List of top Questions asked in JEE Advanced

For a positive integer n let $a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ...+ \frac{1}{(2^n)-1},$ then

For a positive integer n, let $f_n(\theta)=\Bigg(tan\frac{\theta}{2}\Bigg)(1+sec \theta)(1+sec 2\theta)(1+ sec 2^2 \theta)... (1+sec 2^n \theta), then$

Let $a_1,a_2,...,a_{10}$ be in AP and $h_1, h_2$ equal to .....,$h_{10}$ be in HP. If $a_1 = h_1 = 2$ and $ a_{10} = h_{10} = 3,$ then $a_4 h_7$ is

If in the expansion of $(1 + x)^m (1 - x)^n$, the coefficients of $x$ and $x^2$ are 3 and - 6 respectively, then m is euqal to

Let $ S_1, S_2,...$ be squares such that for each $ n \ge 1 $ the length of a side of $ S_n $ equals the length of a diagonal of $ S_{n+1}$. If the length of a side of $ S_1 $ is 10 cm, then for which of the following values of n is the area of $S_n$ less than 1 sq cm?

$ lim_{ n \to \infty} \frac{1}{n} \displaystyle \sum_{r = 1}^ {2n} \frac{r}{ \sqrt{ n^2 + r^2}} $ equals

If two distinct chords, drawn from the point (p, q) on the circle $x^2 + y^2 = px + qy$ (where, $ pq \ne 0$) are bisected by the X-axis, then

$\displaystyle\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos\,x}$ is equal to

A smooth sphere A is moving on a frictionless horizontal plane with angular velocity $?$ and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are $?_A$ and $?_B$ respectively. Then,

A gas will approach ideal behaviour at

A gas $X$ at $1$ atm is bubbled through a solution containing a mixture of $1M$ $Y^-$ and $1 MZ^-$ ions at $25 ^\circ C$. If the reduction potenital of $Z > Y > X$, then

A disc of mass M and radius R is rolling with angular speed to on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

A cubical block of side a moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is

A coil of inductance 8.4 mH and resistance $ 6 \Omega$ is connected to a 12 V battery. The current in the coil is 1A at approximately the time

Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal

A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat plate as shown. The observed interference fringes from this combination shall be

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

A charged particle is released from rest in a region of steady and uniform electric and magnetic fields which are parallel to each other. The particle will move in a

The optically active tartaric acid is named as D-(+)-tartaric acid because it has a positive

On heating ammonium dichromate, the gas evolved is

In compounds of type $EC1_3$, where E = B , P, As or Bi, the angles Cl-E - Cl for different E are in the order

A circular loop of radius R, carrying current I, lies in x-y plane with its centre at origin. The total magnetic flux through x-y plane is

In the compound $CH_2=CH-CH_2-CH_2-C \equiv CH$, the $C_2-C_3$ bonds is of

Among the following compounds, the strongest acid is

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is