Chemistry
1. Which of the following statements is incorrect? 2. The calculated spin-only magnetic moment values in BM for $$\mathrm{[FeCl_4]^-}$$ and $$\mathrm{[Fe(CN)_6]^{3-}}$$ are 3. $$\mathrm{BrF_3}$$ self ionises as following 4. 4f$$^2$$ electronic configuration is found in 5.
The correct order of C = O bond length in ethyl propanoate (I), ethyl propenoate (II) and ethenyl propanoate (III) is 6. Select the molecule in which all the atoms may lie on a single plane is 7. 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) $$\mathrm{{H_2}\mathop C\limits^ \oplus - CH = CH - C 10. The correct order of boiling points of N-ethylethanamine (I), ethoxyethane (II) and butan-2-ol (III) is 11.
Structure of M is, 12.
The correct order of acidity of above compounds is 13.
If all the nucleophilic substitution reactions at saturated carbon atoms in the above sequence of reactions follow SN2 14.
The correct option for the above reaction is 15. Arrange the following in order of increasing mass
I. 1 mole of N$$_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 t 17. 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 abs 20. 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 mag 23. Suppose a gaseous mixture of He, Ne, Ar and Kr is treated with photons of the frequency appropriate to ionize Ar. What i 24. A solution containing 4g of polymer in 4.0 litre solution at 27$$^\circ$$C shows an osmotic pressure of 3.0 $$\times$$ 1 25. The equivalent weight of KIO$$_3$$ in the given reaction is (M = molecular mass):
$$\mathrm{2Cr{(OH)_3} + 4O{H^ - } + KI 26. At STP, the dissociation reaction of water is $$\mathrm{H_2O\rightleftharpoons H^+~(aq.)+OH^-~(aq.)}$$, and the pH of wa 27. Na$$_2$$CO$$_3$$ is prepared by Solvay process but K$$_2$$CO$$_3$$ cannot be prepared by the same because 28. The molecular shapes of SF$$_4$$, CF$$_4$$ and XeF$$_4$$ are 29. The species in which nitrogen atom is in a state of sp hybridisation is 30. The correct statement about the magnetic properties of $${\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$$_4$$]$$^{2-}$$. The 32.
'$$\underline{\underline L} $$' in the above sequence of reaction is/are (where L $$\ne$$ M $$\ne$$ N) 33.
'$$\underline G $$' in the above sequence of reactions is 34. Case - 1 : An ideal gas of molecular weight M at temperature T.
Case - 2 : Another ideal gas of molecular weight 2M at t 35. 63 g of a compound (Mol. Wt. = 126) was dissolved in 500 g distilled water. The density of the resultant solution as 1.1 36. An electron in the 5d orbital can be represented by the following (n, l, m) values 37. The conversion(s) that can be carried out by bromine in carbon tetrachloride solvent is/are 38. The correct set(s) of reactions to synthesize benzoic acid starting from benzene is/are 39. 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 $$f'(x) = {[f(x)]^2} + 4\forall x \in (1,3)$$. Then 4. 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 $$f(x)$$ is 7. 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$$ ... are in 11. If $$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 $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \o 13. Given $${{{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 $$x = 100t - {{25} \over 2}{t 16. If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to th 17. A, B are fixed points with coordinates (0, a) and (0, b) (a > 0, b > 0). P is variable point (x, 0) referred to rectangu 18. The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le 19. The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\w 20. If the vertices of a square are $${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}$$ are in A.P. with increment r, then the difference between the mean of th 22. If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals 23. Reflection of the line $$\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$$ are real, be less than 2 and other be greater than 2, then 25. The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels 26. n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one o 27. Let $$P(n) = {3^{2n + 1}} + {2^{n + 2}}$$ where $$n \in N$$. Then 28. Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the element 29. Let A and B are orthogonal matrices and det A + det B = 0. Then 30. Let $$A = \left( {\matrix{
2 & 0 & 3 \cr
4 & 7 & {11} \cr
5 & 4 & 8 \cr
} } \right)$$. Then 31. If the matrix Mr is given by $${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 compo 35. Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability t 36. Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b 37. If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is
(Here $$n \i 38. The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents 39. 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 perpen 40. If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at 41. The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x 42. ABC is an isosceles triangle with an inscribed circle with centre O. Let P be the midpoint of BC. If AB = AC = 15 and BC 43. Let O be the vertex, Q be any point on the parabola x$$^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 $${{x - 1} \over 2} = {{y 48. The angle between a normal to the plane $$2x - y + 2z - 1 = 0$$ and the X-axis is 49. Let $$f(x) = [{x^2}]\sin \pi x,x > 0$$. Then 50. If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x 51. $$\int\limits_0^{2\pi } {\theta {{\sin }^6}\theta \cos \theta d\theta } $$ is equal to 52. 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 point 56. If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overr 57. Given $$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$$ where a, b, c are positive real numbers. If the equation has no r 59. Let $${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\} $$. Th 62. From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 1 63. The locus of points (x, y) in the plane satisfying $${\sin ^2}x + {\sin ^2}y = 1$$ consists of 64. The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {\left( {{1 \over {2\,.\,3}} + {1 \over {{2^2}\,.\,3}}} \ri 65. The family of curves $$y = {e^{a\sin x}}$$, where 'a' is arbitrary constant, is represented by the differential equation 66. Let f be a non-negative function defined on $$\left[ {0,{\pi \over 2}} \right]$$. If $$\int\limits_0^x {(f'(t) - \sin 2 67. 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 $$f(x) = 3\root 3 \of {{x^2}} - {x^2}$$, then 69. If z$$_1$$ and z$$_2$$ are two complex numbers satisfying the equation $$\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}} 70. A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible 71. If R and R$$^1$$ are equivalence relations on a set A, then so are the relations 72. Let f be a strictly decreasing function defined on R such that $$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 $$\math 2. Three identical convex lenses each of focal length $$\mathrm{f}$$ are placed in a straight line separated by a distance 3.
X-rays of wavelength $$\lambda$$ gets reflected from parallel planes of atoms in a crystal with spacing d between two p 4. If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of n 5.
In the given circuit, find the voltage drop $$\mathrm{V_L}$$ in the load resistance $$\mathrm{R_L}$$. 6.
Consider the logic circuit with inputs A, B, C and output Y. How many combinations of A, B and C gives the output Y = 0 7. A particle of mass m is projected at a velocity u, making an angle $$\theta$$ with the horizontal (x-axis). If the angle 8. A body of mass 2 kg moves in a horizontal circular path of radius 5 m. At an instant, its speed is 2$$\sqrt5$$ m/s and i 9. In an experiment, the length of an object is measured to be 6.50 cm. This measured value can be written as 0.0650 m. The 10. A mouse of mass m jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius R. The fractiona 11. Acceleration due to gravity at a height H from the surface of a planet is the same as that at a depth of H below the sur 12. A uniform rope of length 4 m and mass 0.4 kg is held on a frictionless table in such a way that 0.6 m of the rope is han 13. The displacement of a plane progressive wave in a medium, travelling towards positive x-axis with velocity 4 m/s at t = 14. In a simple harmonic motion, let f be the acceleration and t be the time period. If x denotes the displacement, then |fT 15.
As shown in the figure, a liquid is at same levels in two arms of a U-tube of uniform cross-section when at rest. If th 16. Six molecules of an ideal gas have velocities 1, 3, 5, 5, 6 and 5 m/s respectively. At any given temperature, if $$\math 17.
As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice hav 18.
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 substan 20.
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 linear 22.
12 $$\mu$$C and 6 $$\mu$$C charges are given to the two conducting plates having same cross-sectional area and placed f 23. A wire carrying a steady current I is kept in the x-y plane along the curve $$y=A \sin \left(\frac{2 \pi}{\lambda} x\ri 24.
The figure represents two equipotential lines in x-y plane for an electric field. The x-component E$$_x$$ of the electr 25. An electric dipole of dipole moment $$\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}$$ starts moving from the origin with velocity $$v 28.
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 $$\mathrm{{{{I_{\max } 30.
A circular coil is placed near a current carrying conductor, both lying on the plane of the paper. The current is flowi 31. An amount of charge Q passes through a coil of resistance R. If the current in the coil decreases to zero at a uniform r 32. A modified gravitational potential is given by $$\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 $$\mathrm{m}, \frac{\mathrm{m 34. An earth's satellite near the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also 35.
A bar magnet falls from rest under gravity through the centre of a horizontal ring of conducting wire as shown in figur 36. A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the regi 37. A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead alo 38.
A cyclic process is shown in p-v diagram and T-S diagram. Which of the following statements is/are true? 39.
The figure shows two identical parallel plate capacitors A and B of capacitances C connected to a battery. The key K is 40. A charged particle of charge q and mass m is placed at a distance 2R from the centre of a vertical cylindrical region of
1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
If $${I_n} = \int\limits_0^{{\pi \over 2}} {{{\cos }^n}x\cos nxdx} $$, then I$$_1$$, I$$_2$$, I$$_3$$ ... are in
A
A.P.
B
G.P.
C
H.P.
D
no such relation
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
If $$y = {x \over {{{\log }_e}|cx|}}$$ is the solution of the differential equation $${{dy} \over {dx}} = {y \over x} + \phi \left( {{x \over y}} \right)$$, then $$\phi \left( {{x \over y}} \right)$$ is given by
A
$${{{y^2}} \over {{x^2}}}$$
B
$$ - {{{y^2}} \over {{x^2}}}$$
C
$${{{x^2}} \over {{y^2}}}$$
D
$$ - {{{x^2}} \over {{y^2}}}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
The function $$y = {e^{kx}}$$ satisfies $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \over {dx}} - y} \right) = y{{dy} \over {dx}}$$. It is valid for
A
exactly one value of k.
B
two distinct values of k.
C
three distinct values of k.
D
infinitely many values of k.
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Given $${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$. Changing the independent variable x to z by the substitution $$z = \log \tan {x \over 2}$$, the equation is changed to
A
$${{{d^2}y} \over {d{z^2}}} + {3 \over y} = 0$$
B
$$2{{{d^2}y} \over {d{z^2}}} + {e^y} = 0$$
C
$${{{d^2}y} \over {d{z^2}}} - 4y = 0$$
D
$${{{d^2}y} \over {d{z^2}}} + 4y = 0$$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 75
Physics 40
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