WB JEE 2021
Paper was held on Sat, Jul 17, 2021 4:30 AM
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Chemistry

The exact order of boiling points of the compounds n-pentane, isopentane, butanone and 1-butanol is
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The maximum number of atoms that can be in one plane in the molecule p-nitrobenzonitrile are
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Cyclo [18] carbon is an allotrope of carbon with molecular formula C18. It is a ring of 18 carbon atoms, connected by si
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p-nitro-N, N-dimethylaniline cannot be represented by the resonating structures.
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The relationship between the pair of compounds shown above are respectively
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The exact order of acidity of the compounds p-nitrophenol, acetic acid, acetylene and ethanol is
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The dipeptides which may be obtained from the amino acids glycine, and alanine are
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The compounds A and B above are respectively.
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For a spontaneous reaction at all temperatures which of the following is correct?
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A given amount of Fe2+ is oxidised by x mol of $$MnO_4^ - $$ in acidic medium. The number of moles of $$C{r_2}O_7^{2 - }
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An element crystallises in a body centered cubic lattice. The edge length of the unit cell is 200 pm and the density of
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Molecular velocities of two gases at the same temperature (T) are u1 and u2. Their masses are m1 and m2 respectively. Wh
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When 20 g of naphthoic acid (C11H8O2) is dissolved in 50 g of benzene, a freezing point depression of 2K is observed. Th
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The equilibrium constant for the reaction N2(g) + O2(g) $$\rightleftharpoons$$ 2NO(g) is 4 $$\times$$ 10$$-$$4 at 2000 K
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Under the same reaction conditions, initial concentration of 1.386 mol dm$$-$$3 of a substance becomes half in 40 s and
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Which of the following solutions will have highest conductivity?
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Indicate the products (X) and (Y) in the following reactionsNa2S + nS(n = 1 $$-$$ 8) $$\to$$ (X)Na2SO3 + S $$\to$$ (Y)
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2.5 mL 0.4 M weak monoacidic base (Kb = 1 $$\times$$ 10$$-$$12 at 25$$^\circ$$C) is titrated with 2/15 M HCl in water at
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Solubility products (Ksp) of the salts of types MX, MX2 and M3X at temperature T are 4.0 $$\times$$ 10$$-$$8, 3.2 $$\tim
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The reduction potential of hydrogen half-cell will be negative if
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A saturated solution of BaSO4 at 25$$^\circ$$C is 4 $$\times$$ 10$$-$$5 M. The solubility of BaSO4 in 0.1 M Na2SO4 at th
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A solution is made by a concentrated solution of Co(NO3)2 with a concentrated solution of NaNO2 is 50% acetic acid. A so
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Extraction of a metal (M) from its sulphide ore (M2S) involves the following chemical reactions$$2{M_2}S + 3{O_2}\buildr
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The white precipitate (Y), obtained on passing colorless and odourless gas (X) through an ammoniacal solution of NaCl, l
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Which structure has delocalised $$\pi$$-electrons?
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The H3O+ ions has the following shape
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For the reaction $$_7^{14}N(\alpha ,p)\,{}^{17}O$$, 1.16 MeV (Mass equivalent = 0.00124 amu) of energy is absorbed. Mass
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A solution of NaNO3, when treated with a mixture of Zn dust and 'A' yields ammonia. 'A' can be
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Indicate the number of unpaired electrons in K3[Fe(CN)6] and K4[Fe(CN)6].
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Which of the following compounds have magnetic moment identical with [Cr(H2O)6]3+ ?
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Among the following chlorides the compounds which will be hydrolysed most easily and most slowly in aqueous NaOH solutio
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The products X and Y which are formed in the following sequence of reactions are respectively.
