JEE Mains 2013

The molarity of a solution obtained by mixing

750 mL

0.5 M HCl

with

250 mL

2 M HCl

will be

(a) 0.875 M (b) 1.00 M

(c) 1.75 M (d) 0.0975 M

Topic:

Some Basic Concepts of Chemistry

Exam:

JEE Mains 2013

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Question 2

A gaseous hydrocarbon gives upon combustion,

0.72 g

of water and

3.08 g

CO_{2}

. The empirical formula of the hydrocarbon is

(a) C_{2} H_{4} (b) C_{3} H_{4} (c) C_{6} H_{5} (d) C_{7} H_{8}

Topic:

Some Basic Concepts of Chemistry

Exam:

JEE Mains 2013

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Question 3

Which of the following exists as covalent crystals in the solid state? (b) Silicon (a) Iodine (c) Sulphur (d) Phosphorus

Topic:

The Solid State

Exam:

JEE Mains 2013

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Question 4

Experimentally, it was found that a metal oxide has formula

M_{0.98} O

. Metal

M

, present as

M^{2 +}

in its oxide. Fraction of the metal which exists as

M^{3 +}

M^{3 +}

would be (a)

5.08%

4.08%

6.05%

7.01%

Topic:

The Solid State

Exam:

JEE Mains 2013

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Question 5

In which of the following pairs of molecules/ions both the species are not likely to exist?

$H_{2}^{+}, He_{2}^{2 -}$
$H_{2}^{-}, He_{2}^{2 -}$
$H_{2}^{2 +}, He_{2}$
$H_{2}^{-}, He_{2}^{2 +}$

Topic:

Chemical Bonding and Molecular Structure

Exam:

JEE Mains 2013

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Question 6

Stability of the species

Li_{2}, Li_{2}^{-}

increases in the order of

Li_{2}^{+}

$Li_{2} < Li_{2}^{+} < Li_{2}^{-}$
$Li_{2}^{-} < Li_{2}^{+} < Li_{2}$
$Li_{2} < Li_{2}^{-} < Li_{2}^{+}$
$Li_{2}^{-} < Li_{2} < Li_{2}^{+}$

Topic:

Chemical Bonding and Molecular Structure

Exam:

JEE Mains 2013

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Question 7

This question has Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement I A point particle of mass

m

moving with speed

v

collides with stationary point particle of mass

M

. If the maximum energy loss possible is given as

f (\frac{1}{2} m v^{2})

, then

f = (\frac{m}{M + m})

Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision.
(a) Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I
(c) Statement I is true, Statement II is false
(d) Statement I is false, Statement II is true

Topic:

Laws of motion

Exam:

JEE Mains 2013

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Question 8

What is the minimum energy required to launch a satellite of mass

m

from the surface of a planet of mass

M

and radius

R

in a circular orbit at an altitude of

2 R

?
(a)

\frac{5 G m M}{6 R}

\frac{2 G m M}{3 R}

\frac{G m M}{2 R}

\frac{G m M}{3 R}

Topic:

Gravitation

Exam:

JEE Mains 2013

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Question 9

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible?The surface tension is

T

, density of liquid is

ρ

is its latent heat of vaporisation.

(a)

L

ρ L / T

T / ρ L

T / ρ L

2 T / ρ L

Topic:

Mechanical Properties of Fluids

Exam:

JEE Mains 2013

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Question 10

The amplitude of a damped oscillator decreases to

0.9

times its original magnitude in

5 s

. In another

10 s

, it will decrease to

α

times its original magnitude, where

α

equals

$0.7$
$0.81$
$0.729$
$0.6$

Topic:

Oscillations

Exam:

JEE Mains 2013

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Question 11

This question has Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement I: Higher the range, greater is the resistance of ammeter.
Statement II: To increase the range of ammeter, additional shunt needs to be used across it.
(a) Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I
(c) Statement I is true, Statement II is false
(d) Statement I is false, Statement II is true

Topic:

Current Electricity

Exam:

JEE Mains 2013

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Question 12

In a hydrogen like atom, when an electron jumps from the

M

-shell to the

L

-shell, the wavelength of emitted radiation is

λ

. If an electron jumps from

N

-shell to the

L

-shell, the wavelength of emitted radiation will be
(a)

\frac{27}{20} λ

\frac{25}{16} λ

\frac{20}{27} λ

\frac{16}{25} λ

Topic:

Atoms

Exam:

JEE Mains 2013

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Question 13

In a hydrogen like atom electron make transition from an energy level with quantum number

n

to another with quantum number

(n - 1)

. If

n ≫ 1

, the frequency of radiation emitted is proportional to
(a)

\frac{1}{n}

\frac{1}{n ^{2}}

\frac{1}{n ^{3} /2}

\frac{1}{n ^{3}}

Topic:

Atoms

Exam:

JEE Mains 2013

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Question 14

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4 . Then, the number of spectral lines in the emission spectra will be
(a) 2
(b) 3
(c) 5
(d) 6

Topic:

Atoms

Exam:

JEE Mains 2013

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Question 15

Let

A

be two sets containing 2 elements and 4 elements, respectively. The number of subsets of

B

A \times B

having 3 or more elements is (a) 256 (b) 220 (c) 219 (d) 211

Topic:

Permutations and Combinations

Exam:

JEE Mains 2013

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Question 16

be the number of all possible triangles formed by joining vertices of an

Let

T_{n}

n

-sided regular polygon. If

T_{n + 1} - T_{n} = 10

, then the value of

n

is (a) 7 (b) 5 (c) 10 (d) 8

Topic:

Permutations and Combinations

Exam:

JEE Mains 2013

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Question 17

is (a) 4 (b) 120 (c) 210 (d) 310

The term independent of

x

in the expansion of

(\frac{x + 1}{x ^{2/3} - x ^{1/3} + 1} - \frac{x - 1}{x - x ^{1/2}})^{10}

Topic:

Binomial Theorem

Exam:

JEE Mains 2013

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Question 18

x, y

z

are in AP and

tan^{- 1} x, tan^{- 1} y

tan^{- 1} z

are also in

AP

, then

$x = y = z$
$2 x = 3 y = 6 z$
$6 x = 3 y = 2 z$
$6 x = 4 y = 3 z$

Topic:

Sequences and Series

Exam:

JEE Mains 2013

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Question 19

lim_{x \to 0} \frac{( 1 - c o s 2 x ) ( 3 + c o s x )}{x t a n 4 x}

is equal to (a)

- \frac{1}{4}

\frac{1}{2}

Topic:

Limits and Derivatives

Exam:

JEE Mains 2013

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Question 20

-axis made by tangents to the curve,

The intercepts on

X

y = \int_{0}^{x} ∣ t ∣ d t, x \in R

, which are parallel to the line

y = 2 x

, are equal to (a)

\pm 1

\pm 2

\pm 3