WB JEE 2016 | WB JEE Year Wise Previous Years Questions

Chemistry

Mathematics

1. If the solution of the differential equation $$x{{dy} \over {dx}} + y = x{e^x}\,be\,xy = {e^x}\phi (x) + C$$, then $$\ph 2. The order of the differential equation of all parabolas whose axis of symmetry along X-axis is 3. The line y = x + $$\lambda$$ is tangent to the ellipse 2x2 + 3y2 = 1. Then, $$\lambda$$ is 4. The area enclosed by $$y = \sqrt {5 - {x^2}} $$ and $$y = |x - 1|$$ is 5. Let S be the set of points, whose abscissae and ordinates are natural numbers. Let P $$ \in $$ S, such that the sum of t 6. Time period T of a simple pendulum of length l is given by $$T = 2\pi \sqrt {{l \over g}} $$. If the length is increased 7. The cosine of the angle between any two diagonals of a cube is 8. If x is a positive real number different from 1 such that logax, logbx, logcx are in AP, then 9. If a, x are real numbers and | a | < 1, | x | < 1, then 1 + (1 + a) x + (1 + a + a2) x2 + ..... $$\infty $$ is equ 10. If $${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval 11. The value of $$\sum\limits_{n = 1}^{13} {({i^n} + {i^{n + 1}})} $$, $$i = \sqrt { - 1} $$ is 12. If z1, z2, z3 are imaginary numbers such that $$|{z_1}|\, = \,|{z_2}|\, = \,|{z_3}|\, = \,\left| {{1 \over {{z_1}}} + {1 13. If p, q are the roots of the equation x2 + px + q = 0, then 14. The number of values of k, for which the equation x2 $$-$$ 3x + k = 0 has two distinct roots lying in the interval (0, 1 15. The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is 16. If $${1 \over {{}^5{C_r}}} + {1 \over {{}^6{C_r}}} = {1 \over {{}^4{C_r}}}$$, then the value of r is 17. For positive integer n, n3 + 2n is always divisible by 18. In the expansion of (x $$-$$ 1) (x $$-$$ 2) .... (x $$-$$ 18), the coefficient of x17 is 19. $$1 + {}^n{C_1}\cos \theta + {}^n{C_2}\cos 2\theta + ... + {}^n{C_n}\cos n\theta $$ equals 20. If x, y and z are greater than 1, then the value of $$\left| {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \ 21. Let A be a 3 $$ \times $$ 3 matrix and B be its adjoint matrix. If | B | = 64, then | A | is equal to 22. Let $$Q = \left[ {\matrix{ {\cos {\pi \over 4}} & { - \sin {\pi \over 4}} \cr {\sin {\pi \over 4}} & 23. Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then 24. If A = {5n $$-$$ 4n $$-$$ 1 : n$$ \in $$N} and B = {16(n $$-$$ 1) : n$$ \in $$N}, then 25. If the function f : R $$ \to $$ R is defined by f(x) = (x2 + 1)35, $$\forall $$ x$$ \in $$R, then f is 26. Standard deviation of n observations a1, a2, a3, ....., an is $$\sigma$$. Then, the standard deviation of the observatio 27. Let A and B be two events such that P(A $$ \cap $$ B) = $${1 \over 6}$$, P(A $$\cup$$ B) = $${31 \over 45}$$ and P($$\ov 28. The value of $$\cos 15^\circ \cos 7{{1^\circ } \over 2}\sin 7{{1^\circ } \over 2}$$ is 29. The smallest positive root of the equation tan x $$-$$ x = 0 lies in 30. If in a $$\Delta$$ABC, AD, BE and CF are the altitudes and R is the circumradius, then the radius of the circumcircle of 31. The points ($$-$$a, $$-$$b), (a, b), (0, 0) and (a2, ab), a $$ \ne $$ 0, b $$ \ne $$ 0 are always 32. The line AB cuts off equal intercepts 2a from the axes. From any point P on the line AB perpendiculars PR and PS are dra 33. x + 8y $$-$$ 22 = 0, 5x + 2y $$-$$ 34 = 0, 2x $$-$$ 3y + 13 = 0 are the three sides of a triangle. The area of the trian 34. The line through the points (a, b) and ($$-$$a, $$-$$b), passes through the point 35. The locus of the point of intersection of the straight lines $${x \over a} + {y \over b} = K$$ and $${x \over a} - {y \o 36. The equation of a line parallel to the line 3x + 4y = 0 and touching the circle x2 + y2 = 9 in the first quadrant, is 37. A line passing through the point of intersection of x + y = 4 and x $$-$$ y = 2 makes an angle $${\tan ^{ - 1}}\left( {{ 38. The equation of auxiliary circle of the ellipse $$16{x^2} + 25{y^2} + 32x - 100y = 284$$ is 39. If PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta 40. If the vertex of the conic $${y^2} - 4y = 4x - 4a$$ always lies between the straight lines $$x + y = 3$$ and $$2x + 2y - 41. A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at 42. Angle between the planes x + y + 2z = 6 and 2x $$-$$ y + z = 9 is 43. If $$y = (1 + x)(1 + {x^2})(1 + {x^4})...(1 + {x^{2n}})$$, then the value of $$\left( {{{dy} \over {dx}}} \right)$$ at x 44. If f(x) is an odd differentiable function defined on ($$-$$$$\infty $$, $$\infty $$) such that f'(3) = 2, then f'($$-$$3 45. $$\mathop {\lim }\limits_{x \to 1} {\left( {{{1 + x} \over {2 + x}}} \right)^{{{(1 - \sqrt x )} \over {(1 - x)}}}}$$ is 46. If $$f(x) = {\tan ^{ - 1}}\left[ {{{\log \left( {{e \over {{x^2}}}} \right)} \over {\log (e{x^2})}}} \right] + {\tan ^{ 47. $$\int {{{\log \sqrt x } \over {3x}}} dx$$ is equal to 48. $$\int {{2^x}[f'(x) + f(x)\log 2]dx} $$ is equal to 49. $$\int\limits_0^1 {\log \left( {{1 \over x} - 1} \right)} dx$$ is equal to 50. The value of $$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt {n + 1} + \sqrt {n + 2} + ... + \sqrt {2n - 1} 51. The sum of n terms of the following series $${1^3} + {3^3} + {5^3} + {7^3} + ...$$ is 52. If $$\alpha$$ and $$\beta$$ are roots of ax2 + bx + c = 0, then the equation whose roots are $$\alpha$$2 and $$\beta$$2, 53. If $$\omega$$ is an imaginary cube root of unity, then the value of (2 $$-$$ $$\omega$$) (2 $$-$$ $$\omega$$2) + 2(3 $$- 54. If $${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84$$ and $${}^n{C_{r + 1}} = 126$$, then the value of $${}^n{C_8}$$ is 55. In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probabili 56. The equation x3 $$-$$ yx2 + x $$-$$ y = 0 represents 57. The locus of the mid-points of chords of the circle x2 + y2 = 1, which subtends a right angle at the origin, is 58. The locus of the mid-points of all chords of the parabola y2 = 4ax through its vertex is another parabola with directrix 59. If [x] denotes the greatest integer less than or equal to x, then the value of the integral $$\int\limits_0^2 {{x^2}[x]\ 60. The number of points at which the function f(x) = max {a $$-$$ x, a + x, b}, $$-$$ $$\infty $$ < x < $$\infty $$, 61. For non-zero vectors a and b, if | a + b | < | a $$-$$ b |, then a and b are 62. General solution of $$y{{dy} \over {dx}} + b{y^2} = a\cos x,0 < x < 1$$ is 63. The points of the ellipse 16x2 + 9y2 = 400 at which the ordinate decreases at the same rate at which the abscissa increa 64. The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in an English 65. If the matrix $$A = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 2 & 0 \cr 2 & 0 & 2 \cr 66. On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y, are 67. If $$\phi (t) = \left\{ \matrix{ 1,\,for\,0 \le t < 1, \hfill \cr 0,\,otherwise \hfill \cr} \right.$$, then $$\ 68. If the equation x2 + y2 $$-$$ 10x + 21 = 0 has real roots x = $$\alpha$$ and y = $$\beta$$, then 69. If z = sin$$\theta$$ $$-$$ icos$$\theta$$, then for any integer n, 70. Let f : X $$ \to $$ X be such that f [f(x)] = x, for all x$$\in$$X and X$$ \subseteq $$R, then 71. If A, B are two events such that P(A $$\cup$$ B) $$ \ge $$ $${3 \over 4}$$ and $${1 \over 8}$$ $$ \le $$ P (A $$\cap$$ B 72. If the first and (2n $$-$$ 1)th terms of an AP, GP and HP are equal and their nth terms are respectively a, b, c, then a 73. The coordinates of a point on the line x + y + 1 = 0, which is at a distance $${1 \over 5}$$ unit from the line 3x + 4y 74. If the parabola x2 = ay makes an intercept of length $$\sqrt {40} $$ units on the line y $$-$$ 2x = 1, then, a is equal 75. If f(x) is a function such that f'(x) = (x $$-$$ 1)2(4 $$-$$ x), then

Physics

1. Equivalent capacitance between A and B in the figure is 2. Two wires of same radius having lengths l1 and l2 and resistivities $${{\rho _1}}$$ and $${{\rho _2}}$$ are connected in 3. A hollow metal sphere of radius R is charged with a charge Q. The electric potential and intensity inside the sphere are 4. The potential difference V required for accelerating an electron to have the de-Broglie wavelength of 1 $$\mathop A\limi 5. The work function of Cesium is 2.27 eV. The cut-off voltage which stops the emission of electrons from a cesium cathode 6. The number of de-Broglie wavelengths contained in the second Bohr orbit of hydrogen atom is 7. The wavelength of second Balmer line in hydrogen spectrum is 600 nm. The wavelength for its third line in Lyman series i 8. A ray of light strikes a glass plate at an angle of 60$$^\circ$$. If the reflected and refracted rays are perpendicular 9. Light travels through a glass plate of thickness t and having refractive index $$\mu$$. If c be the velocity of light in 10. If x = at + bt2, where x is in metre (m) and t is in hour (h), then unit of b will be 11. The vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ are such that | $$\overrightarrow A $$ + $$\overrightarrow 12. At a particular height, the velocity of an ascending body is u. The velocity at the same height while the body falls fre 13. Two bodies of masses m1 and m2 are separated by a distance R. The distance of the centre of mass of the bodies from the 14. The velocity of sound in air at 20$$^\circ$$C and 1 atm pressure is 344.2 m/s. At 40$$^\circ$$C and 2 atm pressure, the 15. The perfect gas equation for 4g of hydrogen gas is 16. If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of 17. A particle vibrating simple harmonically has an acceleration of 16 cms$$-$$2 when it is at a distance of 4 cm from the m 18. Work done for a certain spring when stretched through 1 mm is 10 joule. The amount of work that must be done on the spri 19. If the rms velocity of hydrogen gas at a certain temperature is c, then the rms velocity of oxygen gas at the same tempe 20. For air at room temperature, the atmospheric pressure is 1.0 $$ \times $$ 105 Nm$$-$$2 and density of air is 1.2 kgm$$-$ 21. A gas bubble of 2 cm diameter rises through a liquid of density 1.75 g cm$$-$$3 with a fixed speed of 0.35 cms$$-$$1. Ne 22. The temperature of the water of a pond is 0$$^\circ$$C while that of the surrounding atmosphere is $$-$$20$$^\circ$$C. I 23. 1000 droplets of water having 2 mm diameter each coalesce to form a single drop. Given the surface tension of water is 0 24. A Zener diode having break-down voltage 5.6 V is connected in reverse bias with a battery of emf 10 V and a resistance o 25. In case of a bipolar transistor $$\beta$$ = 45. The potential drop across the collector resistance of 1 k$$\Omega$$ is 5 26. An electron enters an electric field having intensity $$E = 3\widehat i + 6\widehat j + 2\widehat k$$ Vm$$-$$1 and magne 27. Two coils of self-inductances 6 mH and 8 mH are connected in series and are adjusted for highest coefficient of coupling 28. A 1 $$\mu$$F capacitor C is connected to a battery of 10 V through a resistance 1 M$$\Omega$$. The voltage across C afte 29. Two equal resistances, 400 $$\Omega$$ each, are connected in series with a 8 V battery. If the resistance of first one i 30. Angle between an equipotential surface and electric lines of force is 31. A current I = I0e$$-$$$$\lambda$$t is flowing in a circuit consisting of a parallel combination of resistance R and capa 32. For Fraunhoffer diffraction to occur 33. The temperature of a blackbody radiation enclosed in a container of volume V is increased from 100$$^\circ$$C to 1000$$^ 34. A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 ms$$-$$2. (ii) 35. The effective resistance between A and B in the figure is $${7 \over {12}}\Omega $$ if each side of the cube has 1$$\Ome 36. A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 37. The distance between a light source and photoelectric cell is d. If the distance is decreased to $${d \over 2}$$, then 38. A train moves from rest with acceleration $$\alpha$$ and in time t1 covers a distance x. It then decelerates to rest at 39. A drop of water detaches itself from the exit of a tap when ($$\sigma$$ = surface tension of water, $$\rho$$ = density o 40. A rectangular coil carrying-current is placed in a non-uniform magnetic field. On that coil, the total

WB JEE 2016

MCQ (Single Correct Answer)

-0.5

If $$\omega$$ is an imaginary cube root of unity, then the value of (2 $$-$$ $$\omega$$) (2 $$-$$ $$\omega$$²) + 2(3 $$-$$ $$\omega$$)(3 $$-$$ $$\omega$$²) + ... + (n $$-$$ 1) (n $$-$$ $$\omega$$)(n $$-$$ $$\omega$$²) is

$${{{n^2}} \over 4}{(n + 1)^2} - n$$

$${{{n^2}} \over 4}{(n + 1)^2} + n$$

$${{{n^2}} \over 4}{(n + 1)^2}$$

$${{{n^2}} \over 4}(n + 1) - n$$

WB JEE 2016

MCQ (Single Correct Answer)

-0.5

If $${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84$$ and $${}^n{C_{r + 1}} = 126$$, then the value of $${}^n{C_8}$$ is

WB JEE 2016

MCQ (Single Correct Answer)

-0.5

In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a person selected at random from the group is aged above 40 yr given that the selected person is a female, is

$${2 \over 7}$$

$${1 \over 2}$$

$${1 \over 4}$$

$${5 \over 6}$$

WB JEE 2016

MCQ (Single Correct Answer)

-0.5

The equation x³ $$-$$ yx² + x $$-$$ y = 0 represents

a hyperbola and two straight lines

a straight line

a parabola and two straight lines

a straight line and a circle