List of top Questions asked in JEE Advanced

In the formula $X = 3Y\, Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. What are the dimensions of $Y$ in $MKSQ$ system?

The orthocentre of the triangle formed by the lines $xy = 0$ and $ x+ y = 1$,is

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non-coplanar unit vectors such that $\overrightarrow{a}\times (\overrightarrow{b} \times\overrightarrow{c}) =\frac{(\overrightarrow{b} +\overrightarrow{c})}{\sqrt 2}$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles triangle ABC, right angled at B. The points A and B are maintained at temperatures T and ($\sqrt 2$)T respectively. In the steady state, the temperature of the point C is $T_c$. Assuming that only heat conduction takes place, T$_c$/T is

A battery is connected between two points A and B on the circumference of a uniform conducting ring of radius r andresistance R. One of the arcs AB of the ring subtends an angle $\theta$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

Two metallic spheres $S_1$, and S$_2$ are made of the same material and have got identical surface finish. The mass of S$_1$ is thrice that of S$_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of $S_1$ to that of S$_2$ is

The pairs of physical quantities that have the same dimensions is (are)

An isosceles prism of angle $120^\circ$ has a refractive index 1.44. Two parallel rays of monochromatic light enter the prism parallel to each other in air as shown. The rays emerging from the opposite face

During paddling of a bicycle, the force of friction exerted by the ground on the two wheels is such that it acts

Two bodies A and B have thermal emissivities of 0.01 and 0.81 respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength $\lambda_B$ corresponding to maximum spectral radiancy in the radiation from B shifted from _the wavelength corresponding to maximum spectral radiancy in the radiation from A, by 1.00 pm. If the temperature of A is 5802 K.

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that centripetal acceleration $a_{c}$ varying with time is $a_{c}=k^{2}\, r \,t^{2}$ where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

Let [.] denote the greatest integer function and $f (x) = [\tan^2 x]$, then:

The value of $ \int^{ \pi / 2}_0 \frac{ dx }{ 1 + \tan^3 \, x } \, is \, $

A current I flows along the length of an infinitely long, straight, thin-walled pipe. Then

Read the following statements carefully Y : The resistivity of semiconductor decreases with increase of temperature. Z : In a conducting solid, the rate of collisions between free electrons and ions increases with increase of temperature Select the correct statement (s) from the following

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant k. A mass m hangs freely from the free end of the spring. The area of cross-section and the Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to

A star initially has $10^{40}$ deuterons. It produces energy via the processes $_1H^2+_1H^2 \rightarrow _1H^3+p$ and $_1H^2+_1H^3 \rightarrow _2{He}^3+n$. If the average power radiated by the star is $10^{16}$ W, the deuteron supply of the star is exhausted in a time o f the order of $M(H)^2=2.014 \, amu;$ $M(n)=1.008 \, amu;$ $M(p)=1.007 \, amu;$ $M(He)^2=4.001 \, amu;$

Which one of the following has the smallest heat of hydrogenation per mole ?

The material used in solar cells contains

Let E and F be two independent events. If the probability that both E and F happen is 1/12 and the probability that neither E nor F happen is 1/2. Then,

Equal weights of ethane and hydrogen are mixed in an empty container at $25^\circ$ C. The fraction of the total pressure exerted by hydrogen is

The locus of the centre of a circle, which touches externally the circle $x^2 + y^2 -6 x - 6y + 14 = 0$ and also touches the Y-axis, is given by the equation

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

An ideal gas is taken from the state A (pressure p, volume V) to the state B (pressure p /2, volume 2 V) along a straight line path in the p-V diagram. Select the correct statements from the following