Question Paper (Section wise)

A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms^-2)

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit its L, about the canter of the Sun, its areal velocity is:

A particle which is experiencing a force, given by  undergoes a displacement of. If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

For equal point charges Q each are placed in the XY plane at (0, 2), (4, 2), (4, - 2) and (0,-2). The work required to put a fifth charge Q at the origin of the coordinate system will be:

For the circuit shown below, the current through the Zener diode is:

The given graph shows variation (with distance r from centre) of:

Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin (450 t – 9x) where distance and time are measured in SI united. The tension in the string is:

In an experiment, electrons are accelerated, from rest, by applying, a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 × 10^-19 C Mass of the electron = 9.1 × 10^-31 kg]

A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in searle’s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8.

The new value of increase in length of the steel wire is:

In a radioactive decay chain, the initial nucleus is  At the end there are 6 α- particles and 4β – particles with are emitted. If the end nucleus is , A and Z are given by:

When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photo current is –V₀/ 2. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is –V₀. The threshold frequency for photoelectric emission is:

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping al throughout. The two climb maximum height h_sph  and h_cyl on the incline. The radio is given by:

The ratio of mass densities of nuclei of ⁴⁰C_a and ¹⁶O is closed to:

A nucleus A, with a finite de – broglie wavelength λ_A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of F. The de – Broglie wavelength λ_B and λ_c of B and C are respectively:

The electric field of light wave is given as. This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

A capacitor with capacitance 5 μF is charged to 5 μC. If the plates are pulled apart to reduce the capacitance to 2 μF, how much work is done?

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

Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm^-2. If the surface has an area of 25 cm², the maximum transferred to the surface in 40 min time duration will be

A submarine experiences a pressure of 0.5 × 10⁶ Pa at a depth of d₁ in a sea. When it goes further to a depth of d₂, it experiences a pressure of 8.08 × 10⁶ Pa. Then d₂ –d₁ is approximately ________ m.

(Density of water = 10³ kg/m³ and acceleration due to gravity = 10 ms^-2)

At 40° C, a brass wire of 1 mm is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40°C to 20°C it regains its original length of 0.2 m. The value of M is close to ______ kg.

(Coefficient of linear expansion and Youngs modules of brass are 10^-5/°C and 10¹¹ N/m², respectively; g = 10 ms^-2).

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 Ω. The internal resistances of the two batteries are 1 Ω and 2 Ω respectively. The voltage across the load will be approximately _______ V.

A satellite orbits around a planet at a height of 20 km from surface. Assuming that only gravitational field of the plant acts on the spaceship. The approximate number of revolution made by the satellite in 12 hours around the plane is ______.

[Given: Mass of plane = 8 × 10²² kg, Radius of planet = 2 × 10⁶ m, Gravitational constant G = 6.67 × 10-11 Nm²/kg²]

A parallel plate capacitor has 1μF capacitance. One of its two plates is given + 2μC charge and the other plate, +4μC charge. The potential difference developed across the capacitor is ________ V.

The major product of the following reaction is

The one that is extensively used as a piezoelectric material is

Which amongst the following is the strongest acid?

The correct match between item ‘I’ and item ‘II’ is:

The pair that contains two P – H bonds in each of the oxoacids is:

Which is the most suitable reagent for the following transformation?

The highest possible oxidation states of uranium and plutonium, respectively, are

The element the usually does NOT show variable oxidation states is:

The major product of the following reaction is:

The major product of the following reaction is:

The two monomers for the synthesis Nylon 6, 6 are:

The pair that does NOT require calcination is:

For a reaction scheme,if the rate formation of B is set to be zero then the concentration of B given by

Given:

Co³⁺e^-→ Co²⁺; E° = 1.81 V

Pb⁴ + 2e^-→ Pb²⁺; E° = +1.67V

Ce⁴⁺ +  e^-→ Ce³⁺; E° + 1.61 V

Bi³⁺ + 3e^-→ Bi; E° = +0.20 V

Oxidising power of the species will increase in the order

But-2-ene on reaction with alkaline KMnO₄ at elevated temperature followed by acidification will give:

The major product of the following reaction is:

The correct order of the oxidation states of nitrogen in NO_, N₂O, NO₂ and N₂O₃ is:

Hydrogen peroxide oxidises [Fe(CN)₆]⁴⁻ to [Fe(CN)₆]³⁻ in acidic medium but reduces [Fe(CN)₆]³⁻ to [Fe(CN)₆]⁴⁻ in alkaline medium. The order product formed are, respectively

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

The major product 'Y' in the following reaction is:-

A solid having density of 9 × 10³ kg m^-3forms face centred cubic crystal of edge length

The molar mass of the solid is ______ kg mol^-1

[Avogadro constant ≅ 6 × 10²³ and mol^-1≅ 3]

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temprature becomes 200 K. If C_v = 28 JK^-1 mol^-1, calculate ΔU for this process.(R = 8.0 J K^-1 mol^-1)

The maximum prescribed concentration of copper in drinking water is_____ ppm.

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M BaCl₂ in water. Assuming complete dissociation of the given ionic compounds in water ,the concentration of XY (in mol L^-1) in solution is

The standard Gibbs energy for the given cell reaction in kJ mol^-1 at 298 K is:

[Faraday’s constant F = 96000 C/mol].

5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is:

Then the sum of the elements in A is:

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

, then f’ (1/2) is :

Consider the following three statements:

P : 5 is a prime number

Q : 7 is a factor of 192

R : L.C.M of 5 and 7 is 35

Then the truth value of which one of the following statements is true?

 Then S represents:

If y(x) is the solution of the differential equation where y(1) , then:

The direction ratio of normal to the plane through the points (0, -1, 0) and (0, 0, 1) and making an angle  with the plane y – z + 5 = 0 is :

 and  be coplanar vectors. Then the non – zero vector  is:

Let f be a differentiable function such that f(1) = 2 and   f ’(x) = f(x) for all x ∈ R. If h(x) = f(f(x)), then h’(1) is equal to :

The set of all values of λ for which the system of linear equations

x – 2y – 2z =λx

x + 2y + z = λy

–x – y = λz,

has a non-trivial solution :

If ⁿC_4, ⁿC₅ and ⁿC₆  are in A. P., then n can be:

Let S(λ) = {(x, y): y²≤ 4x, 0 ≤ x ≤ λ} and A(λ) is the area of the region S(λ). If for λ, 0 < λ < 4, A(λ) : A(4) = 2:5 then λ equals:

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is:

Let f: R→R be a differentiable function satisfying

f’(3) + f’(2) = 0. Then is equal to:

If the fourth term in the Binomial expansion of  is 20 × 8⁷, then the value of x is:

The value of dx is:

Four persons can hit a target correctly with probabilities  respectively. If all hit at the target independently, then the probability that the target would be hit, is:

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 :

The number of real roots of the equation 5+|2^x-1|=2^x(2^x-2) is:

If the of the series

is p, then  is equal to _________.

 then n is equal to ______.

(Here C is a constant of integration)

If m is the minimum value of k for which the function is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the value of (m² + M² – 40) is equal to ________.

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90∘, such that the length (in cm) of their common chord is  cm, then (a – 9b) is equal to _____________.

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag. Its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. Now, if a ball is drawn at random from the bag and the probability of getting this ball as red comes out to be  then p + q is equal to _________