Solved papers for JEE Main & Advanced JEE Main Online Paper (Held on 9 April 2013)

JEE Main Online Paper (Held on 9 April 2013) Total Questions - 90

1)                 Consider two transistors as shown in figure. If 0 volts corresponds to false and 5Volts correspond to true then the output at corresponds to :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                A NAND B

B)

                A OR B

C)

                A AND B

D)

                A NOR B

View Answer
2)                                 In a metre bridge experiment null point is obtained at 40 cm from end of the wire when resistance X is balanced against another resistance Y. if X < Y, then the new position of the null point from the same end, if one decides to balance a resistance of 3X against Y, will be close to :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                80 cm

B)

                75 cm

C)

                                       67 cm

D)

                       50 cm

View Answer
3)                 Two springs of force constants 300 N/m (Spring A) and 400 N/m (Spring B) are joined together in compressed by 8.75 cm. The ratio of energy stored in A and B is\[\frac{{{E}_{A}}}{{{E}_{B}}}\]. The \[{}^{{{E}_{A}}}/{}_{{{E}_{B}}}\]is equal to:         JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\frac{4}{3}\]

B)

                \[\frac{16}{9}\]

C)

                       \[\frac{3}{4}\]

D)

                       \[\frac{9}{16}\]

View Answer
4)                 A person lives in a high-rise building on the bank of a river 50 m wide. Across the river is a well lit tower of height 40 m. When the person, who is at a height of 10 m, looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance X from his building is the least and this corresponds to the light coming from light bulbs at height ?Y? on the tower. The values of X and Y are respectively close to (refractive index of water\[\simeq \frac{4}{3}\])                 JEE Main Online Paper (Held On 09 April 2013)

A)

                25 m, 10 m

B)

                13 m, 27 m

C)

                22 m, 13 m

D)

                17 m, 20 m

View Answer
5) The gravitational filed, due to the 'left over part' of a uniform sphere (from which a part as. Shown, has been 'removed out'), at a very far off point, P, located as shown, would be(nearly):         JEE Main Online Paper (Held On 09 April 2013)

A)

\[\frac{5}{6}\frac{GM}{{{x}^{2}}}\]

B)

\[\frac{8}{9}\frac{GM}{{{x}^{2}}}\]

C)

\[\frac{7}{8}\frac{GM}{{{x}^{2}}}\]

D)

\[\frac{6}{7}\frac{GM}{{{x}^{2}}}\]

View Answer
6)                 A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 Kg It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just ager the bullet embeds into it will be:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                6.25 rad/sec

B)

                0.625 rad/sec

C)

                3.35 rad/sec

D)

                       0.335 rad/sec

View Answer
7)                 On a linear temperature scale Y, water freezes at \[-{{160}^{o}}Y\]and boils at \[-{{50}^{o}}Y\]. On this Y scale, a temperature of 340 K would be read as : (water freezes at 273 K and boils at 373 K)                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[-{{73.7}^{0}}Y\]

B)

                \[-{{233.7}^{0}}Y\]

C)

                \[-{{86.3}^{0}}Y\]

D)

                       \[-{{103.3}^{0}}Y\]

View Answer
8)                                 A uniform electric field \[\vec{E}\] exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to \[\vec{E}\]. The path of the particle between the plates is a:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                straight line

B)

                hyperbola

C)

                parabola

D)

                circle

View Answer
9)                 Photons of an electromagnetic radiation has an energy 11 keV each. To which region of electromagnetic spectrum does it belong?            JEE Main Online Paper (Held On 09 April 2013)

A)

                X-ray region

B)

                Ultra violet region

C)

                      Infrared region

D)

                       Visible region

View Answer
10)                 This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.                 Statement-1: A capillary is dipped in a liquid and liquid rises to a height h in it. As the temperature of the liquid is raised, the height increases (if the density of the liquid and the angle of contact remain the same)                 Statement-2: Surface tension of a liquid decreases with the rise in its temperature.                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Statement -1 is true, Statement-2 is true. Statement-2 is not correct explanation for statement-1.

B)

                Statement -1 is false. Statement -2 is true.

C)

                Statement -1 is true. Statement-2 is false.

D)

                Statement-1 is true, Statement-2 is true. Statement-2 is correct explanation for statement-1.

View Answer
11)                 If a carrier wave \[c(t)=A\sin {{\omega }_{c}}t\] is amplitude modulated by a modulator single \[m(t)=A\sin {{\omega }_{m}}t\]then the equation of modulated signal \[\left[ {{C}_{\operatorname{m}}}\left( \operatorname{t} \right) \right]\]and its modulation index are respectively :               JEE Main Online Paper (Held On 09 April 2013)

A)

                \[{{C}_{\operatorname{m}}}\left( \operatorname{t} \right)=A(1+\sin {{\omega }_{m}}t)\sin {{\omega }_{c}}t\]and 2

B)

                \[{{C}_{\operatorname{m}}}\left( \operatorname{t} \right)=A(1+\sin {{\omega }_{c}}t)\sin {{\omega }_{m}}t\]and 1

C)

                \[{{C}_{\operatorname{m}}}\left( \operatorname{t} \right)=A(1+\sin {{\omega }_{m}}t)\sin {{\omega }_{c}}t\]and 1

D)

                \[{{C}_{\operatorname{m}}}\left( \operatorname{t} \right)=A(1+\sin {{\omega }_{c}}t)\sin {{\omega }_{m}}t\]and 2

View Answer
12) A letter 'A' is constructed of a uniform wire with resistance 1.0 \[\Omega \] per cm. The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is \[{{60}^{0}}\]. The resistance between the ends of the legs is close to:                 JEE Main Online Paper (Held On 09 April 2013)

A)

\[50.0\Omega \]

B)

\[10\Omega \]

C)

\[36.7\Omega \]

D)

\[26.7\Omega \]

View Answer
13)                 An electric current is flowing though a circular coil of radius R. The ratio of the magnetic field at the centre of the centre of the coil and that at a distance \[2\sqrt{2}\]R from the centre the centre of the coil and its axis is:                                JEE Main Online Paper (Held On 09 April 2013)

A)

                \[2\sqrt{2}\]

B)

                27

C)

                36

D)

                8

View Answer
14)                                 Two simple pendulums of length 1m and 4mrespectively are both given small d is placement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to: JEE Main Online Paper (Held On 09 April 2013)

A)

                2

B)

                7

C)

                5

D)

                3

View Answer
15)                                 Light is incident from a medium into air at two possible angles of incidence (a) \[{{20}^{0}}\] and (b)\[{{40}^{0}}\] In the medium light travels 3.0 cm in 0.2ns. The ray will :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                suffer total internal reflection in both cases (a) and (b)

B)

                suffer total internal reflection in cases (b) only

C)

                have partial reflection and partial transmission in case (b)

D)

                have 100% transmission in case (a)

View Answer
16)                 Two point dipoles of dipole moment \[\overset{\to }{\mathop{{{\operatorname{P}}_{1}}}}\,\] and \[\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,\] are at a distance \[x\] from each other and \[\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,||\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,\]. The force between the dipoles is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{4{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{4}}}\]

B)

                \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{3}}}\]

C)

                \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{6{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{4}}}\]

D)

                \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{8{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{4}}}\]

View Answer
17) When two sound waves travel in the same direction in a medium, the displacements of a particle located at \['x'\] at time \['t'\] is given by:                 \[{{y}_{1}}=00.5\,\,\cos \,\,(0.50\,\pi x-100\pi t)\]                 \[{{y}_{2}}=0.05\,\,\cos \,\,(0.46\,\,\pi x-92\pi t)\]                 Where \[{{y}_{1}},{{y}_{2}}\] and \[x\] are in meters and t in seconds. The speed of sound in the medium is:                JEE Main Online Paper (Held On 09 April 2013)

A)

92 m/s

B)

200 m/s

C)

100 m/s

D)

332 m/s

View Answer
18)                 An engine approaches a hill with a constant speed. When it is a distance of 0.9 km it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is 330 m/s, then the speed of the engine is:              JEE Main Online Paper (Held On 09 April 2013)

A)

                32 m/s

B)

                27.5 m/s

C)

                60 m/s

D)

                       30 m/s

View Answer
19)                 Two balls of same mass and carrying equal charge are hung from a fixed support of length \[l\]. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, \[x\] between the balls is proportional to :     JEE Main Online Paper (Held On 09 April 2013)

A)

                \[l\]

B)

                \[{{l}^{2}}\]

C)

                \[{{l}^{2/3}}\]

D)

                \[{{l}^{1/3}}\]

View Answer
20)                                 A uniform sphere of weight W and radius 5cm is being held by a string as shown in the figure. The tension in the string will be:        JEE Main Online Paper (Held On 09 April 2013)

A)

                \[12\frac{W}{5}\]

B)

                \[5\frac{W}{12}\]

C)

                \[13\frac{W}{12}\]

D)

                \[13\frac{W}{12}\]

View Answer
21)                 When Uranium is bombarded with neurons, undergoes fission. The fission reaction can be written as:   \[_{92}{{\bigcup }^{235}}{{+}_{0}}{{n}^{1}}\to 56\operatorname{B}{{a}^{141}}{{+}_{36}}{{\operatorname{Kr}}^{92}}+3x\,+Q(\text{energy)}\]                 where there particles named \[x\] are produced and energy Q is released. What is the name of the particle \[x\]?         JEE Main Online Paper (Held On 09 April 2013)

A)

                electron

B)

                \[\alpha \]-particle

C)

                neutron

D)

                       neutrino

View Answer
22) Two coils, X and Y, are kept in close vicinity of each other. When a varying current, I(t),flows through coil X the induced emf (V (t)) in coil Y, varies in the manner shown here. The variation of I(t), with time, can then be represented by the represented by the graph labeled as graph:

A

B

C

D

                JEE Main Online Paper (Held On 09 April 2013)

A)

A

B)

C

C)

B

D)

D

View Answer
23) A ray of light of intensity I is incident on a parallel glass slab at point A as shown India gram. It undergoes partial reflection and refraction. At each reflection, 25% of incident energy is reflected. The rays AB and A 'B' undergo interference. The ratio of \[{{\operatorname{I}}_{\max }}\] and\[{{\operatorname{I}}_{\min }}\] is :            JEE Main Online Paper (Held On 09 April 2013)

A)

49 : 1

B)

7 : 1

C)

4 : 1

D)

8 : 1

View Answer
24)                                 A shunt of resistance 1\[\Omega \] connected across a galvanometer of 120\[\Omega \]resistance. A current of 5.5 ampere gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly:           JEE Main Online Paper (Held On 09 April 2013)

A)

                5.5 ampere

B)

                0.5 ampere

C)

                0.004 ampere

D)

                0.045 ampere

View Answer
25)                 From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}\,m{{c}^{2}}}\]

B)

                \[\frac{4\pi {{\varepsilon }_{0}}\,{{b}^{2}}}{m{{e}^{2}}}\]

C)

                       \[\frac{m{{c}^{2}}}{4\pi {{\varepsilon }_{0}}\,{{b}^{2}}}\]

D)

                \[\frac{4\pi {{\varepsilon }_{0}}\,m{{c}^{2}}}{{{e}^{2}}}\]

View Answer
26)                 Figure shows the variation in temperature \[(\Delta T)\]with the amount of heat supplied \[(Q)\] in an isobaric process corresponding to a monatomic (M), diatomic (D) and a polyatomic (P) gas. The initial state of all the gases are the same and the scales for the two axes coincide, ignoring vibration degrees of freedom, the lines a, b and c respectively correspond to :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                P, M and D

B)

                M, D and P

C)

                P, D and M

D)

                       D, M and P

View Answer
27)                 In the circuit shown here, the voltage across Land C are respectively300 V and 400 V. The voltage E of the ac source is :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                400 Volt

B)

                500 Volt

C)

                100 Volt

D)

                       700 Volt

View Answer
28)                 If the ratio of lengths, radii and Young? module of steel and brass wires in the figure are a, b and c respectively, then the corresponding ration of increase in lengths is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\frac{3c}{2a{{b}^{2}}}\]

B)

                \[\frac{2{{a}^{2}}c}{b}\]

C)

                       \[\frac{3a}{2{{b}^{2}}c}\]

D)

                \[\frac{2ac}{{{b}^{2}}}\]

View Answer
29)                 In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in \[{{\operatorname{n}}^{\operatorname{th}}}\] exited state, is:           JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\left( \frac{e}{2m} \right)\frac{{{\operatorname{n}}^{2}}h}{2\pi }\]

B)

                \[\left( \frac{e}{m} \right)\frac{\operatorname{n}h}{2\pi }\]

C)

                \[\left( \frac{e}{2m} \right)\frac{\operatorname{n}h}{2\pi }\]

D)

                \[\left( \frac{e}{m} \right)\frac{{{\operatorname{n}}^{2}}h}{2\pi }\]

View Answer
30)                                 There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment 1 is filled with an ideal gas and compartment 3 id filled with a real gas. Compartments 2 and 4 are vacuum. A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum.                 Statement-1: No change in the temperature of the gas takes place when ideal as expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands it expands in vacuum.                 Statement-2: The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential.                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Statement 1 is false and Statement 2is true

B)

                Statement 1 and Statement 2 bath are true. Statement 2 is the correct explanation of Statement 1.

C)

                Statement 1 is true and Statement 2 if false.

D)

                Statement 1 and Statement 2 both are true. Statement 2 is not the correct explanation of Statement 1.

View Answer
31)                 Given:                                 X is:            JEE Main Online Paper (Held On 09 April 2013)

A)



B)



C)



D)



View Answer
32)                 Given: \[\operatorname{X}\operatorname{N}{{\operatorname{a}}_{2}}{{\operatorname{HAsO}}_{3}}+\operatorname{Y}{{\operatorname{NaBrO}}_{3}}+\operatorname{ZHCI}\to \operatorname{NaBr}\]\[\text{+}{{\text{H}}_{\text{2}}}\text{As}{{\text{O}}_{\text{4}}}\text{+NaCl}\]                 The values of X, Y and Z in above reaction are respectively:         JEE Main Online Paper (Held On 09 April 2013)

A)

                2, 1, 2

B)

                2, 1, 3

C)

                3, 1, 6

D)

                3, 1, 4

View Answer
33)                 The migration of dispersion medium under the influence of an electric potential is called:                JEE Main Online Paper (Held On 09 April 2013)

A)

                Catachresis

B)

                Electro osmosis

C)

                Electrophoresis

D)

                       Sedimentation

View Answer
34)                 The addition of HI in the presence of peroxide catalyst does not follow anti-Markovnikov?s rule because:       JEE Main Online Paper (Held On 09 April 2013)

A)

                HI is a strong reducing agent

B)

                H-I bond is too strong to be broken homiletically

C)

                I atom combines with H atom to back HI

D)

                Iodine atom is not reactive enough to add across a double bond

View Answer
35)                 In reaction\[\operatorname{A}+2B\rightleftharpoons 2C+\operatorname{D},\] initial concentration of B was 1.5 tunes of \[\left[ \operatorname{A} \right],\]but at equilibrium the concentrations of A and B became equal. The equilibrium constant for the reaction is:    JEE Main Online Paper (Held On 09 April 2013)

A)

                8

B)

                4

C)

                12

D)

                6

View Answer
36)                 Trigonal bipyramidal geometry is shown by: JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\operatorname{X}e{{\operatorname{OF}}_{2}}\]

B)

                \[\operatorname{X}e{{\operatorname{O}}_{3}}{{F}_{2}}\]

C)

                \[\operatorname{F}\operatorname{X}e\operatorname{O}{{\operatorname{SO}}_{2}}\operatorname{F}\]

D)

                \[{{\left[ \operatorname{X}\operatorname{e}{{\operatorname{F}}_{8}} \right]}^{2-}}\]

View Answer
37)                 If a polythene sample contains two monodisperse fractions in the ration 2: 3 with degree of polymerization 100 and 200, respectively, then its weight average molecular weight will be :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                4900

B)

                                       4600

C)

                4300

D)

                       5200

View Answer
38) The instantaneous rate of disappearance of\[{{\operatorname{MnO}}_{4}}^{-}\operatorname{ion}\] in the following reaction is                 \[4.56\times {{10}^{-3}}\operatorname{M}{{\operatorname{s}}^{-1}}\]                 \[2{{\operatorname{MnO}}_{4}}^{-}+10{{\operatorname{I}}^{-}}+16{{H }^{+}}\to 2{{\operatorname{Mn}}^{2}}^{+}+\] \[5\operatorname{I}+8{{H }_{2}}\operatorname{O}\]                 The rate of appearance \[{{\operatorname{I}}_{2}}\] is :                 JEE Main Online Paper (Held On 09 April 2013)

A)

\[4.56\times {{10}^{-4}}\operatorname{M}{{\operatorname{s}}^{-1}}\]

B)

\[1.14\times {{10}^{-2}}\operatorname{M}{{\operatorname{s}}^{-1}}\]

C)

\[1.14\times {{10}^{-3}}\operatorname{M}{{\operatorname{s}}^{-1}}\]

D)

\[5.7\times {{10}^{-3}}\operatorname{M}{{\operatorname{s}}^{-1}}\]

View Answer
39)                                 Which one of the following is most stable?                 JEE Main Online Paper (Held On 09 April 2013)

A)



B)



C)



D)



View Answer
40)                 In an atom how many orbital (s) will have the quantum numbers: n=3, \[l=2\]and\[{{m}_{l}}=+2?\]                 JEE Main Online Paper (Held On 09 April 2013)

A)

                5

B)

                3

C)

                1

D)

                7

View Answer
41)                 Potassium dichromate when heated with concentrated sulphuric acid and a soluble chloride, gives brown-red vapours of:       JEE Main Online Paper (Held On 09 April 2013)

A)

                \[{{\operatorname{CrO}}_{3}}\]

B)

                \[\operatorname{Cr}{{\operatorname{CI}}_{3}}\]

C)

                \[\operatorname{Cr}{{\operatorname{O}}_{3}}{{\operatorname{CI}}_{2}}\]

D)

                \[{{\operatorname{Cr}}_{2}}{{\operatorname{O}}_{3}}\]

View Answer
42)                 Rate of dehydration of alcohols follows the order:      JEE Main Online Paper (Held On 09 April 2013)

A)

                \[{{2}^{0}}>{{1}^{0}}>{{\operatorname{CH}}_{3}}\operatorname{OH}>{{3}^{0}}\]

B)

                \[{{3}^{0}}>{{2}^{0}}>{{1}^{0}}{{\operatorname{CH}}_{3}}\operatorname{OH}\]

C)

                \[{{2}^{0}}>{{3}^{0}}>{{1}^{0}}{{\operatorname{CH}}_{3}}\operatorname{OH}\]

D)

                \[{{\operatorname{CH}}_{3}}\operatorname{OH}>{{1}^{0}}>{{2}^{0}}>{{3}^{0}}\]

View Answer
43)                 Given                 (A) \[{{\operatorname{H}}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\to {{\operatorname{H}}_{2}}O(l):\] \[\Delta {{\operatorname{H}}^{0}}_{298K}=-285.9\operatorname{k}\operatorname{J}\operatorname{m}\operatorname{o}{{1}^{-1}}\]                 (B)\[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\to {{H}_{2}}O(g);\] \[\Delta {{H}^{0}}_{298K}=-241.8\operatorname{k}\operatorname{j}\operatorname{mo}{{1}^{-1}}\]                 The molar enthalpy of vaporization of water will be:                JEE Main Online Paper (Held On 09 April 2013)

A)

                \[241.8\,\,kJ\,\,mo{{l}^{-1}}\]

B)

                \[22.0\,\,kJ\,\,mo{{l}^{-1}}\]

C)

                \[44.1\,\,kJ\,\,mo{{l}^{-1}}\]

D)

                       \[527.7\,\,kJ\,\,mo{{l}^{-1}}\]

View Answer
44)                 Calcination is the process in which:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                ore is heated above its melting point to expel \[{{H}_{2}}O\] or \[C{{O}_{2}}\] or \[S{{O}_{2}}\]

B)

                ore is heated below its melting point to expel volatile impurities

C)

                ore is heated above its melting point to removes S, As and Sb as \[S{{O}_{2}},A{{s}_{2}}{{O}_{3}}\] and\[S{{b}_{2}}{{O}_{3}}\] respectively

D)

                ore is heated below its melting point to expel \[{{H}_{2}}O\]or\[C{{O}_{2}}\]

View Answer
45)                                 Sodium Carbonate cannot be used in place of   \[{{({{\operatorname{NH}}_{4}})}_{2}}{{\operatorname{CO}}_{3}}\] for the identification of \[C{{a}^{2+}},B{{a}^{2+}}\] and \[\operatorname{S}{{r}^{2+}}\] ions (in group V) during mixture analysis because:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[M{{g}^{2+}}\]ions will also be precipitated

B)

                Concentration of \[CO_{3}^{2-}\] ions is very low

C)

                Sodium ions will acid radicals

D)

                \[{{\operatorname{Na}}^{+}}\] ions will interfere with the detection of \[C{{a}^{2+}},\operatorname{B}{{a}^{2+}},{{\operatorname{Sr}}^{2+}}\] ions

View Answer
46)                 Which one of the following molecules is polar?                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\operatorname{Xe}{{\operatorname{F}}_{4}}\]

B)

                \[{{\operatorname{IF}}_{5}}\]

C)

                \[\operatorname{Sb}{{\operatorname{F}}_{5}}\]

D)

                \[\operatorname{C}{{\operatorname{F}}_{4}}\]

View Answer
47)                 Type of isomerism which exists between                 \[\left[ \operatorname{Pd}{{\left( {{\operatorname{C}}_{6}}{{\operatorname{H}}_{5}} \right)}_{2}}{{\left( \operatorname{SCN} \right)}_{2}} \right]\]and \[\left[ \operatorname{Pd}{{\left( {{\operatorname{C}}_{6}}{{\operatorname{H}}_{5}} \right)}_{2}}{{\left( \operatorname{NCS} \right)}_{2}} \right]\] is                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Linkage isomerism

B)

                Coordination isomerism

C)

                lionization isomerism

D)

                Solvate isomerism

View Answer
48) In which of the following ionization processes the bond energy has increased and also the magnetic behaviour has changed from paramagnetic to diamagnetic?                 JEE Main Online Paper (Held On 09 April 2013)

A)

\[ N\operatorname{O}\to {{\operatorname{NO}}^{+}}\]

B)

\[{{N }_{2}}\to {{\operatorname{N}}_{2}}^{+}\]

C)

\[{{C}_{2}}\to {{C}_{2}}^{+}\]

D)

\[{{O}_{2}}\to {{O}_{2}}^{+}\]

View Answer
49)                 12g of a nonvolatile solute dissolved in 108g of water produces the relative lowering of vapour pressure of 0.1. The molecular mass of the lute is:

A)

                80

B)

                                       60

C)

                20

D)

                       40

View Answer
50)                 Which of the following enzyme converts starch into maltose?                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Diastase

B)

                Maltase

C)

                Zymase

D)

                Invertase

View Answer
51)                 Electrode potentials \[\left( {{E}^{0}} \right)\] are given below:                 \[{{\operatorname{Cu}}^{+}}+\operatorname{Cu}=+0.52V,\]                 \[F{{e}^{3+}}/F{{e}^{2+}}=+0.77V,\]                 \[\frac{1}{2}{{\operatorname{I}}_{2}}\left( s \right)/{{I}^{-}}=+0.54V,\]                                                 \[A{{g}^{+}}/Ag=+0.88V.\]                 Based on the above potentials, strongest oxidizing agent will be:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[{{\operatorname{Cu}}^{+}}\]

B)

                \[{{\operatorname{Fe}}^{3}}^{+}\]

C)

                \[{{\operatorname{Ag}}^{+}}\]

D)

                \[{{\operatorname{I}}_{2}}\]

View Answer
52)                 Aryl fluoride may be prepared from arene diazonium chloride using:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[{{\operatorname{HBF}}_{4}}/\Delta \]

B)

\[{{\operatorname{HBF}}_{4}}/\operatorname{N}a\operatorname{N}{{\operatorname{O}}_{2}},\operatorname{Cu},\Delta \]

C)

                \[\operatorname{Cu}\operatorname{F}/\operatorname{H}\operatorname{F}\]

D)

                \[\operatorname{Cu}/\operatorname{H}\operatorname{F}\]

View Answer
53)                 Anether (A) \[{{\operatorname{C}}_{5}}{{\operatorname{H}}_{12}}\operatorname{O},\]when heated with excess of hot concentrated HI produced two alky halides which when treated with NaOH yielded compounds (B) and (C) Oxidation of (B) and (C) gave a propanone and an ethanoic acid respectively. The IUPAC name of the ether (A) is:         JEE Main Online Paper (Held On 09 April 2013)

A)

                2-ethoxypropane

B)

                ethoxypropane

C)

                methoxybutane

D)

                       2-methoxybutane

View Answer
54)                 Electron gain enthalpy with negative sing of fluorine is less than that of chlorine due to:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                High ionization enthalpy of fluorine

B)

                Smaller size of chlorine atom

C)

                Smaller size of fluorine atom

D)

                Bigger size of \[2p\]orbital of fluorine

View Answer
55)                 Solid \[Ba{{(N{{O}_{3}})}_{2}}\] is gradually dissolved in a \[1.0\times {{10}^{-4}}\,M\,N{{a}_{2}}C{{O}_{3}}\] solution. At which concentration of \[B{{a}^{2+}}\], precipitate of \[BaC{{O}_{3}}\]begins to form? \[({{K}_{sp}}\] for \[BaC{{O}_{3}}=5.1\times {{10}^{-9}})\]              JEE Main Online Paper (Held On 09 April 2013)

A)

                \[5.1\times {{10}^{-5}}\operatorname{M}\]

B)

                \[7.1\times {{10}^{-8}}\operatorname{M}\]

C)

                \[4.1\times {{10}^{-5}}\operatorname{M}\]

D)

                \[8.1\times {{10}^{-7}}\operatorname{M}\]

View Answer
56)                 An element having an atomic radius of 0.14 nm crystallizes in a fcc unit cell. What is the length of a side of the cell?             JEE Main Online Paper (Held On 09 April 2013)

A)

                0.56 nm

B)

                                       0.24 nm

C)

                0.96 nm

D)

                       0.4 nm

View Answer
57)                 Which of the following compounds is not expected to show Lassaignes? test for nitrogen?                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Propanenitrile

B)

                Hydroxylamie hydrochloride

C)

                Niromethane

D)

                Ethanmine

View Answer
58) Formaldehyde can be distinguished from acetaldehyde the use of:                 JEE Main Online Paper (Held On 09 April 2013)

A)

Schiff's reagent

B)

Tollen's reagent

C)

\[{{\operatorname{I}}_{2}}/\]Alkali

D)

Fehling's solution

View Answer
59)                 By how many folds the temperature of a gas would increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from \[5\times {{10}^{4}}\operatorname{cm}/s\] to\[10\times {{10}^{4}}\] cm/s?                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Two

B)

                Three

C)

                Six

D)

                Four

View Answer
60)                 The element which of the following outer electron configuration may exhibit the largest number of oxidation states in its compounds:            JEE Main Online Paper (Held On 09 April 2013)

A)

                \[3{{\operatorname{d}}^{5}}4{{\operatorname{s}}^{2}}\]

B)

                \[3{{\operatorname{d}}^{8}}4{{\operatorname{s}}^{2}}\]

C)

                \[3{{\operatorname{d}}^{7}}4{{\operatorname{s}}^{2}}\]

D)

                \[3{{\operatorname{d}}^{6}}4{{\operatorname{s}}^{2}}\]

View Answer
61)                                 If the lines \[\frac{x+1}{2}=\frac{y-1}{1}=\frac{z+1}{3}\]and \[\frac{x+2}{2}=\frac{y-k}{3}=\frac{z}{3}\] are coplanar, then the value of K is:    JEE Main Online Paper (Held On 09 April 2013)

A)

                        \[\frac{11}{2}\]

B)

                \[-\frac{11}{2}\]

C)

                \[\frac{9}{2}\]

D)

                \[-\frac{9}{2}\]

View Answer
62)                                 Statement 1: The slope of the tangent at any point P on parabola, whose axis is the axis of \[x\] and vertex is the origin, is inversely proportional to the ordinate of the point P.                 Statement 2: The system of parabolas \[{{y}^{2}}=4ax\] satisfies a differential equation of degree 1 and order 1.    JEE Main Online Paper (Held On 09 April 2013)

A)

                Statement -1 is true, Statement -2 is true. Statement -2 is correct explanation for statement-1.

B)

                Statement -1 is true, Statement-2 is true. Statement -2 is not correct explanation for statement-1.

C)

                Statement -1 is false. Statement-2 is true.

D)

                Statement -1 is true. Statement-2 is false.

E)

                Statement -1 is false. Statement-2 is true.

View Answer
63)                 If \[{{Z}_{1}}\ne O\] and \[{{Z}_{2}}\] be two complex numbers such that \[\frac{{{Z}_{2}}}{{{Z}_{1}}}\] is a purely imaginary number, then \[\left| \frac{2{{Z}_{1}}+3{{Z}_{2}}}{2{{Z}_{1}}-3{{Z}_{2}}} \right|\] is equal to:             JEE Main Online Paper (Held On 09 April 2013)

A)

                2

B)

                5

C)

                3

D)

                1

View Answer
64)                 If \[\int{\frac{dx}{x+{{x}^{7}}}=P(x)}\]then,\[\int{\frac{{{x}^{6}}}{x+{{x}^{7}}}=dx}\] is equal to :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[ln\left| x \right|-p(x)+c\]

B)

                \[ln\left| x \right|+p(x)+c\]

C)

                \[x-p(x)+c\]

D)

                \[x+p(x)+c\]

View Answer
65)                                 If each of the lines \[5x+8y=13\] and \[4x-y=13\]contains a diameter of the circle \[{{x}^{2}}+{{y}^{2}}-2({{a}^{2}}-7+11)x-2({{a}^{2}}-6a+6)y\]\[+{{b}^{3}}+1=0,\] then:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[a=5\] and \[b\notin (-1,1)\]

B)

                \[a=1\] and \[b\notin (-1,1)\]

C)

                \[a=2\] and \[b\notin (-\infty ,1)\]

D)

                \[a=5\] and \[b\in (-\infty ,1)\]

View Answer
66)                 If a, b, c, are sides of a scalene triangle, then the value of\[\left| \begin{matrix}    a & b & c \\    b & c & a \\    c & a & b \\ \end{matrix} \right|\]is:    JEE Main Online Paper (Held On 09 April 2013)

A)

                non negative

B)

                negative

C)

                positive

D)

                non-positive

View Answer
67)                 If \[x=\int\limits_{0}^{y}{\frac{dt}{1+{{t}^{2}}},}\] then \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] is equal to:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[y\]

B)

                \[\sqrt{1+{{y}^{2}}}\]

C)

                \[\frac{y}{\sqrt{1+{{y}^{2}}}}\]

D)

                \[{{y}^{2}}\]

View Answer
68)                 Let\[{{a}_{1}},\,\,{{a}_{2}},\,\,{{a}_{3}},..\] be an A.P. such that\[\frac{{{a}_{1}}+{{a}_{2}}+...+{{a}_{p}}}{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}....+{{a}_{q}}}=\frac{{{\operatorname{p}}^{3}}}{{{\operatorname{q}}^{3}}};p\ne q\]. Then\[\frac{{{a}_{6}}}{{{a}_{21}}}\] is equal to: JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\frac{41}{11}\]

B)

                \[\frac{121}{1681}\]

C)

                \[\frac{11}{41}\]

D)

                \[\frac{121}{1861}\]

View Answer
69)                 Statement 1: The equation \[x\log x=2-x\] is satisfied by least one value of \[x\] lying between 1 and 2.                 Statement 2: The function \[f(x)\]= \[x\log x\] is an increasing function is \[[1,2]\] and \[g(x)=2-x\]is a decreasing function in [1,2] and the graphs represented by these functions intersect at a point in [1,2].                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Statement -1 is true, Statement-2 is true. Statement -2 is correct explanation for statement-1.

B)

                Statement -1 is true, Statement -2 is true. Statement -2 is not correct explanation for statement-1.

C)

                Statement -1 is false. Statement-2 is true.

D)

                Statement -1 is true. Statement-2 is false.

View Answer
70)                 Let \[\overset{\to }{\mathop{a}}\,=2\hat{i}-\hat{j}+k,\overset{\to }{\mathop{b}}\,=\hat{i}+2\hat{j}-\hat{k}\]and \[\overset{\to }{\mathop{c}}\,=\hat{i}+\hat{j}-2\overset{\to }{\mathop{k}}\,\]be three vectors. A vector of the type \[\overset{\to }{\mathop{b}}\,+\lambda \overset{\to }{\mathop{c}}\,\] for some scalar\[\lambda ,\] whose projection on \[\overset{\to }{\mathop{a}}\,\] is of magnitude\[\sqrt{\frac{2}{3}},\] is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[2\hat{i}+\hat{j}+5\hat{k}\]

B)

                \[2\hat{i}+3\hat{j}-3\hat{k}\]

C)

                \[2\hat{i}-\hat{j}+5\hat{k}\]

D)

                \[2\hat{i}+3\hat{j}+3\hat{k}\]

View Answer
71)                 The area bounded by the curve \[y=\ln (x)\]and the lines \[y=0,\]\[y=\ln (3)\] and \[x=0\]is equal to:              JEE Main Online Paper (Held On 09 April 2013)

A)

                3

B)

                \[3\,\ln (3)-2\]

C)

                \[3\,\,\ln (3)+2\]

D)

                2

View Answer
72)                 The Values of ?a? for which one root of the equation \[{{x}^{2}}-(a+1)x+{{a}^{2}}+a-8=0\]exceeds 2 and the other is lesser than 2, are given by:       JEE Main Online Paper (Held On 09 April 2013)

A)

                \[3<a<10\]

B)

                \[a\ge 10\]

C)

                \[-2<a<3\]

D)

                (d) \[a\le -2\]

View Answer
73)                 If the surface area of a sphere of radius r is increasing uniformly at the rate \[8{{\operatorname{cm}}^{2}}/s,\]then the rate of change of its volume is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                constant

B)

                proportional to \[\sqrt{r}\]

C)

                proportional to \[{{r}^{2}}\]

D)

                proportional to \[r\]

View Answer
74)                 The probability of a man hitting a target is \[\frac{2}{5}.\] He fires at the target k times (k, a given number). Then the minimum k, so that once is more than \[\frac{7}{10},\] is :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                3

B)

                5

C)

                2

D)

                4

View Answer
75)                 Equation of the line passing though the points of intersection of parabola \[{{x}^{2}}=8y\] and the ellipse\[\frac{{{x}^{2}}}{3}+{{y}^{2}}=1\] is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[y-3=0\]

B)

                \[y+3=0\]

C)

                \[3y+1=0\]

D)

                \[3y-1=0\]

View Answer
76)                 The sum of the series:                 \[1+\frac{1}{1+2}+\frac{1}{1+2+3}+...........\] up to 10 terms, is:      JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\frac{18}{11}\]

B)

                \[\frac{22}{13}\]

C)

                \[\frac{20}{11}\]

D)

                \[\frac{16}{9}\]

View Answer
77)                 A value of \[x\] for which \[\sin ({{\cot }^{-1}}(1+x))=\cos ({{\tan }^{-1}}x),\] is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[-\frac{1}{2}\]

B)

                1

C)

                0

D)

                \[\frac{1}{2}\]

View Answer
78)                 If a and c are positive real numbers and the ellipse\[\frac{{{x}^{2}}}{4{{c}^{2}}}+\frac{{{y}^{3}}}{{{c}^{2}}}=1\]has four distinct points in common with the circle \[{{x}^{2}}+{{y}^{2}}=9{{a}^{2}},\] then                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[9a-9{{a}^{2}}-2{{c}^{2}}<0\]

B)

                \[6ac+9{{a}^{2}}-2{{c}^{2}}<0\]

C)

                \[9ac-9{{a}^{2}}-2{{c}^{2}}>0\]

D)

                \[6ac+9{{a}^{2}}-2{{c}^{2}}>0\]

View Answer
79)                 The vector                 \[\left( \hat{i}\times \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\, \right)\hat{i}+\left( \hat{j}\times \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\, \right)\hat{j}+(\hat{k}\times \overset{\to }{\mathop{a.}}\,\overset{\to }{\mathop{b}}\,)\hat{j}\] \[+(\hat{k}\times \overset{\to }{\mathop{a}}\,.\overset{\to }{\mathop{b}}\,)\hat{k}\]                 is equal to                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[\vec{b}\times \vec{a}\]

B)

                \[\overset{\to }{\mathop{a}}\,\]

C)

                \[\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,\]

D)

                \[\overset{\to }{\mathop{b}}\,\]

View Answer
80)                 A light ray emerging from the point source placed at P(1, 3) is reflected at a point Q in the axis of \[x\]. If the reflected ray passes through the point R(6,7), then the abscissa of is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                1

B)

                3

C)

                \[\frac{7}{2}\]

D)

                \[\frac{5}{2}\]

View Answer
81)                 The mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be:             JEE Main Online Paper (Held On 09 April 2013)

A)

                41

B)

                49

C)

                40.5

D)

                42.5

View Answer
82)                 Let A = {1, 2, 3, 4} and be the relation defined by :                 R = {(1, 1), (2, 3), (3, 4), (4, 2)}. The correct statement is:           JEE Main Online Paper (Held On 09 April 2013)

A)

                R does not have an inverse.

B)

                R is not a one to one function.

C)

                R is an onto function.

D)

                R is not a function

View Answer
83) If the there lines \[x-3y=p,ax+2y=q\]and \[ax+y=r\] form a right - angled triangle then:                 JEE Main Online Paper (Held On 09 April 2013)

A)

\[{{a}^{2}}-9a+18=0\]

B)

\[{{a}^{2}}-6a-12=0\]

C)

\[{{a}^{2}}-6a-18=0\]

D)

\[{{a}^{2}}-9a+12=0\]

View Answer
84)                 The matrix\[{{A}^{2}}+4A-5I,\]where \[I\]is identity matrix and \[A=\left[ \begin{matrix}    1 & 2 \\    4 & -3 \\ \end{matrix} \right]\], equals:               JEE Main Online Paper (Held On 09 April 2013)

A)

                \[4\left[ \begin{matrix}    2 & 1 \\    2 & 0 \\ \end{matrix} \right]\]

B)

                \[4\left[ \begin{matrix}    0 & -1 \\    2 & 2 \\ \end{matrix} \right]\]

C)

                \[32\left[ \begin{matrix}    2 & 1 \\    2 & 0 \\ \end{matrix} \right]\]

D)

                \[32\left[ \begin{matrix}    1 & 1 \\    1 & 0 \\ \end{matrix} \right]\]

View Answer
85)                 The ratio of the coefficient of \[{{x}^{15}}\] to the term in dependent of \[x\] in the expansion of\[{{\left( {{x}^{2}}+\frac{2}{x} \right)}^{15}}\] is:        JEE Main Online Paper (Held On 09 April 2013)

A)

                7 : 16

B)

                7 : 64

C)

                1 : 4

D)

                1 : 32

View Answer
86)                 The value of \[\operatorname{l}\underset{x\to 0}{\mathop{im}}\,\frac{1}{x}\left[ {{\tan }^{-1}}\left( \frac{x+1}{2x+1} \right)-\frac{\pi }{4} \right]\]is : JEE Main Online Paper (Held On 09 April 2013)

A)

                1

B)

                \[-\frac{1}{2}\]

C)

                2

D)

                0

View Answer
87)                 A vector\[\overset{\to }{\mathop{\operatorname{n}}}\,\] is inclined to \[x-\]axis at\[{{45}^{0}}\], to\[y-\]axis at \[{{60}^{0}}\] and at an acute angle to\[z-\]axis.\[\operatorname{If}\]\[\overset{\to }{\mathop{\operatorname{n}}}\,\] is a normal to a plane passing through the point \[(\sqrt{2},-1,1),\] then the equation of the plane is :                 JEE Main Online Paper (Held On 09 April 2013)

A)

                \[4\sqrt{2}x+7y+z=2\]

B)

                \[\sqrt{2}x+y+z=2\]

C)

                \[3\sqrt{2}x-4y-3z=7\]

D)

                \[\sqrt{2}x-y-z=2\]

View Answer
88)                 Statement 1: The statement \[\operatorname{A}\to (\operatorname{B}\to \operatorname{A})\] is equivalent to \[\operatorname{A}\to \]\[\left( \text{A}\wedge \text{B} \right).\]                 Statement 2: The statement                 \[\Rightarrow \]\[\tilde{\ }\left[ \left( \text{A}\wedge \text{B} \right)\to \left( \text{ }\!\!\tilde{\ }\!\!\text{ A}\vee \text{B} \right) \right]\] is a Tautology.                 JEE Main Online Paper (Held On 09 April 2013)

A)

                Statement -1 is false. Statement -2 is true.

B)

Statement -1 is true, Statement-2 is true. Statement -2 is not correct explanation for statement-1.

C)

                Statement -1 is true, Statement-2 is true. Statement -2 is correct explanation for statement-1.

D)

                Statement -1 is true. Statement-2 is false.

View Answer
89)                 A committee of 4 persons is to formed from 2ladies, 2 old men and 4 young men such that it includes at least 1 lady, at lest 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is:                 JEE Main Online Paper (Held On 09 April 2013)

A)

                40

B)

                41

C)

                16

D)

                32

View Answer
90)                                 Let\[f(x)=\frac{{{x}^{2}}-x}{{{x}^{2}}+2x},x\ne 0,-2.\]Then\[\frac{d}{dx}\left[ {{f}^{-1}}(x) \right]\] (wherever it is defined) is equal to :      JEE Main Online Paper (Held On 09 April 2013)

A)

                frac{-1}{{{(1-x)}^{2}}}\]

B)

                \[\frac{3}{{{(1-x)}^{2}}}\]

C)

                \[\frac{1}{{{(1-x)}^{2}}}\]

D)

                \[\frac{-3}{{{(1-x)}^{2}}}\]

View Answer