> WBJEE Sample Papers, Section Wise & Full Mock Tests > WBJEE Previous Year - 2011
Download as PDF

Test Description

1 Crore+ students have signed up on EduRev. Have you? |

WBJEE Previous Year - 2011 - Question 1

The eccentricity of the hyperbola 4x^{2} – 9y^{2} = 36 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 1

WBJEE Previous Year - 2011 - Question 2

The length of the latus rectum of the ellipse 16x^{2} + 25y^{2} = 400 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 2

WBJEE Previous Year - 2011 - Question 3

The vertex of the parabola y^{2} + 6x – 2y + 13 = 0 is

( y −1)^{2}= −6x − 12

( y −1)^{2}= −6(x +12) = 4(-6/4)(x+2)

Vertex →(−2, 1)

WBJEE Previous Year - 2011 - Question 4

The coordinates of a moving point p are (2t^{2} + 4, 4t + 6). Then its locus will be a

Detailed Solution for WBJEE Previous Year - 2011 - Question 4

WBJEE Previous Year - 2011 - Question 5

The equation 8x^{2} + 12y^{2} – 4x + 4y – 1 = 0 represents

Detailed Solution for WBJEE Previous Year - 2011 - Question 5

ax^{2} + by^{2}+ 2hxy + 2gx + 2fy + c = 0

represents ellipse if h^{2 }−ab< 0

3x2 + 12y2− 4x + 4y − 1 = 0

h =0, a= 3, b = 12

h^{2} −ab< 0

WBJEE Previous Year - 2011 - Question 6

If the straight line y = mx lies outside of the circle x^{2} + y^{2} – 20y + 90 = 0, then the value of m will satisfy

Detailed Solution for WBJEE Previous Year - 2011 - Question 6

x^{2} +m^{2} x^{2}− 20mx + 90

x^{2} (1 + m^{2})− 20mx + 90 = 0

D <0

400m^{2} − 4× 90 (1 + m^{2}) < 0

40m^{2 }< 360

m^{2} < 9 ; |m |< 3

WBJEE Previous Year - 2011 - Question 7

The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 7

Centre lies on y-axis locus x = 0

WBJEE Previous Year - 2011 - Question 8

The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are

Detailed Solution for WBJEE Previous Year - 2011 - Question 8

Let p (h, 4 − h)

|h + 2|= 5

h =3,−7 ; p =1, 1

(3,1),(−7,11)

WBJEE Previous Year - 2011 - Question 9

The intercept on the line y = x by the circle x^{2} + y^{2} – 2x = 0 is AB. Equation of the circle with AB as diameter is

Detailed Solution for WBJEE Previous Year - 2011 - Question 9

x^{2} + y^{2} = 0

( 0, 0 ) , (1,1) as diametric ends (x − 0)(x−1) + (y + 0)(y −1) = 0

x^{2} +y^{2}− x − y = 0

WBJEE Previous Year - 2011 - Question 10

If the coordinates of one end of a diameter of the circle x2+y2+4x–8y+5=0, is (2,1), the coordinates of the other end is

Detailed Solution for WBJEE Previous Year - 2011 - Question 10

x^{2} + y^{2}+ 9x − 8y + 5 = 0

Centre circle (–2, 4)

WBJEE Previous Year - 2011 - Question 11

If the three points A(1,6), B(3, –4) and C(x, y) are collinear then the equation satisfying by x and y is

Detailed Solution for WBJEE Previous Year - 2011 - Question 11

⇒ 1(3y+ 4x) − (y − 6x) +1(−4 −18) = 0

⇒ 3y+ 4x − y + 6x −12 = 0

⇒ 2y+ 10x − 22 = 0

y +5x= 11

WBJEE Previous Year - 2011 - Question 12

and θ lies in the second quadrant, then cosθ is equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 12

θ in 2nd quad Cosθ < 0

WBJEE Previous Year - 2011 - Question 13

The solutions set of inequation cos^{–1}x < sin^{–1}x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 13

cos^{–1}x < sin^{–1}x

Detailed Solution for WBJEE Previous Year - 2011 - Question 14

√5 <3 No solution

Detailed Solution for WBJEE Previous Year - 2011 - Question 15

Detailed Solution for WBJEE Previous Year - 2011 - Question 16

WBJEE Previous Year - 2011 - Question 17

If sinθ and cosθ are the roots of the equation ax^{2} – bx + c = 0, then a, b and c satisfy the relation

Detailed Solution for WBJEE Previous Year - 2011 - Question 17

sinθ + cosθ = b/a

sinθ . cosθ = c/a

WBJEE Previous Year - 2011 - Question 18

If A and B are two matrices such that A+B and AB are both defined, then

Detailed Solution for WBJEE Previous Year - 2011 - Question 18

Addition is defined if order of A is equal to order of B

AB is defined if m = n

nxm nxm

⇒ A, B are square matrices of same order

Detailed Solution for WBJEE Previous Year - 2011 - Question 19

A = A^{T}

Detailed Solution for WBJEE Previous Year - 2011 - Question 20

= -(-21-64)-((1-2i)(7(1+2i)+5i(5-3i)))+5i(1+2i)(5+3i)-15i)

= Real

WBJEE Previous Year - 2011 - Question 21

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 21

y = a sin θ

x = a cos θ.

x^{2} + y^{2}= a^{2}

Detailed Solution for WBJEE Previous Year - 2011 - Question 23

Detailed Solution for WBJEE Previous Year - 2011 - Question 24

WBJEE Previous Year - 2011 - Question 25

If y = 2x^{3 }– 2x^{2} + 3x – 5, then for x = 2 and Δ x = 0.1 value of Δ y is

Detailed Solution for WBJEE Previous Year - 2011 - Question 25

WBJEE Previous Year - 2011 - Question 26

The approximate value of 5√33 correct to 4 decimal places is

Detailed Solution for WBJEE Previous Year - 2011 - Question 26

Detailed Solution for WBJEE Previous Year - 2011 - Question 27

WBJEE Previous Year - 2011 - Question 28

For the function f(x) = e^{cos x }, Rolle’s theorem is

Detailed Solution for WBJEE Previous Year - 2011 - Question 28

Detailed Solution for WBJEE Previous Year - 2011 - Question 29

Detailed Solution for WBJEE Previous Year - 2011 - Question 30

Detailed Solution for WBJEE Previous Year - 2011 - Question 31

Detailed Solution for WBJEE Previous Year - 2011 - Question 32

WBJEE Previous Year - 2011 - Question 33

The degree and order of the differential equation are repectively

Detailed Solution for WBJEE Previous Year - 2011 - Question 33

Detailed Solution for WBJEE Previous Year - 2011 - Question 34

WBJEE Previous Year - 2011 - Question 35

The function f(x) = ax + b is strictly increasing for all real x if

Detailed Solution for WBJEE Previous Year - 2011 - Question 35

f′ (x) = a f′(x) > 0 ⇒ a > 0

Detailed Solution for WBJEE Previous Year - 2011 - Question 36

Detailed Solution for WBJEE Previous Year - 2011 - Question 37

Detailed Solution for WBJEE Previous Year - 2011 - Question 38

Detailed Solution for WBJEE Previous Year - 2011 - Question 39

Detailed Solution for WBJEE Previous Year - 2011 - Question 40

C_{2} → C_{2} – C_{3}

C_{3 }→ C_{3} + C_{2}

C_{3} → C_{3} + ωC_{1 }

C_{2} → C_{2} – C_{1}

WBJEE Previous Year - 2011 - Question 41

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

Detailed Solution for WBJEE Previous Year - 2011 - Question 41

WBJEE Previous Year - 2011 - Question 42

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

Detailed Solution for WBJEE Previous Year - 2011 - Question 42

p = 1.1.1.1/2 = 1/2

Detailed Solution for WBJEE Previous Year - 2011 - Question 43

Detailed Solution for WBJEE Previous Year - 2011 - Question 44

Detailed Solution for WBJEE Previous Year - 2011 - Question 45

WBJEE Previous Year - 2011 - Question 46

If A and B are coefficients of xn in the expansions of (1+ x)^{2n} and (1+x)^{2n – 1} respectively, then A/B is equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 46

A = ^{2n}C^{n}

B = ^{2n – 1}C_{n}

WBJEE Previous Year - 2011 - Question 47

If n > 1 is an integer and x ≠0, then (1 + x)^{n} – nx – 1is divisible by

Detailed Solution for WBJEE Previous Year - 2011 - Question 47

(1 + x)n = ^{n}C_{0} + ^{n}C_{1}x + ^{n}C_{2}x² + ^{n}C_{3}x^{3} + .......

= 1 + nx + x² (^{n}C_{2} + ^{n}C_{3} x + .........) (1 + x)n – nx – 1

= x² (^{n}C_{2}+ ^{n}C_{3}x + ........)

WBJEE Previous Year - 2011 - Question 48

If ^{n}C_{4}, ^{n}C_{5} and ^{n}C_{6} are in A.P., then n is

Detailed Solution for WBJEE Previous Year - 2011 - Question 48

^{n}C_{4}, ^{n}C_{5} and ^{n}C_{6}

WBJEE Previous Year - 2011 - Question 49

The number of diagonals in a polygon is 20. The number of sides of the polygon is

Detailed Solution for WBJEE Previous Year - 2011 - Question 49

^{n}C_{2} –n = 20

n = 8

Detailed Solution for WBJEE Previous Year - 2011 - Question 50

WBJEE Previous Year - 2011 - Question 51

Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax^{2} + bx + c = 0

Detailed Solution for WBJEE Previous Year - 2011 - Question 51

WBJEE Previous Year - 2011 - Question 52

If the ratio of the roots of the equation px^{2} + qx + r = 0 is a : b, then ab/(a + b)^{2 }is

Detailed Solution for WBJEE Previous Year - 2011 - Question 52

WBJEE Previous Year - 2011 - Question 53

If α and β are the roots of the equation x^{2 }+ x + 1 = 0, then the equation whose roots are α^{19} and β^{7} is

Detailed Solution for WBJEE Previous Year - 2011 - Question 53

α and β are the roots of x^{2} + x + 1 = 0

α = ω

β=ω^{2}

α^{19} = ω

β^{7} = ω^{2}

x^{2} – (α^{19 }+ β^{7})x + α^{19} β^{7} = 0

Thou, x^{2} – (ω + ω^{ 2}) x + ω . ω^{ 2} = 0

x^{2} + x + 1 = 0

WBJEE Previous Year - 2011 - Question 54

For the real parameter t, the locus of the complex number z = (1 – t²) + i√(1 + t^{2}) in the complex plane is

Detailed Solution for WBJEE Previous Year - 2011 - Question 54

Let z = x + iy

x = 1 – t^{2}

y^{2} = 1 + t^{2}

Thus, x + y^{2} = 2

y^{2} = 2 – x

y^{2} = – (x – 2)

Thus parabola

WBJEE Previous Year - 2011 - Question 55

if x + 1/x = 2cosθ, then for any integer n , x^{n} + 1/x_{n}

Detailed Solution for WBJEE Previous Year - 2011 - Question 55

x + 1/x = 2cosθ

Let x = cos θ + 1 sin θ

1/x = cosθ − 1sinθ

thus, x^{n} + 1/x_{n} = 2 cos nθ

WBJEE Previous Year - 2011 - Question 56

If ω ≠ 1 is a cube root of unity, then the sum of the series S = 1 + 2ω + 3ω ² + .......... + 3nω^{ 3n – 1} is

Detailed Solution for WBJEE Previous Year - 2011 - Question 56

S = 1 + 2ω + 3ω ² + .......... + 3nω^{ 3n – 1}

Sω = ω + ω ² + .......... + (3n-1)ω^{ 3n – 1} + 3nω^{n}

s(1 – ω) = 1 + ω + ω² + ...........+ ω^{3n–1} – 3nω^{3h}

= 0 – 3n

WBJEE Previous Year - 2011 - Question 57

If log_{3}x + log_{3}y = 2 + log_{3}2 and log_{3}(x + y) = 2, then

Detailed Solution for WBJEE Previous Year - 2011 - Question 57

log_{3}x + log_{3}y = 2 + log_{3}2

⇒ x.y = 18 log (x + y) = 2

⇒ x + y = 9

we will get x = 3 and y = 6

Detailed Solution for WBJEE Previous Year - 2011 - Question 58

log_{49}28 = log_{72}4 × 7

WBJEE Previous Year - 2011 - Question 59

The sequence log a, log a^{2}/b, loga^{3}/b^{2}, ....... is

Detailed Solution for WBJEE Previous Year - 2011 - Question 59

log a . (2log a – log b)(3log a – 2 log b)

= T_{2} – T_{1} = log a – log b

= T_{3}– T_{2} = log a – log b

WBJEE Previous Year - 2011 - Question 60

If in a triangle ABC, sin A, sin B, sin C are in A.P., then

Detailed Solution for WBJEE Previous Year - 2011 - Question 60

Detailed Solution for WBJEE Previous Year - 2011 - Question 61

c_{1} → c_{1 }+ c_{2} + c_{3}

Detailed Solution for WBJEE Previous Year - 2011 - Question 62

WBJEE Previous Year - 2011 - Question 63

Let f(x) = x^{3}e^{–3x}, x > 0. Then the maximum value of f(x) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 63

f(x) = x^{3}e^{–3x}

= f′(x) = 3x^{2}e^{–3x} + x^{3} e^{–3x }(–3)

= x^{2}3e^{–3x}[1 – x] = 0, x = 1

Maximum at x = 1

f(1) = e^{–3}

Detailed Solution for WBJEE Previous Year - 2011 - Question 64

WBJEE Previous Year - 2011 - Question 65

The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2. The time taken by the particle to move the second metre is

Detailed Solution for WBJEE Previous Year - 2011 - Question 65

Detailed Solution for WBJEE Previous Year - 2011 - Question 66

WBJEE Previous Year - 2011 - Question 67

Integrating Factor (I.F.) of the defferential equation

Detailed Solution for WBJEE Previous Year - 2011 - Question 67

WBJEE Previous Year - 2011 - Question 68

The differential equation of y = ae^{bx} (a & b are parameters) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 68

y = a.e^{bx} ............ (i)

y_{1} = abe^{bx}

y_{1} = by............(ii)

y_{2} = by_{1} ...........(iii)

Detailed Solution for WBJEE Previous Year - 2011 - Question 69

Detailed Solution for WBJEE Previous Year - 2011 - Question 70

Detailed Solution for WBJEE Previous Year - 2011 - Question 71

I = ∫ 2x f ′(x)dx+∫ 2x f (x) log 2dx

= 2^{x}f(x)

WBJEE Previous Year - 2011 - Question 72

Let f(x) = tan^{–1}x. Then f′(x) + f′′(x) is = 0, when x is equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 72

f(x) = tan^{–1}x

Detailed Solution for WBJEE Previous Year - 2011 - Question 73

Detailed Solution for WBJEE Previous Year - 2011 - Question 74

Detailed Solution for WBJEE Previous Year - 2011 - Question 75

Detailed Solution for WBJEE Previous Year - 2011 - Question 76

WBJEE Previous Year - 2011 - Question 77

if f(x) is continuous at x = 2, the value of λ will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 77

Detailed Solution for WBJEE Previous Year - 2011 - Question 78

Detailed Solution for WBJEE Previous Year - 2011 - Question 79

WBJEE Previous Year - 2011 - Question 80

The locus of the middle points of all chords of the parabola y^{2} = 4ax passing through the vertex is

Detailed Solution for WBJEE Previous Year - 2011 - Question 80

2h = x, 2k = y

y^{2} = 4ax

k^{2} = 2ah

y^{2} = 2ax

WBJEE Previous Year - 2011 - Question 81

The charge on the capacitor of capacitance C shown in the figure below will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 81

∴ Potential difference across R_{2} ,

∴ Charge on the capacitor

WBJEE Previous Year - 2011 - Question 82

The resistance across A and B in the figure below will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 82

Resistance are in parallel = R/3

WBJEE Previous Year - 2011 - Question 83

Five equal resistance, each of resistance R, are connected as shown in figure below. A battery of V volt is connected between A and B. The current flowing in FC will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 83

WBJEE Previous Year - 2011 - Question 84

Two cells with the same e.m.f. E and different internal resistances r_{1} and r_{2} are connected in series to an external resistance R. The value of R so that the potential difference across the first cell be zero is

Detailed Solution for WBJEE Previous Year - 2011 - Question 84

WBJEE Previous Year - 2011 - Question 85

Current through ABC and A'B'C' is I. What is the magnetic field at P? BP = PB' = r (Here C'B' PBC are collinear)

Detailed Solution for WBJEE Previous Year - 2011 - Question 85

WBJEE Previous Year - 2011 - Question 86

The magnetic field at the point of intersection of diagonals of a square wire loop of side L carrying a current I is

Detailed Solution for WBJEE Previous Year - 2011 - Question 86

WBJEE Previous Year - 2011 - Question 87

In an inelastic collision an electron excites as hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-State and ionizes it. At least how much energy the second electron transfers to the atom in the M-state?

Detailed Solution for WBJEE Previous Year - 2011 - Question 87

Minimum energy required by electron should be +1.51 eV

WBJEE Previous Year - 2011 - Question 88

A radioactive nucleus of mass number A, initially at rest, emits an α-particle with a speed ν . The recoil speed of the daughter nucleus will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 88

From conservation of momentum

WBJEE Previous Year - 2011 - Question 90

Which type of Gate the following truth table represents?

