JEE Advanced 2008 Question Paper with Solutions

A spherically symmetric gravitational system of particles has a mass density ρ = { ρ 0 f o r r ≤ R 0 f o r r > R Where ρ 0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r ( 0 < r < ∞ ) from the centre of the system is represented by

STATEMENT - 1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first. and STATEMENT - 2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

STATEMENT - 1 : The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down. and STATEMENT - 2 : In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

The speed of the block at point C, immediately before it leaves the second incline is

If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

Aqueous solutions of Na 2 S 2 O 3 on reaction with Cl 2 gives:

A gas described by van Der Waals equation

Hyperconjugation involves overlapping of the following orbitals:

STATEMENT - 1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45 o slope as the atomic number is increased. STATEMENT - 2 : Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides

The correct statement(s) concerning the structures E, F and G is(are) :

Let ${S_n} = \sum\limits_{k = 1}^n {{n \over {{n^2} + kn + {k^2}}}}$ and ${T_n} = \sum\limits_{k = 0}^{n - 1} {{n \over {{n^2} + kn + {k^2}}}}$ for $n$ $=1, 2, 3, ............$ Then,

Let $P\left( {{x_1},{y_1}} \right)$ and $Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,$ be the end points of the latus rectum of the ellipse ${x^2} + 4{y^2} = 4.$ The equations of parabolas with latus rectum $PQ$ are :

Points E and F are given by

Let z be any point in A ∩ B ∩ C Then, | z + 1 − i | 2 + | z − 5 − i | 2 lies between :

Let z be any point A ∩ B ∩ C and let w be any point satisfying | w − 2 − i | < 3 . Then, | z | − | w | + 3 lies between :

In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is λ . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

A particle of mass m and charge q, moving with velocity v enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is l . Choose the correct choice (s).

STATEMENT - 1 In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance. and STATEMENT - 2 Resistance of a metal increases with increase in temperature.

The wavelength of light emitted in the visible region by He + ions after collisions with H atoms is

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60 $^\circ$ ). In the position of minimum deviation, the angle of refraction will be :

Let $g(x) = {{{{(x - 1)}^n}} \over {\log {{\cos }^m}(x - 1)}};0 < x < 2,m$ and $n$ are integers, $m \ne 0,n > 0$ , and let $p$ be the left hand derivative of $|x - 1|$ at $x = 1$ . If $\mathop {\lim }\limits_{x \to {1^ + }} g(x) = p$ , then

Consider the system of equations: x − 2 y + 3 z = − 1 − x + y − 2 z = k x − 3 y + 4 z = 1 Statement - 1 : The system of equations has no solution for k ≠ 3 . and Statement - 2 : The determinant | 1 3 − 1 − 1 − 2 k 1 4 1 | ≠ 0 , for k ≠ 3 .

Let f and g be real valued functions defined on interval ( − 1 , 1 ) such that g ″ ( x ) is continuous, g ( 0 ) ≠ 0. g ′ ( 0 ) = 0 , g ″ ( 0 ) ≠ 0 , and f ( x ) = g ( x ) sin ⁡ x STATEMENT - 1: lim x → 0 [ g ( x ) cot ⁡ x − g ( 0 ) cos ⁡ e c x ] = f ″ ( 0 ) and STATEMENT - 2: f ′ ( 0 ) = g ( 0 )

The area of the region bounded by the curve $y=f(x),$ the $x$ -axis, and the lines $x=a$ and $x=b$ , where $- \infty < a < b < - 2,$ is :

If $f\left( { - 10\sqrt 2 } \right) = 2\sqrt 2 ,$ then $f''\left( { - 10\sqrt 2 } \right) =$

Among the following, the correct statement is :

Water is added to the solution M such that the fraction of water in the solution becomes 0.9 mole. The boiling point of this solution is:

Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of:

The freezing point of the solution M is :

Among the following, the correct statement is: