Recent questions in JEEMAIN PAST PAPERS

Boron cannot form which one of the following anions ?

asked Dec 11, 2018 by pady_1

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A vessel at 1000 K contains $CO_2$ with a pressure of 0.5 atm. Some of the $CO_2$ is converted into $CO$ on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of $K$ is

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a' and 'b' are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because

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The degree of dissociation $(\alpha$) of a weak electrolyte $A_xB_y$ is related to vant Hoff factor (i) by the expression :

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The strongest acid amongst the following compounds is :

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The reduction potential of hydrogen half cell will be negative if :

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Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is :

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Trichloroacetaldehyde was subjected to Cannizzaro's reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :

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The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?

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Among the following the maximum covalent character is shown by the compound :

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For $x \in (0, \frac{5 \pi}{2})$, define $f(x) = \int_0^x \;\sqrt{t} \;\sin t \;dt$. Then $f$ has

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The area of the region enclosed by the curves $ y = x,\; \; x = e, \; \; y = \frac{1}{x}$ are the positive x-axis is

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The value of p and q for which the function $ f(x) = \begin{cases} \frac{\sin (p+1) x + \sin x}{x} &, x < 0 \\ \; \; \;\; \;q &, x = 0 \\ \frac{\sqrt{x+x^2} - \sqrt{x}}{x^{3/2}} & , x > 0 \end{cases} $ is continuous for all $x$ in $R$, is

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If $\omega (\neq 1)$ is a cube root of unity, and $(1 + \omega)^7 = A + B \omega$. Then $(A, B)$ equals

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Let A and B be two symmetric matrices of order 3. Statement-1 : A (BA) and (AB) A are symmetric matrices. Statement -2 : AB is symmetric matrix if matrix multiplication of A and B is commutative.

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Statement-1 : The point A (1, 0, 7) is the mirror image of the point B (1, 6, 3) in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ Statement-2 : The line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ bisects the line segment joining A (1, 0, 7) and B (1, 6, 3)

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If the mean deviation about the medium of the numbers a, 2a, . . . ., 50a is 50, then |a| equals

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

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Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negative of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

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The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z=0; 2x + 2y + z = 0 possess a non-zero solution is

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If C and D are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among the following is

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The two circles $x^2+y^2=ax$ and $x^2+y^2 =c^2 (c>0)$ touch each other if

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The vector $\overrightarrow{a}$ and $\overrightarrow{b}$ are not perpendicular and $\overrightarrow{c}$ and $\overrightarrow{d}$ are two vectors satisfying : $\overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{b} \times \overrightarrow{d}$ and $\overrightarrow{a}.\overrightarrow{d} =0$. Then the vector $\overrightarrow{d}$ is equal to

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Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity $\sqrt{\frac{2}{5}}$ is

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If $\overrightarrow{a} = \frac{1}{\sqrt{10}} (3 \hat{i} + \hat{k})$ and $\overrightarrow{b} =\frac{1}{7} (2 \hat{i} + 3 \hat{j} - 6\hat{k})$, then the value of $(2 \overrightarrow{a} - \overrightarrow{b} ) . [ (\overrightarrow{a} \times \overrightarrow{b} ) \times (\overrightarrow{a} + \overrightarrow{2b} ) ]$ is

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If the angle between the line $x= \frac{y-1}{2} = \frac{z-3}{\lambda}$ and the plane $x + 2y + 3z = 4$ is $\cos^{-1} (\sqrt{\frac{5}{14}})$, then $\lambda$ equals

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The domain of the function $f(x) = \frac{1}{\sqrt{|x|-x}}$ is

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A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

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Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then p lies in the interval

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Let $\alpha, \beta$ be real and $z$ be a complex number. If $z^2 + \alpha z + \beta = 0$ has two distinct roots on the line $Rez=1$, then it is necessary that

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The value of $\begin{align} \int_0^1 \frac{8 \log (1+x)}{1+x^2} dx \end{align} $ is

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Let R be the set of real numbers Statement-1 : $A = \{ (x,y) \in R \times R : y - x$ is an integer $\}$ is an equivalence relation on R. Statement-2 : B = $\{ (x,y) \in R \times R : x = \alpha y$ for some rational number $\alpha \}$ is an equivalence relation on R.

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If $\frac{dy}{dx} = y + 3 > 0$ and $y(0) = 2$, then $y(In2)$ is equal to

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$\frac{d^2x}{dy^2}$ equals

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Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is $^9C_3$ Statement-2 : The number of ways of choosing any 3 places from 9 different places is $^9C_3$.

asked Dec 11, 2018 by pady_1

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$ \displaystyle{\lim_{x \to 2} ( \frac{\sqrt{1-\cos \{ 2 (x-2) \} }}{x-2} } )$

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The coefficient of $x^7$ in the expansion of $(1 - x - x^2 + x^3)^6$ is

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If $A = \sin^2 x + \cos^2 x $, then for all real $x$

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The lines $L_1 : y - x = 0$ an $L_2 : 2x + y =0$ intersect the line $L_3 : y + 2 = 0$ at P and Q respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersect $L_3$ at R. Statement-1 : The ratio PR : RQ equals $2\sqrt{2}:\sqrt{5}$. Statement -2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

asked Dec 11, 2018 by pady_1

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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 metallic surface is irradiated by a monochromatic light of frequency $v > v_0$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $K_{max}$ and $V_0$ respectively. If the frequency incident on the surface doubled, both the $K_{max}$ and $V_0$ are also doubled. Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

asked Dec 11, 2018 by pady_1

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The half life of a radioactive substance is 20 minutes. The aproximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ and $\frac{1}{3}$ of it had decayed is :

asked Dec 11, 2018 by pady_1

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100 g of water is heated from $30^{\circ}C$ to $50^{\circ}C$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4148 J/Kg/K) :

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A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is :

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The electrostatic potential inside a charged spherical ball is given by $\phi = \alpha \rho^2 + b$ where r is the distance from the centre, a, b are constants. Then the charge density inside ball is

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Energy required for the electron excitation in $Li^{++}$ from the first to the third Bohr orbit is :

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A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is :

asked Dec 11, 2018 by pady_1

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Direction : The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane - convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement-1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi$. Statement-2:The centre of the interference pattern is dark.

asked Dec 11, 2018 by pady_1

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If a wire is stretched to make it 0.1% longer, its resistance will :

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A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 $K$, its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are, respectively :

asked Dec 11, 2018 by pady_1

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A resistor 'R' and $2 \mu F$ capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. ($\log_{10} 2.5 = 0.4$)

asked Dec 11, 2018 by pady_1

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