Detailed Solution for WBJEE Previous Year - 2011 - Question 90

WBJEE Previous Year - 2011 - Question 91

Given A =2iˆ+ 3ˆj and B = ˆi+ˆj. The component of vector A along vector B is

Detailed Solution for WBJEE Previous Year - 2011 - Question 91

WBJEE Previous Year - 2011 - Question 92

A cubical vessel of height 1 m is full of water. What is the amount of work done in pumping water out of the vessel? (Take g = 10 m s^{–2})

Detailed Solution for WBJEE Previous Year - 2011 - Question 92

V = l^{3}=1m^{3}

m = 1 x 1000 = 1000kg

w = mgh = 1000 x 10 x 1/2= 5000J

WBJEE Previous Year - 2011 - Question 93

A stone of relative density K is released from rest on the surface of a lake. If viscous effects are ignored, the stone sinks in water with an acceleration of

Detailed Solution for WBJEE Previous Year - 2011 - Question 93

WBJEE Previous Year - 2011 - Question 94

If a person can throw a stone to maximum height of h metre vertically, then the maximum distance through which it can be thrown horizontally by the same person is

Detailed Solution for WBJEE Previous Year - 2011 - Question 94

WBJEE Previous Year - 2011 - Question 95

A body of mass 6 kg is acted upon by a force which causes a displacement in it given x = t^{2}/4 metre where t is the time in second. The work done by the force in 2 seconds is

Detailed Solution for WBJEE Previous Year - 2011 - Question 95

WBJEE Previous Year - 2011 - Question 96

A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

Detailed Solution for WBJEE Previous Year - 2011 - Question 96

WBJEE Previous Year - 2011 - Question 97

A particle is moving with a constant speed ν in a circle. What is the magnitude of average velocity after half rotation?

Detailed Solution for WBJEE Previous Year - 2011 - Question 97

WBJEE Previous Year - 2011 - Question 98

A cricket ball of mass 0.25 kg with speed 10 m/s collides with a bat and returns with same speed within 0.01 S. The force acted on bat is

Detailed Solution for WBJEE Previous Year - 2011 - Question 98

WBJEE Previous Year - 2011 - Question 99

If the Earth were to suddenly contract to 1/n th of its present radius without any change in its mass, the duration of the new day will be nearly

Detailed Solution for WBJEE Previous Year - 2011 - Question 99

I_{1}ω_{1}=I _{2} ω_{ 2}

WBJEE Previous Year - 2011 - Question 100

If g is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass m raised from the earth’s surface to a height equal to the radius R of the earth is

Detailed Solution for WBJEE Previous Year - 2011 - Question 100

WBJEE Previous Year - 2011 - Question 101

A material has Poisson’s ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2 × 10^{–3}, then the percentage change in volume is

WBJEE Previous Year - 2011 - Question 102

Two identical springs are connected to mass m as shown (k = spring constant). If the period of the configuration in (a) is 2S, the period of the configuration (b) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 102

T = 1S

WBJEE Previous Year - 2011 - Question 103

An object weighs m_{1} in a liquid of density d_{1} and that in liquid of density d_{2} is m_{2}. The density d of the object is

Detailed Solution for WBJEE Previous Year - 2011 - Question 103

V(d – d_{1})g = m_{1}g

V(d – d_{2})g = m_{2}g

WBJEE Previous Year - 2011 - Question 104

A body floats in water with 40% of its volume outside water. When the same body floats in an oil, 60% of its volume remains outside oil. The relative density of oil is

Detailed Solution for WBJEE Previous Year - 2011 - Question 104

Vσg = 0.6 Vσ_{1}g ...... (1)

Vσg = 0.4 Vσ_{2}g .................. (2)

Dividing (1) and (2)

= 3/2

WBJEE Previous Year - 2011 - Question 105

Two soap bubbles of radii x and y coalesee to constitute a bubble of radius z. Then z is requal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 105

n = n1 + n2

pv = p1v1 + p2v2

WBJEE Previous Year - 2011 - Question 106

A particle of mass m is located in a one dimensional potential field where potential energy is given by : V(x) = A(1 – cos px), where A and p are constants. The period of small oscillations of the particle is

Detailed Solution for WBJEE Previous Year - 2011 - Question 106

v _{x} =A(1− cos px )

WBJEE Previous Year - 2011 - Question 107

The period of oscillation of a simple pendulum of length l suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α, is given by

Detailed Solution for WBJEE Previous Year - 2011 - Question 107

WBJEE Previous Year - 2011 - Question 108

In Young’s double slit experiment the two slits are d distance apart. Interference pattern is observed on a screen at a distance D from the slits. A dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is

Detailed Solution for WBJEE Previous Year - 2011 - Question 108

WBJEE Previous Year - 2011 - Question 109

A plane progressive wave is given by y = 2 cos 6.284 (330 t – x). What is period of the wave ?

Detailed Solution for WBJEE Previous Year - 2011 - Question 109

y = 2 cos 2π (330 t – x)

ω = 2π × 330

T = 1/330 S

WBJEE Previous Year - 2011 - Question 110

The displacement of a particle in S.H.M. varies according to the relation x = 4(cos πt + sin πt). The amplitude of the particle is

Detailed Solution for WBJEE Previous Year - 2011 - Question 110

R sin δ = 4

R cos δ = 4

R = 4√2

WBJEE Previous Year - 2011 - Question 111

Two temperature scales A and B are related by At which temperature two scales have the same reading ?

Detailed Solution for WBJEE Previous Year - 2011 - Question 111

, A = B

2A – 84 = A – 72

A = 12

WBJEE Previous Year - 2011 - Question 112

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume (γ = 1.4 and 2^{-14}= 0.38). The ratio of the final to initial pressure is

Detailed Solution for WBJEE Previous Year - 2011 - Question 112

WBJEE Previous Year - 2011 - Question 113

Air inside a closed container is saturated with water vapour. The air pressure is p and the saturated vapour pressure of water is p^{-} . If the mixture is compressed to one half of its volume by maintaining temperature constant, the pressure becomes

WBJEE Previous Year - 2011 - Question 114

1.56 × 10^{5} J of heat is conducted through a 2 m^{2} wall of 12 cm thick in one hour. Temperature difference between the two sides of the wall is 20^{0}C. The thermal conductivity of the material of the wall is (in W m^{–1 }K^{–1})

Detailed Solution for WBJEE Previous Year - 2011 - Question 114

WBJEE Previous Year - 2011 - Question 115

A diver at a depth of 12 m in water ( μ = 4/3) sees the sky in a cone of semivertical angle :

Detailed Solution for WBJEE Previous Year - 2011 - Question 115

sin^{-1}(4/3)

WBJEE Previous Year - 2011 - Question 116

Two thin lenses of focal lengths 20 cm and 25 cm are placed in cotact. The effective power of the combination is

Detailed Solution for WBJEE Previous Year - 2011 - Question 116

P = P_{1} + P_{2}

WBJEE Previous Year - 2011 - Question 117

A convex lens of focal length 30 cm produces 5 times magnified real image of an object. What is the object distance ?

Detailed Solution for WBJEE Previous Year - 2011 - Question 117

WBJEE Previous Year - 2011 - Question 118

If the focal length of the eye piece of a telescope is doubled, its magnifying power (m) will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 118

m = -f_{0}/f_{e}

m' = m/2

WBJEE Previous Year - 2011 - Question 119

A plano-concave lens is made of glass of refractive index 1.5 and the radius of curvature of its curved face is 100 cm. What is the power of the lens ?

Detailed Solution for WBJEE Previous Year - 2011 - Question 119

WBJEE Previous Year - 2011 - Question 120

Four charges equal to –Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is

Detailed Solution for WBJEE Previous Year - 2011 - Question 120

WBJEE Previous Year - 2011 - Question 121

Two aromatic compounds having formula C7H8O which are easily identifiable by FeCl_{3} solution test (violet colouration) are

Detailed Solution for WBJEE Previous Year - 2011 - Question 121

O – cresol contains phenolic group, thus it gives violet coloration with FeCl_{3} where as benzylalchol donot contains phenolic group, hence no coloration with FeCl_{3}. Hence Identifiable

WBJEE Previous Year - 2011 - Question 122

The ease of dehydrohalogenation of alkyl halide with alcoholic KOH is

Detailed Solution for WBJEE Previous Year - 2011 - Question 122

Such dehydrohalogenation follows E_{2 }mechanism. The driving force of such reactions is the stability of alkene produced. Since tetriary alkyl halide can give more substituted alkene, it reacts fastest followed by secondary and primary i.e. 3^{o} > 2^{o} > 1^{o}.

WBJEE Previous Year - 2011 - Question 123

The ease of Nitration of the following three hydrocarbons follows the order

WBJEE Previous Year - 2011 - Question 124

The correct order of decreasing acidity of nitrophenols will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 124

Due to – I and – R influence, NO_{2} in ortho-postion should have raised the acidity to the maximum extent. But it is due to intramolecular H – bonding, ortho-nitrophenol is less acidic than para – nitrophenol.

WBJEE Previous Year - 2011 - Question 125

Among the alkenes which one produces tertiary bytyl alcohol on acid hydration

Detailed Solution for WBJEE Previous Year - 2011 - Question 125

WBJEE Previous Year - 2011 - Question 126

Which of the following compounds has maximum volatility?

A.

B.

C.

D.

Detailed Solution for WBJEE Previous Year - 2011 - Question 126

Due to intramolecular H – bonding

WBJEE Previous Year - 2011 - Question 127

Which one of the following will show optical isomerism?

Detailed Solution for WBJEE Previous Year - 2011 - Question 127

The central carbon is attached to four different substituents, hence it is chiral carbon, therefore optically active.

WBJEE Previous Year - 2011 - Question 128

The pH of an aqueous solution of CH_{3}COONa of concentrated C(M) is given by

Detailed Solution for WBJEE Previous Year - 2011 - Question 128

In case of Hydrolysis of salt of weak acid and strong base, the pH is given by

WBJEE Previous Year - 2011 - Question 129

The standard reduction potential E^{o} for half reations are

Zn = Zn^{+2} + Ze E^{o} = +0.76 V

Fe = Fe^{+2 }+ Ze E^{o }= + 0.41 V

The EMF of hte cell reaction

Fe^{+2 }+ Zn = Zn^{+2} + Fe

WBJEE Previous Year - 2011 - Question 130

If the equilibrium constants of the following equilibria

are given by K_{1 }and K_{2} respectively, which of the following relations is correct

Detailed Solution for WBJEE Previous Year - 2011 - Question 130

WBJEE Previous Year - 2011 - Question 131

The energy of an electron in first Bohr orbit of H – atom is – 13.6 eV. The possible energy value of electron in the excited state of Li^{2+} is

Detailed Solution for WBJEE Previous Year - 2011 - Question 131

For the excited state, n = 2 and for Li^{++ }ion, z = 3

WBJEE Previous Year - 2011 - Question 132

The amount of the heat released when 20 ml 0.5 M NaOH is mixed with 100 ml 0.1 M HCl is x kJ. The heat of neutralization is

Detailed Solution for WBJEE Previous Year - 2011 - Question 132

During formation of 10 millimole of H2O the heat released is x KJ. Therefore heat of neutralisation is – 100 x KJ/mol (heat released hence negative)

WBJEE Previous Year - 2011 - Question 133

Which one of the following has the lowest ionization energy?

Detailed Solution for WBJEE Previous Year - 2011 - Question 133

It’s an alkalimetal; hence least I.P

Detailed Solution for WBJEE Previous Year - 2011 - Question 134

WBJEE Previous Year - 2011 - Question 135

2 gm of metal carbonate is neutralized completely by 100 ml of 0.1 (N) HCl. The equivalent weight of metal carbonate is

Detailed Solution for WBJEE Previous Year - 2011 - Question 135

Number of gram equivalents of HCl = 100 x 0.1/1000 = 0.01

Number of gram equivalents of metal carbonate required for neutralisation must also be 0.01. Thus, mass of 1 gram eqivalent of carbonate salt 2/0.01= 200g

WBJEE Previous Year - 2011 - Question 136

Which one of the following is not true at room temperature and pressure

Detailed Solution for WBJEE Previous Year - 2011 - Question 136

SO_{3} is a colourless gas, crystalline transparent solid at room temperature.

WBJEE Previous Year - 2011 - Question 137

An electric current is passed through an aqueous solution of a mixture of alanine (isoelectric point 6.0) glutamic acid (3.2) and arginine (10.7) buffered at pH 6. What is the fate of the three acids?

Detailed Solution for WBJEE Previous Year - 2011 - Question 137

At pH = 6, glutamic acid exists as a dianionic species & migrates to anode while arginine exists as cationic species & moves to cathode. Alanine does not migrate to any electrode at its isoelectric point .

WBJEE Previous Year - 2011 - Question 138

The representation of the ground state electronic configuration of He by box – diagram as ↑↑ is wrong because it violates

Detailed Solution for WBJEE Previous Year - 2011 - Question 138

According to Pauli Exclusion Principle, In any orbital, maximum two electrons can exist, having opposite spin.

WBJEE Previous Year - 2011 - Question 139

The electronic transitions from n = 2 to n = 1 will produce shortest wavelength in (where n = principal quantum state)

Detailed Solution for WBJEE Previous Year - 2011 - Question 139

Hence, for shortest λ, z must be maximum, which is for Li^{+2}.

WBJEE Previous Year - 2011 - Question 140

In the following electron – dot structure, calculate the formal charge from left to right nitrogen atom;

Detailed Solution for WBJEE Previous Year - 2011 - Question 140

Formal chargl = Number of electrons in

Valence shell –(1/2) x numbers of electrons as bond pair + numbers of electrons as lone pair)

WBJEE Previous Year - 2011 - Question 141

If the molecular wt. of Na_{2}S_{2}O_{3 }and I_{2} are M_{1} and M_{2} respectively, then what will be the equivalent wt. of Na_{2}S_{2}O_{3 }and I_{2} in the following reaction?

Detailed Solution for WBJEE Previous Year - 2011 - Question 141

WBJEE Previous Year - 2011 - Question 142

A radioactive atom _{y}^{x}M emits two α particles and one β particle successively. The number of neutrons in the nucleus of the product will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 142

Number of neutrons

= Mass no. – Atomic no.

= X – 8 – Y + 3

= X – Y – 5

WBJEE Previous Year - 2011 - Question 143

An element belongs to Group 15 and third period of the periodic table. Its electonic configuration will be

Detailed Solution for WBJEE Previous Year - 2011 - Question 143

General valence shell electronic configuration of 15 group elements is ns^{2}np^{3}. where n = period number.

Detailed Solution for WBJEE Previous Year - 2011 - Question 144

WBJEE Previous Year - 2011 - Question 145

Platinum, Palladium and Iridium are called noble metals because

Detailed Solution for WBJEE Previous Year - 2011 - Question 146

Guanine is the constituent of nucleic acid and not guanidine.

WBJEE Previous Year - 2011 - Question 147

The sp^{3}d^{2} hybridization of central atom of a molecule would lead to

Detailed Solution for WBJEE Previous Year - 2011 - Question 148

WBJEE Previous Year - 2011 - Question 149

Which of the following is used to prepare Cl_{2} gas at room temperature from concentrated HCl?

Detailed Solution for WBJEE Previous Year - 2011 - Question 149

2MnO_{4}^{-}+ 16 H^{+} + 10Cl^{– }→ 2Mn^{2+} + 5Cl_{2} + 8H_{2}O

Detailed Solution for WBJEE Previous Year - 2011 - Question 150

Detailed Solution for WBJEE Previous Year - 2011 - Question 151

Volume strength = 5.6 × normality

30 = 5.6 × N

N = 30/5.6 = 5.3

Detailed Solution for WBJEE Previous Year - 2011 - Question 152

6HCHO + 4NH_{3} → (CH_{2})_{6 }N_{4} + 6H_{2}O

WBJEE Previous Year - 2011 - Question 153

A plot of In k against 1/T (abscissa) is expected to be a straight line with intercept on ordinate axis equal to

Detailed Solution for WBJEE Previous Year - 2011 - Question 153

ΔG° = – RT InK

or, ΔH° – TΔS° = – RT InK

WBJEE Previous Year - 2011 - Question 154

Which of the following represents the composition of Carnallite mineral?

WBJEE Previous Year - 2011 - Question 155

The solubility of Ca3(PO4)2 in water is y moles / litre. Its solubility product is

Detailed Solution for WBJEE Previous Year - 2011 - Question 155

Detailed Solution for WBJEE Previous Year - 2011 - Question 156

Detailed Solution for WBJEE Previous Year - 2011 - Question 157

WBJEE Previous Year - 2011 - Question 158

Which one of the following is s-butyl phynylvinyl methane?

Detailed Solution for WBJEE Previous Year - 2011 - Question 158

WBJEE Previous Year - 2011 - Question 159

Hybridization of C_{2} and C_{3} of H_{3}C – CH = C = CH – CH_{3} are

Detailed Solution for WBJEE Previous Year - 2011 - Question 159

WBJEE Previous Year - 2011 - Question 160

Which of the following compounds is not formed in iodoform reaction of acetone

Detailed Solution for WBJEE Previous Year - 2011 - Question 160

Detailed Solution for WBJEE Previous Year - 2011 - Question 161

Glucose and amino acids are reabsorbed in the proximal tubule of nephron.

Detailed Solution for WBJEE Previous Year - 2011 - Question 162

The amount of CSF in the cranial cavity is 140 ml.

Detailed Solution for WBJEE Previous Year - 2011 - Question 163

Proline and hydroxyproline are imino acids.

WBJEE Previous Year - 2011 - Question 164

The main difference between Gram positive and Gram negative bacteria is

Detailed Solution for WBJEE Previous Year - 2011 - Question 165

ACTH is secreted from anterior pituitary

WBJEE Previous Year - 2011 - Question 166

Which of the following is the correct pathway for propagation of cardiac impulse?

WBJEE Previous Year - 2011 - Question 167

Inner surface of the bronchi, bronchioles and fallopian tubes are lined by

Detailed Solution for WBJEE Previous Year - 2011 - Question 167

Ciliated epithelium is found in inner surface of bronchi, bronchioles and fallopian tubes