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The total length of a sonometer wire between fixed ends is 110 cm. Two bridges are placed to divide the length of wire in ratio 6 : 3 : 2. The tension in the wire is 400 N and the mass per unit length is 0.01 kg/m. What is the minimum common frequency with which three parts can vibrate?
Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be
Interference pattern is observed at ‘P’ due to superimposition of two rays coming out from a source ‘S’ as shown in the figure. The value of l for which maxima is obtained at ‘P’ is ( R is perfect reflection surface):
Two bodies of masses 1 kg and 4 kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25 rad/s, and amplitude 1.6 cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g = 10 ms^{2}).
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V_{0} and its pressure is P_{0}. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T_{M}. If the Young’s modulus of the material of the wire is Y then is equal to : (ggravitational acceleration)
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion the average time of collision between molecules increases as V^{q}, where V is the volume of the gas. The value of q is :
An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section 0.8 × 10^{2}m^{2}. Initially the gas is at 300 K and occupies a volume of 2.4 × 10^{3}m^{3} and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 10^{5} N/m^{2}. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be ( Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)
The temperatureentropy diagram of a reversible engine cycle is given in the figure. Its efficiency is
A black coloured solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature T_{0}. The initial temperature of sphere is 3T_{0}. If the specific heat of the material of the sphere varies as αT^{3} with the temperature T of the sphere, where a is a constant, then the time taken for the sphere to cool down to temperature 2T_{0} will be (σ is StafanBoltzmann constant )
A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? (Given: cross section of the tube can be assumed to be uniform)
A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
A small particle of mass m is projected at an angle θ with the xaxis with an initial velocity v_{0} in the xy plane as shown in the figure. At a time t < , the angular momentum of the particle is
Consider a cylinder of mass M resting on a rough horizontal rough that it pulled out from under it with acceleration ‘a’ perpendicular to the axis of cylinder. What is F_{friction} at point P? It is assumed that the cylinder does not slip.
A mass m moves with a velocity u and collides elastically with another identical mass at rest. After collision the first mass moves with celcity in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.
The acceleration experienced by a moving motor boat, after its engine is cut off, is given by .Where k is constant. If v_{0} is the magnitude of velocity at cutoff, the magnitude of the velocity at a time t after the cut off is
The distance between the object and its doubly magnified real image by a concave mirror of focal length f is
The diameter of objective lens of microscope makes an angle β at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of microscope.
In a Young’s double slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single slit diffraction pattern is:
An isolated sphere S of radius R carries an electric charge. S is momentarily connected to a distant uncharged sphere T which has a radius r. The ratio of surface charge density of S to that of T is
In post office box, the graph of galvanometer deflection versus resistance R ( pulled out of resistance box) for the ratio 100:1 is given as shown ( due to unsuitable values of R, galvanometer shows deflection).The two consecutive values of R are shown in the figure.The value of unknown resistance would be
A sphere encloses an electric dipole within it. The total flux across the sphere is
The output of a 2 input NAND gate is fed to a NOT gate. The Truth table for the output of the combination for all possible input of A and B is
A zener diode is operating in its normal region i.e., the breakdown region for which the circuit diagram is as shown in the figure
Here, Take V_{Z }= 7V and R = 10 W. For potential difference equal to 8V across AB, what is the current through microammeter?
Voltage with appreciable ripple expressed as V = V_{1}+V_{2} cos wt is applied to a resistor R. The average amount of heat generated per second is
An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q_{0} and then connected to the L and R as shown.If a student plots graphs of the square of maximum charge Q^{2}_{max} on the capacitor with time (t) for two different values L_{1} and L_{2} (L_{1}>L_{2}) of L then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale)
In the given circuit, charge Q_{2} on the 2µF capacitor changes as C is varied from 1µF to 3µF. Q_{2} as a function of ‘C’ is given properly by:
An inductor (L=0.03H) and a resistor (R=0.15kW) are connected in series to a battery of 15V EMF in a circuit shown. The key K_{1} has been kept closed for a long time. Then at t = 0, K_{1} is opened and key K_{2} is closed simultaneously. At t = 1 ms, the current in the circuit will be : (e^{5}=150)
An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity B, The magnetic field B_{s} inside the superconductor will be such that:
A compound A and B are interconverting. Structures of A and B are shown below:
Which of the following statement is correct regarding the equililbrium constant of A B.
Which of the following statement is correct regarding the product of the following reaction?
