Solved papers for JEE Main & Advanced AIEEE Solved Paper-2013

done AIEEE Solved Paper-2013 Total Questions - 90

• question_answer1) A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged n a liquid  of density $\sigma$ at equilibrium position. The extension${{x}_{0}}$of the spring when it is in equilibrium is: (Here, k is spring constant)   AIEEE Solevd Paper-2013

A)
$\frac{Mg}{k}$

B)
$\frac{Mg}{k}\left( 1-\frac{LA\sigma }{M} \right)$

C)
$\frac{Mg}{k}\left( 1-\frac{LA\sigma }{2M} \right)$

D)
$\frac{Mg}{k}\left( 1+\frac{LA\sigma }{M} \right)$

• question_answer2) A metallic rod of length$\ell$ is tied to a string of length$2\ell$and made to rotate with angular speed$\omega$on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is: AIEEE Solevd Paper-2013

A)
$\frac{2B\omega {{\ell }^{2}}}{2}$

B)
$\frac{3B\omega {{\ell }^{2}}}{2}$

C)
$\frac{4B\omega {{\ell }^{2}}}{2}$

D)
$\frac{5B\omega {{\ell }^{2}}}{2}$

• question_answer3) This question has statement I and Statement II. Of the four choice 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 $f\left( \frac{1}{2}m{{v}^{2}} \right)$then$f=\left( \frac{m}{M+m} \right)$ Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.     AIEEE Solevd Paper-2013

A)
Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement - I

B)
Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement - I

C)
Statement - I is true, Statement - II is false

D)
Statement - I is false, Statement - II is true

• question_answer4) Let$[{{\varepsilon }_{0}}]$denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = Time and A = electric current, then:     AIEEE Solevd Paper-2013

A)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{2}}A]$

B)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}}]$

C)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}{{A}^{-2}}]$

D)
$[{{\varepsilon }_{0}}]=[{{M}^{-1}}{{L}^{2}}{{T}^{-1}}A]$

• question_answer5) A Projectile is given an initial velocity of$(\hat{i}+2\hat{j})m/s$+ where$\hat{i}$is along the ground and $\hat{j}$is along the vertical. If$g=10\text{ }m/{{s}^{2}},$the equation of its trajectory is :     AIEEE Solevd Paper-2013

A)
$y=x-5{{x}^{2}}$

B)
$y=2x-5{{x}^{2}}$

C)
$4y=2x-5{{x}^{2}}$

D)
$4y=2x-25{{x}^{2}}$

• question_answer6) The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to $\alpha$ times its original magnitude, where α equals:     AIEEE Solevd Paper-2013

A)
0.7

B)
0.81

C)
0.729

D)
0.6

• question_answer7) Two capacitors${{C}_{1}}$and${{C}_{2}}$are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then:     AIEEE Solevd Paper-2013

A)
$5{{C}_{1}}=3{{C}_{2}}$

B)
$3{{C}_{1}}=5{{C}_{2}}$

C)
$3{{C}_{1}}+5{{C}_{2}}=0$

D)
$9{{C}_{1}}=4{{C}_{2}}$

• question_answer8) A sonometer wire of length 1.5 m is made of steel. The tension in it produce an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times {{10}^{3}}kg/{{m}^{3}}$ and $2.2\times {{10}^{11}}$ $N/{{m}^{2}}$respectively?     AIEEE Solevd Paper-2013

A)
188.5 Hz

B)
178.2 Hz

C)
200.5 Hz

D)
770 Hz

• question_answer9) A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is:     AIEEE Solevd Paper-2013

A)
$9.1\times {{10}^{-11}}weber$

B)
$6\times {{10}^{-11}}weber$

C)
$3.3\times {{10}^{-11}}weber$

D)
$6.6\times {{10}^{-9}}weber$

• question_answer10) Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is$2\times {{10}^{8}}m/s,$ the focal length of the lens is:     AIEEE Solevd Paper-2013

A)
15 cm

B)
20 cm

C)
30 cm

D)
10 cm

• question_answer11) 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 2R?     AIEEE Solevd Paper-2013

A)
$\frac{5GmM}{6R}$

B)
$\frac{2GmM}{3R}$

C)
$\frac{GmM}{2R}$

D)
$\frac{GmM}{3R}$

• question_answer12) A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.     AIEEE Solevd Paper-2013

A)
10.62 MHz

B)
10.62 kHz

C)
5.31 MHz

D)
5.31 kHz

• question_answer13) A beam of unpolarised light of intensity${{I}_{0}}$is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of$45{}^\circ$ relative to that of A. The intensity of the emergent light is:     AIEEE Solevd Paper-2013

A)
${{I}_{0}}$

B)
${{I}_{0}}/2$

C)
${{I}_{0}}/4$

D)
${{I}_{0}}/8$

• question_answer14) The supply voltage to a room is 120 V. The resistance of the lead wires is$6\Omega .$ A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?     AIEEE Solevd Paper-2013

A)
zero Volt

B)
2.9 Volt

C)
13.3 Volt

D)
10.04 Volt

• question_answer15) The above $p-v$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is: AIEEE Solevd Paper-2013

A)
${{p}_{0}}{{v}_{0}}$

B)
$\left( \frac{13}{2} \right){{p}_{0}}{{v}_{0}}$

C)
$\left( \frac{11}{2} \right){{p}_{0}}{{v}_{0}}$

D)
$4{{p}_{0}}{{v}_{0}}$

• question_answer16) A hoop of radius r and mass m rotating with an angular velocity ${{\omega }_{0}}$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?     AIEEE Solevd Paper-2013

A)
$\frac{r{{\omega }_{0}}}{4}$

B)
$\frac{r{{\omega }_{0}}}{3}$

C)
$\frac{r{{\omega }_{0}}}{2}$

D)
$r{{\omega }_{0}}$

• question_answer17) An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is ${{V}_{0}}$ and its pressure is${{P}_{0}}$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:     AIEEE Solevd Paper-2013

A)
$\frac{1}{2\pi }\frac{{{A}_{\gamma }}{{P}_{0}}}{{{V}_{0}}M}$

B)
$\frac{1}{2\pi }\frac{{{V}_{0}}M{{P}_{0}}}{{{A}^{2}}\gamma }$

C)
$\frac{1}{2\pi }\sqrt{\frac{{{A}^{2}}\gamma {{P}_{0}}}{M{{V}_{0}}}}$

D)
$\frac{1}{2\pi }\sqrt{\frac{M{{V}_{0}}}{{{A}_{\gamma }}{{P}_{0}}}}$

• question_answer18) If a piece of metal is heated to temperature$\theta$ and then allowed to cool in a room which is at temperature${{\theta }_{0}},$the graph between the temperature T of the metal and time t will be closed to:     AIEEE Solevd Paper-2013

A) B) C) D) • question_answer19) 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.     AIEEE Solevd Paper-2013

A)
Statement - I is true, Statements - II is true, Statement - II is the correct explanation of Statements ? 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.

• question_answer20) In an LCR circuit as shown below both switches are open initially. Now switch${{S}_{1}}$is closed,${{S}_{2}}$kept open. (q is charge on the capacitor and$\tau =RC$is Capacitive time constant). Which of the following statement is correct? AIEEE Solevd Paper-2013

A)
Work done by the battery is half of the energy dissipated in the resistor

B)
$At\text{ }t=\tau ,\text{ }q=CV/2$

C)
$~At\text{ }t=2\tau ,\text{ }q=CV(1-{{e}^{-2}})$

D)
$At\text{ }t=\frac{\tau }{2},q=CV(1-{{e}^{-1}})$

• question_answer21) Two coherent point sources${{S}_{1}}$and${{S}_{2}}$are separated by a small distance 'd' as shown. The fringes obtained on the screen will be: AIEEE Solevd Paper-2013

A)
points

B)
straight lines

C)
semi−circles

D)
concentric circles

• question_answer22) The magnetic field in a travelling electromagnetic wave has a peak value of 20 $nT$. The peak value of electric field strength is:     AIEEE Solevd Paper-2013

A)
$\frac{3V}{m}$

B)
$\frac{6V}{m}$

C)
$\frac{9V}{m}$

D)
$\frac{12V}{m}$

• question_answer23) The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:     AIEEE Solevd Paper-2013

A) B) C) D) • question_answer24) The I − V characteristic of an LED is:     AIEEE Solevd Paper-2013

A) B) C) D) • question_answer25) 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$\rho$and L is its latent heat of vaporization.     AIEEE Solevd Paper-2013

A)
$\frac{\rho L}{T}$

B)
$\sqrt{\frac{T}{\rho L}}$

C)
$\frac{T}{\rho L}$

D)
$\frac{2T}{\rho L}$

• question_answer26) In a hydrogen like atom electron makes 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:     AIEEE Solevd Paper-2013

A)
$\frac{1}{n}$

B)
$\frac{1}{{{n}^{2}}}$

C)
$\frac{1}{{{n}^{3/2}}}$

D)
$\frac{1}{{{n}^{3}}}$

• question_answer27) The graph between angle of deviation $(\delta )$ and angle of incidence (i) for a triangular prism is represented by:     AIEEE Solevd Paper-2013

A) B) C) D) • question_answer28) Two charges, each equal to q, are kept at $x=-a$ and$x=a$ on the x−axis. A particle of mass m and charge${{q}_{0}}=\frac{q}{2}$ is placed at the origin. If charge${{q}_{0}}$is given a small displacement$(y<<a)$ along the y−axis, the net force acting on the particle is proportional to:     AIEEE Solevd Paper-2013

A)
y

B)
− y

C)
$\frac{1}{y}$

D)
$-\frac{1}{y}$

• question_answer29) Two short bar magnets of length 1 cm each have magnetic moments 1.20$A{{m}^{2}}$and 1.00$A{{m}^{2}}$respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centre is close to (Horizontal component of earth′s magnetic induction is$3.6\times {{10}^{-5}}Wb/{{m}^{2}}$)     AIEEE Solevd Paper-2013

A)
$3.6\times {{10}^{-5}}Wb/{{m}^{2}}$

B)
$2.56\times {{10}^{-4}}Wb/{{m}^{2}}$

C)
$3.50\times {{10}^{-4}}Wb/{{m}^{2}}$

D)
$5.80\times {{10}^{-4}}Wb/{{m}^{2}}$

• question_answer30) A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is: AIEEE Solevd Paper-2013

A)
$\frac{Q}{8\pi {{\varepsilon }_{0}}L}$

B)
$\frac{3Q}{4\pi {{\varepsilon }_{0}}L}$

C)
$\frac{Q}{4\pi {{\varepsilon }_{0}}L\ell n2}$

D)
$\frac{Q\ell n2}{4\pi {{\varepsilon }_{0}}L}$

• question_answer31) Which of the following complex species is not expected to exhibit optical isomerism?     AIEEE Solevd Paper-2013

A)
${{[Co{{(en)}_{3}}]}^{3+}}$

B)
${{[Co{{(en)}_{2}}C{{l}_{2}}]}^{+}}$

C)
$[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]$

D)
${{[Co(en){{(N{{H}_{3}})}_{2}}C{{l}_{2}}]}^{+}}$

• question_answer32) Which one of the following molecules is expected to exhibit diamagnetic behaviour?     AIEEE Solevd Paper-2013

A)
${{C}_{2}}$

B)
${{N}_{2}}$

C)
${{O}_{2}}$

D)
${{S}_{2}}$

• question_answer33) A solution of (−)−1 − chloro − 1− phenylethane in toluene racemises slowly in the presence of a small amount of $SbC{{l}_{5}},$ due to the formation of:     AIEEE Solevd Paper-2013

A)
carbanion

B)
carbene

C)
carbocation

D)

• question_answer34)   Given: $E_{C{{r}^{3+}}/Cr}^{0}=-0.74V;$           $E_{MnO_{4}^{-}/M{{n}^{2+}}}^{0}\text{=}1.51\text{ }V$ $E_{C{{r}_{2}}o_{7}^{2-}/C{{r}^{3+}}}^{0}\text{=}1.33\text{ }V;$            $E_{Cl/C{{l}^{-}}}^{0}\text{=}1.36\text{ }V$ Based on the data given above, strongest oxidizing agent will be:     AIEEE Solevd Paper-2013

A)
$C{{l}^{-}}$

B)
$C{{r}^{3+}}$

C)
$M{{n}^{2+}}$

D)
$MnO_{4}^{-}$

• question_answer35) A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of$37.0{}^\circ C.$ As it does so, it absorbs 208 J of heat. The values of q and w for the process will be: $(R=8.314\text{ }J/mol\text{ }K)\text{ }(ln\text{ }7.5=2.01)$     AIEEE Solevd Paper-2013

A)
$q=+208\text{ }J,\text{ }w=-208\text{ }J$

B)
$q=-208\text{ }J,\text{ }w=-208\text{ }J$

C)
$q=-208\text{ }J\text{ },\text{ }w=+208\text{ }J$

D)
$q=+208\text{ }J\text{ },\text{ }w=+208\text{ }J$

• question_answer36) The molarity of a solution obtained by mixing 750 mL of 0.5(M)$HCl$with 250 mL of 2(M) $HCl$will be :     AIEEE Solevd Paper-2013

A)
0.875 M

B)
1.00 M

C)
1.75 M

D)
0.975 M

• question_answer37) Arrange the following compounds in order of decreasing acidity : AIEEE Solevd Paper-2013

A)
$II>IV>I>III$

B)
$I>II>III>IV$

C)
$III>I>II>IV$

D)
$IV>III>I>II$

• question_answer38) For a gaseous state, if most probable speed I denoted by ${{C}^{*}}$, average speed by$\overline{C}$and mean square speed by C, then for a large number of molecules the ratios of these speeds are:     AIEEE Solevd Paper-2013

A)
$C*:\overline{C}:C=1.225:1.128:1$

B)
$C*:\overline{C}:C=1.128:1.225:1$

C)
$C*:\overline{C}:C=1:1.128:1.225$

D)
$C*:\overline{C}:C=1:1.225:1.128$

• question_answer39) The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation of such a reaction will be: ($R=8.314\text{ }J{{K}^{-1}}$and$log2=0.301$)     AIEEE Solevd Paper-2013

A)
$53.6\text{ }kJ\text{ }mo{{l}^{-1}}$

B)
$48.6\text{ }kJ\text{ }mo{{l}^{-1}}$

C)
$58.5\text{ }kJ\text{ }mo{{l}^{-1}}$

D)
$60.5\text{ }kJ\text{ }mo{{l}^{-1}}$

• question_answer40) A compound with molecular mass 180 is acylated with$C{{H}_{3}}COCl$to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:     AIEEE Solevd Paper-2013

A)
2

B)
5

C)
4

D)
6

• question_answer41) Which of the following arrangements does not represent the correct order of the property stated against it?     AIEEE Solevd Paper-2013

A)
${{V}^{2+}}<C{{r}^{2+}}<M{{n}^{2+}}<F{{e}^{2+}}$: paramagnetic behavior

B)
$N{{i}^{2+}}<C{{o}^{2+}}<F{{e}^{2+}}<M{{n}^{2+}}$: ionic size

C)
$C{{o}^{3+}}<F{{e}^{3+}}<C{{r}^{3+}}<S{{c}^{3+}}$: stability in aqueous solution

D)
$Sc<Ti<Cr<Mn$: number of oxidation states

• question_answer42) The order of stability of the following carbocations: is:     AIEEE Solevd Paper-2013

A)
III > II > I

B)
II > III > I

C)
I > II > III

D)
III > I > II

• question_answer43) Consider the following reaction: $xMnO_{4}^{-}+y{{C}_{2}}O_{4}^{2-}+z{{H}^{+}}\to xM{{n}^{2+}}+2yC{{O}_{2}}+\frac{z}{2}{{H}_{2}}O$ The values of x, y and z in the reaction are, respectively:     AIEEE Solevd Paper-2013

A)
5, 2 and 16

B)
2, 5 and 8

C)
2, 5 and 16

D)
5, 2 and 8

• question_answer44) Which of the following is the wrong statement?     AIEEE Solevd Paper-2013

A)
$ONCl$and$ON{{O}^{-}}$are not isoelectronic

B)
${{O}_{3}}$molecule is bent

C)
Ozone is violet − black in solid state

D)
Ozone is diamagnetic gas.

• question_answer45) A gaseous hydrocarbon gives upon combustion 0.72 g. of water and 3.08 g of $C{{O}_{2}}.$The empirical formula of the hydrocarbon is:     AIEEE Solevd Paper-2013

A)
${{C}_{2}}{{H}_{4}}$

B)
${{C}_{3}}{{H}_{4}}$

C)
${{C}_{6}}{{H}_{5}}$

D)
${{C}_{7}}{{H}_{8}}$

• question_answer46) In which of the following pairs of molecules/ ions , both the species are not likely to exist?     AIEEE Solevd Paper-2013

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

B)
$H_{2}^{-},He_{2}^{2-}$

C)
$H_{2}^{2+},H{{e}_{2}}$

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

• question_answer47) Which of the following exists as covalent crystals in the solid state?     AIEEE Solevd Paper-2013

A)
Iodine

B)
Silicon

C)
Sulphur

D)
Phosphorus

• question_answer48) Synthesis of each molecule of glucose in photosynthesis involves :     AIEEE Solevd Paper-2013

A)
18 molecules of ATP

B)
10 molecules of ATP

C)
8 molecules of ATP

D)
6 molecules of ATP

• question_answer49) The coagulating power of electrolytes having ions$N{{a}^{+}},\text{ }A{{l}^{3+}}$and$B{{a}^{2+}}$for arsenic sulphide sol increases in the order:     AIEEE Solevd Paper-2013

A)
$A{{l}^{3+}}<B{{a}^{2+}}<N{{a}^{+}}$

B)
$N{{a}^{+}}<B{{a}^{2+}}<A{{l}^{3+}}$

C)
$B{{a}^{2+}}<N{{a}^{+}}<A{{l}^{3+}}$

D)
$A{{l}^{3+}}<N{{a}^{+}}<B{{a}^{2+}}$

• question_answer50) Which of the following represents the correct order of increasing first ionization enthalpy for$Ca,Ba,S,Se$and$Ar$?     AIEEE Solevd Paper-2013

A)
$Ca<S<Ba<Se<Ar$

B)
$S<Se<Ca<Ba<Ar$

C)
$Ba<Ca<Se<S<Ar$

D)
$Ca<Ba<S<se<Ar$

• question_answer51) Energy of an electron is given by$E=-2.178\times$${{10}^{18}}J\left( \frac{{{Z}^{2}}}{{{n}^{2}}} \right)$. Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be: ($h=6.62\times {{10}^{-34}}Js$and$c=3.0\times {{10}^{-8}}m{{s}^{-1}}$)     AIEEE Solevd Paper-2013

A)
$1.214\times {{10}^{-7}}m$

B)
$2.816\times {{10}^{-7}}m$

C)
$6.500\times {{10}^{-7}}m$

D)
$8.500\times {{10}^{-7}}m$

• question_answer52) Compound (A),${{C}_{8}}{{H}_{9}}Br,$gives a white precipitate when warmed with alcoholic $AgN{{O}_{3}}.$ Oxidation of (A) gives an acid (B) , ${{C}_{8}}{{H}_{6}}{{O}_{4}}.$(B) easily forms anhydride on heating. Identify the compound (A) .     AIEEE Solevd Paper-2013

A) B) C) D) • question_answer53) Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest$E_{{{M}^{3+}}/{{M}^{2+}}}^{0}$value?     AIEEE Solevd Paper-2013

A)
$Cr(Z=24)$

B)
$Mn(Z=25)$

C)
$Fe(Z=26)$

D)
$Co(Z=27)$

• question_answer54) How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?     AIEEE Solevd Paper-2013

A)
0.1 L

B)
0.9 L

C)
2.0 L

D)
9.0 L

• question_answer55) The first ionisation potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be :     AIEEE Solevd Paper-2013

A)
$-2.55\text{ }eV$

B)
$-5.1\text{ }eV$

C)
$-10.2\text{ }eV$

D)
$+2.55\text{ }eV$

• question_answer56) An organic compound A upon reacting with $N{{H}_{3}}$gives B. On heating, B gives C. C in presence of$KOH$reacts with$B{{r}_{2}}$to give $C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}.$A is:     AIEEE Solevd Paper-2013

A)
$C{{H}_{3}}COOH$

B)
$C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COOH$

C)
$C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-COOH$

D)
$C{{H}_{3}}C{{H}_{2}}COOH$

• question_answer57) Stability of the species$L{{i}_{2}},Li_{2}^{-}$and$Li_{2}^{+}$increases in the order of :     AIEEE Solevd Paper-2013

A)
$L{{i}_{2}}<Li_{2}^{+}<Li_{2}^{-}$

B)
$Li_{2}^{-}<Li_{2}^{+}<L{{i}_{2}}$

C)
$L{{i}_{2}}<Li_{2}^{-}<Li_{2}^{+}$

D)
$Li_{2}^{-}<L{{i}_{2}}<Li_{2}^{+}$

• question_answer58) An unknown alcohol is treated with the 'Lucas reagent' to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:     AIEEE Solevd Paper-2013

A)
secondary alcohol by${{S}_{N}}1$

B)
tertiary alcohol by${{S}_{N}}1$

C)
secondary alcohol by${{S}_{N}}2$

D)
tertiary alcohol by${{S}_{N}}2$

• question_answer59) The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:     AIEEE Solevd Paper-2013

A)
Methylisocyanate

B)
Methylamine

C)
Ammonia

D)
Phosgene

• question_answer60) Experimentally it was found that a metal oxide has formula${{M}_{0}}{{.}_{98}}O.$Metal M, is present as${{M}^{2+}}$and${{M}^{3+}}$in its oxide. Fraction of the metal which exists as${{M}^{3+}}$would be:     AIEEE Solevd Paper-2013

A)
7.01 %

B)
4.08 %

C)
6.05 %

D)
5.08 %

• question_answer61) Distance between two parallel planes$2x+y$ $+2z=8$ and$4x+2y+4z+5=0\text{ }is:$     AIEEE Solevd Paper-2013

A)
$\frac{3}{2}$

B)
$\frac{5}{2}$

C)
$\frac{7}{2}$

D)
$\frac{9}{2}$

• question_answer62) At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by$\frac{dp}{dx}=100-12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is:     AIEEE Solevd Paper-2013

A)
2500

B)
3000

C)
3500

D)
4500

• question_answer63) Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of$A\times B$ having 3 or more elements is:     AIEEE Solevd Paper-2013

A)
256

B)
220

C)
219

D)
211

• question_answer64) If the lines$\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$and$\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$are coplanar, then k can have:     AIEEE Solevd Paper-2013

A)
any value

B)
exactly one value

C)
exactly two values

D)
exactly three values

• question_answer65) If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$are the sides of a triangle ABC, then the length of the median through A is:     AIEEE Solevd Paper-2013

A)
$\sqrt{18}$

B)
$\sqrt{72}$

C)
$\sqrt{33}$

D)
$\sqrt{45}$

• question_answer66) The real number k for which the equation, $2{{x}^{3}}+3x+k=0$has two distinct real roots in [0, 1]     AIEEE Solevd Paper-2013

A)
lies between 1 and 2

B)
lies between 2 and 3

C)
lies between −1 and 0

D)
does not exist

• question_answer67) The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ??, is :     AIEEE Solevd Paper-2013

A)
$\frac{7}{81}(179-{{10}^{-20}})$

B)
$\frac{7}{9}(99-{{10}^{-20}})$

C)
$\frac{7}{81}(179+{{10}^{-20}})$

D)
$\frac{7}{9}(99+{{10}^{-20}})$

• question_answer68) A ray of light along$x+\sqrt{3}y=\sqrt{3}$gets reflected upon reaching x−axis, the equation of the reflected ray is:     AIEEE Solevd Paper-2013

A)
$y=x+\sqrt{3}$

B)
$\sqrt{3y}=x-\sqrt{3}$

C)
$y=\sqrt{3}x-\sqrt{3}$

D)
$\sqrt{3}y=x-1$

• question_answer69) The number of values of k, for which the system of equations: $(k+1)x+8y=4k$ $kx+(k+3)y=3k-1$ has no solution, is:     AIEEE Solevd Paper-2013

A)
in finite

B)
1

C)
2

D)
3

• question_answer70) If the equations${{x}^{2}}+2x+3=0$and$a{{x}^{2}}+bx+$ $c=0,\text{ }a,b,c\in R,$have a common root, then $a:b:c$ is     AIEEE Solevd Paper-2013

A)
1 : 2 : 3

B)
3 : 2 : 1

C)
1 : 3 : 2

D)
3 : 1 : 2

• question_answer71) The circle passing through (1, −2) and touching the axis of$x$at (3, 0) also passes through the point :     AIEEE Solevd Paper-2013

A)
(−5, 2)

B)
(2, −5)

C)
(5, −2)

D)
(−2, 5)

• question_answer72) If$x,y,z$are in A.P. and$ta{{n}^{-1}}x,ta{{n}^{-1}}y$and $ta{{n}^{-1}}z$ are also in A.P., then :     AIEEE Solevd Paper-2013

A)
$x=y=z$

B)
$2x=3y=6z$

C)
$6x=3y=2z$

D)
$6x=4y=3z$

• question_answer73) Consider: Statement − I:$(p\wedge \sim q)\wedge (\sim p\wedge q)$is a fallacy. Statement II:$(p\to q)\leftrightarrow (\sim q\to \sim p)$is a tautology.     AIEEE Solevd Paper-2013

A)
Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement I.

B)
Statement − I is true; Statement − II is true; Statement − II is not a correct explanation for Statement − I.

C)
Statement − I is true; Statement − II is false.

D)
Statement − I is false; Statement − II is true.

• question_answer74) If$\int f(x)dx=\psi (x),$ then$\int {{x}^{5}}f({{x}^{3}})dx$is equal to:     AIEEE Solevd Paper-2013

A)
$\frac{1}{3}\left[ {{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{2}}\psi ({{x}^{3}})dx} \right]+C$

B)
$\frac{1}{3}{{x}^{3}}\psi ({{x}^{3}})-3\int{{{x}^{3}}\psi ({{x}^{3}})dx}+C$

C)
$\frac{1}{3}{{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{3}}\psi ({{x}^{3}})dx}+C$

D)
$\frac{1}{3}\left[ {{x}^{3}}\psi ({{x}^{3}})-\int{{{x}^{3}}\psi ({{x}^{3}})dx} \right]+C$

• question_answer75) $\underset{x\to 0}{\mathop{\lim }}\,\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$is equal to:     AIEEE Solevd Paper-2013

A)
$-\frac{1}{4}$

B)
$\frac{1}{2}$

C)
1

D)
2

• question_answer76) Statement − I: The value of the integral$\int\limits_{\pi /6}^{\pi /3}{\frac{dx}{1+\sqrt{\tan x}}}$is equal to $\frac{\pi }{6}$ Statement − II: $\int\limits_{a}^{b}{f(x)dx}\int\limits_{a}^{b}{f(a+b-x)dx}$     AIEEE Solevd Paper-2013

A)
Statement − I is true; Statement − II is true; Statement − II is a correct explanation for Statement − I.

B)
Statement − I is true; Statement − II is true; Statement − II is a not a correct explanation for Statement − I.

C)
Statement − I is true; Statement − II is false.

D)
Statement − I is false; Statement − II is true.

• question_answer77) The equation of the circle passing through the foci of the ellipse$\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1,$and having centre at (0, 3) is :     AIEEE Solevd Paper-2013

A)
${{x}^{2}}+{{y}^{2}}-6y-7=0$

B)
${{x}^{2}}+{{y}^{2}}-6y+7=0$

C)
${{x}^{2}}+{{y}^{2}}-6y-5=0$

D)
${{x}^{2}}+{{y}^{2}}-6y+5=0$

• question_answer78) A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:     AIEEE Solevd Paper-2013

A)
$\frac{17}{{{3}^{5}}}$

B)
$\frac{13}{{{3}^{5}}}$

C)
$\frac{11}{{{3}^{5}}}$

D)
$\frac{10}{{{3}^{5}}}$

• question_answer79) The x−coordinate of the in centre of the triangle that has the coordinates of mid points of its sides as (0, 1) (1, 1) and (1, 0) is:     AIEEE Solevd Paper-2013

A)
$2+\sqrt{2}$

B)
$2-\sqrt{2}$

C)
$1+\sqrt{2}$

D)
$1-\sqrt{2}$

• question_answer80) The term independent of x in expansion of ${{\left( \frac{x+1}{{{x}^{2/3}}-{{x}^{1/3}}+1}-\frac{x}{x-{{x}^{1/2}}} \right)}^{10}}$is:     AIEEE Solevd Paper-2013

A)
4

B)
120

C)
210

D)
310

• question_answer81) The area (in square units) bounded by the curves$y=\sqrt{x},\text{ }2y-x+3=0,$x−axis, and lying in the first quadrant is:     AIEEE Solevd Paper-2013

A)
9

B)
36

C)
18

D)
$\frac{27}{4}$

• question_answer82) Let${{T}_{n}}$be the number of all possible triangles formed by joining vertices of a n−sided regular polygon. If${{T}_{n+1}}-{{T}_{n}}=1$then the value of n is:     AIEEE Solevd Paper-2013

A)
7

B)
5

C)
10

D)
8

• question_answer83) If z is a complex number of unit modulus and argument $\theta$, then $\arg \left( \frac{1+z}{1+z} \right)$ equals:     AIEEE Solevd Paper-2013

A)
$-\theta$

B)
$\frac{\pi }{2}-\theta$

C)
$\theta$

D)
$\pi -\theta$

• question_answer84) ABCD is a trapezium such that AB and CD are parallel and$BC\bot CD$. If$\angle ADB=\theta ,\text{ }BC=p$ and$CD=q,$then AB is equal to:     AIEEE Solevd Paper-2013

A)
$\frac{({{p}^{2}}\text{+}{{q}^{2}})sin\theta }{p\,cos\,\theta +q\,sin\,\theta }$

B)
$\frac{{{p}^{2}}+{{q}^{2}}cos}{p\,cos\,\theta +q\,sin\,\theta }$

C)
$\frac{{{p}^{2}}+{{q}^{2}}}{{{p}^{2}}cos\,\theta +{{q}^{2}}sin\,\theta }$

D)
$\frac{({{p}^{2}}+{{q}^{2}})\sin \theta }{{{(pcos\,\theta +qsin\,\theta )}^{2}}}$

• question_answer85) If$P=\left[ \begin{matrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \\ \end{matrix} \right]$is the ad joint of$3\times 3$matrix A and $|A|=4,$ then $\alpha$ is equal to:     AIEEE Solevd Paper-2013

A)
4

B)
11

C)
5

D)
0

• question_answer86) The intercepts on x−axis made by tangents to the curve,$y=\int\limits_{0}^{x}{|t|}dt,x\in R,$which are parallel to the line$y=2x,$are equal to     AIEEE Solevd Paper-2013

A)
$\pm 1$

B)
$\pm 2$

C)
$\pm 3$

D)
$\pm 4$

• question_answer87) Given: A circle,$2{{x}^{2}}+2{{y}^{2}}=5$and a parabola, ${{y}^{2}}=4\sqrt{5}x.$ Statement − I: An equation of a common tangent to these curves is$y=x+5.$ Statement − II: If the line,$y=mx+\frac{\sqrt{5}}{m}(m\ne 0)$is their common tangent, then ?m? satisfies${{m}^{4}}-3{{m}^{2}}+2=0.$     AIEEE Solevd Paper-2013

A)
Statement−I is true; Statement−II is true; Statement − II is a correct explanation for Statement − I.

B)
Statement−I is true; Statement−II is true; Statement − II is not a correct explanation for Statement − I.

C)
Statement−I is true; Statement−II is false.

D)
Statement−I is false; Statement−II is true.

• question_answer88) If$y=sec(ta{{n}^{-1}}x),$then$\frac{dy}{dx}$at$x=1$is equal to:     AIEEE Solevd Paper-2013

A)
$\frac{1}{\sqrt{2}}$

B)
$\frac{1}{2}$

C)
1

D)
$\sqrt{2}$

• question_answer89) The expression$\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$can be written as:     AIEEE Solevd Paper-2013

A)
$sinA\text{ }cosA+1$

B)
$secA\text{ }cosecA+1$

C)
$tanA+cotA$

D)
$secA+cosecA$

• question_answer90) All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?     AIEEE Solevd Paper-2013

A)
mean

B)
median

C)
mode

D)
variance

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