WB JEE 2022
JEE 2022 Previous Year
3 hDuration
200Total Marks
155Questions
3Sections
Instructions
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Paper Structure
Chemistry
Chemistry
Q1.
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The product of the following reaction is :
Q2.
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The product of the following hydrogenation reaction is:
Q3.
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The above conversion can be carried out by,
The above conversion can be carried out by,
Q4.
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Which of the following is radioactive?
Q5.
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The metal-pair that can produce nascent hydrogen in alkaline medium is :
Q6.
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The correct pair of electron affinity order is
Q7.
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The correct order of acidity of the following hydra acids is
Q8.
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Oxidation states of Cr in K~2~Cr~2~O~7~ and CrO~5~ are respectively
Q9.
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In Bohr model of atom, radius of hydrogen atom in ground state is r~1~ and radius of He^(+) ion in ground state is r~2~. Which of the following is correct?
Q10.
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Which one of the following is the correct set of four quantum numbers (n, 1, m, s) ?
Q11.
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The number of unpaired electron in Mn^(2+) ion is
Q12.
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The de-Broglie wavelength ($$\lambda$$) for electron (e), proton (p) and He^(2+) ion ($$\alpha$$) are in the following order. Speed of e, p and $$\alpha$$ are the same
Q13.
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During the preparation of NH~3~ in Haber's process, the promoter(s) used is/are -
Q14.
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What is the correct order of acidity of salicylic acid, 4-hydroxybenzoic acid, and 2, 6-dihydroxybenzoic acid ?
Q15.
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The boiling point of the water is higher than liquid HF. The reason is that
Q16.
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XeF~2~, NO~2~, HCN, ClO~2~, CO~2~.
Identify the non-linear molecule-pair from the above mentioned molecules.
Q17.
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The correct bond order of B-F bond in BF~3~ molecule is :
Q18.
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Which of the statements are incorrect?
Q19.
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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 above equation. What is the volume of oxygen (at STP) needed for complete combustion of 39 gram of liquid benzene?
Q20.
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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 mass of M is
Q21.
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1 mL of water has 25 drops. Let N~0~ be the Avogadro number. What is the number of molecules present in 1 drop of water ? (Density of water = 1 g/mL)
Q22.
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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 solution in water?
Q23.
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The correct statement(s) about B~2~H~6~ is /are :
Q24.
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To a solution of colourless sodium salt, a solution of lead nitrate was added to have a white precipitate which dissolves in warm water and reprecipitates on cooling. Which of the following acid radical is present in the salt?
Q25.
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A sample of MgCO~3~ is dissolved in dil. HCl and the solution is neutralized with ammonia and buffered with NH~4~Cl / NH~4~OH. Disodium hydrogen phosphate reagent is added to the resulting solution. A white precipitate is formed. What is the formula of the precipitate?
Q26.
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The average speed of H~2~ at T~1~K is equal to that of O~2~ at T~2~K. The ratio T~1~ : T~2~ is
Q27.
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Avogadro's law is valid for
Q28.
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Let (C~rms~)~H2~ is the r.m.s. speed of H~2~ at 150 K. At what temperature, the most probable speed of helium [C~mp~)~He~] will be half of (C~rms~)~H2~ ?
Q29.
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Hybridisation of the negative carbons in (1) and (2) are
Hybridisation of the negative carbons in (1) and (2) are
Q30.
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The correct order of relative stability for the given free radicals is :
Q31.
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Pick the correct statement.
Q32.
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Choose the correct statement for the [Ni(CN)~4~]^(2$$-$$) complex ion (Atomic no. of Ni = 28)
Q33.
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Sodium nitroprusside is :
Q34.
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How many monobriminated product(s) (including stereoisomers) would form in the free radical bromination of n-butane?
Q35.
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The enol form in which ethyle-3-oxobutanoate exists is
Q36.
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The correct order of relative stability of the given conformers of n-butane is
Q37.
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The correct relationship between molecules I and II is
The correct relationship between molecules I and II is
Q38.
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The major product of the following reaction is
$${F_3}C - CH = C{H_2} + HBr \to $$
Q39.
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The number of atoms in body centred and face centred cubic unit cell respectively are
Q40.
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Which of the following would produce enantiomeric products when reacted with methyl magnesium iodide?
Mathematics
Mathematics
Q1.
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Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then
Q2.
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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 lengths of the sides of a triangle which is
Q3.
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If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow \gamma = \widehat i + \widehat k$$ then the maximum value of $$\left[ {\overrightarrow \alpha \overrightarrow \beta \overrightarrow \gamma } \right]$$ is
Q4.
