List of top Questions asked in JEE Main

Which of the following statements is false?

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$ . If $F$ is the focus of the parabola, then the area of the triangle $PFQ$ (in s units) is equal to :

The curve satisfying the differential equation, $(x^2 - y^2) dx + 2xydy = 0$ and passing through the point $(1, 1)$ is :

The locus of the point of intersection of the lines, $\sqrt{2} x-y + 4 \sqrt{2} \, k=0$ and $\sqrt{2} k x+k \, y-4 \sqrt{2} = 0$ (k is any non-zero real parameter), is :

A box contains 5 black and 4 white balls. A ball is drawn at random and its colour is noted. The ball is then put back in the box along with two additional balls of its opposite colour. If a ball is drawn again from the box, then the probability? that the ball drawn now is black, is :

The length of the projection of the line segment joining the points $ (5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x + y + z = 7$ is:

If sum of all the solutions of the equation $8 \cos x.\left(\cos \left(\frac{\pi}{6} + x\right). \cos\left(\frac{\pi}{6} - x\right) - \frac{1}{2}\right)= 1 $ in $\left[0, \pi\right]$ is $ k \pi $, then $k$ is equal to :

The ratio of mass percent of $C$ and $H$ of an organic compound $\left( C _{ X } H _{ Y } O _{ Z }\right)$ is $6: 1 .$ If one molecule of the above compound $\left( C _{ X } H _{ Y } O _{ Z }\right)$ contains half as much oxygen as required to burn one molecule of compound $C _{X} H_{Y}$ completely to $CO _{2}$ and $H _{2} O$. The empirical formula of compound $C _{ X } H _{ Y } O _{ Z }$ is

Two compounds I and II are eluted by column chromatography (adsorption of I > II). Which one of following is a correct statement ?

Hydrogen peroxide oxidises $[Fe(CN)6]^{4-}$ to $[Fe(CN)6]^{3-}$ in acidic medium but reduces $[Fe(CN)6]^{3-}$ to$[Fe(CN)6]^{4-}$ in alkaline medium. The other products formed are, respectively

The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with 1000 turns/cm. The current that should be passed in the solenoid to demagnetise the ferromagnet completely is :

The dipole moment of a circular loop carrying a current $I$, is $m$ and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is :

If $\tan \, A$ and $\tan \, B$ are the roots of the quadratic equation, $3x^2 - 10x - 25 = 0$, then the value of $3 \, \sin^2(A + B) -10 \, \sin ( A + B)?\cos(A + B)-25 \cos^2(A+B) $ is :

When $9.65\,A$ current was passed for $1.0\, hour$ into nitrobenzene in acidic medium, the amount of p-aminophenol produced is_____.

A man in a car at location $Q$ on a straight highway is moving with speed $v$. He decides to reach a point $P$ in a field at a distance d from the highway (point $M$) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance $RM$, so that the time taken to reach $P$ is minimum ?

A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90^{\circ}$ with respect to each other. The mass of unknown particle is :

The set of all $\alpha \epsilon R$, for which $w = \frac{1 + (1 - 8 \alpha)z}{1 - z}$ is a purely imaginary number, for all $z \neq 1$, is :

If for a matrix A, |A| = 6 and adj $A = \begin{bmatrix}1&-2&4\\ 4&1&1\\ -1&k&0\end{bmatrix}$ , then k is equal to :

The negation of $A \to (A \vee \sim B)$ is :

If $L_1$ is the line of intersection of the planes $2x - 2y + 3z - 2 =0, x - y + z + 1 = 0$ and $L_2$ is the line of intersection of the planes $x + 2y - z - 3 = 0, 3x - y + 2z - 1 = 0,$ then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$, is:

The solution of the differential equation $\frac{y dx + x dy}{y dx - x dy} = \frac{x^{2} e^{xy}}{y^{4}} $ satisfying $y(0) = 1$, is :

$\displaystyle\lim_{x \to0} \frac{x \tan2x - 2x \tan x}{\left(1-\cos2x\right)^{2}} $ equals :

From a point A with position vector $p(\hat{i} + \hat{j} + \hat{k})$, AB and AC are drawn perpendicular to the lines $\vec{r} = \hat{k} + \lambda (\hat{i} + \hat{j})$ and $\vec{r} = - \hat{k} + \mu (\hat{i} - \hat{j})$, respectively. A value of p is equal to :

If the tangents drawn to the hyperbola $4y^2 = x^2 + 1$ intersect the co-ordinate axes at the distinct points $A$ and $B$ , then the locus of the mid point of $AB$ is :

The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point $(0, 3)$ is :