List of top Questions asked in JEE Main- 2013

Choose the correct sketch of the magnetic field lines of a circular current loop shown by the dot ? and the cross ?.

If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to

Arrange in the correct order of stability (decreasing order) for the following molecules :

A tennis ball (treated as hollow spherical shell) starting from $O$ rolls down a hill. At point A the ball becomes air borne leaving at an angle of $30^\circ$ with the horizontal. The ball strikes the ground at $B$. What is the value of the distance $AB$ ? (Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter $=\frac{2}{3}mR^{2}$ )

In which of the following exothermic reactions, the heat liberated per mole is the highest ?

A block is placed on a rough horizontal plane. A time dependent horizontal force $F = kt$ acts on the block, where $k$ is a positive constant. The acceleration - time graph of the block is:

A light ray emerging from the point source placed at $P( 1,3)$ is reflected at a point $Q$ in the axis of $x$. If the reflected ray passes through the point $R (6, 7)$, then the abscissa of $Q$ is:

Let the equations of two ellipses be $E_{1} : \frac{x^{2}}{3}+\frac{y^{2}}{2}=1 and E_{2} : \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$, If the product of their eccentricities is $\frac{1}{2}$, then the length of the minor axis of ellipse $E_2$ is:

If two vertices of an equilateral triangle are $A (- a, 0)$ and $B (a, 0), a > 0$, and the third vertex $C$ lies above x-axis then the equation of the circumcircle of $\Delta ABC$ is :

If the three lines $x - 3y = p, \,ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then :

If the image of point $P(2, 3)$ in a line $L$ is $Q(4,5)$, then the image of point $R(0,0)$ in the same line is:

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as $(0, 1), (1, 1)$ and $(1,0)$ is

If the extremities of the base of an isosceles triangle are the points $(2a, 0)$ and $(0, a)$ and the equation of one of the sides is $x = 2a$, then the area of the triangle, in square units, is :

The line $x - 2y = 2$ meets the parabola, $y^2 + 2x = 0$ only at the point $(- 2,-2)$. The line $ y=mx-\frac{1}{2m}\left(m\ne0\right)$ is tangent to the parabola, $y^{2} = - 2x$ at the point $\left(-\frac{1}{2m^{2}}, -\frac{1}{m}\right).$

\(12\, g\) of a nonvolatile solute dissolved in \(108\, g\) of water produces the relative lowering of vapor pressure of \(0.1.\)The molecular mass of the solute is :

A compound with molecular mass $180$ is acylated with $CH_3COCl$ to get a compound with molecular mass $390$. The number of amino groups present per molecule of the former compound is

A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is :

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of a for which the vectors $\vec{u}=\left(\alpha-2\right)\vec{a}+\vec{b}$ and $\vec{v}=\left(2+3\alpha\right)\vec{a}-3\vec{b}$ are collinear is :

The expression$\frac{tan\, A}{1-cot\, A}+\frac{cot\, A}{1-tan \, A}$ can be written as

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC$ $\perp$ $CD$, if $\angle $ $ADB = \theta, BC = p$ and $CD = q$, then $AB$ is equal to

Bond distance in $HF$ is $9.17 \times 10^{-11}\, m$. Dipole moment of $HF$ is $6.10^4 \times 10^{-30}\, Cm$ . The percentage ionic character in $HF$ will be : (electron charge $= 1.60 \times 10^{-19}\, C$)

Which one of the following molecules is polar?

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 $g = 10 m/s^2$, then the equation of its trajectory is

A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\vec{E}=\vec{E}_{0}\left(4\times10^{-7}\,x-50t\right)$ with distance being in meter and time in seconds. The dielectric constant of the medium is: