Chemistry
1. For the above three esters, the order of rates of alkaline hydrolysis is 2. Ph$$ - $$
CDO$$\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{Warm}^{50\% aq.NaOH}} $$
Ph$$ - $$
COO$$\mathop H\limi 3. The correct order of acidity for the following compounds is : 4. The reduction product of ethyl 3-oxobutanoate by NaBH4 in methanol is 5. What is the major product of the following reaction? 6. The maximum number of electrons in an atom in which the last electron filled has the quantum numbers n = 3, l = 2 and m 7. In the face centered cubic lattice structure of gold the closest distance between gold atoms is ('a' being the edge leng 8. The equilibrium constant for the following reactions are given at 25$$^\circ $$C$$2A$$ $$\rightleftharpoons$$ B + C, K1 9. Among the following, the ion which will be more effective for flocculation of Fe(OH)3 solution is : 10. The mole fraction of ethanol in water is 0.08. Its molality is 11. 5 mL of 0.1 M Pb(NO3)2 is mixed with 10 mL of 0.02 M KI. The amount of PbI2 precipitated will be about 12. At 273 K temperature and 76 cm Hg pressure the density of a gas is 1.964 g L-1. The gas is 13. Equal masses of ethane and hydrogen are mixed in an empty container at 298 K. The fraction of total pressure exerted by 14. An ideal gas expands adiabatically against vacuum. Which of the following is correct for the given process? 15. Kf (water) = 1.86 K kg mol-1. The temperature at which ice begins to separate from a mixture of 10 mass % ethylene glyco 16. The radius of the first Bohr orbit of a hydrogen atom is 0.53 $$\times {10^-8}$$ cm. The velocity of the electron in the 17. Which of the following statements is not true for the reaction, 2F2 + 2H2O $$ \to $$ 4HF + O2 ? 18. The number of unpaired electrons in the uranium (92U) atom is 19. How and why does the density of liquid water change on prolonged electrolysis? 20. The difference between orbital angular momentum of an electron in a 4f -orbital and another electron in a 4s-orbital is 21. Which of the following has the largest number of atoms? 22. Indicate the correct IUPAC name of the coordination compound shown in the figure. 23. What will be the mass of one atom of 12C? 24. Bond order of He2, $$He_2^ + $$ and $$He_2^{2 + }$$ are respectively 25. To a solution of a colourless efflorescent sodium salt, when dilute acid is added, a colourless gas is evolved along wit 26. The reaction for obtaining the metal (M) from its oxide (M2O3) ore is given by$${M_2}{O_3}(s) + 2Al(l)\buildrel {Heat} \ 27. In the extraction of Ca by electro reduction of molten CaCl2 some CaF2 is added to the electrolyte for the following rea 28. The total number of alkyl bromides (including stereoisomers) formed in the reaction $$M{e_3}C - CH = C{H_2} + HBr \to $$ 29. The product in the above reaction is 30. Which of the following compounds is asymmetric? 31. For a reaction 2A + B $$ \to $$ P, when concentration of B alone is doubled, t1/2 does not change and when concentration 32. A solution is saturated with SrCO3 and SrF2. The $$[CO_3^{2 - }]$$ is found to be 1.2 $$ \times $$ 10-3 M. The concentra 33. A homonuclear diatomic gas molecule shows 2-electron magnetic moment. The one-electron and two-electron reduced species 34. $$C{H_3} - O - C{H_2} - Cl\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_\Delta ^{aq{.^\Theta }OH}} C{H_3} - O - C{H_ 35. Which of the following reactions give(s) a meso-compound as the main product? 36. For spontaneous polymerisation, which of the following is (are) correct? 37. Which of the following statement(s) is/are incorrect? 38. SiO2 is attacked by which one/ones of the following? 39. $$Me - C \equiv C - Me\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{EtOH, - 33^\circ C}^{Na/N{H_3}(liq.)}} \underli 40. For the following carbocations, the correct order of stability is I. $$^ \oplus C{H_2} - COC{H_3}$$II. $$^ \oplus C{H_2}
Mathematics
1. Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then 2. Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) < 0$$ in [0, 1], then 3. $$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = } $$ 4. The value of $$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^ 5. $$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to 6. If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is 7. If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = } $$ 8. Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over 9. Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty } f(x) = 0.$$ If $$y' + yf'(x) - f(x)f'(x 10. If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $ 11. Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then 12. If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respect 13. If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a} 14. If 2 log(x + 1) $$ - $$ log(x2 $$ - $$ 1) = log 2, then x = 15. The number of complex numbers p such that $$\left| p \right| = 1$$ and imaginary part of p4 is 0, is 16. The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circle of radius 17. The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if 18. In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. I 19. If the total number of m-element subsets of the set A = {a1, a2, ..., an} is k times the number of m element subsets con 20. Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then 21. If c0, c1, c2, ......, c15 are the binomial coefficients in the expansion of (1 + x)15, then the value of $${{{c_1}} \ov 22. Let A = $$\left( {\matrix{