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If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ and $$\overrightarrow c $$ is unit vector perpendicular to $$\overrightarrow a $$ and coplanar with $$\overrightarrow a $$ and $$\overrightarrow b $$, then unit vector $$\overrightarrow d $$ perpendicular to both $$\overrightarrow a $$ and $$\overrightarrow c $$ is
Q5.
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Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is
Q6.
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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 $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int\limits_0^x {f(t)dt} } $$ and f (0) = 0. Then
Q7.
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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 that the determinant chosen is non-zero is
Q8.
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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 $$P(C) = {{1 - 2x} \over 2}$$. Then the set of possible values of x are in
Q9.
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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 the least value is
Q10.
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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
Q11.
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The values of a, b, c for which the function $$f(x) = \left\{ \matrix{
{{\sin (a + 1)x + \sin x} \over x},x 0 \hfill \cr} \right.$$ is continuous at x = 0, are
Q12.
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$$\mathop {\lim }\limits_{x \to 0} \left( {{1 \over x}\ln \sqrt {{{1 + x} \over {1 - x}}} } \right)$$ is
Q13.
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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
Q14.
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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
Q15.
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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. Then f(x) is differentiable at x = 0
Q16.
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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 are positive constants. The maximum velocity attained by the particle is
Q17.
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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 above the ground when the stone reaches the ground after 4 sec is [g = 32 ft/sec^(2)]
Q18.
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If $$\Delta (x) = \left| {\matrix{
{x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr
{x - 1} & {{x^2}} & {{{(x + 1)}^3}} \cr
x & {{{(x + 1)}^2}} & {{{(x + 2)}^3}} \cr
} } \right|$$, then coefficient of x in $$\Delta$$x is
Q19.
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Let $$\Delta = \left| {\matrix{
{\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr
{\cos \theta \cos \phi } & {\cos \theta \sin \phi } & { - \sin \theta } \cr
{ - \sin \theta \sin \phi } & {\sin \theta \cos \phi } & 0 \cr
} } \right|$$. Then
Q20.
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Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{
1 & 2 & 4 \cr
2 & 1 & 2 \cr
1 & 2 & {(a - 4)} \cr
} } \right)\left( {\matrix{
x \cr
y \cr
z \cr
} } \right) = \left( {\matrix{
6 \cr
4 \cr
a \cr
} } \right)$$ possesses(possess) unique solution ?
Q21.
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The solution of $$\det (A - \lambda {I_2}) = 0$$ be 4 and 8 and $$A = \left( {\matrix{
2 & 2 \cr
x & y \cr
} } \right)$$. Then
(I~2~ is identity matrix of order 2)
Q22.
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If $$p = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \right]$$ is the adjoint of the $$3 \times 3$$ matrix A and det A = 4, then $$\alpha$$ is equal to
Q23.
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If $$A = \left( {\matrix{
1 & 1 \cr
0 & i \cr
} } \right)$$ and $${A^{2018}} = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$, then $$(a + d)$$ equals
Q24.
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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 to the x-axis is
Q25.
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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
Q26.
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If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 < {\alpha _1},{\alpha _2},....\,{\alpha _n} < \pi /2$$, then the maximum value of $$(\cos {\alpha _1})(\cos {\alpha _2}).....(\cos {\alpha _n})$$ is given by
Q27.
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$$I = \int {\cos (\ln x)dx} $$. Then I =
Q28.
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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 of integration)
Q29.
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If P~1~P~2~ and P~3~P~4~ are two focal chords of the parabola y^(2) = 4ax then the chords P~1~P~3~ and P~2~P~4~ intersect on the
Q30.
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AB is a chord of a parabola y^(2) = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is
Q31.
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Let the tangent and normal at any point P(at^(2), 2at), (a > 0), on the parabola y^(2) = 4ax meet the axis of the parabola at T and G respectively. Then the radius of the circle through P, T and G is
Q32.
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From the point ($$-$$1, $$-$$6), two tangents are drawn to y^(2) = 4x. Then the angle between the two tangents is
Q33.
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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 is
Q34.
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The point of contact of the tangent to the parabola y^(2) = 9x which passes through the point (4, 10) and makes an angle $$\theta$$ with the positive side of the axis of the parabola where tan$$\theta$$ > 2, is
Q35.
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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 positive direction of x-axis. If this line meets the curve $${x^2} = 4y - 9$$ at A and B, then |AB| is equal to
Q36.
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The number of zeros at the end of $$\left| \!{\underline {\,
{100} \,}} \right. $$ is
Q37.
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If x satisfies the inequality $${\log _{25}}{x^2} + {({\log _5}x)^2} < 2$$, then x belongs to
Q38.
