List of top Questions asked in JEE Advanced- 2012

Consider a disc rotating in the horizontal plane with a constant angular speed to about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) \(\omega\) remains constant throughout. Then

Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field and the electric potential $V (r)$ with the distance $r$ from the centre, is best represented by which graph?

If $S$ be the area of the region enclosed by $ y = e^{-x^2} $, $y = 0,x = 0$ and $x = 1$ . Then,

If the straight lines \(\frac{x-1}{2}=\frac{y+1}{K} = \frac{z}{2}\) and \(\space20mm \frac{x+1}{5}=\frac{y+1}{2} = \frac{z}{k}\) are coplanar, then the plane(s) containing these two lines is/are

In allene $(C_3H_4)$ the type(s) of hybridisation of the carbon atoms, is (are)

Let $P=[a_{ij}]$ be a $3\times3$ matrix and let $Q=[b_{ij}]$ where $b_{ij}=2^{i+j} a_{ij}$ for $1 \le i, j \le $.If the determinant of $P$ is $2$, then the determinant of the matrix $Q$ is

For the resistance network shown in the figure, choose the correct option(s).

For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in 100g of water, the elevation in boiling point at 1 atm pressure is 2$^{\circ}$C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (take $K_b = 0.76 K kg mol^{-1}).$

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $- q$ at $(0,- \frac{a}{4} ,0), + 3q$ at $(0, 0, 0)$ and $- q$ at $(0,+ \frac{a}{4},0)$. Choose the correct option(s).

Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is

The reaction of white phosphorus with aqueous $NaOH$ gives phosphine along with another phosphorus containing compound. The reaction type, the oxidation states of phosphorus in phosphine and the other product respectively are

The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball is

If PQR is a triangle of area $\triangle$ with a = 2, b = $ \frac{7}{2}$ and c = $ \frac{5}{2}$, where a, b and c are the lengths of the sides of ' the triangle opposite to the angles a t P ,Q and R, respectively. Then, $ \frac{ 2 \, sin \, P - sin \, 2 P }{ 2 \, sin \, P + sin \, 2P }$ equals

With respect to graphite and diamond, which of the statement(s) given below is/are correct?

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [$a_0$ is Bohr radius]

The value of the integral $ \int ^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \bigg ( x^2 + \log \frac{\pi - x }{ \pi + x } \bigg ) \, \cos \, x \, dx $

In the given circuit, the AC source has ? = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)

If $a_1, a_2, a_3,... $ are in harmonic progression with $a_1 = 5$ and $ a_{20} = 25.$ Then, the least positive integer $n$ for which $a_n < 0,$ is

Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction, as shown in the given scheme.

For one mole of a van der Waals' gas when $b = 0$ and $T = 300\, K$. the $pV\, vs \,1/V$ plot is shown below. The value of the van der Waals' constant a (atm $L\, mol^{-2}$)

The carboxyl functional group $(- COOH)$ is present in

The compound that undergoes decarboxylation most readily under mild condition is

The shape of $XeO_2F_2$ molecule is

The number of optically active products obtained from the complete ozonolysis of the given compound, is

In the cyanide extraction process of silver from argentite ore, the oxidising and reducing agents used are