{3 - t} \cr
{ - 1} \cr
0 \cr
} \matrix{
{} \cr
{} \cr
{} \cr
23. Let $$A = \left[ {\matrix{
{12} & {24} & 5 \cr
x & 6 & 2 \cr
{ - 1} & { - 2} & 3 \ 24. Let $$A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$ be a 2 $$ \times $$ 2 real matrix with 25. If $$\left| {\matrix{
{{a^2}} & {bc} & {{c^2} + ac} \cr
{{a^2} + ab} & {{b^2}} & {ca} \cr
{ 26. If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{
27. Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then 28. The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ respectively with $$\alpha = 2\widehat i + 29. Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the g 30. A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire 31. $$\cos (2x + 7) = a(2 - \sin x)$$ can have a real solution for 32. The differential equation of the family of curves y = ex (A cos x + B sin x) where, A, B are arbitrary constants is 33. The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents 34. The locus of the centre of the circles which touch both the circles x2 + y2 = a2 and x2 + y2 = 4ax externally is 35. Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the ori 36. A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. Th 37. Area in the first quadrant between the ellipses x2 + 2y2 = a2 and 2x2 + y2 = a2 is 38. The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point 39. The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\a 40. A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OP 41. If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over 42. The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. 43. The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines$${{x - 1} \over 2} = {{y + 2} \o 44. The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the pl 45. Let f(x) = sin x + cos ax be periodic function. Then, 46. The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is 47. Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is 48. If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right)^{{1 \over x}}} = 4$$, then $$\mathop { 49. Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is continuous) such that f(0) = f(1) = f'(0 50. Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.Then 51. The area of the region$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is 52. In open interval $$\left( {0,\,{\pi \over 2}} \right)$$ 53. If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $ 54. If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\wideha 55. Let z1 and z2 be two imaginary roots of z2 + pz + q = 0, where p and q are real. The points z1, z2 and origin form an eq 56. If P(x) = ax2 + bx + c and Q(x) = $$ - $$ax2 + dx + c, where ac $$ \ne $$ 0 [a, b, c, d are all real], then P(x).Q(x) = 57. Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then 58. Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given functions. If S be the domain of fog and T b 59. Let p1 and p2 be two equivalence relations defined on a non-void set S. Then 60. Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of 61. Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of 62. A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutt 63. Let $$0 < \alpha < \beta < 1$$. Then, $$\mathop {\lim }\limits_{n \to \infty } \int\limits_{1/(k + \beta )}^{ 64. $$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}} \right)$$ 65. Let $$y = {1 \over {1 + x + lnx}}$$, then 66. Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then 67. The area of the figure bounded by the parabola $$x = - 2{y^2},\,x = 1 - 3{y^2}$$ is 68. A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then 69. The equation $${x^{{{(\log 3x)}^2}}} - {9 \over 2}\log 3\,x + 5 = 3\sqrt 3 $$ has 70. In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i 71. A and B are independent events. The probability that both A and B occur is $${1 \over {20}}$$ and the probability that n 72. The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose su 73. Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ at any point. The locus of the mid-point 74. Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is 75. Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive integer k such that $$\mathop {\lim }\limits_{ 76. Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A a
Physics
1. The intensity of light emerging from one of the slits in a Young's double slit experiment is found to be 1.5 times the i 2. In a Fraunhofer diffraction experiment, a single slit of width 0.5 mm is illuminated by a monochromatic light of wavelen 3. If R is the Rydberg constant in cm-1, then hydrogen atom does not emit any radiation of wavelength in the range of 4. A nucleus X emits a $$\beta $$-particle to produce a nucleus Y. If their atomic masses are Mx and My respectively, then 5. For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV 6. A common emitter transistor amplifier is connected with a load resistance of 6 k$$\Omega $$
. When a small AC signal of 7. In the circuit shown, the value of $$\beta $$ of the transistor is 48. If the supplied base current is 200 $$\mu $$A, wh 8. The frequency v of the radiation emitted by an atom when an electron jumps from one orbit to another is given by v = k$$ 9. Consider the vectors $$A = \hat i + \hat j - \hat k$$
,$$B = 2\hat i - \hat j + \hat k$$ and $$C = {1 \over {\sqrt 5 }}\ 10. A fighter plane, flying horizontally with a speed 360 km/h at an altitude of 500 m drops a bomb for a target straight ah 11. A block of mass m rests on a horizontal table with a coefficient of static friction $$\mu $$. What minimum force must be 12. A tennis ball hits the floor with a speed v at an angle $$\theta $$ with the normal to the floor. If the collision is in 13. The bob of a swinging second pendulum (one whose time period is 2 s) has a small speed v0 at its lowest point. It height 14. A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm2 hang from a ceiling and are 15 cm apar 15. Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body fallin 16. An ideal gas undergoes the cyclic process abca as shown in the given p - V diagramIt rejects 50J of heat during ab and a 17. A container AB in the shape of a rectangular parallelopiped of length 5 m is divided internally by a movable partition P 18. When 100 g of boiling water at 100$$^\circ $$
C is added into a calorimeter containing 300 g of cold water at 10$$^\circ 19. As shown in the figure, a point charge q1 = + 1 $$ \times $$ 10-6 C is placed at the origin in xy-plane and another poin 20. Four identical point masses, each of mass m and carrying charge + q are placed at the corners of a square of sides a on 21. A very long charged solid cylinder of radius a contains a uniform charge density p. Dielectric constant of the material 22. A galvanometer can be converted to a voltmeter of full scale deflection V0 by connecting a series resistance R1 and can 23. As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius r concentrical 24. As shown in the figure, a wire is bent to form a D-shaped closed loop, carrying current I, where the curved part is a se 25. What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figu 26. When a DC voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current graduall 27. Consider the circuit shown.If all the cells have negligible internal resistance, what will be the current through the 2$ 28. Consider a conducting wire of length L bent in the form of a circle of radius R and another conductor of length a (a < 29. An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the ob 30. A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the ve 31. A conducting circular loop of resistance 20$$\Omega $$
and cross-sectional area 20 $$ \times $$ 10-2 m2 is placed perpe 32. A pair of parallel metal plates are kept with a separation d. One plate is at a potential + V and the other is at ground 33. A metallic block of mass 20 kg is dragged with a uniform velocity of 0.5 ms-1 on a horizontal table for 2.1 s. The coeff 34. Consider an engine that absorbs 130 cal of heat from a hot reservoir and delivers 30 cal heat to a cold reservoir in eac 35. Two pith balls, each carrying charge + q are hung from a hook by two springs. It is found that when each charge is tripl 36. A point source of light is used in an experiment of photoelectric effects. If the distance between the source and the ph 37. Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. The 38. A simple pendulum of length l is displaced, so that its taught string is horizontal and then released. A uniform bar piv 39. A 400$$\Omega $$ resistor, a 250 mH inductor and a 2.5 $$\mu $$F capacitor are connected in series with an AC source of 40. A charged particle moves with constant velocity in a region, where no effect of gravity is felt but an electrostatic fie
1
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is
A
0.01
B
0.18
C
$$ - $$0.05
D
0.07
2
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right)^{{1 \over x}}} = 4$$, then $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + 2cx} \over {1 - 2cx}}} \right)^{{1 \over x}}}$$ is
A
2
B
4
C
16
D
64
3
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is continuous) such that f(0) = f(1) = f'(0) = 0. Then
A
f"(c) = 0 for some c $$ \in $$ R
B
there is no point for which f"(x) = 0
C
at all points f"(x) > 0
D
at all points f"(x) < 0
4
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.
Then
Then
A
f(x) has 13 non-zero real roots
B
f(x) has exactly one real root
C
f(x) has exactly one pair of imaginary roots
D
f(x) has no real root
Paper analysis
Total Questions
Chemistry
40
Mathematics
76
Physics
40
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