Recent questions in JEEMAIN PAST PAPERS

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is $\frac{1}{2}$. Then the length of the semi-major axis is

asked Nov 29, 2018 by pady_1

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A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $P (A\cup B)$ is

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It is given that the events A and B are such that $P(A)=\frac{1}{4}P\bigg(\frac{A}{B}\bigg)=\frac{1}{2}$$P\bigg(\frac{B}{A}\bigg)=\frac{2}{3}$.Then P(B) is

asked Nov 29, 2018 by pady_1

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AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is $60^\circ$. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is $45^\circ$. Then the height of the pole is

asked Nov 29, 2018 by pady_1

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In conversion of limestone to lime, $CaCO_3 (s) \to CaO(s) + CO_2(g)$ the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are $+179.1\;kJ\; mol^{-1}$ and $160.2\;J/K$ respectively at 298 K and 1 bar. Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is :

asked Nov 29, 2018 by pady_1

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A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm) at the same temperature will be:

asked Nov 29, 2018 by pady_1

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The first and second dissociation constants of an acid $H_2A$ are $1.0 \times 10^{-5}$ and $5.0 \times 10^{-10}$ respectively. The overall dissociation constant of the acid will be :

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The density (in $g\; mL^{-1}$) of a 3.60 M sulphuric acid solution that is $29\% \; H_2SO_4$ (molar mass =$98\;g\;mol^{-1}$) by mass will be :

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The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species, $K^+, Ca^{2+}, Mg^{2+}, Be^{2+}$ ?

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Identify the incorrect statement among the following :

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The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence :

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Which of the following species exhibits the diamagnetic behaviour ?

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The compound formed as a result of oxidation of ethyl benzene by $KMnO_4$ is

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Which one of the following is the strongest base in aqueous solution ?

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The equivalent conductances of two strong electrolytes at infinite dilution in $H_2O$ (where ions move freely through a solution) at $25^{\circ}C$ are given below : $\bigwedge^{\circ}_{CH_3COONa }= 91.0\;S \;cm^2/equiv $ $ \bigwedge^{\circ}_{HCl} = 426.2 \; S\;cm^2/equiv$ What additional information/quantity one needs to calculate $\bigwedge^{\circ}$ of an aqueous solution of acetic acid ?

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Which of the following nuclear reactions will generate an isotope ?

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Identify the correct statement regarding a spontaneous process :

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Regular use of which of the following fertilisers increases the acidity of soil ?

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In the reaction, $ 2Al (s) + 6 HCl (aq) \to 2Al^{3+} (aq) + 6 Cl^- (aq) + 3H_2(g)$

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Which of the following hydrogen bonds is the strongest ?

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Which of the following sets of quantum numbers represents the highest energy of an atom ?

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In the following sequence of reactions, $CH_3CH_2OH \xrightarrow{P + I_2} A \xrightarrow[\text{ether }]{\text{Mg}} B \xrightarrow{HCHO} C \xrightarrow{H_2O} D$ the compound 'D' is :

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Which of the following is the correct order of decreasing $S_N2$ reactivity ? (X = a halogen)

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Which one of the following conformations of cyclohexane is chiral ?

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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room ?

asked Nov 29, 2018 by pady_1

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In a saturated solution of the sparingly soluble strong electrolyte $AgIO_3$ (Molecular mass = 283) the equilibrium which sets in is $AgIO_3(s) \rightleftharpoons Ag^+ (aq) + IO_3^- (ag)$ if the solubility product constant $K_{sp}$ of $AgIO_3$ at a given temperature is $1.0 \times 10^{-8}$, what is the mass of $AgIO_3$ contained in 100 mL of its saturated solution ?

asked Nov 29, 2018 by pady_1

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Assuming that water vapour is an ideal gas, the internal energy change ($\Delta U$) when 1 mole of water is vapourised at 1 bar pressure and $100^{\circ}C$, (Given : molar enthalpy of vaporisation of water at 1 bar and 373 K = 41 kJ mol$^{-1}$ and R = 8.3 J mol$^{-1}$ K$^{-1}$ ) will be :

asked Nov 29, 2018 by pady_1

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A 5.25% solution of a substance is isotonic with a 1.5% solution of urea (molar mass = $60 \; g\; mol^{-1}$) in the same solvent. If the densities of both the solutions are assumed to be equal to $1.0\; g\; cm^{-3}$, molar mass of the substance will be :

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Equal masses of methane and oxygen are mixed in an empty container at $25^{\circ}C$. The fraction of the total pressure exerted by oxygen is :

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The actinoids exhibit more number of oxidation states in general than the lanthanoids. This is because :

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In which of the following ionisation processes, the bond order has increased and the magnetic behaviour has changed ?

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Presence of a nitro group in a benzene ring :

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The reaction of toluene with $Cl_2$ in presence of $FeCl_3$ gives predominantly :

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In the chemical reaction, $CH_3CH_2NH_2 + CHCl_3 + 3 KOH \to$ $(A) + (B) + 3H_2O$, the compounds $(A)$ and $(B)$ are respectively :

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Which of the following reactions will yield, 2, 2-dibromopropane ?

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The secondary structure of a protein refers to :

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Which of the following molecules is expected to rotate the plane of plane-polarised light ?

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Which one of the following has a square planar geometry ? (At. no. Co = 27, Ni = 28, Fe = 26, Pt = 78)

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Identify the incorrect statement among the following :

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Consider the reaction, $2A + B \to products$ When concentration of B alone was doubled, the half-life did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is :

asked Nov 29, 2018 by pady_1

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The $pK_a$ of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which 50% of the acid ionised is :

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The cell $Zn|Zn^{2+} (1M) || Cu^{2+} (1M) | Cu \; (E^{\circ} cell = 1.10 V)$, was allowed to be completely discharged at 298 K. The relative concentration of $Zn^{2+}$ to $Cu^{2+} \begin{pmatrix} \frac{[Zn^{2+}]}{[Cu^{2+}]} \end{pmatrix} $ is :

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The energies of activation for forward and reverse reactions for $A_2 + B_2 \leftrightharpoons 2AB$ are $180\; kJ\;mol^{-1}$ and $200 \; kJ \;mol^{-1}$ respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by $100\; kJ\; mol^{-1}$. The enthalpy change of the reaction ($A_2 + B_2 \to 2AB$) in the presence of catalyst will be (in $kJ\;mol^{-1}$) :

asked Nov 29, 2018 by pady_1

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A particle of mass m executes simple harmonic motion with amplitude $a$ and frequency $v$. The average kinetic energy during its motion from the position of equilibrium to the end is :

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When a system is taken from state $i$ to state $f$ along the path $iaf$, it is found that $Q=50 \;cal$ and $W=20\; cal$. Along the path $ibf$ Q = 36 cal. W along the path $ibf$ is :

asked Nov 29, 2018 by pady_1

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Two springs, of force constants $k_1$ and $k_2$ are connected to a mass m as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes :

asked Nov 29, 2018 by pady_1

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In a Young's double slit experiment the intensity at a point where the path difference is $\frac{\lambda}{6}$ ($\lambda$ being the wavelength of the light used) is $I$. If $I_0$ denotes the maximum intensity, $I/ I_0$ is equal to :

asked Nov 29, 2018 by pady_1

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A particle is projected at $60^{\circ}$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is :

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A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by :

asked Nov 29, 2018 by pady_1

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