List of top Questions asked in JEE Main

Statement 1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x+y=5 \, is\, x^{2}+y^{2}-6x+2y=0.$ Statement 2 : $2x + y = 5$ is a normal to the circle $x^{2}+y^{2}-6x+2y=0.$

A common tangent to the conics $x^{2}=6y$ and $2x^{2}-4y^{2}=9$ is:

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

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 $=\frac{2}{3}mR^{2}$ )

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:

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 :

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 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 :

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:

\(12\, g\) 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 :

$ABCD$ 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:

If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is

If $z$ is a complex number of unit modulus and argument $\theta ,$ then $ \, arg \left(\frac{1 + z}{1 + \bar{z}}\right)$ is equal to

Monocarboxylic acids are functional isomers of:

The Wurtz-Fittig reaction involves condensation of:

A solution of $(-) 1-chloro-1-$phenylethane in toluene racemises slowly in the presence of a small amount of $SbCl_5$, due to the formation of

A major component of Borsch reagent is obtained by reacting hydrazine hydrate with which of the following ?

Arrange the following compounds in the order of decreasing acidity

An ether (A), $C_5H_{12}O$, when heated with excess of hot concentrated $HI$ produced two alkyl halides which when treated with $NaOH$ yielded compounds (B) and (C). Oxidation of (B) and (C) gave a propanone and an ethanoic acid respectively. The IUPAC name of the ether (A) is :