Question Paper (Section wise)

One mole of ideal gas passes through a process where pressure and volume obey the relation. Here P₀ and V₀ are constant. Calculate the change in the temperature of the gas if its volume change from V₀ to 2V₀

A bullet of mass 20 g has an initial speed of 1 ms^-1 just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers mean resistance of 2.5 × 10^-2 N, the speed of the bullet after emerging from the other side of the wall is close to

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of  and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let l₁ be the moment of inertia of the disc about its axis and l₂ be the moment of inertia of the new sphere about its axis. The ratio of l₁/l₂ is given by:

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 mm² are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produce a new elongation of 0.2 mm is [ Given, the Young’s Modulus for steel and brass are respectively 120 × 10⁹ N/m² and 60 × 10⁹ N/m² ]

Two radioactive substance A and B have decay constant 5λ and λ respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become will be

When heat Q is supplied to a diatomic gas of rigid molecules at constant volume its temperature increase by ∆T. The heat required to produce the same change in temperature, at constant pressure is

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

A plane is inclined at an angle α = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms^-1, from the base of the plant, making an angle θ = 15° with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to Take g = 10 ms²

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is:  [ Take µ₀ = 4π × 10^-7 NA^-2 ]

Two blocks A and B of masses m_A = 1kg and m_B = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontal, so that the block A does not slide over the block B is:

The major product obtained in the given reaction is

The difference between ∆H and ∆U ( ∆H - ∆U ), when the combustion of one mole of heptane ( I ) is carried out a temperature T is equal to

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are:

For the reaction of H₂ with I₂, the rate constant is 2.5 × 10^-4 dm³ mol^–1 s^–1 at 327°C and 1.0 dm³ mol^–1 s^–1 at 527°C. The activation energy for the reaction, in kJ mol^–1 is: ( R = 8.314 J K^–1 mol^–1 )

Which of these factors does not govern the stability of a conformation in acyclic compounds?

Air pollution that occurs in sunlight is:

The INCORRECT statement is:

The correct statement is:

The correct match between Item-I and Item-II is:

Points I, II and III in the following plot respectively correspond to ( V_mp : most probable velocity )

The sum of real roots of the equation

at a point ( α, β ) ≠ ( 0, 0 ) on it is parallel to the line 2x + 6y – 11 = 0 then

The locus of the centres of the circles, which touch the circle, x² + y² = 1 externally, also touch the y-axis and lie in the first quadrant is :

Let f( x ) = log_e ( sin x ), ( 0 < x < π ) and g( x ) = sin^-1( e^-x ), ( x ≥ 0 ) If α is a positive real number such that a = ( fog )’( α ) and b = ( fog )( α ), then

If 5x + 9 = 0 is the directrix of the hyperbola 16x² – 9y² = 144, then its corresponding focus is:

Let a₁, a₂, a₃,…. be an A. P with a₆ = 2. Then the common difference of this A. P., which maximizes the product a₁a₄a₅ is: