Chemistry
1. Which of the following statements is incorrect?2. The calculated spin-only magnetic moment values in BM for $$\mathrm{[FeCl_4]^-}$$ and $$\mathrm{[Fe(CN)_6]^{3-}}$$ are3. $$\mathrm{BrF_3}$$ self ionises as following4. 4f$$^2$$ electronic configuration is found in5.
The correct order of C = O bond length in ethyl propanoate (I), ethyl propenoate (II) and ethenyl propanoate (III) is6. Select the molecule in which all the atoms may lie on a single plane is7. The IUPAC name of
8.
The relationship between the pair of compounds shown above are respectively,9. The correct stability order of the following carbocations is
(I) $$\mathrm{{H_2}\mathop C\limits^ \oplus - CH = CH - C10. The correct order of boiling points of N-ethylethanamine (I), ethoxyethane (II) and butan-2-ol (III) is11.
Structure of M is,12.
The correct order of acidity of above compounds is13.
If all the nucleophilic substitution reactions at saturated carbon atoms in the above sequence of reactions follow SN2 14.
The correct option for the above reaction is15. Arrange the following in order of increasing mass
I. 1 mole of N$$_2$$
II. 0.5 mole of O$$_3$$
III. $$3.011\times10^{23}16. Two base balls (masses : m$$_1$$ = 100 g, and m$$_2$$ = 50 g) are thrown. Both of them move with uniform velocity, but t17. What is the edge length of the unit cell of a body centred cubic crystal of an element whose atomic radius is 75 pm?18. The root mean square (rms) speed of X$$_2$$ gas is x m/s at a given temperature. When the temperature is doubled, the X$19. Which of the following would give a linear plot?
(k is the rate constant of an elementary reaction and T is temp. in abs20. The equivalent conductance of NaCl, HCl and CH$$_3$$COONa at infinite dilution are 126.45, 426.16 and 91 ohm$$^{-1}$$cm$21. For the reaction A + B $$\to$$ C, we have the following data:
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{22. If in case of a radio isotope the value of half-life (T$$_{1/2}$$) and decay constant ($$\lambda$$) are identical in mag23. Suppose a gaseous mixture of He, Ne, Ar and Kr is treated with photons of the frequency appropriate to ionize Ar. What i24. A solution containing 4g of polymer in 4.0 litre solution at 27$$^\circ$$C shows an osmotic pressure of 3.0 $$\times$$ 125. The equivalent weight of KIO$$_3$$ in the given reaction is (M = molecular mass):
$$\mathrm{2Cr{(OH)_3} + 4O{H^ - } + KI26. At STP, the dissociation reaction of water is $$\mathrm{H_2O\rightleftharpoons H^+~(aq.)+OH^-~(aq.)}$$, and the pH of wa27. Na$$_2$$CO$$_3$$ is prepared by Solvay process but K$$_2$$CO$$_3$$ cannot be prepared by the same because28. The molecular shapes of SF$$_4$$, CF$$_4$$ and XeF$$_4$$ are29. The species in which nitrogen atom is in a state of sp hybridisation is30. The correct statement about the magnetic properties of $${\left[ {Fe{{(CN)}_6}} \right]^{3 - }}$$ and $${\left[ {Fe{F_6}31. Nickel combines with a uninegative monodentate ligand (X$$^-$$) to form a paramagnetic complex [NiX$$_4$$]$$^{2-}$$. The32.
'$$\underline{\underline L} $$' in the above sequence of reaction is/are (where L $$\ne$$ M $$\ne$$ N)33.
'$$\underline G $$' in the above sequence of reactions is34. Case - 1 : An ideal gas of molecular weight M at temperature T.
Case - 2 : Another ideal gas of molecular weight 2M at t35. 63 g of a compound (Mol. Wt. = 126) was dissolved in 500 g distilled water. The density of the resultant solution as 1.136. An electron in the 5d orbital can be represented by the following (n, l, m) values37. The conversion(s) that can be carried out by bromine in carbon tetrachloride solvent is/are38. The correct set(s) of reactions to synthesize benzoic acid starting from benzene is/are39. Which statement(s) is/are applicable above critical temperature?40. Which of the following mixtures act(s) as buffer solution?
Mathematics
1. $$\mathop {\lim }\limits_{x \to \infty } \left\{ {x - \root n \of {(x - {a_1})(x - {a_2})\,...\,(x - {a_n})} } \right\}$2. Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{
1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr
{e^3. Let $$f:[1,3] \to R$$ be continuous and be derivable in (1, 3) and $$f'(x) = {[f(x)]^2} + 4\forall x \in (1,3)$$. Then4. f(x) is a differentiable function and given $$f'(2) = 6$$ and $$f'(1) = 4$$, then $$L = \mathop {\lim }\limits_{h \to 0}5. Let $${\cos ^{ - 1}}\left( {{y \over b}} \right) = {\log _e}{\left( {{x \over n}} \right)^n}$$, then $$A{y_2} + B{y_1} +6. If $$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then $$f(x)$$ is7. If $$\int {{{dx} \over {(x + 1)(x - 2)(x - 3)}} = {1 \over k}{{\log }_e}\left\{ {{{|x - 3{|^3}|x + 1|} \over {{{(x - 2)}8. the expression $${{\int\limits_0^n {[x]dx} } \over {\int\limits_0^n {\{ x\} dx} }}$$, where $$[x]$$ and $$\{ x\} $$ are 9. The value $$\int\limits_0^{1/2} {{{dx} \over {\sqrt {1 - {x^{2n}}} }}} $$ is $$(n \in N)$$10. If $${I_n} = \int\limits_0^{{\pi \over 2}} {{{\cos }^n}x\cos nxdx} $$, then I$$_1$$, I$$_2$$, I$$_3$$ ... are in11. If $$y = {x \over {{{\log }_e}|cx|}}$$ is the solution of the differential equation $${{dy} \over {dx}} = {y \over x} + 12. The function $$y = {e^{kx}}$$ satisfies $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \o13. Given $${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$. Changing the independent variable x 14. Let $$f(x) = \left\{ {\matrix{
{x + 1,} & { - 1 \le x \le 0} \cr
{ - x,} & {0 15. A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t16. If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to th17. A, B are fixed points with coordinates (0, a) and (0, b) (a > 0, b > 0). P is variable point (x, 0) referred to rectangu18. The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le19. The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\w20. If the vertices of a square are $${z_1},{z_2},{z_3}$$ and $${z_4}$$ taken in the anti-clockwise order, then $${z_3} = $$21. If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of th22. If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals23. Reflection of the line $$\overline a z + a\overline z = 0$$ in the real axis is given by :24. If one root of $${x^2} + px - {q^2} = 0,p$$ and $$q$$ are real, be less than 2 and other be greater than 2, then25. The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels 26. n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one o27. Let $$P(n) = {3^{2n + 1}} + {2^{n + 2}}$$ where $$n \in N$$. Then28. Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the element29. Let A and B are orthogonal matrices and det A + det B = 0. Then30. Let $$A = \left( {\matrix{
2 & 0 & 3 \cr
4 & 7 & {11} \cr
5 & 4 & 8 \cr
} } \right)$$. Then31. If the matrix Mr is given by $${M_r} = \left( {\matrix{
r & {r - 1} \cr
{r - 1} & r \cr
} } \right)$$ for r 32. Let $$\alpha,\beta$$ be the roots of the equation $$a{x^2} + bx + c = 0,a,b,c$$ real and $${s_n} = {\alpha ^n} + {\beta 33. Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:34. Let X be a nonvoid set. If $$\rho_1$$ and $$\rho_2$$ be the transitive relations on X, then
($$\circ$$ denotes the compo35. Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability t36. Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b37. If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is
(Here $$n \i38. The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents39. Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpen40. If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at41. The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x 42. ABC is an isosceles triangle with an inscribed circle with centre O. Let P be the midpoint of BC. If AB = AC = 15 and BC43. Let O be the vertex, Q be any point on the parabola x$$^2$$ = 8y. If the point P divides the line segment OQ internally 44. The tangent at point $$(a\cos \theta ,b\sin \theta ),0 45. Let $$A(2\sec \theta ,3\tan \theta )$$ and $$B(2\sec \phi ,3\tan \phi )$$ where $$\theta + \phi = {\pi \over 2}$$ be 46. If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$,47. If the distance between the plane $$\alpha x - 2y + z = k$$ and the plane containing the lines $${{x - 1} \over 2} = {{y48. The angle between a normal to the plane $$2x - y + 2z - 1 = 0$$ and the X-axis is49. Let $$f(x) = [{x^2}]\sin \pi x,x > 0$$. Then50. If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x51. $$\int\limits_0^{2\pi } {\theta {{\sin }^6}\theta \cos \theta d\theta } $$ is equal to52. If $$x = \sin \theta $$ and $$y = \sin k\theta $$, then $$(1 - {x^2}){y_2} - x{y_1} - \alpha y = 0$$, for $$\alpha=$$53. In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.54. The average ordinate of $$y = \sin x$$ over $$[0,\pi ]$$ is :55. The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point56. If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overr57. Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$58. Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no r59. Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} + 60. Let $$A = \left( {\matrix{
0 & 0 & 1 \cr
1 & 0 & 0 \cr
0 & 0 & 0 \cr
} } \right),B = \left( {\matrix{
61. Let $$\rho$$ be a relation defined on set of natural numbers N, as $$\rho = \{ (x,y) \in N \times N:2x + y = 4\} $$. Th62. From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 163. The locus of points (x, y) in the plane satisfying $${\sin ^2}x + {\sin ^2}y = 1$$ consists of64. The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {\left( {{1 \over {2\,.\,3}} + {1 \over {{2^2}\,.\,3}}} \ri65. The family of curves $$y = {e^{a\sin x}}$$, where 'a' is arbitrary constant, is represented by the differential equation66. Let f be a non-negative function defined on $$\left[ {0,{\pi \over 2}} \right]$$. If $$\int\limits_0^x {(f'(t) - \sin 267. A balloon starting from rest is ascending from ground with uniform acceleration of 4 ft/sec$$^2$$. At the end of 5 sec, 68. If $$f(x) = 3\root 3 \of {{x^2}} - {x^2}$$, then69. If z$$_1$$ and z$$_2$$ are two complex numbers satisfying the equation $$\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}}70. A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible71. If R and R$$^1$$ are equivalence relations on a set A, then so are the relations72. Let f be a strictly decreasing function defined on R such that $$f(x) > 0,\forall x \in R$$. Let $${{{x^2}} \over {f({a^73. A rectangle ABCD has its side parallel to the line y = 2x and vertices A, B, D are on lines y = 1, x = 1 and x = $$-$$1 74. Let $$f(x) = {x^m}$$, m being a non-negative integer. The value of m so that the equality $$f'(a + b) = f'(a) + f'(b)$$ 75. Which of the following statements are true?
Physics
1. A ray of monochromatic light is incident on the plane surface of separation between two media $$\mathrm{X}$$ and $$\math2. Three identical convex lenses each of focal length $$\mathrm{f}$$ are placed in a straight line separated by a distance 3.
X-rays of wavelength $$\lambda$$ gets reflected from parallel planes of atoms in a crystal with spacing d between two p4. If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of n 5.
In the given circuit, find the voltage drop $$\mathrm{V_L}$$ in the load resistance $$\mathrm{R_L}$$.6.
Consider the logic circuit with inputs A, B, C and output Y. How many combinations of A, B and C gives the output Y = 07. A particle of mass m is projected at a velocity u, making an angle $$\theta$$ with the horizontal (x-axis). If the angle8. A body of mass 2 kg moves in a horizontal circular path of radius 5 m. At an instant, its speed is 2$$\sqrt5$$ m/s and i9. In an experiment, the length of an object is measured to be 6.50 cm. This measured value can be written as 0.0650 m. The10. A mouse of mass m jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius R. The fractiona11. Acceleration due to gravity at a height H from the surface of a planet is the same as that at a depth of H below the sur12. A uniform rope of length 4 m and mass 0.4 kg is held on a frictionless table in such a way that 0.6 m of the rope is han13. The displacement of a plane progressive wave in a medium, travelling towards positive x-axis with velocity 4 m/s at t = 14. In a simple harmonic motion, let f be the acceleration and t be the time period. If x denotes the displacement, then |fT15.
As shown in the figure, a liquid is at same levels in two arms of a U-tube of uniform cross-section when at rest. If th16. Six molecules of an ideal gas have velocities 1, 3, 5, 5, 6 and 5 m/s respectively. At any given temperature, if $$\math17.
As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice hav18.
A given quantity of gas is taken from A to C in two ways; a) directly from A $$\to$$ C along a straight line and b) in 19.
Two substances A and B of same mass are heated at constant rate. The variation of temperature $$\theta$$ of the substan20.
Consider a positively charged infinite cylinder with uniform volume charge density $$\rho > 0$$. An electric dipole 21.
A thin glass rod is bent in a semicircle of radius R. A charge is non-uniformly distributed along the rod with a linear22.
12 $$\mu$$C and 6 $$\mu$$C charges are given to the two conducting plates having same cross-sectional area and placed f23. A wire carrying a steady current I is kept in the x-y plane along the curve $$y=A \sin \left(\frac{2 \pi}{\lambda} x\ri24.
The figure represents two equipotential lines in x-y plane for an electric field. The x-component E$$_x$$ of the electr25. An electric dipole of dipole moment $$\vec{p}$$ is placed at the origin of the co-ordinate system along the $$\mathrm{z}26. The electric field of a plane electromagnetic wave of wave number k and angular frequency $$\omega$$ is given $$\vec{E}=27. A charged particle in a uniform magnetic field $$\vec{B}=B_{0} \hat{k}$$ starts moving from the origin with velocity $$v28.
In an experiment on a circuit as shown in the figure, the voltmeter shows 8 V reading. The resistance of the voltmeter 29. An interference pattern is obtained with two coherent sources of intensity ratio n : 1. The ratio $$\mathrm{{{{I_{\max }30.
A circular coil is placed near a current carrying conductor, both lying on the plane of the paper. The current is flowi31. An amount of charge Q passes through a coil of resistance R. If the current in the coil decreases to zero at a uniform r32. A modified gravitational potential is given by $$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{r}}+\frac{\mathrm{A}}{\mathrm{r}33. There are n elastic balls placed on a smooth horizontal plane. The masses of the balls are $$\mathrm{m}, \frac{\mathrm{m34. An earth's satellite near the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also35.
A bar magnet falls from rest under gravity through the centre of a horizontal ring of conducting wire as shown in figur36. A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the regi37. A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead alo38.
A cyclic process is shown in p-v diagram and T-S diagram. Which of the following statements is/are true?39.
The figure shows two identical parallel plate capacitors A and B of capacitances C connected to a battery. The key K is40. A charged particle of charge q and mass m is placed at a distance 2R from the centre of a vertical cylindrical region of
1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le x \le 2a$$, is :
A
$$b\{ 2\sqrt 3 - \ln (2 + \sqrt 3 )\} $$
B
$$b\{ 3\sqrt 2 + \ln (3 + \sqrt 2 )\} $$
C
$$a\{ 2\sqrt 5 - \ln (2 + \sqrt 5 )\} $$
D
$$a\{ 5\sqrt 2 + \ln (5 + \sqrt 2 )\} $$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\widehat j + \widehat k,\overrightarrow \beta = \widehat j + a\widehat k$$ and $$\overrightarrow \gamma = a\widehat i + \widehat k$$ is maximum, is
A
3
B
$$-$$3
C
$$ - {1 \over {\sqrt 3 }}$$
D
$${1 \over {\sqrt 3 }}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
If the vertices of a square are $${z_1},{z_2},{z_3}$$ and $${z_4}$$ taken in the anti-clockwise order, then $${z_3} = $$
A
$$ - i{z_1} - (1 + i){z_2}$$
B
$${z_1} - (1 + i){z_2}$$
C
$${z_1} + (1 + i){z_2}$$
D
$$ - i{z_1} + (1 + i){z_2}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of their squares & the square of their mean is
A
$${{{r^2}\{ {{(n - 1)}^2} - 1\} } \over {12}}$$
B
$${{{r^2}} \over {12}}$$
C
$${{{r^2}({n^2} - 1)} \over {12}}$$
D
$${{{n^2} - 1} \over {12}}$$
Paper analysis
Total Questions
Chemistry
40
Mathematics
75
Physics
40
More papers of WB JEE
WB JEE
Papers
2024
2023
2022
2021
2020
2019
2018
2017
2016