Recent questions in JEEMAIN PAST PAPERS

In the chemical reactions, the compounds ‘A’ and ‘B’ respectively are

asked Dec 11, 2018 by pady_1

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From amongst the following alcohols the one that would react fastest with conc. $HCl$ and anhydrous $ZnCl_2$, is

asked Dec 11, 2018 by pady_1

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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 mol of sodium sulphate is dissolved in 1 kg of water, is $(K_f = 1.86\; K\; kg\; mol^{–1})$

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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If $10^{–4 }dm^3$ of water is introduced into a $1.0\; dm^{3}$ flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ? (Given : Vapour pressure of $H_2O$ at $300\; K$ is $3170 \;Pa ; R = 8.314 J K^{–1} mol^{–1})$

asked Dec 11, 2018 by pady_1

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Consider the reaction : $Cl_2(aq) + H_2S(aq) \to S(s) + 2H^{+}(aq) + 2Cl^{–} (aq)$ The rate equation for this reaction is rate $= k [Cl_2] [H_2S]$ Which of these mechanisms is/are consistent with this rate equation ?
 (A) $Cl_2 + H_{2}S \to H^+ + Cl^- + Cl^+ + HS^- \;$ (slow)
$Cl^{+} + HS^{–} \to H^+ + Cl^- + S (fast)$
 $(B)\; H_2S \Leftrightarrow H^+ + HS^- $(fast equilibrium)
$Cl_2 + HS^{–} \to 2Cl^{–} +H^+ + S$ (slow)

asked Dec 11, 2018 by pady_1

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A solution containing $2.675\; g$ of $CoCl_3. 6 NH_3$ (molar mass =$ 267.5 \;g \;mol^{–1})$ is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of $AgNO_3$ to give $4.78\; g$ of $AgCl$ (molar mass $= 143.5\; g \;mol^{–1}$). The formula of the complex is (At. Mass of $Ag = 108 \;u$)

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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The standard enthalpy of formation of $NH_3$ is $–46.0\; kJ mol^{–1}.$ If the enthalpy of formation of $H_2$ from its atoms is $–436\; kJ mol^{–1}$ and that of $N_2$ is $–712\; kJ mol^{–1},$ the average bond enthalpy of $N–H$ bond in $NH_3$ is

asked Dec 11, 2018 by pady_1

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Let A be a $2 \times 2$ matrix Statement-1: adj (adj A) = A Statement-2 : |adj A| = |A|

asked Nov 29, 2018 by pady_1

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Statement -1 : $\sim (p \leftrightarrow \sim q) $ is equivalent to $p \leftrightarrow q$ Statement -2: $\sim (p \leftrightarrow \sim q) $ is a tautology.

asked Nov 29, 2018 by pady_1

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Statement -1: The variance of first n even natural numbers is $\frac{n^2-1}{4}$ Statement -2 :The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$

asked Nov 29, 2018 by pady_1

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Let $f(x) = x|x| $ and $g(x) = \sin x$ Statement -1 : gof is differentiable at $x=0$ and its derivative is continuous at the point. Statement -2 : gof is twice differentiable at $x=0$

asked Nov 29, 2018 by pady_1

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Let $f(x) = (x+1)^2 - 1, x \geq -1$ Statement -1 : The set $\{ x : f(x) = f^{-1} (x) \} = \{0, -1\}$ Statement-2: f is a bijection.

asked Nov 29, 2018 by pady_1

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The shortest distance between the line $y - x = 1$ and the curve $x = y^2$ is

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Given $P(x) = x^4 + ax^3 + bx^2+cx+d$ such that $x=0$ is the only real root of $P'(x) = 0$. If $P(-1) < P(1)$, then in the interval $[-1, 1]$

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The area of the region bounded by the parabola $(y-2)^2 = x-1$, the tangent to the parabola at the point (2, 3) and the x-axis is

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Let $y$ be an implicit function of $x$ defined by $x^{2x} - 2x^{x} \cot y -1 =0$. Then $y'(1)$ equals

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One ticket is selected at random from 50 tickets numbered $00, 01, 02, .....49$. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

asked Nov 29, 2018 by pady_1

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The differential equation which represents the family of curves $y = c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants is

asked Nov 29, 2018 by pady_1

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The sum of the infinity of the series $1 + \frac{2}{3} + \frac{6}{3^2} + \frac{10}{3^3}+\frac{14}{3^4} + . . . . $ is

asked Nov 29, 2018 by pady_1

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The ellipse $x^2+4y^2 = 4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

asked Nov 29, 2018 by pady_1

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The remainder left out when $8^{2n} - (62)^{2n+1}$ is divided by 9 is

asked Nov 29, 2018 by pady_1

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Three distinct points A, B and C are given in the 2-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (-1, 0) is equal to $\frac{1}{3}$. Then the circumcentre of the triangle ABC is at the point

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If $|z - \frac{4}{z}| = 2$, then the maximum value of $|z|$ is equal to

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The projections of a vector on the three coordinate axis are 6, -3, 2 respectively. The direction consines of the vector are

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If P and Q are the points of intersection of the circles $x^2+y^2+3x+7y+2p-5=0$ and $x^2+y^2+2x+2y-p^2 = 0$ then there is a circle passing through P, Q and (1, 1) for

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In a binomial distribution $B ( n, p = \frac{1}{4})$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then $n$ is greater than

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For real $x$, let $f(x) = x^3 + 5x + 1$, then

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$\begin{align} \int_0^{\pi} [\cot x] dx, \;[.] \end{align} $ denotes the greatest integer function, is equal to

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From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

asked Nov 29, 2018 by pady_1

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Let the line $\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}$ lies in the plane $x+3y -\alpha z + \beta = 0$. Then $(\alpha, \beta)$ equals

asked Nov 29, 2018 by pady_1

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If $\overrightarrow{u}, \overrightarrow{v}, \overrightarrow{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $[3\overrightarrow{u} \;\; p\overrightarrow{v} \;\; p\overrightarrow{w}] - [p \overrightarrow{v} \;\; \overrightarrow{w}\; \; q \overrightarrow{u}] - [2 \overrightarrow{w}\; \; q \overrightarrow{v}\;\;q \overrightarrow{u}] = 0$ holds for

asked Nov 29, 2018 by pady_1

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If A, B and C are three sets suct that $A \cap B = A \cap C$ and $A \cup B = A \cup C$, then

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The lines $p(p^2+1) x-y+q = 0$ and $(p^2 + 1)^2 x + (p^2+1)y + 2q = 0$ are perpendicular to a common line for

asked Nov 29, 2018 by pady_1

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Let A and B denote the statements A : $\cos \alpha + \cos \beta + \cos \gamma = 0$ $B: \sin \alpha + \sin \beta + \sin \gamma = 0$ If $\cos (\beta-\gamma) + \cos(\gamma - \alpha) + \cos (\alpha - \beta) = -\frac{3}{2}$, then

asked Nov 29, 2018 by pady_1

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If the roots of the equation $bx^2 + cx + a = 0$ be imaginary, then for all real values of $x$, the expression $3b^2x^2 + 6bcx+2c^2$ is

asked Nov 29, 2018 by pady_1

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If the mean deviation of number $1, 1+d, 1 +2d, . . . ., 1 + 100d$ from their mean is 255, then the $d$ is equal to

asked Nov 29, 2018 by pady_1

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Let a, b, c be such that $b(a+c) \neq 0$. If $\begin{vmatrix} a & a+1 & a-1 \\ -b & b+1 & b-1 \\ c & c-1 & c+1 \end{vmatrix}$ + $\begin{vmatrix} a+1 & b+1 & c-1 \\ a-1 & b-1 & c+1 \\ (-1)^{n+2}a & (-1)^{n+1}b & (-1)^n c \end{vmatrix} = 0$, then the value of 'n' is

asked Nov 29, 2018 by pady_1

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Buna-N synthetic rubber is a copolymer of :

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Which of the following pairs represents linkage isomers ?

asked Nov 29, 2018 by pady_1

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In Cannizzaro reaction given below $2 Ph \; CHO \xrightarrow{\overset{(-)}{: OH}} Ph \; CH_2OH + PhC\overset{..}{O}_2^{(-)}$ the slowest step is :

asked Nov 29, 2018 by pady_1

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The bond dissociation energy of $B-F$ in $BF_3$ is $646 \; kJ\; mol^{-1}$ whereas that of $C-F$ in $CF_4$ is $515 \; kJ\; mol^{-1}$. The correct reason for higher $B-F$ bond dissociation energy as compared to that of $C-F$ is :

asked Nov 29, 2018 by pady_1

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The two functional groups present in a typical carbohydrate are:

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The set representing the correct order of ionic radius is :

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The IUPAC name of neopentane is

asked Nov 29, 2018 by pady_1

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The number of stereoisomers possible for a compound of the molecular formula $CH_3 - CH = CH - CH(OH)-Me$ is :

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A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?

asked Nov 29, 2018 by pady_1

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Calculate the wavelength (in nanometer) associated with a proton moving at $1.0 \times 10^3 \; ms^{-1}$ (Mass of proton = $1.67 \times 10^{-27} kg$ and $h = 6.63 \times 10^{-34} Js$ ):

asked Nov 29, 2018 by pady_1

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In context with the transition elements, which of the following statements is incorrect ?

asked Nov 29, 2018 by pady_1

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