AIEEE 2010 PYQ Mock Test

The standard enthalpy of formation of ${\text{NH}}_3$ is $-46.0{\text{kJ mol}}^{-1}$. If the enthalpy of formation of ${\text{H}}_2$ from its atoms is $-436{\text{kJ mol}}^{-1}$ and that of ${\text{N}}_2$ is $-712{\text{kJ mol}}^{-1}$, the average bond enthalpy of $\text{N}-\text{H}$ bond in ${\text{NH}}_3$ is:

The time for half life period of a certain reaction $\text{A}\to \text{products}$ is $1\text{hour}$. When the initial concentration of the reactant '$\text{A}$ ', is $2.0{\text{mol L}}^{-1}$, how much time does it take for its concentration to come from $0.50$ to $0.25{\text{mol L}}^{-1}$ if it is a zero order reaction?

A solution containing $2.675\text{g}$ of ${\text{CoCl}}_3\cdot 6{\text{NH}}_3$ (molar mass $=267.5{\text{g mol}}^{-1}$) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of ${\text{AgNO}}_3$ to give $4.78\text{g}$ of $\text{AgCl}$ (molar mass $=143.5{\text{g mol}}^{-1}$). The formula of the complex is (At. Mass of $\text{Ag}=108\text{u}$):

Consider the reaction:${\text{Cl}}_2(aq)+{\text{H}}_2\text{S}(aq)\to \text{S}(s)+2{\text{H}}^{+}(aq)+2{\text{Cl}}^{-}(aq)$ The rate equation for this reaction is $\text{rate}=k[{\text{Cl}}_2][{\text{H}}_2\text{S}]$.Which of these mechanisms is/are consistent with this rate equation?(A) ${\text{Cl}}_2+{\text{H}}_2\text{S}\to {\text{H}}^{+}+{\text{Cl}}^{-}+{\text{Cl}}^{+}+{\text{HS}}^{-}$ (slow)${\text{Cl}}^{+}+{\text{HS}}^{-}\to {\text{H}}^{+}+{\text{Cl}}^{-}+\text{S}$ (fast)(B) ${\text{H}}_2\text{S}\rightleftharpoons {\text{H}}^{+}+{\text{HS}}^{-}$ (fast equilibrium)${\text{Cl}}_2+{\text{HS}}^{-}\to 2{\text{Cl}}^{-}+{\text{H}}^{+}+\text{S}$ (slow)

If $10^{-4}{\text{dm}}^3$ of water is introduced into a $1.0{\text{dm}}^3$ flask to $300\text{K}$, how many moles of water are in the vapour phase when equilibrium is established?(Given: Vapour pressure of ${\text{H}}_2\text{O}$ at $300\text{K}$ is $3170\text{Pa}$; $R=8.314{\text{J K}}^{-1}{\text{mol}}^{-1}$)

One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of $44\text{u}$. The alkene is:

If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water ($\Delta T_f$), when $0.01\text{mol}$ of sodium sulphate is dissolved in $1\text{kg}$ of water, is ($K_f=1.86{\text{K kg mol}}^{-1}$):

From amongst the following alcohols the one that would react fastest with conc. $\text{HCl}$ and anhydrous ${\text{ZnCl}}_2$, is:

In the chemical reactions, the compounds 'A' and 'B' respectively are:

$29.5\text{mg}$ of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in $20\text{mL}$ of $0.1\text{M HCl}$ solution. The excess of the acid required $15\text{mL}$ of $0.1\text{M NaOH}$ solution for complete neutralization. The percentage of nitrogen in the compound is:

The energy required to break one mole of $\text{Cl}-\text{Cl}$ bonds in ${\text{Cl}}_2$ is $242{\text{kJ mol}}^{-1}$. The longest wavelength of light capable of breaking a single $\text{Cl}-\text{Cl}$ bond is ($c=3\times 10^8{\text{m s}}^{-1}$ and $N_A=6.02\times 10^{23}{\text{mol}}^{-1}$):

Ionisation energy of ${\text{He}}^{+}$ is $19.6\times 10^{-18}{\text{J atom}}^{-1}$. The energy of the first stationary state ($n=1$) of ${\text{Li}}^{2+}$ is:

Consider the following bromides:

The correct order of ${\text{S}}_{\text{N}}1$ reactivity is:

Which one of the following has an optical isomer? (en = ethylenediamine)

