JEE Advanced 2013 Question Paper

The major product(s) of the following reaction is (are) -

In the following reaction, the product (s) formed is (are)

Upon treatment with ammonical H2S , the metal ion that precipitates as a sulfide is -

Among P, Q, R and S, the aromatic compound(s) is / are :

After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are)Reaction I : Reaction II :

Let f(x) = x sin π x, x > 0. Then for all natural numbers n, f′(x) vanishes at -

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio of 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners.If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

The area enclosed by the curve y = sinx + cosx and y = |cosx - sinx| over the interval is

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length or y-axis is (are)

Let complex numbers α and lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2 respectively. If z0 = x0 + iy0 satisfies the equation 2|z0|2 = r2 + 2, then |α| =

The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a0, where a0 is the Bohr radius. Its orbital angular momentum is It is given that h is Planck constant and R is Rydberg constant. The possible wavelength (s), when the atom de-excites, is (are) :-

In the circuit shown in the figure, there are two parallel plate capacitors each of the capacitance C.The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed, After some time,

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 108 ms-1. The final momentum of the object is :-

Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and -ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region :-

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale excatly coincides with one of the main scale divisions. The diameter of the cylinder is :-