JEE (Advanced) 2008 Paper-2

Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Consider all possible permutations  of the letters of the word ENDEANOEL. Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Consider a system of three charges $$\frac{q}{3}, \frac{q}{3}$$ and $$-\frac{2q}{3}$$ placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle $$CAB = 60^\circ$$

A radioactive sample S1 having an activity of $$5 \mu Ci$$ has twice the number of nuclei as another sample S2 which has anactivity of $$10 \mu Ci$$. The half lives of S1 and S2
can be

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the waveis 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is

A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio $$\frac{y}{x}$$ is

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle $$\theta$$ at which the speed of the bob is half of that at A, satisfies 

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension ofthe string is slightly increased the numberof beats reduces to 2 per second. Assuming the velocity of soundin air to be 340 m/s, the frequency n of the tuning fork in Hz is

A parallel plate capacitor C with plates of unit area and separation is filled with a liquid of dielectric constant K = 2. The level of liquid is $$\frac{d}{3}$$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is