List of top Questions asked in JEE Main

If a, b and c are the greatest values of $^{19}C_{p}, \, ^{20}C_{q}$ and $^{21}C_{r}$ respectively, then :

Let the latus ractum of the parabola $y^{2}=4x$ be the common chord to the circles $C _{1}$ and $C _{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C _{1}$ and $C _{2}$ is:

Which of the following statements is a tautology?

If a hyperbola passes through the point $P(10,16)$ and it has vertices at $( ? 6,0)$, then the equation of the normal to it at P is :

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to $50 .$ A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :

If $\frac{dy}{dx}=\frac{xy}{x^{2}+y^{2}}; y\left(1\right)=1;$ then a value of $x$ satisfying $y(x) = e$ is :

Let $a_n$ be the $n^{th}$ term of a G.P. of positive terms. If $x=\displaystyle \sum_{n=1}^{100}a_{2n+1}=200$ and $x=\displaystyle \sum_{n=1}^{100}a_{2n}=100$, $x=\displaystyle \sum_{n=1}^{200}a_n$ is equal to :

If speed $V$, area $A$ and force $F$ are chosen as fundamental units, then the dimension of Young's modulus will be :

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is $M ,$ radius of its top, $R$ and height, $H ,$ then its moment of inertia about its axis is: 

If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then :

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{i}}{\sqrt{2}},$ with its polarization along the direction $\hat{k}.$ The correct form of the magnetic field of the wave would be (here $B_0$ is an appropriate constant):

Proton with kinetic energy of $1 \,MeV$ moves from south to north It gets an acceleration of $10^{12} \, m/s^2$ by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is $1.6 \times 10^{-27}\, kg$)

$\displaystyle \lim_{x \to 1}$$\left\{log_{e}\left(e^{x\left(x-1\right)}-e^{x\left(1-x\right)}\right)-log_{e}\left(4x\left(x-1\right)\right)\right\}$ is equal to :

In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A $ wins the game if he throws a total of $6$ before $B$ throws a total of $7$ and $B$ wins the game if he throws a total of $7 $before $A$ throws a total of six The game stops as soon as either of the players wins. The probability of $A$ winning the game is :

Let A and B be two independent events such that $P\left(A\right) = \frac{1}{3}$ and $P\left(B\right) = \frac{1}{6}.$ Then, which of the following is TRUE ?

Which of the following statement is not true for glucose?

Which of the following is not an essential amino acid:

Kjeldahl's method cannot be used to estimate nitrogen for which of the following compounds ?

The true statement amongst the following is :

A graph of vap our pressure and temperature for three different liquids X, Y, and Z is shown below : The following inferences are made : (A) X has higher intermolecular interactions compared to Y. (B) X has lower intermolecular interactions compared to Y. (C) Z has lower intermolecular interactions compared to Y. The correct inference(s) is/are :

At 35$^{\circ}$C, the vapour pressure of $CS_2$ is 512 mm Hg and that of acetone is 344 mm Hg. A solution of $CS_2$, in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is :

Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non volatile solute are together sealed in a container. Over time:

The de Broglie wavelength of an electron in the $4^{th}$ Bohr orbit is :

If the sum of the series $20+19 \frac{3}{5}+19 \frac{1}{5}+18 \frac{4}{5}+\ldots $ upto $n^ {th }$ term is $488$ and the $n ^ {th }$ term is negative, then :

The dimension of stopping potential $V_0$ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :