Solved papers for JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

JEE Main Paper (Held On 26 May 2012) Total Questions - 90

1) Three positive charges of equal value q are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in JEE Main Online Paper (Held On 26-May-2012)

A)



B)



C)



D)



View Answer
2) In Young's double slit interference experiment, the slit widths are in the ratio 1: 25. Then the ratio of intensity at the maxima and minima in the interference pattern is JEE Main Online Paper (Held On 26-May-2012)

A)

3:2

B)

                       1:25

C)

                       9:4

D)

                       1:5

View Answer
3) Which of the plots shown in the figure represents speed (v) of the electron in a hydrogen atom as a function of the principal quantum number (n)? JEE Main Online Paper (Held On 26-May-2012)

A)

B

B)

                       D

C)

                       C

D)

                       A

View Answer
4) A radio transmitter transmits at 830 kHz. At a certain distance from the transmitter magnetic field has amplitude \[4.82\times {{10}^{-11}}T.\]The electric field and the wavelength are respectively JEE Main Online Paper (Held On 26-May-2012)

A)

0.014N/C, 36m

B)

                       0.14N/C, 36m

C)

                       0.14N/C, 360m

D)

                       0.014N/C, 360m

View Answer
5) A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of\[\frac{dM}{dt}=\alpha v\] where M is the mass (of satellite t+ dust) at that instant. The instantaneous acceleration of the satellite is JEE Main Online Paper (Held On 26-May-2012)

A)

\[-\frac{\alpha {{v}^{2}}}{2M}\]

B)

                       \[-\frac{\alpha {{v}^{2}}}{M}\]

C)

                       \[-\alpha {{v}^{2}}\]

D)

                       \[-\frac{2\alpha {{v}^{2}}}{M}\]

View Answer
6) Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. The force acting on the conductor B, which is situated at 10 cm distance from A will be JEE Main Online Paper (Held On 26-May-2012)

A)

\[8\times {{10}^{-5}}N\]

B)

                       \[5\times {{10}^{-5}}N\]

C)

                       \[8\pi \times {{10}^{-7}}N\]

D)

                       \[4\pi \times {{10}^{-7}}N\]

View Answer
7) 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: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is\[6.4\times {{10}^{6}}m.\] JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

B)

Statement 1 is false, Statement 2 is true.

C)

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

D)

Statement 1 is true, Statement 2 is false.

View Answer
8) The resistance of a wire is R. It is bent at the middle by 180° and both the ends are twisted together to make a shorter wire. The resistance of the new wire is JEE Main Online Paper (Held On 26-May-2012)

A)

2R

B)

                       R/2

C)

                       R/4

D)

                       R/S

View Answer
9) An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (velocity of sound = 330 m/s) JEE Main Online Paper (Held On 26-May-2012)

A)

125.00

B)

                       93.75

C)

                       62.50

D)

                       187.50

View Answer
10) The electrical resistance R of a conductor of length \[l\] and area of cross section a is given by\[R=\frac{\rho l}{a}\]where \['\rho '\]is the electrical resistivity. What is the dimensional formula for electrical conductivity' \['\sigma '\]which is reciprocal of resistivity? JEE Main Online Paper (Held On 26-May-2012)

A)

\[[{{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}}]\]

B)

                       \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{2}}]\]

C)

                       \[[M{{L}^{-3}}{{T}^{-3}}{{A}^{-2}}]\]

D)

                       \[[{{M}^{-2}}{{L}^{3}}{{T}^{2}}{{A}^{-1}}]\]

View Answer
11) The frequency of X-rays;\[\gamma \text{-}\]rays and ultraviolet rays are respectively a, b and c then. JEE Main Online Paper (Held On 26-May-2012)

A)

\[a<b;b>c\]

B)

                       \[a>b;b>c\]

C)

                       \[a<b<c\]

D)

                       \[a=b=c\]

View Answer
12) The figure shows a combination of two NOT gates and a NOR gate. The combination is equivalent to a. JEE Main Online Paper (Held On 26-May-2012)

A)

NAND gate

B)

                       NOR gate

C)

                       AND gate

D)

                       OR gate

View Answer
13) Photoelectrons are ejected from a metal when light of frequency u falls on it. Pick out the wrong statement from the following. JEE Main Online Paper (Held On 26-May-2012)

A)

No electrons are emitted if o is less than W/h, where W is the work function of the metal

B)

                       The ejection of the photoelectrons is instantaneous.

C)

                       The maximum energy of the photo electrons is\[h\upsilon .\]

D)

                       The maximum energy of the photoelectrons is independent of the intensity of the light.

View Answer
14) The counting rate observed from a radioactive source at t = 0 was 1600 counts \[{{s}^{-1}}.\], and t = 8 s, it was 100 counts \[{{s}^{-1}}.\]. The counting rate observe das counts \[{{s}^{-1}}.\] at t = 6 s will be. JEE Main Online Paper (Held On 26-May-2012)

A)

250

B)

                       400

C)

                       300

D)

                       200

View Answer
15) A point particle is held on the axis of a ring of mass m and radius r at a distance r from its centre C. When released, it reaches C under the gravitational attraction of the ring. Its speed at C will be. JEE Main Online Paper (Held On 26-May-2012)

A)

\[\sqrt{\frac{2Gm}{r}\left( \sqrt{2}-1 \right)}\]

B)

                       \[\sqrt{\frac{Gm}{r}}\]

C)

                       \[\sqrt{\frac{2Gm}{r}\left( 1-\frac{1}{\sqrt{2}} \right)}\]

D)

                       \[\sqrt{\frac{2Gm}{r}}\]

View Answer
16) A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face AB. The refractive indices of the material for the above red, green and blue colours are 1.39, 1.44 and 1.47 respectively. A person looking on surface A C of the prism will see JEE Main Online Paper (Held On 26-May-2012)

A)

no light

B)

                       green and blue colours

C)

                       red and green colours

D)

                       Red colour only

View Answer
17) The force \[\overset{\to }{\mathop{F}}\,=F\hat{i}\] on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x = 0. What is the kinetic energy of the particle at\[x=8m?\] JEE Main Online Paper (Held On 26-May-2012)

A)

34J

B)

                       34.5 J

C)

                       4.5J

D)

                       29.4J

View Answer
18) The door of a working refrigerator is left open in a well insulated room. The temperature of air in the room will JEE Main Online Paper (Held On 26-May-2012)

A)

decrease

B)

                       increase in winters and decrease in summers

C)

remain the same

D)

                       increase

View Answer
19) The terminal velocity of a small sphere of radius a in a viscous liquid is proportional to JEE Main Online Paper (Held On 26-May-2012)

A)

\[{{a}^{2}}\]

B)

                       \[{{a}^{3}}\]

C)

                       a

D)

                       \[{{a}^{-1}}\]

View Answer
20) A stone of mass m, tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by \[T=A{{r}^{n}},\]where A is a constant, r is the instantaneous radius of the circle. The value of n is equal to. JEE Main Online Paper (Held On 26-May-2012)

A)

-1

B)

-2

C)

-4

D)

-3

View Answer
21) The disturbance y (x, t) of a wave propagating in the positive x-direction is given by \[y=\frac{1}{1+{{x}^{2}}}\] at time t = 0 and by \[y=\frac{1}{\left[ 1+{{\left( x-1 \right)}^{2}} \right]}\]at t = 2 s, where x and y are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in m/s is. JEE Main Online Paper (Held On 26-May-2012)

A)

2.0

B)

4.0

C)

0.5

D)

1.0

View Answer
22) An ideal monatomic gas with pressure P, volume V and temperature T is expanded isothermally to a volume 2V and a final pressure \[{{P}_{i}}.\] If the same gas is expanded adiabatically to a volume 2V, the final pressure is \[{{P}_{a}}.\]The ratio \[\frac{{{P}_{a}}}{{{P}_{i}}}\]is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[{{2}^{-1/3}}\]

B)

\[{{2}^{1/3}}\]

C)

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

D)

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

View Answer
23) A telescope of aperture \[3\times {{10}^{-2}}m\] diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing \[2\times {{10}^{-3}}m\]. Given:\[\lambda =5.5\times {{10}^{-7}}m,\]which of the following is true for observing the mesh through the telescope? JEE Main Online Paper (Held On 26-May-2012)

A)

Yes, it is possible with the same aperture size.

B)

Possible also with an aperture half the present diameter.

C)

No, it is not possible.

D)

Given data is not sufficient.

View Answer
24) 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 charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is false, Statement 2 is time.

B)

Statement 1 is time, Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.

C)

Statement 1 is true. Statement 2 is false.

D)

Statement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.

View Answer
25) A ball is dropped vertically downwards from a height h above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents variation between speed (v) and height (h) correctly? JEE Main Online Paper (Held On 26-May-2012)

A)

B)

C)

D)

View Answer
26) A thick-walled hollow sphere has outside radius\[{{R}_{0}}.\]It rolls down an incline without slipping and its speed at the bottom is \[{{v}_{0}}.\].Now the incline is waxed, so that it is practically frictionless and the sphere is observed to slide down (without any rolling). Its speed at the bottom is observed to be\[5{{v}_{0}}/4.\]The radius of gyration of the hollow sphere about an axis through its centre is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[3{{R}_{0}}/2\]

B)

\[3{{R}_{0}}/4\]

C)

\[9{{R}_{0}}/16\]

D)

\[3{{R}_{0}}\]

View Answer
27) In a cylindrical water tank, there are two small holes A and B on the wall at a depth of\[{{h}_{1}},\] from the surface of water and at a height of \[{{h}_{2}}\] from the bottom of water tank. Surface of water is at height of\[{{h}_{2}}\] from the bottom of water tank. Surface of water is at height H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S. Find the ratio of \[{{h}_{1}}\]and \[{{h}_{2}}\] JEE Main Online Paper (Held On 26-May-2012)

A)

Depends on H

B)

1:1

C)

2:2

D)

1:2

View Answer
28) 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: If you push on a cart being pulled by a horse so that it does not move, the cart pushes you back with an equal and opposite force. Statement 2: The cart does not move because the force described in statement 1 cancel each other. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is time, Statement 2 is time, Statement 2 is the correct explanation of Statement 1.

B)

Statement 1 is false, Statement 2 is time.

C)

Statement 1 is true. Statement 2 is false.

D)

Statement 1 is time. Statement 2 is time, Statement 2 is not the correct explanation of Statement 1.

View Answer
29) In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length \[\ell \]is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance R, If R is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be. JEE Main Online Paper (Held On 26-May-2012)

A)

\[\ell \]

B)

                       \[2\ell \]

C)

                       \[\ell /2\]

D)

                       \[\ell /4\]

View Answer
30) The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the resonance frequency of the circuit is 10 kHz. When the container is filled with a gas, the resonance frequency changes by 50 Hz. The dielectric constant of the gas is. JEE Main Online Paper (Held On 26-May-2012)

A)

1.001

B)

                       2.001

C)

                       1.01

D)

                       3.01

View Answer
31) The following sets of quantum numbers represent four electrons in an atom. JEE Main Online Paper (Held On 26-May-2012)

(i) \[n=4,l=1\]

(ii) \[n=4,l=0\]

(iii)\[n=3,l=2\]

(iv) \[n=3,l=1\]

The sequence representing increasing order of energy, is

A)

(iii)<(i)<(iv)<(ii)

B)

(iv)<(ii)<(iii)<(i)

C)

(i)<(iii)<(ii)<(iv)

D)

(ii)<(iv)<(i)<(iii)

View Answer
32) 'The substance used as froth stabilisers in forth-floatation process is . JEE Main Online Paper (Held On 26-May-2012)

A)

Potassium ethyl xanthate

B)

                       Aniline

C)

                       Sodium cyanide

D)

                       Copper sulphate

View Answer
33) The activation energy for a reaction which doubles the rate when the temperature is raised from 298 K to 308 K is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[52.2\,kJ\,mo{{l}^{-1}}\]

B)

                       \[39.2\,kJ\,mo{{l}^{-1}}\]

C)

                       \[52.9\,kJ\,mo{{l}^{-1}}\]

D)

                       \[29.5\,kJ\,mo{{l}^{-1}}\]

View Answer
34) Tollen's reagent and Fehling solutions are used to distinguish between. JEE Main Online Paper (Held On 26-May-2012)

A)

acids and alcohols

B)

                       alkanes and alcohols

C)

                       ketones and aldehydes

D)

                       n-alkaens and branched alkanes

View Answer
35) In the following compounds : the order of basicity is as follows. JEE Main Online Paper (Held On 26-May-2012)

A)

\[IV>III>II>I\]

B)

                       \[III>I>II>IV\]

C)

                       \[II>III>I>IV\]

D)

                       \[I>III>II>IV\]

View Answer
36) Maleic acid and fumaric acids are. JEE Main Online Paper (Held On 26-May-2012)

A)

Chain isomers

B)

                       Functional isomers

C)

                       Tautomers

D)

                       Geometrical isomers

View Answer
37) Which of the following compounds are anti-aromatic . JEE Main Online Paper (Held On 26-May-2012)

A)

(I) and (V)

B)

(II) and (V)

C)

(I) and (IV)

D)

(III) and (VI)

View Answer
38) The freezing point of a 1.00 m aqueous solution of HF is found to be \[-1.91\text{ }{}^\circ C\]. The freezing point constant of water, K. is 1.86 K kg \[\text{mo}{{\text{l}}^{-1}}\] The percentage dissociation of HF at this concentration is. JEE Main Online Paper (Held On 26-May-2012)

A)

30%

B)

10%

C)

5.2%

D)

2.7%

View Answer
39) Which of the following presents the correct order of second ionization enthalpies of C, N, O and F? JEE Main Online Paper (Held On 26-May-2012)

A)

\[F>O>N>C\]

B)

                       \[O>N>F>C\]

C)

                       \[C>N>O>F\]

D)

                       \[O>F>N>C\]

View Answer
40) A transition metal M forms a volatile chloride which has a vapour density of 94.8. If it contains74.75% of chlorine the formula of the metal chloride will be . JEE Main Online Paper (Held On 26-May-2012)

A)

\[MC{{l}_{3}}\]

B)

\[MC{{l}_{2}}\]

C)

\[MC{{l}_{4}}\]

D)

\[MC{{l}_{5}}\]

View Answer
41) Among the following species which two have trigonal bipyramidal shape? JEE Main Online Paper (Held On 26-May-2012)

(I) \[N{{I}_{3}}\]

(II) \[I_{3}^{-}\]

(III) \[SO_{3}^{2-}\]

(IV) \[NO_{3}^{-}\]

A)

l and III

B)

IIl and IV

C)

l and IV

D)

II and III

View Answer
42) Consider the following sequence of reactions \[C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[700K]{C{{l}_{2}}}A\xrightarrow[420K,12atm]{N{{a}_{2}}C{{O}_{3}}}\]\[B\xrightarrow[(ii)NaOH]{(i)HOCl}C\] Compound 'C' is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[\underset{\begin{align} & | \\ & CHOH \\ & | \\ & C{{H}_{2}}OH \\ \end{align}}{\mathop{C{{H}_{2}}OH}}\,\]

B)

\[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,COONa\]

C)

\[HOC{{H}_{2}}-CH=C{{H}_{2}}\]

D)

\[C{{H}_{3}}\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,COCl\]

View Answer
43) Fire extinguishers contain \[{{H}_{2}}S{{O}_{4}}\] and which one of the following? JEE Main Online Paper (Held On 26-May-2012)

A)

\[NaHC{{O}_{3}}\]and\[N{{a}_{2}}C{{O}_{3}}\]

B)

                       \[N{{a}_{2}}C{{O}_{3}}\]

C)

                       \[NaHC{{O}_{3}}\]

D)

                       \[CaC{{O}_{3}}\]

View Answer
44) Which one of the following depletes ozone layer? JEE Main Online Paper (Held On 26-May-2012)

A)

CO

B)

                       NO and freons

C)

                       \[S{{O}_{2}}\]

D)

                       \[C{{O}_{2}}\]

View Answer
45) Dipole moment is shown by. JEE Main Online Paper (Held On 26-May-2012)

A)

1,2-dichlorobenzene

B)

                       trans 2,3-dichloro-2-butene

C)

                       1,4-chlorobenzene

D)

                       trans-1,2-dinitroethene

View Answer
46) Which of the following statements is correct? JEE Main Online Paper (Held On 26-May-2012)

A)

RNA controls the synthesis of proteins.

B)

                       The sugar present in DNA is D-(-)-ribose.

C)

                       RNA has double stranded a-helix structure.

D)

                       DNA mainly occurs in the cytoplasm of the cell.

View Answer
47) The solubility of\[PB{{I}_{2}}\]at 25°C is \[0.7g\,{{L}^{-1}}.\] The solubility product of\[Pb{{I}_{2}}\] at this temperature is(molar mass of\[Pb{{I}_{2}}=461.2\,g\,\text{mo}{{\text{l}}^{-1}}\]). JEE Main Online Paper (Held On 26-May-2012)

A)

\[1.40\times {{10}^{-9}}\]

B)

                       \[0.14\times {{10}^{-9}}\]

C)

                       \[140\times {{10}^{-9}}\]

D)

                       \[14.0\times {{10}^{-9}}\]

View Answer
48) Bakelite is obtained from phenol by reacting it with. JEE Main Online Paper (Held On 26-May-2012)

A)

Acetaldehyde

B)

                       Chlorobenzene

C)

                       Formaldehyde

D)

                       Acetamide

View Answer
49) Among the following the incorrect statement is. JEE Main Online Paper (Held On 26-May-2012)

A)

Density of crystals remains unaffected due to Frenkel defect.

B)

                       In BCC unit cell the void space is 32%.

C)

                       Density of crystals decreases due to Schottky defect.

D)

                       Electrical conductivity of semiconductors and metals increases with increase in temperature.

View Answer
50) Which of the following forms stable + 4 oxidationstate? JEE Main Online Paper (Held On 26-May-2012)

A)

La(Z=57)

B)

                       Eu(Z=63)

C)

                       Ce(Z=58)

D)

                       Gd(Z=64)

View Answer
51) Colloidal solutions can be purified by. JEE Main Online Paper (Held On 26-May-2012)

A)

emulsification

B)

                       electrodialysis

C)

                       peptization

D)

                       using Tyndall effect

View Answer
52) Given\[E_{C{{u}^{2+}}/Cu}^{o}=0.34V,E_{C{{u}^{2+}}/Cu}^{o}=0.15V\] Standard electrode potential for the half cell \[C{{u}^{+}}/Cu\]is. JEE Main Online Paper (Held On 26-May-2012)

A)

0.38V

B)

                       0.53V

C)

                       0.19V

D)

                       0.49V

View Answer
53) The complex ion \[{{[Pt(N{{O}_{2}})(Py)(N{{H}_{3}})(N{{H}_{2}}OH)]}^{+}}\]will give. JEE Main Online Paper (Held On 26-May-2012)

A)

2 isomers (Geometrical)

B)

                       3 isomers (Geometrical)

C)

                       6 isomers (Geometrical)

D)

                       4 isomers (Geometrical)

View Answer
54) The hydration of propyne results in formation of. JEE Main Online Paper (Held On 26-May-2012)

A)

Acetone

B)

                       Propanol-1

C)

                       Propene

D)

                       Propanal

View Answer
55) One mole of an ideal gas is expanded isothermally and reversibly to half of its initial pressure. \[\Delta S\]for the process in \[J\,{{K}^{-1}}\,mo{{l}^{-1}}\] is [\[\ell n2=0.693\]and\[R=8.314J/(mol\,K)\]]. JEE Main Online Paper (Held On 26-May-2012)

A)

6.76

B)

                                       5.76

C)

                       10.76

D)

                       8.03

View Answer
56) The number of S-S bonds in\[S{{O}_{3}},{{S}_{2}}O_{3}^{2-}{{S}_{2}}O_{6}^{2-}\]and\[{{S}_{2}}O_{8}^{2-}\]respectively are. JEE Main Online Paper (Held On 26-May-2012)

A)

1,0,0,1

B)

1,0,1,0

C)

0,1,1,0

D)

0,1,0,1

View Answer
57) Sulphonamides act as. JEE Main Online Paper (Held On 26-May-2012)

A)

Antiseptic

B)

                       Analgesic

C)

                       Antimicrobials

D)

                       Antipyretic

View Answer
58) The relationship among most probable velocity, average velocity and root mean square velocity is respectively. JEE Main Online Paper (Held On 26-May-2012)

A)

\[\sqrt{2}:\sqrt{3}:\sqrt{8/\pi }\]

B)

                       \[\sqrt{2}:\sqrt{8/\pi }:\sqrt{3}\]

C)

                       \[\sqrt{8/\pi }:\sqrt{3}:\sqrt{2}\]

D)

                       \[\sqrt{3}:\sqrt{8/\pi }:\sqrt{2}\]

View Answer
59) The number of unpaired electrons in Gadolinium\[[Z=64]\]is. JEE Main Online Paper (Held On 26-May-2012)

A)

3

B)

                       8

C)

                       6

D)

                       2

View Answer
60) One mole of\[{{O}_{2(g)}}\]and two moles of\[S{{O}_{2(g)}}\] were heated in a closed vessel of one-litre capacity at1098 K. At equilibrium 1.6 moles of\[S{{O}_{3(g)}}\] were found. The equilibrium constant \[{{K}_{c}}\] of the reaction would be. JEE Main Online Paper (Held On 26-May-2012)

A)

30

B)

                       40

C)

                       80

D)

                       60

View Answer
61) The distance of the point \[-\hat{i}+2\hat{j}+6\hat{k}\]from the straight line that passes through the point \[2\hat{i}+3\hat{j}-4\hat{k}\] and is parallel to the vector \[6\hat{i}+3\hat{j}-4\hat{k}\] is JEE Main Online Paper (Held On 26-May-2012)

A)

9

B)

                       8

C)

                       7

D)

                       10

View Answer
62) Consider the following planes \[P:x+y-2z+7=0\] \[Q:x+y+2z+2=0\] \[R:3x+3y-6z-11=0\] JEE Main Online Paper (Held On 26-May-2012)

A)

P and R are perpendicular

B)

                       Q and R are perpendicular

C)

                       P and g are parallel

D)

                       P and R are parallel

View Answer
63) If\[A=\left[ \begin{matrix}    1 & 0 & 0 \\    2 & 1 & 0 \\    -3 & 2 & 1 \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix}    1 & 0 & 0 \\    -2 & 1 & 0 \\    7 & -2 & 1 \\ \end{matrix} \right]\] then AB equals. JEE Main Online Paper (Held On 26-May-2012)

A)

I

B)

                       A

C)

                       B

D)

                       0

View Answer
64) If the A.M. between \[{{\text{p}}^{\text{th}}}\]and \[{{\text{q}}^{\text{th}}}\]terms of an A.P. is equal to the A.M. between \[{{\text{r}}^{\text{th}}}\]and \[{{\text{s}}^{\text{th}}}\] terms of the same A.P., then p + q is equal to. JEE Main Online Paper (Held On 26-May-2012)

A)

r+s-1

B)

r+s-2

C)

r+s+1

D)

r+s

View Answer
65) The value of cos \[225{}^\circ \] + sin \[195{}^\circ \] is'. JEE Main Online Paper (Held On 26-May-2012)

A)

\[\frac{\sqrt{3}-1}{2\sqrt{2}}\]

B)

\[\frac{\sqrt{3}-1}{\sqrt{2}}\]

C)

\[-\frac{\sqrt{3}-1}{\sqrt{2}}\]

D)

\[\frac{\sqrt{3}+1}{\sqrt{2}}\]

View Answer
66) The middle term in the expansion of \[{{\left( 1-\frac{1}{x} \right)}^{n}}{{\left( 1-x \right)}^{n}}\] in powers of x is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[{{-}^{2n}}{{C}_{n-1}}\]

B)

                       \[{{-}^{2n}}{{C}_{n}}\]

C)

                       \[^{2n}{{C}_{n-1}}\]

D)

                       \[^{2n}{{C}_{n}}\]

View Answer
67) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin \left( \pi {{\cos }^{2}}x \right)}{{{x}^{2}}}\] equals. JEE Main Online Paper (Held On 26-May-2012)

A)

\[-\pi \]

B)

                       1

C)

                       \[-1\]

D)

                       \[\pi \]

View Answer
68) The line parallel to x-axis and passing through the point of intersection of lines \[ax+2by+3b=0\]and \[bx-2ay-3a=0,\] where \[(a,b)\ne (0,0)\] is. JEE Main Online Paper (Held On 26-May-2012)

A)

above x-oxis ata distance 2/3 from it

B)

                       above x-axis at a distance 3/2 from it

C)

                       below x-axis at a distance 3/2 from it

D)

                       below x-axis at a distance 2/3 from it

View Answer
69) The chord PQ of the parabola \[{{y}^{2}}=x,\]where one end P of the chord is at point (4, - 2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[-4\]

B)

                       \[-\frac{1}{4}\]

C)

                       4

D)

                       \[\frac{1}{4}\]

View Answer
70) Let p and q denote the following statements p : The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[q\Rightarrow \tilde{\ }p\]

B)

                       \[q\wedge \tilde{\ }p\]

C)

                       \[p\wedge \tilde{\ }q\]

D)

                       \[\tilde{\ }q\Rightarrow \tilde{\ }p\]

View Answer
71) If the sum of the series \[{{\text{1}}^{\text{2}}}+\text{2}.{{\text{2}}^{\text{2}}}+{{\text{3}}^{\text{2}}}+\text{2}.{{\text{4}}^{\text{2}}}+{{\text{5}}^{\text{2}}}+\]\[~...\text{ 2}.{{\text{6}}^{\text{2}}}+...\] upto n terms, when n is even, is\[\frac{n{{\left( n+1 \right)}^{2}}}{2},\]then the sum of the series, when n is odd, is , JEE Main Online Paper (Held On 26-May-2012)

A)

\[{{n}^{2}}(n+1)\]

B)

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

C)

                       \[\frac{{{n}^{2}}(n+1)}{2}\]

D)

                       \[{{n}^{2}}(n-1)\]

View Answer
72) The area bounded by the parabola \[{{y}^{2}}=4x\] and the line \[\text{2x}-\text{3y}+\text{4}=0,\] in square unit, is. JEE Main Online Paper (Held On 26-May-2012)

A)

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

B)

                       \[\frac{1}{3}\]

C)

                       \[1\]

D)

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

View Answer
73) Let \[f;\left( -\infty ,\infty \right)\to \left( -\infty ,\infty \right)\] be defined by \[f(x)={{x}^{3}}+1.\] Statement 1: The function f has a local extremumatx=0 Statement 2: The function f is continuous and differentiable on \[\left( -\infty ,\infty \right)\] and f'(0)=0. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is true. Statement 2 is false.

B)

                       Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

C)

                       Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

D)

                       Statement 1 is false, Statement 2 is true.

View Answer
74) Let A and B be nonempty sets in R and\[f:A\to B\] is a objective function. Statement 1: fis an onto function. Statement 2: There exists a function \[g:B\to A\] such that \[fog={{I}_{B}}.\]. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is true, Statement 2 is false.

B)

                       Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

C)

                       Statement 1 is false. Statement 2 is true.

D)

                       Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

View Answer
75) The number of common tangents of the circles given by\[{{x}^{2}}+{{y}^{2}}-8x-2y+1=0\]and\[{{x}^{2}}+{{y}^{2}}+6x+8y=0\]is. JEE Main Online Paper (Held On 26-May-2012)

A)

one

B)

                       four

C)

                       two

D)

                       three

View Answer
76) \[{{\left| {{z}_{1}}+{{z}_{2}} \right|}^{2}}+{{\left| {{z}_{1}}-{{z}_{2}} \right|}^{2}}\] is equal to. JEE Main Online Paper (Held On 26-May-2012)

A)

\[2\left( \left| {{z}_{1}}-{{z}_{2}} \right| \right)\]

B)

                       \[2\left( {{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}} \right)\]

C)

                       \[\left| {{z}_{1}} \right|\left| {{z}_{2}} \right|\]

D)

                       \[{{\left| {{z}_{1}} \right|}^{2}}+{{\left| {{z}_{2}} \right|}^{2}}\]

View Answer
77) \[f\left( x \right)=\frac{dx}{{{\sin }^{6}}x}\]is a polynomial of degree. JEE Main Online Paper (Held On 26-May-2012)

A)

5 in cot x

B)

                       5 in tan x

C)

                       3 in tan x

D)

                       3 in cot x

View Answer
78) The equation of a plane containing the line \[\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\] and the point (0,7, - 7) is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[x+y+z=0\]

B)

                       \[x+2y+z=21\]

C)

                       \[3x-2y+5z+35=0\]

D)

                       \[3x+2y+5z+21=0\]

View Answer
79) Statement-1: The vectors \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,\]and \[\overset{\to }{\mathop{c}}\,\] lie in the same plane if and only if \[\overset{\to }{\mathop{a}}\,.\left( \overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\, \right)=0\] Statement-2: The vectors \[\overset{\to }{\mathop{u}}\,\]and \[\overset{\to }{\mathop{v}}\,\] are perpendicular if and only if \[\overset{\to }{\mathop{u}}\,.\overset{\to }{\mathop{v}}\,=0\]where\[\overset{\to }{\mathop{u}}\,\times \overset{\to }{\mathop{v}}\,\]is a vector perpendicular to the plane of. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is false. Statement 2 is true.

B)

Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement!.

C)

Statement 1 is true, Statement 2 is false.

D)

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

View Answer
80) Statement 1: If the system of equations\[x+ky+3z=0,\]\[3x+ky-2z=0,\]\[2x+3y-4z=0\]has anon- trivial solution, then the value of k is\[\frac{31}{2}.\] Statement 2: A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is false, Statement 2 is true.

B)

                       Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

C)

                       Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

D)

                       Statement 1 is true, Statement 2 is false.

View Answer
81) The normal at \[\left( 2,\frac{3}{2} \right)\]to the ellipse,\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{3}=1\] touches a parabola, whose equation is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[{{y}^{2}}=-104x\]

B)

                       \[{{y}^{2}}=14x\]

C)

                       \[{{y}^{2}}=26x\]

D)

                       \[{{y}^{2}}=-14x\]

View Answer
82) If [x] is the greatest integer \[\le x,\] then the value of the integral\[\int\limits_{-0.9}^{0.9}{\left( \left[ {{x}^{2}} \right]+\log \left( \frac{2-x}{2+x} \right) \right)dx}\]is. JEE Main Online Paper (Held On 26-May-2012)

A)

0.486

B)

                       0.243

C)

                       1.8

D)

                       0

View Answer
83) If\[a,b,c\in R\] and 1 is a root of equation \[a{{x}^{2}}+bx+c=0,\]then the curve \[y=4a{{x}^{2}}+3bx+2c,a\ne 0\]intersect x-axis at. JEE Main Online Paper (Held On 26-May-2012)

A)

two distinct points whose coordinates are always rational numbers

B)

       no point

C)

                       exactly two distinct points

D)

                       exactly one point

View Answer
84) If\[f(x)=a|\sin x|+b{{e}^{|x|}}+c|x{{|}^{3}},\] where \[a,b,c\in R\], is differentiable at x = 0, then. JEE Main Online Paper (Held On 26-May-2012)

A)

\[a=0,b\]and c are any real numbers

B)

                       \[c=0,a=0,b\] is any real number

C)

                       \[b=0,c=0,a\] is any real number

D)

                       \[a=0,b=0,c\] is any real number

View Answer
85) The integrating factor of the differential equation \[\left( {{x}^{2}}-1 \right)\frac{dy}{dx}+2xy=x\] is. JEE Main Online Paper (Held On 26-May-2012)

A)

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

B)

                       \[{{x}^{2}}-1\]

C)

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

D)

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

View Answer
86) Consider the straight lines \[{{L}_{1}}:x-y=1\] \[{{L}_{2}}:x+y=1\] \[{{L}_{3}}:2x+2y=5\] \[{{L}_{4}}:2x-2y=7\] The correct statement is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[{{L}_{1}}||{{L}_{4}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\]intersect \[{{L}_{4}}.\]

B)

\[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{2}}.\]

C)

\[{{L}_{1}}\bot {{L}_{2}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{4}}.\]

D)

\[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{2}}\] intersect \[{{L}_{4}}.\]

View Answer
87) Statement-1: The variance of first n odd natural numbers is\[\frac{{{n}^{2}}-1}{3}\] Statement-2: The sum of first n odd natural number is n2 and the sum of square of first n odd natural numbers is \[\frac{n\left( 4{{n}^{2}}+1 \right)}{3}.\]. JEE Main Online Paper (Held On 26-May-2012)

A)

Statement 1 is true, Statement 2 is false.

B)

Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

C)

Statement 1 is false, Statement 2 is true.

D)

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

View Answer
88) If a metallic circular plate of radius 50 cm is heated so that its radius increases at the rate of 1 mm per hour, then the rate at which, the area of the plate increases (in \[\text{c}{{\text{m}}^{\text{2}}}\]/hour) is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[5\pi \]

B)

                                       \[10\pi \]

C)

                       \[100\pi \]

D)

                       \[50\pi \]

View Answer
89) If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[6!7!\]

B)

                       \[{{(6!)}^{2}}\]

C)

                       \[{{(7!)}^{2}}\]

D)

                       \[7!\]

View Answer
90) There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the um and there after a ball is drawn at random from the um, then the probability that it is white is. JEE Main Online Paper (Held On 26-May-2012)

A)

\[\frac{1}{4}\]

B)

\[\frac{2}{3}\]

C)

\[\frac{1}{5}\]

D)

\[\frac{1}{3}\]

View Answer