Chemistry
1. A sample of MgCO3 is dissolved in dil. HCl and the solution is neutralized with ammonia and buffered with NH4Cl / NH4OH. 2. XeF2, NO2, HCN, ClO2, CO2.
Identify the non-linear molecule-pair from the above mentioned molecules. 3. The number of atoms in body centred and face centred cubic unit cell respectively are 4. The number of unpaired electron in Mn2+ ion is 5. The average speed of H2 at T1K is equal to that of O2 at T2K. The ratio T1 : T2 is 6. Sodium nitroprusside is : 7. Choose the correct statement for the [Ni(CN)4]2$$-$$ complex ion (Atomic no. of Ni = 28) 8. The boiling point of the water is higher than liquid HF. The reason is that 9. The metal-pair that can produce nascent hydrogen in alkaline medium is : 10. The correct bond order of B-F bond in BF3 molecule is : 11. Which of the following is radioactive? 12. The correct order of acidity of the following hydra acids is 13. To a solution of colourless sodium salt, a solution of lead nitrate was added to have a white precipitate which dissolve 14. Oxidation states of Cr in K2Cr2O7 and CrO5 are respectively 15. The correct order of relative stability for the given free radicals is :
16.
Hybridisation of the negative carbons in (1) and (2) are 17.
The correct relationship between molecules I and II is 18. The enol form in which ethyle-3-oxobutanoate exists is 19. How many monobriminated product(s) (including stereoisomers) would form in the free radical bromination of n-butane? 20. What is the correct order of acidity of salicylic acid, 4-hydroxybenzoic acid, and 2, 6-dihydroxybenzoic acid ? 21. How much solid oxalic acid (Molecular weight 126) has to be weighed to prepare 100 ml. exactly 0.1 (N) oxalic acid solut 22. The major product of the following reaction is
$${F_3}C - CH = C{H_2} + HBr \to $$ 23. The correct order of relative stability of the given conformers of n-butane is
24. $${C_6}{H_6}(liq) + {{15} \over 2}{O_2}(g) \to 6C{O_2}(g) + 3{H_2}O(liq)$$
Benzene burns in oxygen according to the abov 25. Avogadro's law is valid for 26. 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 27. The de-Broglie wavelength ($$\lambda$$) for electron (e), proton (p) and He2+ ion ($$\alpha$$) are in the following orde 28. 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 ? 29. 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 30. Which one of the following is the correct set of four quantum numbers (n, 1, m, s) ? 31. 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 32. The correct pair of electron affinity order is 33. The product of the following reaction is :
34. The product of the following hydrogenation reaction is:
35. Pick the correct statement. 36. During the preparation of NH3 in Haber's process, the promoter(s) used is/are - 37. The correct statement(s) about B2H6 is /are : 38. Which of the following would produce enantiomeric products when reacted with methyl magnesium iodide? 39.
The above conversion can be carried out by, 40. Which of the statements are incorrect?
Mathematics
1. The values of a, b, c for which the function $$f(x) = \left\{ \matrix{
{{\sin (a + 1)x + \sin x} \over x},x 0 \hfill 2. Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is 3. Let $$f(x) = {a_0} + {a_1}|x| + {a_2}|x{|^2} + {a_3}|x{|^3}$$, where $${a_0},{a_1},{a_2},{a_3}$$ are real constants. The 4. If $$y = {e^{{{\tan }^{ - 1}}x}}$$, then 5. $$\mathop {\lim }\limits_{x \to 0} \left( {{1 \over x}\ln \sqrt {{{1 + x} \over {1 - x}}} } \right)$$ is 6. Let f : [a, b] $$\to$$ R be continuous in [a, b], differentiable in (a, b) and f(a) = 0 = f(b). Then 7. $$I = \int {\cos (\ln x)dx} $$. Then I =
8. Let f be derivable in [0, 1], then 9. Let $$\int {{{{x^{{1 \over 2}}}} \over {\sqrt {1 - {x^3}} }}dx = {2 \over 3}g(f(x)) + c} $$ ; then
(c denotes constant o 10. The value of $$\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{\sin x}}} \over {{{(\cos x)}^{\sin x}} + {{(\sin x)}^{\cos 11. Let $$\mathop {\lim }\limits_{ \in \to 0 + } \int\limits_ \in ^x {{{bt\cos 4t - a\sin 4t} \over {{t^2}}}dt = {{a\sin 4x 12. Let $$f(x) = \int\limits_{\sin x}^{\cos x} {{e^{ - {t^2}}}dt} $$. Then $$f'\left( {{\pi \over 4}} \right)$$ equals 13. If $$x{{dy} \over {dx}} + y = x{{f(xy)} \over {f'(xy)}}$$, then $$|f(xy)|$$ is equal to 14. A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes 15. The solution of $$\cos y{{dy} \over {dx}} = {e^{x + \sin y}} + {x^2}{e^{\sin y}}$$ is $$f(x) + {e^{ - \sin y}} = C$$ (C 16. The point of contact of the tangent to the parabola y2 = 9x which passes through the point (4, 10) and makes an angle $$ 17. Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then 18. If $$\overrightarrow a = \widehat i + \widehat j - \widehat k$$, $$\overrightarrow b = \widehat i - \widehat j + \wide 19. If the equation of one tangent to the circle with centre at (2, $$-$$1) from the origin is 3x + y = 0, then the equation 20. Area of the figure bounded by the parabola $${y^2} + 8x = 16$$ and $${y^2} - 24x = 48$$ is 21. A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k 22. If a, b, c are in G.P. and log a $$-$$ log 2b, log 2b $$-$$ log 3c, log 3c $$-$$ log a are in A.P., then a, b, c are the 23. Let $${a_n} = {({1^2} + {2^2} + .....\,{n^2})^n}$$ and $${b_n} = {n^n}(n!)$$. Then 24. The number of zeros at the end of $$\left| \!{\underline {\,
{100} \,}} \right. $$ is 25. If $$|z - 25i| \le 15$$, then Maximum arg(z) $$-$$ Minimum arg(z) is equal to
(arg z is the principal value of argument 26. If z = x $$-$$ iy and $${z^{{1 \over 3}}} = p + iq(x,y,p,q \in R)$$, then $${{\left( {{x \over p} + {y \over q}} \right) 27. If a, b are odd integers, then the roots of the equation $$2a{x^2} + (2a + b)x + b = 0$$, $$a \ne 0$$ are 28. 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 29. Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then 30. 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 $$ 31. Under which of the following condition(s) does(do) the system of equations $$\left( {\matrix{
1 & 2 & 4 \cr
2 & 32. If $$\Delta (x) = \left| {\matrix{
{x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr
{x - 1} & {{x^2}} & {{{(x + 1)}^3}} 33. If $$p = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \right]$$ is the adjoint 34. If $$A = \left( {\matrix{
1 & 1 \cr
0 & i \cr
} } \right)$$ and $${A^{2018}} = \left( {\matrix{
a & b \c 35. 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 36. For the mapping $$f:R - \{ 1\} \to R - \{ 2\} $$, given by $$f(x) = {{2x} \over {x - 1}}$$, which of the following is c 37. A, B, C are mutually exclusive events such that $$P(A) = {{3x + 1} \over 3}$$, $$P(B) = {{1 - x} \over 4}$$ and $$P(C) = 38. A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability 39. If $$(\cot {\alpha _1})(\cot {\alpha _2})\,......\,(\cot {\alpha _n}) = 1,0 40. 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 41. 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 42. If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is 43. A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the po 44. 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 45. Let $$P(3\sec \theta ,2\tan \theta )$$ and $$Q(3\sec \phi ,2\tan \phi )$$ be two points on $${{{x^2}} \over 9} - {{{y^2} 46. Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)2 = 2(x $$-$$ 4). Then the locus of mid-point of PQ i 47. AB is a chord of a parabola y2 = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The 48. AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right 49. The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y $$-$$ z + 4 = 0 and parallel 50. The line $$x - 2y + 4z + 4 = 0$$, $$x + y + z - 8 = 0$$ intersect the plane $$x - y + 2z + 1 = 0$$ at the point 51. If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx} $$, $${I_2} = \int\limits_0^1 {{e^{ - {x^ 52. $$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + 1} \over {x + 1}} - ax - b} \right),(a,b \in R)$$ = 0. Then 53. If the transformation $$z = \log \tan {x \over 2}$$ reduces the differential equation $${{{d^2}y} \over {d{x^2}}} + \cot 54. From the point ($$-$$1, $$-$$6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is 55. If $${\overrightarrow \alpha }$$ is a unit vector, $$\overrightarrow \beta = \widehat i + \widehat j - \widehat k$$, 56. The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is 57. A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the ori 58. Let the tangent and normal at any point P(at2, 2at), (a > 0), on the parabola y2 = 4ax meet the axis of the parabola at 59. The value of a for which the sum of the squares of the roots of the equation $${x^2} - (a - 2)x - a - 1 = 0$$ assumes th 60. If x satisfies the inequality $${\log _{25}}{x^2} + {({\log _5}x)^2} 61. The solution of $$\det (A - \lambda {I_2}) = 0$$ be 4 and 8 and $$A = \left( {\matrix{
2 & 2 \cr
x & y \cr
} 62. If P1P2 and P3P4 are two focal chords of the parabola y2 = 4ax then the chords P1P3 and P2P4 intersect on the 63. $$f:X \to R,X = \{ x|0 64. Let f be a non-negative function defined in $$[0,\pi /2]$$, f' exists and be continuous for all x and $$\int\limits_0^x 65. PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OP 66. From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon ab 67. Let $$f(x) = {x^2} + x\sin x - \cos x$$. Then 68. Let z1 and z2 be two non-zero complex numbers. Then 69. Let $$\Delta = \left| {\matrix{
{\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr
{\cos 70. Let R and S be two equivalence relations on a non-void set A. Then 71. Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on 72. Consider the equation $$y - {y_1} = m(x - {x_1})$$. If m and x1 are fixed and different lines are drawn for different va 73. Let p(x) be a polynomial with real co-efficient, p(0) = 1 and p'(x) > 0 for all x $$\in$$ R. Then 74. Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of t 75. The line y = x + 5 touches
Physics
1.
Two infinite line-charges parallel to each other are moving with a constant velocity v in the same direction as shown i 2. The electric potential for an electric field directed parallel to X-axis is shown in the figure. Choose the correct plot 3. An electron revolves around the nucleus in a circular path with angular momentum $$\overrightarrow L $$. A uniform magne 4. A straight wire is placed in a magnetic field that varies with distance x from origin as $$\overrightarrow B = {B_0}\le 5. In a closed circuit there is only a coil of inductance L and resistance 100 $$\Omega$$. The coil is situated in a unifor 6. When an AC source of emf E with frequency $$\omega$$ = 100 Hz is connected across a circuit, the phase difference betwee 7.
A battery of emf E and internal resistance r is connected with an external resistance R as shown in the figure. The bat 8. If the kinetic energies of an electron, an alpha particle and a proton having same de-Broglie wavelength are $${\varepsi 9. In a Young's double slit experiment, the intensity of light at a point on the screen where the path difference between t 10. In Young's double slit experiment with a monochromatic light, maximum intensity is 4 times the minimum intensity in the 11. The human eye has an approximate angular resolution of $$\theta$$ = 5.8 $$\times$$ 10$$-$$4 rad and typical photo printe 12. Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of $${h \over {2\pi }}$$ 13. A Zener diode having break down voltage Vz = 6V is used in a voltage regulator circuit as shown in the figure. The minim 14. The expression $$\overline A (A + B) + (B + AA)(A + \overline B )$$ simplifies to 15. Given : The percentage error in the measurements of A, B, C and D are respectively, 4%, 2%, 3% and 1%. The relative erro 16. The Entropy (S) of a black hole can be written as $$S = \beta {k_B}A$$, where kB is the Boltzmann constant and A is the 17. The kinetic energy (Ek) of a particle moving along X-axis varies with its position (X) as shown in the figure. The force 18.
A particle is moving in an elliptical orbit as shown in figure. If $$\overrightarrow p $$, $$\overrightarrow L $$ and $ 19. A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency 20. A body of mass m is thrown with velocity u from the origin of a co-ordinate axes at an angle $$\theta$$ with the horizon 21. Three particles, each of mass 'm' grams situated at the vertices of an equilateral $$\Delta$$ABC of side 'a' cm (as show 22. A body of mass m is thrown vertically upward with speed $$\sqrt3$$ ve, where ve is the escape velocity of a body from ea 23. If a string, suspended from the ceiling is given a downward force F1, its length becomes L1. Its length is L2, if the do 24. 27 drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy? 25. Certain amount of an ideal gas is taken from its initial state 1 to final state 4 through the paths 1 $$\to$$ 2 $$\to$$ 26. Consider a thermodynamic process where integral energy $$U = A{P^2}V$$ (A = constant). If the process is performed adiab 27. One mole of a diatomic ideal gas undergoes a process shown in P-V diagram. The total heat given to the gas (ln 2 = 0.7) 28. Two charges, each equal to $$-$$q are kept at ($$-$$a, 0) and (a, 0). A charge q is placed at the origin. If q is given 29.
A neutral conducting solid sphere of radius R has two spherical cavities of radius a and b as shown in the figure. Cent 30. Consider two concentric conducting sphere of radii R and 2R respectively. The inner sphere is given a charge +Q. The oth 31. A horizontal semi-circular wire of radius r is connected to a battery through two similar springs X and Y to an electric 32. Find the equivalent capacitance between A and B of the following arrangement :
33. A golf ball of mass 50 gm placed on a tee, is struck by a golf-club. The speed of the golf ball as it leaves the tee is 34. Three concentric metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities +$$\sigm 35. One mole of an ideal monoatomic gas expands along the polytrope PV3 = constant from V1 to V2 at a constant pressure P1. 36.
As shown in figure, a rectangular loop of length 'a' and width 'b' and made of a conducting material of uniform cross-s 37. A sample of hydrogen atom in its ground state is radiated with photons of 10.2 eV energies. The radiation from the sampl 38. A particle is moving in x-y plane according to $$\overrightarrow r = b\cos \omega t\widehat i + b\sin \omega t\widehat 39.
Two wires A and B of same length are made of same material. Load (F) vs. elongation (x) graph for these two wires is 40.
A hemisphere of radius R is placed in a uniform electric field E so that its axis is parallel to the field. Which of th
1
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
$$\mathop {\lim }\limits_{x \to 0} \left( {{1 \over x}\ln \sqrt {{{1 + x} \over {1 - x}}} } \right)$$ is
A
$${1 \over 2}$$
B
0
C
1
D
does not exist
2
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Let f : [a, b] $$\to$$ R be continuous in [a, b], differentiable in (a, b) and f(a) = 0 = f(b). Then
A
there exists at least one point $$c \in (a,b)$$ for which $$f'(c) = f(c)$$
B
$$f'(x) = f(x)$$ does not hold at any point of (a, b)
C
at every point of $$(a,b),f'(x) > f(x)$$
D
at every point of $$(a,b),f'(x) < f(x)$$
3
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
$$I = \int {\cos (\ln x)dx} $$. Then I =
A
$${x \over 2}\{ \cos (\ln x) + \sin (\ln x)\} + c$$ (c denotes constant of integration)
B
$${x^2}\{ \cos (\ln x) - \sin (\ln x)\} + c$$ (c denotes constant of integration)
C
$${x^2}\sin (\ln x) + c$$ (c denotes constant of integration)
D
$$x\cos (\ln x) + c$$ (c denotes constant of integration)
4
WB JEE 2022
MCQ (Single Correct Answer)
+1
-0.25
Let f be derivable in [0, 1], then
A
there exists $$c \in (0,1)$$ such that $$\int\limits_0^c {f(x)dx = (1 - c)f(c)} $$
B
there does not exist any point $$d \in (0,1)$$ for which $$\int\limits_0^d {f(x)dx = (1 - d)f(d)} $$
C
$$\int\limits_0^c {f(x)dx} $$ does not exist, for any $$c \in (0,1)$$
D
$$\int\limits_0^c {f(x)dx} $$ is independent of $$c,c \in (0,1)$$
Paper analysis
Total Questions
Chemistry
40
Mathematics
75
Physics
40
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