Chemistry
1. One of the products of the following reaction is P.Structure of P is 2. For the reaction below, the product is Q.The compound Q is 3. Cyclopentanol on reaction with NaH followed by CS2 and CH3I produces a/an 4. The compound, which evolves carbon dioxide on treatment with aqueous solution of sodium bicarbonate at 25$$^\circ$$C, is 5. The indicated atom is not a nucleophilic site in 6. The charge carried by 1 millimole of Mn+ ions is 193 coulombs. The value of n is 7. Which of the following mixtures will have the lowest pH at 298 K? 8. Consider the following two first order reactions occurring at 298 K with same initial concentration of A :(1) A $$\to$$ 9. For the equilibrium, H2O(l) $$\rightleftharpoons$$ H2O(v), which of the following is correct? 10. For a van der Waals' gas, the term $$\left( {{{ab} \over {{V^2}}}} \right)$$ represents some 11. In the equilibrium, H2 + I2 $$\rightleftharpoons$$ 2HI, if at a given temperature the concentration of the reactants are 12. If electrolysis of aqueous CuSO4 solution is carried out using Cu-electrodes, the reaction taking place at the anode is 13. Which one of the following electronic arrangements is absurd? 14. The quantity hv/KB corresponds to 15. In the crystalline solid MSO4 . nH2O of molar mass 250 g mol$$-$$1, the percentage of anhydrous salt is 64 by weight. Th 16. At S.T.P. the volume of 7.5 g of a gas is 5.6 L. The gas is 17. The half-life period of $${}_{53}{I^{125}}$$ is 60 days. The radioactivity after 180 days will be 18. Consider, the radioactive disintegration $${}_{82}{A^{210}}\buildrel {} \over
\longrightarrow B\buildrel {} \over
\lon 19. The second ionization energy of the following elements follows the order 20. The melting points of (i) BeCl2 (ii) CaCl2 and (iii) HgCl2 follows the order 21. Which of these species will have non-zero magnetic moment? 22. The first electron affinity of C, N and O will be of the order 23. The H - N - H angle in ammonia is 107.6$$^\circ$$ while the H - P - H angle in phosphine is 93.5$$^\circ$$. Relative to 24. The reactive species in chlorine bleach is 25. The conductivity measurement of a coordination compound of cobalt (III) shows that it dissociates into 3 ions in solutio 26. In the Bayer's process, the leaching of alumina is done by using 27. Which atomic species cannot be used as a nuclear fuel? 28. The molecule/molecules that has/have delocalised lone pair(s) of electrons is/are 29. The conformations of n-butane, commonly known as eclipsed, gauche and anti-conformations can be interconverted by 30. The correct order of the addition reaction rates of halogen acids with ethylene is 31. The total number of isomeric linear dipeptides which can be synthesised from racemic alanine is 32. The kinetic study of a reaction like vA $$\to$$ P at 300 K provides the following curve, where concentration is taken in 33. At constant pressure, the heat of formation of a compound is not dependent on temperature, when 34. A copper coin was electroplated with Zn and then heated at high temperature until there is a change in colour. What will 35. Oxidation of allyl alcohol with a peracid gives a compound of molecular formula C3H6O2, which contains an asymmetric car 36. Haloform reaction with I2 and KOH will be respond by 37. Identify the correct statement(s) : 38. Compounds with spin only magnetic moment equivalent to five unpaired electrons are 39. Which of the following chemicals may be used to identify three unlabelled beakers containing conc. NaOH, conc. H2SO4 and 40. The compound (s), capable of producing achiral compound on heating at 100$$^\circ$$ is/are
Mathematics
1. $$\mathop {\lim }\limits_{x \to {0^ + }} ({x^n}\ln x),\,n > 0$$ 2. If $$\int {\cos x\log \left( {\tan {x \over 2}} \right)} dx$$ = $$\sin x\log \left( {\tan {x \over 2}} \right)$$ + f(x), 3. y = $$\int {\cos \left\{ {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right\}} dx$$ is an equation of a family o 4. The value of the integration $$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over 5. The value of $$\mathop {\lim }\limits_{x \to 0} {1 \over x}\left[ {\int\limits_y^a {{e^{{{\sin }^2}t}}dt - } \int\limits 6. If $$\int {{2^{{2^x}}}.\,{2^x}dx} = A\,.\,{2^{{2^x}}} + C$$, then A is equal to 7. The value of the integral $$\int\limits_{ - 1}^1 {\left\{ {{{{x^{2015}}} \over {{e^{|x|}}({x^2} + \cos x)}} + {1 \over { 8. $$\mathop {\lim }\limits_{n \to \infty } {3 \over n}\left[ {1 + \sqrt {{n \over {n + 3}}} + \sqrt {{n \over {n + 6}}} 9. The general solution of the differential equation $$\left( {1 + {e^{{x \over y}}}} \right)dx + \left( {1 - {x \over y}} 10. General solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2},a \ne 0$$ is (C is an arbitrary constant) 11. Let P(4, 3) be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at P in 12. If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by 13. The three sides of a right angled triangle are in GP (geometric progression). If the two acute angles be $$\alpha$$ and 14. If $$\log _2^6 + {1 \over {2x}} = {\log _2}\left( {{2^{{1 \over x}}} + 8} \right)$$, then the value of x are 15. Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z $$-$$ arg($$-$$ z) is 16. The general value of the real angle $$\theta$$, which satisfies the equation, $$(\cos \theta + i\sin \theta )(\cos 2\th 17. Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + bx + c = 0 has imaginary roots. 18. A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 ques 19. There are 7 greeting cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The numbe 20. 72n + 16n $$-$$1 (n$$ \in $$ N) is divisible by 21. The number of irrational terms in the expansion of $${\left( {{3^{{1 \over 8}}} + {5^{{1 \over 4}}}} \right)^{84}}$$ is 22. Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matr 23. If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') $$-$$ (adj M)' is equal to 24. If $$A = \left( {\matrix{
5 & {5x} & x \cr
0 & x & {5x} \cr
0 & 0 & 5 \cr
} } \ 25. Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then, 26. Let P and T be the subsets of k, y-plane defined byP = {(x, y) : x > 0, y > 0 and x2 + y2 = 1}T = {(x, y) : x > 27. Let $$f:R \to R$$ be defined by $$f(x) = {x^2} - {{{x^2}} \over {1 + {x^2}}}$$ for all $$x \in R$$. Then, 28. Let the relation $$\rho $$ be defined on R as a$$\rho $$b if 1 + ab > 0. Then, 29. A problem in mathematics is given to 4 students whose chances of solving individually are $${{1 \over 2}}$$, $${{1 \over 30. If X is a random variable such that $$\sigma$$(X) = 2.6, then $$\sigma$$(1 $$-$$ 4X) is equal to 31. If $${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$$, then the number of real values of x is 32. The angles of a triangle are in the ratio 2 : 3 : 7 and the radius of the circumscribed circle is 10 cm. The length of t 33. A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be c 34. A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If 35. A variable line passes through the fixed point $$(\alpha ,\beta )$$. The locus of the foot of the perpendicular from the 36. If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by $$-$$ d = 0 lies in the 4th quadrant and is eq 37. A variable circle passes through the fixed point A(p, q) and touches X-axis. The locus of the other end of the diameter 38. If P(0, 0), Q(1, 0) and R$$\left( {{1 \over 2},{{\sqrt 3 } \over 2}} \right)$$ are three given points, then the centre o 39. For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the foll 40. S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentr 41. The equation of the directrices of the hyperbola $$3{x^2} - 3{y^2} - 18x + 12y + 2 = 0$$ is 42. P is the extremity of the latusrectum of ellipse $$3{x^2} + 4{y^2} = 48$$ in the first quadrant. The eccentric angle of 43. The direction ratios of the normal to the plane passing through the points (1, 2, $$-$$3), ($$-$$1, $$-$$2, 1) and paral 44. The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is 45. The limit of the interior angle of a regular polygon of n sides as n $$ \to $$ $$\infty $$ is 46. Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \lo 47. Consider the function f(x) = cos x2. Then, 48. $$\mathop {\lim }\limits_{x \to {0^ + }} {({e^x} + x)^{1/x}}$$ 49. Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then, 50. Let $$f:[1,3] \to R$$ be a continuous function that is differentiable in (1, 3) an f'(x) = | f(x) |2 + 4 for all x$$ \in 51. Let $$a = \min \{ {x^2} + 2x + 3:x \in R\} $$ and $$b = \mathop {\lim }\limits_{\theta \to 0} {{1 - \cos \theta } \over 52. Let a > b > 0 and I(n) = a1/n $$-$$ b1/n, J(n) = (a $$-$$ b)1/n for all n $$ \ge $$ 2, then 53. Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \, 54. The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\wideh 55. A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves $${1 \over 2}$$ 56. For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is 57. The system of equations$$\eqalign{
& \lambda x + y + 3z = 0 \cr
& 2x + \mu y - z = 0 \cr
& 5x + 7y 58. Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation) 59. Let S, T, U be three non-void sets and f : S $$ \to $$ T, g : T $$ \to $$ U be so that gof : s $$ \to $$ U is surjective 60. The polar coordinate of a point P is $$\left( {2, - {\pi \over 4}} \right)$$. The polar coordinate of the point Q which 61. The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is 62. The value of $$\mathop {\lim }\limits_{x \to {0^ + }} {x \over p}\left[ {{q \over x}} \right]$$ is 63. Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then 64. The graphs of the polynomial x2 $$-$$ 1 and cos x intersect 65. A point is in motion along a hyperbola $$y = {{10} \over x}$$ so that its abscissa x increases uniformly at a rate of 1 66. Let $${I_n} = \int\limits_0^1 {{x^n}} {\tan ^{ - 1}}xdx$$. If $${a_n}{I_{n + 2}} + {b_n}{I_n} = {c_n}$$ for all n $$ \ge 67. Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes 68. The area bounded by y = x + 1 and y = cos x and the X-axis, is 69. Let x1, x2 be the roots of $${x^2} - 3x + a = 0$$ and x3, x4 be the roots of $${x^2} - 12x + b = 0$$. If $${x_1} < {x 70. If $$\theta \in R$$ and $${{1 - i\cos \theta } \over {1 + 2i\cos \theta }}$$ is real number, then $$\theta $$ will be ( 71. Let $$A = \left[ {\matrix{
3 & 0 & 3 \cr
0 & 3 & 0 \cr
3 & 0 & 3 \cr
} } \right 72. Straight lines x $$-$$ y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB 73. Equation of a tangent to the hyperbola 5x2 $$-$$ y2 = 5 and which passes through an external point (2, 8) is 74. Let f and g be differentiable on the interval I and let a, b $$ \in $$ I, a < b. Then, 75. Consider the function $$f(x) = {{{x^3}} \over 4} - \sin \pi x + 3$$
Physics
1. A ray of light is reflected by a plane mirror. $${\widehat e_0}$$, $$\widehat e$$ and $$\widehat n$$ be the unit vectors 2. A parent nucleus X undergoes $$\alpha$$-decay with a half-life of 75000 yrs. The daughter nucleus Y undergoes $$\beta$$- 3. A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2 4. To which of the following the angular velocity of the electron in the n-th Bohr orbit is proportional? 5. In the circuit shown, what will be the current through the 6V zener? 6. Each of the two inputs A and B can assume values either 0 or 1. Then which of the following will be equal to $$\overline 7. The correct dimensional formula for impulse is given by 8. The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the 9. Two weights of the mass m1 and m2 (> m1) are joined by an inextensible string of negligible mass passing over a fixed 10. A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The 11. Two particles are simultaneously projected in the horizontal direction from a point P at a certain height. The initial v 12. Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also move aro 13. A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the 14. A small spherical body of radius r and density $$\rho $$ moves with the terminal velocity v in a fluid of coefficient of 15. Two black bodies A and B have equal surface areas are maintained at temperatures 27$$^\circ$$C and 177$$^\circ$$C respec 16. What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules? 17. Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature 18. Five identical capacitors, of capacitance 20$$\mu$$F each, are connected to a battery of 150V, in a combination as shown 19. Eleven equal point charges, all of them having a charge +Q, are placed at all the hour positions of a circular clock of 20. A negative charge is placed at the midpoint between two fixed equal positive charges, separated by a distance 2d. If the 21. To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a 22. An electric current 'I' enters and leaves a uniform circular wire of radius r through diametrically opposite points. A p 23. A current 'I' is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing a 24. A square conducting loop is placed near an infinitely long current carrying wire with one edge parallel to the wire as s 25. What is the current I shown in the given circuit? 26. When the value of R in the balanced Wheatstone bridge, shown in the figure, is increased from 5$$\Omega $$ to 7$$\Omega 27. When a 60 mH inductor and a resistor are connected in series with an AC voltage source, the voltage leads the current by 28. A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens a 29. In Young's experiment for the interference of light, the separation between the slits is d and the distance of the scree 30. When the frequency of the light used is changed from $$4 \times {10^{14}}{s^{ - 1}}$$ to $$5 \times {10^{14}}{s^{ - 1}}$ 31. A capacitor of capacitance C is connected in series with a resistance R and DC source of emf E through a key. The capaci 32. A horizontal fire hose with a nozzle of cross-sectional area $${5 \over {\sqrt {21} }} \times {10^{ - 3}}{m^2}$$ deliver 33. Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the m 34. A particle with charge q moves with a velocity v in a direction perpendicular to the directions of uniform electric and 35. A parallel plate capacitor in series with a resistance of 100$$\Omega $$, an inductor of 20 mH and an AC voltage source 36. Electrons are emitted with kinetic energy T from a metal plate by an irradiation of light of intensity J and frequency v 37. The initial pressure and volume of a given mass of an ideal gas with $$\left( {{{{C_p}} \over {{C_V}}} = \gamma } \right 38. A projectile thrown with an initial velocity of 10 ms$$-$$1 at an angle $$\alpha$$ with the horizontal, has a range of 5 39. In the circuit shown in the figure all the resistance are identical and each has the value r$$\Omega $$. The equivalent 40. A metallic loop is placed in a uniform magnetic field B with the plane of the loop perpendicular to B. Under which condi
1
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
72n + 16n $$-$$1 (n$$ \in $$ N) is divisible by
A
65
B
63
C
61
D
64
2
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
The number of irrational terms in the expansion of $${\left( {{3^{{1 \over 8}}} + {5^{{1 \over 4}}}} \right)^{84}}$$ is
A
73
B
74
C
75
D
76
3
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix $$A - 3{I_3}$$ is
A
invertible
B
orthogonal
C
non-invertible
D
real Skew Symmetric matrix
4
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') $$-$$ (adj M)' is equal to
A
M
B
M'
C
null matrix
D
identity matrix
Paper analysis
Total Questions
Chemistry
40
Mathematics
75
Physics
40
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