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The atomic masses of helium and neon are 4.0 and 20.0 amu respectively. The value of the de-Broglie wavelength of helium
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The mole fraction of a solute in a binary solution is 0.1 at 298 K, molarity of this solution is same as its molality. D
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5.75 mg of sodium vapour is converted to sodium ion. If the ionisation energy of sodium is 490 kJ mol$$-$$1 and atomic w
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The product(s) in the following sequence of reactions will be
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The compounds X and Y are respectively
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Aqueous solution of HNO3, KOH, CH3COOH and CH3COONa of identical concentration are provided. The pair(s) of solutions wh
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Reaction of silver nitrate solution with phosphorus acid produces
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N2H4 and H2O2 show similarity in
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Mathematics

If $$I = \mathop {\lim }\limits_{x \to 0} sin\left( {{{{e^x} - x - 1 - {{{x^2}} \over 2}} \over {{x^2}}}} \right)$$, the
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Let f : R $$\to$$ R be such that f(0) = 0 and $$\left| {f'(x)} \right| \le 5$$ for all x. Then f(1) is in
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If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \ov
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Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt} $$ where x > 0 and f be continuous function and f(2x) = f(x), then
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$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx} $$ is equal to
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The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \r
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If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}} $$, then the value of x is
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The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P
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The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where $$y^{
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If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is equal to (where k is an arbitrary positive
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The straight the through the origin which divides the area formed by the curves y = 2x $$-$$ x2, y = 0 and x = 1 into tw
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The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx} $$ is
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A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a po
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Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes
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let $$\alpha$$, $$\beta$$, $$\gamma$$ be three non-zero vectors which are pairwise non-collinear. if $$\alpha$$ + 3$$\be
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Let f : R $$\to$$ R be given by f(x) = | x2 $$-$$ 1 |, x$$\in$$R. Then,
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Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2
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Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p
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If |z| = 1 and z $$\ne$$ $$\pm$$ 1, then all the points representing $${z \over {1 - {z^2}}}$$ lie on
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Let C denote the set of all complex numbers. Define A = {(z, w) | z, w$$\in$$C and |z| = |w|}, B = {z, w} | z, w$$\in$$C
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Let $$\alpha$$, $$\beta$$ be the roots of the equation x2 $$-$$ 6x $$-$$ 2 = 0 with $$\alpha$$ > $$\beta$$. If an = $$\a
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For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ..... + {x^{2016}}
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Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each
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What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any
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The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is
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If M is a 3 $$\times$$ 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to
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Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos t} & {\sin t} \cr 0 & { - \sin t} & {\cos t} \cr } }
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Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)$$-$$1(AB$$-$$1)T is equal to
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If an (> 0) be the nth term of a G.P. then$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}}
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Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote t
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Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3
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Four persons A, B, C and D throw and unbiased die, turn by turn, in succession till one gets an even number and win the
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The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two successes
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Let $${S_n} = {\cot ^{ - 1}}2 + {\cot ^{ - 1}}8 + {\cot ^{ - 1}}18 + {\cot ^{ - 1}}32 + ....$$ to nth term. Then $$\math
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If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos$$\theta$$, b sin$$\
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Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular
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A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the
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The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}x - 12a$$ is
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A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X-axis, the equation of the reflected ray
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Two tangents to the circle x2 + y2 = 4 at the points A and B meet at M($$-$$4, 0). The area of the quadrilateral MAOB, w
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From a point (d, 0) three normal are drawn to the parabola y2 = x, then
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If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the
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The co-ordinate of a point on the auxiliary circle of the ellipse x2 + 2y2 = 4 corresponding to the point on the ellipse
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The locus of the centre of a variable circle which always touches two given circles externally is
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A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angle with co-ordinate a
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For $$y = {\sin ^{ - 1}}\left\{ {{{5x + 12\sqrt {1 - {x^2}} } \over {13}}} \right\};\left| x \right| \le 1$$, if $$a(1 -
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f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =
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Consider the functions f1(x) = x, f2(x) = 2 + loge x, x > 0. The graphs of the functions intersect
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The equation 6x + 8x = 10x has
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Let f : D $$\to$$ R where D = [$$-$$0, 1] $$\cup$$ [2, 4] be defined by $$f(x) = \left\{ {\matrix{ {x,} & {if} & {x \
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Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx} $$. Then
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If $$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt} $$, then $$\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}}
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The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is
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Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be def
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The $$\mathop {\lim }\limits_{x \to \infty } {\left( {{{3x - 1} \over {3x + 1}}} \right)^{4x}}$$ equals
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The area bounded by the parabolas $$y = 4{x^2},y = {{{x^2}} \over 9}$$ and the straight line y = 2 is
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If a($$\alpha$$ $$\times$$ $$\beta$$) + b($$\beta$$ $$\times$$ $$\gamma$$) + c($$\gamma$$ + $$\alpha$$) = 0, where a, b,
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If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x =
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The coefficient of a3b4c5 in the expansion of (bc + ca + ab)6 is
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Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right)
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The determinant $$\left| {\matrix{ {{a^2} + 10} & {ab} & {ac} \cr {ab} & {{b^2} + 10} & {bc} \cr {ac} & {bc
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Let R be the real line. Let the relations S and T or R be defined by $$S = \{ (x,y):y = x + 1,0
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The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle $$\alpha$$. The eq
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The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 =
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Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx} $$. Then
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If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$$ for a complex number z, then z is equa
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$$\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1} \cr {7x - 2} & {17x + 6} & {12x -
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The remainder when $${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7) is divided by 48 is
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Whichever of the following is/are correct?
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A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of $$\Delta$$ABC is (1
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Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, t
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$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt n } \over {\sqrt {{n^3}} }} + {{\sqrt n } \over {\sqrt {{{(n +
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Let $$f(x) = \left\{ {\matrix{ {0,} & {if} & { - 1 \le x \le 0} \cr {1,} & {if} & {x = 0} \cr {2,} & {if} &
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The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3
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Let f and g be periodic functions with the periods T1 and T2 respectively. Then f + g is
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Physics

A spherical convex surface of power 5 D separates object and image space of refractive indices 1.0 and $$4\over3$$ , res
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In Young's double slit experiment, light of wavelength $$\lambda$$ passes through the double slit and forms interference
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A 12.5 eV electron beam is used to bombard gaseous hydrogen at ground state. The energy level upto which the hydrogen at
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Let r, v, E be the radius of orbit, speed of electron and total energy of electron respectively in H-atom. Which of the
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What is the value of current through the diode in the circuit given?
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For the given logic circuit, the output Y for inputs (A = 0, B = 1) and (A = 0, B = 0) respectively are
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From dimensional analysis, the Rydberg constant can be expressed in terms of electric charge (e), mass (m) and Planck co
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Three blocks are pushed with a force F across a frictionless table as shown in figure above. Let N1 be the contact force
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A block of mass m slides with speed v on a frictionless table towards another stationary block of mass m. A massless spr
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The acceleration versus distance graph for a particle moving with initial velocity 5 m/s is shown in the figure. The vel
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A simple pendulum, consisting of a small ball of mass m attached to a massless string hanging vertically from the ceilin
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In case of projectile motion, which one of the following figures represent variation of horizontal component of velocity
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A uniform thin rod of length L, mass m is lying on a smooth horizontal table. A horizontal impulse P is suddenly applied
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Centre of mass (CM) of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and CM of another syste
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A body of density 1.2 $$\times$$ 103 kg/m3 is dropped from rest from a height 1 m into a liquid to density 2.4 $$\times$
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Two solid spheres S1 and S2 of same uniform density fall from rest under gravity in a viscous medium and after sometime,
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In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas
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If pressure of real gas O2, in a container is given by $$p = {{RT} \over {2V - b}} - {a \over {4{b^2}}}$$, then the mass
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300 g of water at 25$$^\circ$$C is added to 100 g of ice at 0$$^\circ$$C. The final temperature of the mixture is
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The variation of electric field along the Z-axis due to a uniformly charged circular ring of radius a in XY-plane as sho
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A metal sphere of radius R carrying charge q is surrounded by a thick concentric metal shell of inner and outer radii a
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Three infinite plane sheets carrying uniform charge densities $$-$$ $$\sigma$$, 2$$\sigma$$, 4$$\sigma$$ are placed para
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Two point charges +q1 and +q2 are placed a finite distance d apart. It is desired to put a third charge q3 in between th
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Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire pass
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A thin charged rod is bent into the shape of a small circle of radius R, the charge per unit length of the rod being $$\
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For two types of magnetic materials A and B, variation of $$1\over\chi$$ ($$\chi$$ : susceptibility) versus temperature
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The rms value of potential difference V shown in the figure is
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The carbon resistor with colour code is shown in the figure. There is no fourth band in the resistor. The value of the r
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Consider a pure inductive AC circuit as shown in the figure. If the average power consumed is P, then
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The cross-section of a reflecting surface is represented by the equation x2 + y2 = R2 as shown in the figure. A ray trav
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For a plane electromagnetic wave, the electric field is given by$$ \overrightarrow{E} = 90\sin (0.5 \times {10^3}x + 1.5
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Two metal wires of identical dimensions are connected in series. If $$\sigma$$1 and $$\sigma$$2 are the electrical condu
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A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity $$\omega
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An ideal gas of molar mass M is contained in a very tall vertical cylindrical column in the uniform gravitational field.
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Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the exte
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A small bar magnet of dipole moment M is moving with speed v along x-direction towards a small closed circular conductin
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Electric field component of an EM radiation varies with time as E = a (cos$$\omega$$0t + sin$$\omega$$t cos$$\omega$$0t)
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Consider the p - V diagram for 1 mole of an ideal monatomic gas shown in the figure. Which of the following statements i
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The potential energy of a particle of mass 0.02 kg moving along X-axis is given by V = Ax (x $$-$$ 4) J, where x is in m
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A particle of mass m and charge q moving with velocity v enters region-b from region-a along the normal to the boundary
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