potential difference VBC between the points B and C is

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If the pressure, temperature and density of an ideal gas are denoted by p, T and $$\rho $$, respectively, the velocity o

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Two long parallel wires separated by 0.1 m carry currents of 1A and 2A, respectively in opposite directions. A third cur

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If $$\chi $$ stands for the magnetic susceptibility of a substance, $$\mu$$ for its magnetic permeability and $$\mu$$0 f

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Let vn and En be the respective speed and energy of an electron in the nth orbit of radius rn, in a hydrogen atom, as pr

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A small steel ball bounces on a steel plate held horizontally. On each bounce the speed of the ball arriving at the plat

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