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WBJEE Previous Year - 2011


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240 Questions MCQ Test WBJEE Sample Papers, Section Wise & Full Mock Tests | WBJEE Previous Year - 2011

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WBJEE Previous Year - 2011 - Question 1

The eccentricity of the hyperbola  4x2 – 9y2 = 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 16x2 + 25y2 = 400 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 2

WBJEE Previous Year - 2011 - Question 3

The vertex of  the parabola  y2 + 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 (2t2 + 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  8x2 + 12y2 – 4x + 4y – 1 = 0  represents

Detailed Solution for WBJEE Previous Year - 2011 - Question 5

ax2 + by2+ 2hxy + 2gx + 2fy + c = 0

represents ellipse if h2 −ab< 0

3x2 + 12y2− 4x + 4y − 1 = 0

h =0, a= 3, b = 12

h2 −ab< 0

WBJEE Previous Year - 2011 - Question 6

If the straight line  y = mx lies outside of the circle x2 + y2 – 20y + 90 = 0, then the value of  m will satisfy

Detailed Solution for WBJEE Previous Year - 2011 - Question 6

x2 +m2 x2− 20mx + 90

x2 (1 + m2)− 20mx + 90 = 0

D <0

400m2 − 4× 90 (1 + m2) < 0

40m2 < 360

m2 < 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 x2 + y2 – 2x = 0 is  AB.  Equation of the circle with AB as diameter is

Detailed Solution for WBJEE Previous Year - 2011 - Question 9

x2 + y2 = 0

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

x2 +y2− 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

x2 + y2+ 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–1x < sin–1x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 13

cos–1x < sin–1

WBJEE Previous Year - 2011 - Question 14

The number of solutions of  2sinx + cos x = 3 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 14

√5 <3      No solution

WBJEE Previous Year - 2011 - Question 15

Detailed Solution for WBJEE Previous Year - 2011 - Question 15

 

WBJEE Previous Year - 2011 - Question 16

If  θ+ φ = π/4 then (1 + tanθ)(1 + tanφ)  is equal to

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  ax2 – 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

WBJEE Previous Year - 2011 - Question 19

  is a symmetric matrix, then the value of  x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 19

A = AT

WBJEE Previous Year - 2011 - Question 20

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.

x2 + y2= a2

WBJEE Previous Year - 2011 - Question 22

If sinθ + cosθ = 0 and 0 < θ < π, then θ

WBJEE Previous Year - 2011 - Question 23

The value of cos 15o – sin 15o is

Detailed Solution for WBJEE Previous Year - 2011 - Question 23

WBJEE Previous Year - 2011 - Question 24

he period of the function f(x) = cos 4x + tan 3x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 24

WBJEE Previous Year - 2011 - Question 25

If y = 2x3 – 2x2 + 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

WBJEE Previous Year - 2011 - Question 27

The value of  2-2  xcos + xsinx + 1

Detailed Solution for WBJEE Previous Year - 2011 - Question 27

WBJEE Previous Year - 2011 - Question 28

For the function f(x) = ecos x , Rolle’s theorem is

Detailed Solution for WBJEE Previous Year - 2011 - Question 28

WBJEE Previous Year - 2011 - Question 29

The general solution of the differential equation 

Detailed Solution for WBJEE Previous Year - 2011 - Question 29

WBJEE Previous Year - 2011 - Question 30

Detailed Solution for WBJEE Previous Year - 2011 - Question 30

WBJEE Previous Year - 2011 - Question 31

Detailed Solution for WBJEE Previous Year - 2011 - Question 31

WBJEE Previous Year - 2011 - Question 32

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

WBJEE Previous Year - 2011 - Question 34

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

WBJEE Previous Year - 2011 - Question 36

Detailed Solution for WBJEE Previous Year - 2011 - Question 36

WBJEE Previous Year - 2011 - Question 37

Detailed Solution for WBJEE Previous Year - 2011 - Question 37

WBJEE Previous Year - 2011 - Question 38

The general solution of the differential equation 

Detailed Solution for WBJEE Previous Year - 2011 - Question 38

WBJEE Previous Year - 2011 - Question 39

Detailed Solution for WBJEE Previous Year - 2011 - Question 39

WBJEE Previous Year - 2011 - Question 40

Detailed Solution for WBJEE Previous Year - 2011 - Question 40

C2 → C2 – C3

C3 → C3 + C2

C3 → C3 + ωC1

C2 → C2 – C1

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

WBJEE Previous Year - 2011 - Question 43

The coefficient of xn in the expansion of 

Detailed Solution for WBJEE Previous Year - 2011 - Question 43

WBJEE Previous Year - 2011 - Question 44

The sum of the series 

Detailed Solution for WBJEE Previous Year - 2011 - Question 44

WBJEE Previous Year - 2011 - Question 45

The number (101)100– 1 is divisible by

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 = 2nCn  

B = 2n – 1Cn

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 = nC0 + nC1x + nC2x² + nC3x3 + .......              

= 1 + nx + x² (nC2 + nC3 x + .........)  (1 + x)n – nx – 1

= x² (nC2+ nC3x + ........)

WBJEE Previous Year - 2011 - Question 48

If  nC4, nC5 and nC6  are in A.P., then n is

Detailed Solution for WBJEE Previous Year - 2011 - Question 48

nC4, nC5 and nC6

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

nC2 –n = 20  

n = 8

WBJEE Previous Year - 2011 - Question 50

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 ax2 + 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 px2 + qx + r = 0 is a : b, then ab/(a + b)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 x2 + x + 1 = 0, then the equation whose roots are α19 and β7 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 53

 α  and β are the roots of x2 + x + 1 = 0

α = ω

β=ω2 

α19 = ω

β7 = ω2

x2 – (α19 + β7)x + α19 β7 = 0

Thou, x2 – (ω + ω 2) x + ω . ω 2 = 0

x2 + 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 + t2) in the complex plane is

Detailed Solution for WBJEE Previous Year - 2011 - Question 54

 Let z = x + iy  

x = 1 – t2 

y2 = 1 + t2

Thus, x + y2 = 2          

y2 = 2 – x        

y2 = – (x – 2)    

Thus  parabola

WBJEE Previous Year - 2011 - Question 55

if x + 1/x = 2cosθ, then for any integer n , xn + 1/xn

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, xn + 1/xn = 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 + 3nωn

s(1 – ω) = 1 + ω + ω² + ...........+ ω3n–1 – 3nω3h

 = 0 – 3n

WBJEE Previous Year - 2011 - Question 57

If log3x + log3y = 2 + log32 and log3(x + y) = 2, then

Detailed Solution for WBJEE Previous Year - 2011 - Question 57

log3x + log3y = 2 + log32

⇒ x.y = 18  log (x + y) = 2  

⇒  x + y = 9

we will get x = 3 and y = 6

WBJEE Previous Year - 2011 - Question 58

If log 7 2 = λ, then the value of log49 (28) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 58

  log4928 = log724 × 7

WBJEE Previous Year - 2011 - Question 59

The sequence log a, log a2/b, loga3/b2,  ....... is

Detailed Solution for WBJEE Previous Year - 2011 - Question 59

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

 = T2 – T1 = log a – log b

= T3– T2 = 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

WBJEE Previous Year - 2011 - Question 61

Detailed Solution for WBJEE Previous Year - 2011 - Question 61

 c1 → c1 + c2 + c3

WBJEE Previous Year - 2011 - Question 62

The area enclosed between y2 = x and y = x is

Detailed Solution for WBJEE Previous Year - 2011 - Question 62

WBJEE Previous Year - 2011 - Question 63

Let f(x) = x3e–3x, x  > 0. Then the maximum value of f(x) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 63

f(x) = x3e–3x

= f′(x) = 3x2e–3x + x3 e–3x (–3)

= x23e–3x[1 – x] = 0, x = 1

Maximum at x = 1

f(1) = e–3

WBJEE Previous Year - 2011 - Question 64

The area bounded by y2 = 4x and x2 = 4y is

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

WBJEE Previous Year - 2011 - Question 66

The solution of

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 = aebx (a & b are parameters) is

Detailed Solution for WBJEE Previous Year - 2011 - Question 68

y = a.ebx ............ (i)

y1 = abebx

y1 = by............(ii)

y2 = by1 ...........(iii)

WBJEE Previous Year - 2011 - Question 69

The value of

Detailed Solution for WBJEE Previous Year - 2011 - Question 69

WBJEE Previous Year - 2011 - Question 70

Detailed Solution for WBJEE Previous Year - 2011 - Question 70

WBJEE Previous Year - 2011 - Question 71

∫ 2x (f ′(x) + f (x) log 2)dx is

Detailed Solution for WBJEE Previous Year - 2011 - Question 71

I = ∫ 2x f ′(x)dx+∫ 2x f (x) log 2dx

= 2xf(x)

WBJEE Previous Year - 2011 - Question 72

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

Detailed Solution for WBJEE Previous Year - 2011 - Question 72

f(x) = tan–1x

WBJEE Previous Year - 2011 - Question 73

Detailed Solution for WBJEE Previous Year - 2011 - Question 73

WBJEE Previous Year - 2011 - Question 74

Detailed Solution for WBJEE Previous Year - 2011 - Question 74

WBJEE Previous Year - 2011 - Question 75

Detailed Solution for WBJEE Previous Year - 2011 - Question 75

WBJEE Previous Year - 2011 - Question 76

If the function

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

WBJEE Previous Year - 2011 - Question 78

The even function of the following is

Detailed Solution for WBJEE Previous Year - 2011 - Question 78

WBJEE Previous Year - 2011 - Question 79

If f(x + 2y, x – 2y) = xy, then f(x, y) is equal to

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 y2 = 4ax passing through the vertex is

Detailed Solution for WBJEE Previous Year - 2011 - Question 80

2h = x,  2k = y

y2 = 4ax

k2 = 2ah

y2 = 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 R2 ,

∴ 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  r1 and r2  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 89

In the nuclear reaction

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 = l3=1m3

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 = t2/4 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

I1ω1=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 m1 in a liquid of density d1 and that in liquid of density d2 is m2. The density d of the object is

Detailed Solution for WBJEE Previous Year - 2011 - Question 103

V(d – d1)g = m1g

V(d – d2)g = m2g

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 Vσ1g ...... (1)

Vσg = 0.4 Vσ2g  .................. (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 × 105 J of heat is conducted through a 2 m2 wall of 12 cm thick in one hour. Temperature difference between the two sides of the wall is 200C. 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 = P1 + P2

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 = -f0/fe

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 FeCl3 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 FeCl3  where as benzylalchol donot contains phenolic group, hence no coloration with FeCl3. 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 E2 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. 3o > 2o > 1o.

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,  NO2 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 CH3COONa 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 Eo for half reations are

Zn = Zn+2 + Ze Eo = +0.76 V

Fe = Fe+2 + Ze Eo = + 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 K1 and K2 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 Li2+ 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

WBJEE Previous Year - 2011 - Question 134

The ozone layer forms naturally by

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

SO3 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 Na2S2O3 and I2 are M1 and M2 respectively, then what will be the equivalent wt. of Na2S2Oand I2 in the following reaction?

Detailed Solution for WBJEE Previous Year - 2011 - Question 141

WBJEE Previous Year - 2011 - Question 142

A radioactive atom yxM 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 ns2np3. where n = period number.

WBJEE Previous Year - 2011 - Question 144

Which one of the following is paramagnetic?

Detailed Solution for WBJEE Previous Year - 2011 - Question 144

WBJEE Previous Year - 2011 - Question 145

Platinum, Palladium and Iridium are called noble metals because

WBJEE Previous Year - 2011 - Question 146

Which one is not a constituent of nucleic acid?

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 sp3d2 hybridization of central atom of a molecule would lead to

WBJEE Previous Year - 2011 - Question 148

In aqueous solution glucose remains as

Detailed Solution for WBJEE Previous Year - 2011 - Question 148

WBJEE Previous Year - 2011 - Question 149

Which of the following is used to prepare Cl2 gas at room temperature from concentrated HCl?

Detailed Solution for WBJEE Previous Year - 2011 - Question 149

2MnO4-+ 16 H+ + 10Cl→ 2Mn2+ + 5Cl2 + 8H2O

WBJEE Previous Year - 2011 - Question 150

NO2 is not obtained on heating

Detailed Solution for WBJEE Previous Year - 2011 - Question 150

WBJEE Previous Year - 2011 - Question 151

The normality of 30 volume H2O2 is

Detailed Solution for WBJEE Previous Year - 2011 - Question 151

Volume strength = 5.6 × normality      

30 = 5.6 × N

N = 30/5.6 = 5.3

 

WBJEE Previous Year - 2011 - Question 152

Reaction of formaldehyde and ammonia gives

Detailed Solution for WBJEE Previous Year - 2011 - Question 152

6HCHO + 4NH3 → (CH2)6 N4 + 6H2O

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

WBJEE Previous Year - 2011 - Question 156

Paracetamol is

Detailed Solution for WBJEE Previous Year - 2011 - Question 156

WBJEE Previous Year - 2011 - Question 157

Anhydrous ferric chloride is prepared by

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 C2 and C3 of H3C – CH = C = CH – CH3 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

WBJEE Previous Year - 2011 - Question 161

Glucose and amino acids are reabosorbed in the

Detailed Solution for WBJEE Previous Year - 2011 - Question 161

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

WBJEE Previous Year - 2011 - Question 162

The amount of CSF in the cranial cavity

Detailed Solution for WBJEE Previous Year - 2011 - Question 162

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

WBJEE Previous Year - 2011 - Question 163

Which one is imino acid?

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

WBJEE Previous Year - 2011 - Question 165

ACTH is secreted from

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

WBJEE Previous Year - 2011 - Question 168

Electric potential of the brain is recorded by