List of top Questions asked in JEE Advanced- 2012

Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?

Choose the correct reason(s) for the stability of the lyophobic colloidal particles.

If $ lim_{ x \to \infty} \bigg( \frac{x^2 + x + 1}{x + 1} - ax - b \bigg) $ = 4, then

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, as a function of the radial distance $r$ from the axis is best represented by

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $\omega$, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $|\tau|$ on the system about O, as a function of time is best represented by which plot?

If $X$ and $Y$ are two events such that $P (X | Y )=\frac{1}{2}, P(X | Y)=\frac{1}{3.} \, and \, P(X \cap Y)\frac{1}{6}$ Then, which of the following is/are correct?

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1.$ The points of contacts of the tangents on the hyperbola are

Four fair dice $D_1, D_2, D_3$ and $D_4$ each having six faces numbered $1, 2, 3, 4, 5$ and $6$ are rolled simultaneously. The probability that D$_4$ shows a number appearing on one of $D_1, D_2$ and $D_3$, is

The point $P$ is the intersection of the straight line joining the points $Q(2, 3, 5)$ and $R (1, - 1, 4)$ with the plane $5x - 4y - z = 1$. If $S$ is the foot of the perpendicular drawn from the point $T (2,1, 4)$ to $QR$, then the length of the line segment $PS$ is

The equation of a plane passing through the line of intersection of the planes $x + 2y + 3z = 2$ and $x - y + z = 3$ and at a distance $\frac{2}{\sqrt 3}$ from the point $(3,1, -1)$ is

If $\overrightarrow{a} $ and $ \overrightarrow{b}$ are vectors such that $| \overrightarrow{a}+\overrightarrow{b} |=\sqrt{29}$ and $\overrightarrow{a}\times(2\widehat{i}+3\widehat{j}+4\widehat{k})=(2\widehat{i}+3\widehat{j}+4\widehat{k})\times\overrightarrow{b},$ then a possible value of $ (\overrightarrow{a}+\overrightarrow{b})(-7\widehat{i}+2\widehat{j}+3\widehat{k} is $

A ship is fitted with three engines $ E_1, E_2$ and $E_3 $ The engines function independently of each other with respective probabilities $\frac {1}{2}, \frac {1}{4}$ and $\frac{1}{4}$. For the ship to be operational at least two of its engines must function. Let $X$ denotes the event that the ship is operational and let $ X_1 , X _2 $ and $ X_ 3 $ denote, respectively the events that the engines $ E_1 , E_2$ and $E_3 $ are functioning. Which of the following is/are true?

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $\bigg(\frac{ v_{rms}(helium)}{v_{rms(argon)}}\bigg)$ is

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed $ \omega$. If the angular momentum of the system, calculated about O and P are denoted by $ L_o$ and $ L_p $ respectively, then

A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces are of the same radius of curvature $R\, = \,14\, cm$.For this bi-convex lens, for an object distance of $40\, cm$, the image distance will be

Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe widths recorded are $\beta_G,\beta_R$ and $\beta_B$ respectively. Then,