JEE Mains 2006

combines with a uninegative monodentate ligand

Nickel

(Z = 28)

X^{-}

to form a paramagnetic complex

[NiX_{4}]^{2 -}

. The number of unpaired electron (s) in the nickel and geometry of this complex ion are, respectively

one, tetrahedral
two, tetrahedral
one, square planar
two, square planar

Topic:

Coordination Compounds

Exam:

JEE Mains 2006

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Question 3

Fe (CO)_{5}

, the

Fe - C

bond possesses

$π$ -character only
both $σ$ and $π$ -characters
ionic character
$σ$ -character only

Topic:

Coordination Compounds

Exam:

JEE Mains 2006

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Question 4

Total volume of atoms present in a face-centred cubic unit cell of a metal is (

r

is atomic radius)

$\frac{20}{3} π r^{3}$
$\frac{24}{3} π r^{3}$
$\frac{12}{3} π r^{3}$
$\frac{16}{3} π r^{3}$

Topic:

The Solid State

Exam:

JEE Mains 2006

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Question 5

How many moles of magnesium phosphate,

Mg_{3} (PO_{4})_{2}

will contain

0.25

mole of oxygen atoms? (a) 0.02 (b)

3.125 \times 1 0^{- 2}

1.25 \times 1 0^{- 2}

2.5 \times 1 0^{- 2}

Topic:

Some Basic Concepts of Chemistry

Exam:

JEE Mains 2006

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Question 6

The decreasing values of bond angles from

NH_{3} (10 7^{\circ})

SbH_{3} (9 1^{\circ})

down group-15 of the periodic table is due to

increasing $b p - b p$ repulsion
increasing $p$ -orbital character in $s p^{3}$
decreasing $lp$ - bp repulsion
decreasing electronegativity

Topic:

Chemical Bonding and Molecular Structure

Exam:

JEE Mains 2006

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Question 7

Which of the following molecules/ions does not contain unpaired electrons?

$O_{2}^{2 -}$
$B_{2}$
$N_{2}^{+}$
$O_{2}$

Topic:

Chemical Bonding and Molecular Structure

Exam:

JEE Mains 2006

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Question 8

The potential energy of a

1 kg

particle free to move along the

x

-axis is given by

V (x) = (\frac{x ^{4}}{4} - \frac{x ^{2}}{2}) J

The total mechanical energy of the particle is

2 J

. Then, the maximum speed (in

ms^{- 1}

) is
(a)

\frac{3}{2}

2

\frac{1}{2}

(d) 2

Topic:

Work, Energy and Power

Exam:

JEE Mains 2006

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Question 9

Consider a two particle system with particles having masses

m_{1}

. If the first particle is pushed towards the centre of mass through a distance

m_{2}

d

, by what distance should the second particle be moved, so as to keep the centre of mass at the same position? (a)

\frac{m _{2}}{m _{1}} d

\frac{m _{1}}{m _{1} + m _{2}} d

\frac{m _{1}}{m _{2}} d

d

Topic:

System of Particles and Rotational Motion

Exam:

JEE Mains 2006

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Question 10

Consider a two particle system with particles having masses

m_{1}

. If the first particle is pushed towards the centre of mass through a distance

m_{2}

d

, by what distance should the second particle be moved, so as to keep the centre of mass at the same position? (a)

\frac{m _{2}}{m _{1}} d

\frac{m _{1}}{m _{1} + m _{2}} d

\frac{m _{1}}{m _{2}} d

d

Topic:

System of Particles and Rotational Motion

Exam:

JEE Mains 2006

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Question 11

If the terminal speed of a sphere of gold (density

= 19.5 kgm^{- 3}

) is

0.2 ms^{- 1}

in a viscous liquid (density

= 1.5 kgm^{- 3}

), find the terminal speed of a sphere of silver (density

= 10.5 kg / m^{3}

) of the same size in the same liquid. (a)

0.4 ms^{- 1}

0.133 ms^{- 1}

0.1 ms^{- 1}

0.2 ms^{- 1}

Topic:

Mechanical Properties of Fluids

Exam:

JEE Mains 2006

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Question 12

is performed in order to compress one kilo mole of a gas adiabatically and in this process, the temperature of the gas increases by

The work of

146 kJ

7^{\circ} C

. The gas is

(R = 8.3 J mol^{- 1} K^{- 1}

)
(a) diatomic
(b) triatomic
(c) a mixture of monatomic and diatomic
(d) monatomic

Topic:

Thermodynamics

Exam:

JEE Mains 2006

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Question 13

A string is stretched between fixed points separated by

75.0 cm

. It is observed to have resonant frequencies of

420 Hz

. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
(a)

315 Hz

105 Hz

1.05 Hz

1050 Hz

10.5 Hz

Topic:

Waves

Exam:

JEE Mains 2006

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Question 14

A whistle producing sound waves of frequencies

9500 Hz

and above is approaching a stationary person with speed

v ms^{- 1}

. The velocity of sound in air is

300 ms^{- 1}

. If the person can hear frequencies upto a maximum of

10000 Hz

, the maximum value of

v

upto which he can hear the whistle is (a)

152 ms^{- 1}

15/ 2 ms^{- 1}

15 ms^{- 1}

The maximum velocity of a particle, executing simple harmonic motion with an amplitude

30 ms^{- 1}

Topic:

Waves

Exam:

JEE Mains 2006

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Question 15

Easy

7 mm

, is

4.4 ms^{- 1}

. The period of oscillation is

$0.01 s$
$10 s$
$0.1 s$
$100 s$

Topic:

Oscillations

Exam:

JEE Mains 2006

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Question 16

Starting from the origin, a body oscillates simple harmonically with a period of

2 s

. After what time will its kinetic energy be

75%

of the total energy?

$\frac{1}{6} s$
$\frac{1}{4} s$
$\frac{1}{3} s$
$\frac{1}{12} s$

Topic:

Oscillations

Exam:

JEE Mains 2006

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Question 17

Easy

Two spherical conductors

A

B

of radii

1 mm

are separated by a distance of

2 mm

5 cm

and are uniformly charged. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres

A

B

is
(a)

4 : 1

1 : 2

2 : 1

1 : 4

Topic:

Electric Charges and Fields

Exam:

JEE Mains 2006

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Question 18

has twice the specific resistance of

A material

B

A

. A circular wire made of

B

has twice the diameter of a wire made of

A

. Then, for the two wires to have the same resistance, the ratio

l_{B} / l_{A}

of their respective lengths must be
(a) 1
(b)

1/2

1/4

(d) 2

Topic:

Current Electricity

Exam:

JEE Mains 2006

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Question 19

An electric bulb is rated

220 V - 100 W

. The power consumed by it when operated on

110 V

will be
(a)

75 W

40 W

25 W

50 W

Topic:

Current Electricity

Exam:

JEE Mains 2006

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Question 20

The resistance of a bulb filament is

100Ω

at a temperature of

10 0^{\circ} C

. If its temperature coefficient of resistance is

0.005

per

^{\circ} C

, its resistance will become

200Ω

at a temperature of (a)

30 0^{\circ} C

40 0^{\circ} C

50 0^{\circ} C