A face centred cubic lattice is made up of hollow spheres of X. Spheres of solid Y are present in hollow sphere X. Radius of Y is half of radius of X. What is the ratio of total volume of spheres of X unoccupied by Y in a Unitcell and volume of unit cell.
[HXeO_{4}]^{} + OH^{} → [A] +[B] + O_{2} + H_{2}O.
The products in [A] and [B] in unbalanced reaction are:
B(OH)_{3} + NaOH Na[B(OH)_{4}] (aq)
Addition of compound X makes the reaction to proceed in forward direction, compound X is:
During the transition of an electron from n = n level to n = 1 level in H (Hydrogen), D (Deuterium) and T (Tritium) if the wavelengths of emitted photons are λ_{H}, λ_{D} and λ_{T}. Then which of the following statement is correct?
Which of the following diatomic molecules would be stabilized by the removal of an electron?
The approximate pH of a solution formed by mixing equal volumes of solution of 0.1 M sodium propanoate and 0.1 M propanoic acid (k_{a} for propanoic acid = 1.3 × 10^{5} mol dm^{3}) will be:
A catalyst lowers the activation energy of a reaction from 20 kJ mole^{–1} to 10 kJ mole^{–1}. The temperature at which the uncatalysed reaction will have the same rate as that of the catalysed at 27°C is
The velocity of electron in the second orbit of He^{+} will be
20 ml of 0.2 M Al_{2}(SO_{4})_{3} is mixed with 20 ml of 0.6 M BaCl_{2}. Concentration of Al^{3+} ion in the solution will be
The circulation of blood in human body supplies O_{2} and releases CO_{2}. the concentration of O_{2} and CO_{2} is variable but on an average, 100 ml blood contains 0.02 g of O_{2} and 0.08 g of CO_{2}. The volume of O_{2} and CO_{2} at 1 atm and at body temperature 37^{o}C, assuming 10 lt blood in human body, is
A 3 mol sample of a gas having = 1.33 at 300 K is allowed to expand under reversible adiabatic condition from 5 L to 40 L. The value of H is
Aqueous solution of a salt (Y) is alkaline to litmus. On strong heating, it swellsup to give a glassy material. When conc. H_{2}SO_{4} is added to a hot concentrated solution of (Y), white crystals of a weak acid separates out. Hence, the compound (Y) is
A white powder when strongly heated gives off brown fumes. A solution of this powder gives a yellow precipitate with a solution of KI. When a solution of barium chloride is added to a solution of powder, a white precipitate results. This white powder may be
Which nitrogen in the following compound has least pK_{b} value?
The slag obtained during the extraction of copper pyrites is composed mainly of
Chlorination of toluene in presence of light and heat followed by treatment with aqueous NaOH gives
The reaction A Product, is zero order while the reaction B Product, is first order reaction. For what initial concentration of A are the half lives of the two reactions equal? (Rate constant value are same for both two reaction).
Two substances A and B are present such that [A_{0}] = 4[B_{0}] and halflife of A is 5 minutes and that of B is 15 minutes. If they start decaying at the same time following first order kinetics how much time later will the concentration of both of them would be same?
40% of a mixture of 0.2 mol of N_{2} and 0.6 mol of H_{2} react to give NH_{3} according to the equation,N_{2}(g) + 3H_{2}(g) → 2NH_{3}(g), at constant temperature and pressure. Then the ratio of the final volume to the initial volume of gases are
Equation of the bisector of the acute angle between lines 3x + 4y + 5 = 0 and 12x – 5y – 7 = 0 is
If α and β are the roots of the equation x^{2 } 2x + 4 = 0, then the value of α^{n} + β^{n} will be
If AM and HM between two numbers are 27 and 12 respectively, then their GM is
A bag contains 3 white and 5 black balls. One ball is drawn at random. Then, the probability that it is white, is
In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes?
If the domain of the function f (x) = x^{2}  6x + 7 is (∞ , ∞) , then the range of function is
In order that the function f (x) = (x + 1)^{1/x} is continuous at x = 0,f (0) must be defined as
The line x + y = 4 divides the line joining the points (1,1) and (5,7) in the ratio
The angle between the pair of lines given by equation x^{2 }+ 2xy – y^{2 }= 0, is
The length of tangent from point (5,1) to the circle x^{2} + y^{2} + 6x  4y 3 = 0 is
If projection of any line on coordinate axes are 3, 4 and 5, then its length is
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60° with the horizontal and height of the house be , then the length of the ladder is
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