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Consider the equation $$y - {y_1} = m(x - {x_1})$$. If m and x~1~ are fixed and different lines are drawn for different values of y~1~, then
Q39.
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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
Q40.
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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, then the line passes through the fixed point
Q41.
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Let R and S be two equivalence relations on a non-void set A. Then
Q42.
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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 $$\cap$$ Q = $$\varphi $$ is
Q43.
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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 defined. Let g . f be injective mapping. Then
Q44.
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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 correct?
Q45.
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If z = x $$-$$ iy and $${z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)$$, then $${{\left( {{x \over p} + {y \over q}} \right)} \over {({p^2} + {q^2})}}$$ is equal to
Q46.
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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 of z)
Q47.
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Let z~1~ and z~2~ be two non-zero complex numbers. Then
Q48.
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The line y = x + 5 touches
Q49.
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Let $$P(3\sec \theta ,2\tan \theta )$$ and $$Q(3\sec \phi ,2\tan \phi )$$ be two points on $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ such that $$\theta + \phi = {\pi \over 2},0 < \theta ,\phi < {\pi \over 2}$$. Then the ordinate of the point of intersection of the normals at P and Q is
Q50.
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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 $$\Delta OPQ$$ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies
Q51.
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Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is
Q52.
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The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is
Q53.
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Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then
Q54.
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Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then
Q55.
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$$f:X \to R,X = \{ x|0 < x < 1\} $$ is defined as $$f(x) = {{2x - 1} \over {1 - |2x - 1|}}$$. Then
Q56.
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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
Q57.
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Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then
Q58.
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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 is arbitrary real constant) where f(x) is equal to
Q59.
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If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to
Q60.
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If the transformation $$z = \log \tan {x \over 2}$$ reduces the differential equation
$${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$ into the form $${{{d^2}y} \over {d{z^2}}} + ky = 0$$ then k is equal to
Q61.
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+2 / 0.5
A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is
Q62.
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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 common chord PQ. The equation of PQ is
Q63.
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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 angle is always constant and is $$\alpha$$. Let x-axis be along AB and the origin be at A. Then the locus of the vertex is
Q64.
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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 of the other tangent through the origin is
Q65.
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+2 / 0
Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed be greatest?
Q66.
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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 is bisected at the point of contact. The equation of the curve is
Q67.
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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 angle at the origin O, then $${1 \over {O{A^2}}} + {1 \over {O{B^2}}}$$ equals to
Q68.
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Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
Q69.
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If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then
Q70.
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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 a row so that neighbouring balls are of different colours is
Q71.
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If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} $$, $${I_2} = \int\limits_0^1 {{e^{ - {x^2}}}{{\cos }^2}x\,dx} $$, $${I_3} = \int\limits_0^1 {{e^{ - {x^2}}}dx} $$, $${I_4} = \int\limits_0^1 {{e^{ - {x^2}/2}}dx} $$, then
Q72.
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Let f be derivable in [0, 1], then
Q73.
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Let $$\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x} \over x} - 1,\left( {0 < x < {\pi \over 4}} \right)} $$. Then a and b are given by
Q74.
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The value of $$\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{\sin x}}} \over {{{(\cos x)}^{\sin x}} + {{(\sin x)}^{\cos x}}}}dx} $$ is
Q75.
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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
Physics
Physics
Q1.
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The kinetic energy (E~k~) of a particle moving along X-axis varies with its position (X) as shown in the figure. The force acting on the particle at X = 10 m is
Q2.
mcq multi
+2 / 0
A particle is moving in x-y plane according to $$\overrightarrow r = b\cos \omega t\widehat i + b\sin \omega t\widehat j$$, where $$\omega$$ is constant. Which of the following statement(s) is/are true?
Q3.
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The expression $$\overline A (A + B) + (B + AA)(A + \overline B )$$ simplifies to
Q4.
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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 minimum current required to pass through the Zener to act as a voltage regulator is 10 mA and maximum allowed current through Zener is 40 mA. The maximum value of R~s~ for Zener to act as a voltage regulator is
Q5.
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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 the interfering waves is $$\lambda$$, ($$\lambda$$ being the wavelength of light used) is I. The intensity at a point where the path difference is $${\lambda \over 4}$$ will be (assume two waves have same amplitude)
Q6.
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In Young's double slit experiment with a monochromatic light, maximum intensity is 4 times the minimum intensity in the interference pattern. What is the ratio of the intensities of the two interfering waves?
Q7.
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A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motion, the phase difference ($$\delta$$) between the two motion is
Q8.
mcq single
+1 / 0.25
A particle is moving in an elliptical orbit as shown in figure. If $$\overrightarrow p $$, $$\overrightarrow L $$ and $$\overrightarrow r $$ denote the linear momentum, angular momentum and position vector of the particle (from focus O) respectively at a point A, then the direction of $$\overrightarrow \alpha $$ = $$\overrightarrow p $$ $$\times$$ $$\overrightarrow L $$ is along.
A particle is moving in an elliptical orbit as shown in figure. If $$\overrightarrow p $$, $$\overrightarrow L $$ and $$\overrightarrow r $$ denote the linear momentum, angular momentum and position vector of the particle (from focus O) respectively at a point A, then the direction of $$\overrightarrow \alpha $$ = $$\overrightarrow p $$ $$\times$$ $$\overrightarrow L $$ is along.
Q9.
mcq single
+1 / 0.25
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. The magnitude of the angular momentum of the particle about the origin at time t when it is at the maximum height of the trajectory is proportional to
Q10.
mcq single
+1 / 0.25
Three particles, each of mass 'm' grams situated at the vertices of an equilateral $$\Delta$$ABC of side 'a' cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC in g-cm^(2) units will be
Q11.
mcq single
+1 / 0.25
In a closed circuit there is only a coil of inductance L and resistance 100 $$\Omega$$. The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by 5 Weber. What amount of charge will flow in the circuit as a result?
Q12.
mcq single
+1 / 0.25
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) is
Q13.
mcq single
+1 / 0.25
Consider a thermodynamic process where integral energy $$U = A{P^2}V$$ (A = constant). If the process is performed adiabatically, then
Q14.
mcq single
+1 / 0.25
Certain amount of an ideal gas is taken from its initial state 1 to final state 4 through the paths 1 $$\to$$ 2 $$\to$$ 3 $$\to$$ 4 as shown in figure. AB, CD, EF are all isotherms. If v~p~ is the most probable speed of the molecules, then
Q15.
mcq single
+2 / 0.5
One mole of an ideal monoatomic gas expands along the polytrope PV^(3) = constant from V~1~ to V~2~ at a constant pressure P~1~. The temperature during the process is such that molar specific heat $${C_V} = {{3R} \over 2}$$. The total heat absorbed during the process can be expressed as
Q16.
mcq single
+1 / 0.25
27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?
Q17.
mcq multi
+2 / 0
Two wires A and B of same length are made of same material. Load (F) vs. elongation (x) graph for these two wires is shown in the figure. Then which of the following statement(s) is/are true?
Two wires A and B of same length are made of same material. Load (F) vs. elongation (x) graph for these two wires is shown in the figure. Then which of the following statement(s) is/are true?
Q18.
mcq multi
+2 / 0
A hemisphere of radius R is placed in a uniform electric field E so that its axis is parallel to the field. Which of the following statement(s) is/are true?
A hemisphere of radius R is placed in a uniform electric field E so that its axis is parallel to the field. Which of the following statement(s) is/are true?
Q19.
mcq single
+1 / 0.25
The electric potential for an electric field directed parallel to X-axis is shown in the figure. Choose the correct plot of electric field strength.
Q20.
mcq single
+1 / 0.25
Consider two concentric conducting sphere of radii R and 2R respectively. The inner sphere is given a charge +Q. The other sphere is grounded. The potential at $$r = {{3R} \over 2}$$ is
Q21.
mcq single
+1 / 0.25
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 a small displacement along y direction, the force acting on q is proportional to
Q22.
mcq single
+1 / 0.25
A neutral conducting solid sphere of radius R has two spherical cavities of radius a and b as shown in the figure. Centre to centre distance between two cavities is c. q~a~ and q~b~ charges are placed at the centres of cavities respectively. The force between q~a~ and q~b~ is
A neutral conducting solid sphere of radius R has two spherical cavities of radius a and b as shown in the figure. Centre to centre distance between two cavities is c. q~a~ and q~b~ charges are placed at the centres of cavities respectively. The force between q~a~ and q~b~ is
Q23.
mcq single
+1 / 0.25
A body of mass m is thrown vertically upward with speed $$\sqrt3$$ v~e~, where v~e~ is the escape velocity of a body from earth surface. The final velocity of the body is
Q24.
mcq single
+2 / 0.5
Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities +$$\sigma$$, $$-$$$$\sigma$$ and +$$\sigma$$ respectively. The potential of shell B is
Q25.
mcq single
+2 / 0.5
Find the equivalent capacitance between A and B of the following arrangement :
Q26.
mcq single
+1 / 0.25
The human eye has an approximate angular resolution of $$\theta$$ = 5.8 $$\times$$ 10^($$-$$4) rad and typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance d should a printed page be held so that one does not see the individual dots?
Q27.
mcq single
+1 / 0.25
The Entropy (S) of a black hole can be written as $$S = \beta {k_B}A$$, where k~B~ is the Boltzmann constant and A is the area of the black hole. The $$\beta$$ has dimension of
Q28.
mcq single
+1 / 0.25
Given : The percentage error in the measurements of A, B, C and D are respectively, 4%, 2%, 3% and 1%. The relative error in $$Z = {{{A^4}{B^{{1 \over 3}}}} \over {C{D^{{3 \over 2}}}}}$$ is
Q29.
mcq multi
+2 / 0
A sample of hydrogen atom in its ground state is radiated with photons of 10.2 eV energies. The radiation from the sample is absorbed by excited ionized He^(+). Thenwhich of the following statement/s is/are true?
Q30.
mcq single
+1 / 0.25
Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of $${h \over {2\pi }}$$. The largest possible wavelength emitted by hydrogen atoms in visible range in a world according to Bohr's model will be,
(Consider hc = 1242 Mev-fm)
Q31.
mcq single
+1 / 0.25
If the kinetic energies of an electron, an alpha particle and a proton having same de-Broglie wavelength are $${\varepsilon _1},{\varepsilon _2}$$ and $${\varepsilon _3}$$ respectively, then
Q32.
mcq single
+1 / 0.25
If a string, suspended from the ceiling is given a downward force F~1~, its length becomes L~1~. Its length is L~2~, if the downward force is F~2~. What is its actual length?
Q33.
mcq single
+2 / 0.5
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 100 m/s, the time of contact on the ball is 0.02 s. If the force decreases to zero linearly with time, then the force at the beginning of the contact is
Q34.
mcq single
+1 / 0.25
A straight wire is placed in a magnetic field that varies with distance x from origin as $$\overrightarrow B = {B_0}\left( {2 - {x \over a}} \right)\widehat k$$. Ends of wire are at (a, 0) and (2a, 0) and it carries a current I. If force on wire is $$\overrightarrow F = I{B_0}\left( {{{ka} \over 2}} \right)\widehat j$$, then value of k is
Q35.
mcq single
+1 / 0.25
An electron revolves around the nucleus in a circular path with angular momentum $$\overrightarrow L $$. A uniform magnetic field $$\overrightarrow B $$ is applied perpendicular to the plane of its orbit. If the electron experiences a torque $$\overrightarrow T $$, then
Q36.
mcq multi
+2 / 0
As shown in figure, a rectangular loop of length 'a' and width 'b' and made of a conducting material of uniform cross-section is kept in a horizontal plane where a uniform magnetic field of intensity B is acting vertically downward. Resistance per unit length of the loop is $$\lambda$$ $$\Omega$$/m. If the loop is pulled with uniform velocity 'v' in horizontal direction, which of the following statement is/are true?
As shown in figure, a rectangular loop of length 'a' and width 'b' and made of a conducting material of uniform cross-section is kept in a horizontal plane where a uniform magnetic field of intensity B is acting vertically downward. Resistance per unit length of the loop is $$\lambda$$ $$\Omega$$/m. If the loop is pulled with uniform velocity 'v' in horizontal direction, which of the following statement is/are true?
Q37.
mcq single
+1 / 0.25
Two infinite line-charges parallel to each other are moving with a constant velocity v in the same direction as shown in the figure. The separation between two line-charges is d. The magnetic attraction balances the electric repulsion when, [ c = speed of light in free space ]
Two infinite line-charges parallel to each other are moving with a constant velocity v in the same direction as shown in the figure. The separation between two line-charges is d. The magnetic attraction balances the electric repulsion when, [ c = speed of light in free space ]
Q38.
mcq single
+2 / 0.5
A horizontal semi-circular wire of radius r is connected to a battery through two similar springs X and Y to an electric cell, which sends current I through it. A vertically downward uniform magnetic field B is applied on the wire, as shown in the figure. What is the force acting on each spring?
Q39.
mcq single
+1 / 0.25
A battery of emf E and internal resistance r is connected with an external resistance R as shown in the figure. The battery will act as a constant voltage source if
A battery of emf E and internal resistance r is connected with an external resistance R as shown in the figure. The battery will act as a constant voltage source if
Q40.
mcq single
+1 / 0.25
When an AC source of emf E with frequency $$\omega$$ = 100 Hz is connected across a circuit, the phase difference between E and current I in the circuit is observed to be $${\pi \over 4}$$ as shown in the figure. If the circuit consist of only RC or RL in series, then
