JEE (Advanced) 2012 Paper-1

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

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

A small block of mass of 0.1 kg lies on fixed inclined plane PQ which makes an angle $$\theta$$ with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10 $$m/s^2$$)

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $$\overrightarrow{E} = E_0 \hat{j}$$ and $$\overrightarrow{B} = B_0 \hat{j}$$. At time t = 0, this charge has velocity $$\overrightarrow{v}$$ in the x-y plane, making an angle $$\theta$$ with the x-axis. Which of the following option(s) is (are) correct for time t > 0?

A person blowsinto open-end of a long pipe. As a result, a high-pressure pulseof air travels down the pipe. Whenthis pulse reachesthe other endof the pipe,

An infinitely long solid cylinder of radius R has a uniform volume charge density p. It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression $$\frac{23 \rho R}{16k ε_0}$$. The value of k is

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density/ flows along the length. If the magnitude of the magnetic field at the point P is given by $$\frac{N}{12}\mu_0 aJ$$, then the value of N is

A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and is $$I_O$$ and $$I_P$$, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $$\frac{I_P}{I_O}$$ to the nearest integer is

A circular wire loop of radius R is placed in the x-y plane centeredat the origin O. A square loop of side a (a << R) having twoturnsis placed with its center at $$z = \sqrt{3}R$$ along the axis of the circular wire loop, as shownin figure. The plane of the square loop makes an angle of $$45^\circ$$ with respectto the z-axis. If the mutual inductance between the loops is given by $$\frac{\mu_0 a^2}{2^{\frac{p}{2}}R}$$, then the value of p is

A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the protonatits start is: (take the proton mass, $$m_p = \left(\frac{5}{3}\right) \times 10^{-27}$$ kg; $$h/e = 4.2 \times 10^{-15}$$ J.s/C; $$\frac{1}{4 \pi ε_0} = 9 \times 10^9$$ m/f; 1 fm = $$10^{-15}$$ m)