On mixing, heptane and octane form an ideal solution. At $373\text{K}$, the vapour pressures of the two liquid components (heptane and octane) are $105\text{kPa}$ and $45\text{kPa}$ respectively. Vapour pressure of the solution obtained by mixing $25.0\text{g}$ of heptane and $35\text{g}$ of octane will be (molar mass of heptane $=100{\text{g mol}}^{-1}$ and of octane $=114{\text{g mol}}^{-1}$):

The main product of the following reaction is
:

Three reactions involving ${\text{H}}_2{\text{PO}}_4^{-}$ are given below:(i) ${\text{H}}_3{\text{PO}}_4+{\text{H}}_2\text{O}\to {\text{H}}_3{\text{O}}^{+}+{\text{H}}_2{\text{PO}}_4^{-}$ (ii) ${\text{H}}_2{\text{PO}}_4^{-}+{\text{H}}_2\text{O}\to {\text{HPO}}_4^{2-}+{\text{H}}_3{\text{O}}^{+}$ (iii) ${\text{H}}_2{\text{PO}}_4^{-}+{\text{OH}}^{-}\to {\text{H}}_3{\text{PO}}_4+{\text{O}}^{2-}$ (Inconsistent stoichiometry)In which of the above does ${\text{H}}_2{\text{PO}}_4^{-}$ act as an acid?

In aqueous solution the ionization constants for carbonic acid are $K_1=4.2\times 10^{-7}$ and $K_2=4.8\times 10^{-11}$. Select the correct statement for a saturated $0.034\text{M}$ solution of the carbonic acid.

The edge length of a face centered cubic cell of an ionic substance is $508\text{pm}$. If the radius of the cation is $110\text{pm}$, the radius of the anion is:

The correct order of increasing basicity of the given conjugate bases ($\text{R}={\text{CH}}_3$) is:

The correct sequence which shows decreasing order of the ionic radii of the elements is:

Solubility product of silver bromide is $5.0\times 10^{-13}$. The quantity of potassium bromide (molar mass taken as $120{\text{g mol}}^{-1}$) to be added to $1\text{litre}$ of $0.05\text{M}$ solution of silver nitrate to start the precipitation of $\text{AgBr}$ is:

The Gibbs energy for the decomposition of ${\text{Al}}_2{\text{O}}_3$ at $500^{\circ }\text{C}$ is as follows:$\frac{2}{3}{\text{Al}}_2{\text{O}}_3\to \frac{4}{3}\text{Al}+{\text{O}}_2,{\Delta }_{r}G=+966{\text{kJ mol}}^{-1}$ The potential difference needed for electrolytic reduction of ${\text{Al}}_2{\text{O}}_3$ at $500^{\circ }\text{C}$ is at least:

At $25^{\circ }\text{C}$, the solubility product of ${\text{Mg(OH)}}_2$ is $1.0\times 10^{-11}$. At which pH, will ${\text{Mg}}^{2+}$ ions start precipitating in the form of ${\text{Mg(OH)}}_2$ from a solution of $0.001{\text{M Mg}}^{2+}$ ions?

Percentage of free space in cubic close packed structure and in body centred packed structure are respectively:

Out of the following, the alkene that exhibits optical isomerism is:

Biuret test is not given by:

The correct order of $E_{M^{2+}/M}^{\circ }$ values with negative sign for the four successive elements $\text{Cr, Mn, Fe}$ and $\text{Co}$ is:

The polymer containing strong intermolecular forces e.g. hydrogen bonding, is:

For a particular reversible reaction at temperature $T$, $\Delta H$ and $\Delta S$ were found to be both $+\text{ve}$. If $T_e$ is the temperature at equilibrium, the reaction would be spontaneous when:

A rectangular loop has a sliding connector $\text{PQ}$ of length $l$ and resistance $R\Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field $B$ going into the plane of the paper. The three currents $I_1,I_2$ and $I$ (where $I$ is through the connector) are:

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be:

Statement-1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.Statement-2: Principle of conservation of momentum holds true for all kinds of collisions.

Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by X-rays, both $V_0$ and $K_{max}$ increase.Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

A ball is made of a material of density $\rho$ where ${\rho }_{oil}<\rho <{\rho }_{water}$ with ${\rho }_{oil}$ and ${\rho }_{water}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following describes its equilibrium position?

A particle is moving with velocity $\vec{v}=K(y\hat{i}+x\hat{j})$, where $K$ is a constant. The general equation for its path is:

Two long parallel wires are at a distance $2d$ apart. They carry steady equal current $I$ flowing out of the plane of the paper. The variation of the magnetic field $B$ along the line $X{X}^{\prime }$ (perpendicular to wires) is zero at what point?

In a circuit containing a battery of emf $V$, a resistor $R_2$ in series with an inductor $L$ and resistor $R_1$ in parallel, the key $K$ is closed at $t=0$. The current through the battery is:

The figure shows the position–time ($x-t$) graph of one-dimensional motion of a body of mass $0.4\text{kg}$. If the graph is a sawtooth wave with peaks at $2\text{m}$ every $2\text{seconds}$, the magnitude of each impulse is:

A nucleus of mass $M+\Delta m$ is at rest and decays into two daughter nuclei of equal mass $M/2$ each. Speed of light is $c$. If the binding energy per nucleon for the parent nucleus is $E_1$ and that for the daughter nuclei is $E_2$, then:

A nucleus of mass $M+\Delta m$ is at rest and decays into two daughter nuclei of equal mass $M/2$ each. The speed of daughter nuclei is:

A radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits $3\alpha$ -particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be:

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the centre $O$ is:

A logic gate circuit has two inputs $A$ and $B$. Both are passed through NOT gates, then through a NAND gate, and finally through another NOT gate. This combination yields:

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from $V$ to $32V$, the efficiency of the engine is:

If a source of power $4\text{kW}$ produces $10^{20}$ photons/second, the radiation belongs to a part of the spectrum called:

The respective number of significant figures for the numbers $23.023$, $0.0003$ and $2.1\times 10^{-3}$ are:

In a series $\text{LCR}$ circuit $R=200\Omega$ and the voltage and the frequency of the main supply is $220\text{V}$ and $50\text{Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ }$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ }$. The power dissipated in the $\text{LCR}$ circuit is:

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)={\rho }_0(\frac{5}{4}-\frac{r}{R})$ up to $r=R$, and $\rho (r)=0$ for $r>R$. The electric field at a distance $r(r<R)$ from the origin is given by:

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D=[U(x=\infty )-U_{atequilibrium}]$, $D$ is:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8{\text{g cm}}^{-3}$, the angle remains the same. If density of the material of the sphere is $16{\text{g cm}}^{-3}$, the dielectric constant of the liquid is:

Two conductors have the same resistance at $0^{\circ }\text{C}$ but their temperature coefficients of resistance are ${\alpha }_1$ and ${\alpha }_2$. The respective temperature coefficients of their series and parallel combinations are nearly:

A point $P$ moves in counter-clockwise direction on a circular path of radius $20\text{m}$. The movement of '$P$ ' is such that it sweeps out a length $s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The acceleration of '$P$ ' when $t=2\text{s}$ is nearly:

Two fixed frictionless inclined planes making an angle $30^{\circ }$ and $60^{\circ }$ with the vertical are shown. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

For a particle in uniform circular motion the acceleration $\vec{a}$ at a point $P(R,\theta )$ on the circle of radius $R$ is (here $\theta$ is measured from the $x$ -axis):

An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I)={\mu }_0+{\mu }_{2}I$, where ${\mu }_0$ and ${\mu }_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium, it will:

An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I)={\mu }_0+{\mu }_{2}I$. The initial shape of the wave front of the beam is:

An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I)={\mu }_0+{\mu }_{2}I$. The speed of light in the medium is:

A small particle of mass $m$ is projected at an angle $\theta$ with the $x$ -axis with an initial velocity $v_0$ in the $x-y$ plane. At a time $t<\frac{v_0\sin \theta }{g}$, the angular momentum of the particle about the origin is:

The equation of a wave on a string of linear mass density $0.04{\text{kg m}}^{-1}$ is given by $y=0.02(m)\sin [2\pi (\frac{t}{0.04(s)}-\frac{x}{0.50(m)})]$. The tension in the string is:

Let $\cos (\alpha +\beta )=\frac{4}{5}$ and let $\sin (\alpha -\beta )=\frac{5}{13}$, where $0\le \alpha ,\beta \le \frac{\pi }{4}$, then $\tan 2\alpha =$

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:$P$: There is a rational number $x\in S$ such that $x>0$.Which of the following statements is the negation of the statement $P$?

Let $\vec{a}=\hat{j}-\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$. Then vector $\vec{b}$ satisfying $\vec{a}\times \vec{b}+\vec{c}=\vec{0}$ and $\vec{a}\cdot \vec{b}=3$ is:

The equation of the tangent to the curve $y=x+\frac{4}{x^2}$, that is parallel to the $x$ -axis, is:

Solution of the differential equation $\cos xdy=y(\sin x-y)dx$, $0<x<\frac{\pi }{2}$ is:

The area bounded by the curves $y=\cos x$ and $y=\sin x$ between the ordinates $x=0$ and $x=\frac{3\pi }{2}$ is:

If two tangents drawn from a point $P$ to the parabola $y^2=4x$ are at right angles, then the locus of $P$ is:

If the vectors $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$, $\vec{b}=2\hat{i}+4\hat{j}+\hat{k}$ and $\vec{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k}$ are mutually orthogonal, then $(\lambda ,\mu )=$

Consider the following relations:$R=\{(x,y)|x,y\in \mathbb{R}\text{ and }x=wy\text{ for some rational number }w\}$;$S=\{(\frac{m}{n},\frac{p}{q})|m,n,p,q\in \mathbb{Z},n,q\ne 0\text{ and }qm=pn\}$. Then:

Let $f:\mathbb{R}\to \mathbb{R}$ be defined by $f(x)=\{\begin{array}{ll}k-2x,& \text{if }x\le -1\\ 2x+3,& \text{if }x>-1\end{array}$. If $f$ has a local minimum at $x=-1$, then a possible value of $k$ is:

The number of $3\times 3$ non-singular matrices, with four entries as $1$ and all other entries as $0$, is:

Four numbers are chosen at random (without replacement) from the set $\{1,2,3,\dots ,20\}$.Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$.Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is $\{\pm 1,\pm 2,\pm 3,\pm 4,\pm 5\}$.

Statement-1: The point $A(3,1,6)$ is the mirror image of the point $B(1,3,4)$ in the plane $x-y+z=5$.Statement-2: The plane $x-y+z=5$ bisects the line segment joining $A(3,1,6)$ and $B(1,3,4)$.

Let $S_1={\sum }_{j=1}^{10}j(j-1)\left(\genfrac{}{}{0ex}{}{10}{j}\right)$, $S_2={\sum }_{j=1}^{10}j\left(\genfrac{}{}{0ex}{}{10}{j}\right)$ and $S_3={\sum }_{j=1}^{10}{j}^2\left(\genfrac{}{}{0ex}{}{10}{j}\right)$.Statement-1: $S_3=55\times 2^9$ Statement-2: $S_1=90\times 2^8$ and $S_2=10\times 2^8$.

Let $A$ be a $2\times 2$ matrix with non-zero entries and let $A^2=I$.Statement-1: $\text{Tr}(A)=0$ Statement-2: $|A|=1$

Let $f:\mathbb{R}\to \mathbb{R}$ be a continuous function defined by $f(x)=\frac{1}{e^x+2e^{-x}}$.Statement-1: $f(c)=\frac{1}{3}$, for some $c\in \mathbb{R}$.Statement-2: $0<f(x)\le \frac{1}{2\sqrt{2}}$, for all $x\in \mathbb{R}$.

For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A false statement among the following is:

If $\alpha$ and $\beta$ are the roots of the equation $x^2-x+1=0$, then ${\alpha }^{2009}+{\beta }^{2009}=$

The number of complex numbers $z$ such that $|z-1|=|z+1|=|z-i|$ equals:

A line $AB$ in three-dimensional space makes angles $45^{\circ }$ and $120^{\circ }$ with the positive $x$ -axis and the positive $y$ -axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$ -axis, then $\theta$ equals:

The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is:

A person is to count $4500$ currency notes. Let $a_n$ denote the number of notes he counts in the $n^{\text{th}}$ minute. If $a_1=a_2=\cdots =a_{10}=150$ and $a_{10},a_{11},\dots$ are in A.P. with common difference $-2$, then the time taken by him to count all notes is:

Let $f:\mathbb{R}\to \mathbb{R}$ be a positive increasing function with ${\lim }_{x\to \infty }\frac{f(3x)}{f(x)}=1$. Then ${\lim }_{x\to \infty }\frac{f(2x)}{f(x)}=$

Let $p(x)$ be a function defined on $\mathbb{R}$ such that $p^{\prime }(x)=p^{\prime }(1-x)$, for all $x\in [0,1]$, $p(0)=1$ and $p(1)=41$. Then ${\int }_0^{1}p(x)dx$ equals:

Let $f:(-1,1)\to \mathbb{R}$ be a differentiable function with $f(0)=-1$ and $f^{\prime }(0)=1$. Let $g(x)=[f(2f(x)+2){]}^2$. Then $g^{\prime }(0)=$

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is: