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The self inductance of an electric fan motor is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of
A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then the maximum velocity with which the car can move is
Directions: This question has two statements, Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement 1: DavissonGermer experiment proved the wave nature of electrons.
Statement 2: If electrons have wave nature, then they can interfere and show diffraction.
A semi circular wire of radius 'r' is charged uniformly with a charge 'Q' as shown in the figure. Then, the force experienced by a charge 'q' kept at its centre is
A shell is fired from a cannon with a speed of 100 ms^{1} at an angle 30° with the vertical (ydirection). At the highest point of its trajectory, the shell explodes into two fragments of masses in the ratio 1 : 2. The lighter fragment moves vertically upwards with an initial speed of 200 ms1. What is the speed of the heavier fragment at the time of explosion?
Consider a solid sphere of mass M and radius R. The energy released in forming this solid sphere is
A block of mass m is placed on a surface with a vertical crosssection given by y = x^{3}/6. If the coefficient of friction is 0.5, then the maximum height above the ground at which the block can be placed without slipping is
The logic gate circuit shown in the figure realises which of the following functions?
A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is
The magnetism of a magnet is due to which of the following?
The resistance of the rod is 1 Ω. It is bent in form of a square. What is the resistance across adjacent corners?
Figure shows the vertical crosssection of a vessel filled with a liquid of density ρ. The normal thrust per unit area on the walls of the vessel at point P, as shown will be
A conducting ring of mass 2 kg and radius 0.5 m is placed on a smooth horizontal plane. The ring carries a current i = 4 A. A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in the figure. The initial angular acceleration of the ring will be
A stone is dropped from a height of 45 m on a horizontal level ground. There is the horizontal wind blowing due to which horizontal acceleration of the stone becomes 10 m s^{−2}. (Take g = 10 m s^{−2}). The time taken (t)t by stone to reach the ground and the net horizontal displacement (x) of the stone from the time it is dropped and till it reaches the ground are respectively
The current (I) in the inductance is varying with time according to the plot shown in the figure.
The correct variation of voltage with time in the coil is
Two charges q_{1} and q_{2} are placed 30 cm apart, as shown in the figure. A third charge q_{3} is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is
A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. Calculate the thickness of the shell if the temperature difference between the outer and inner surfaces of the shell in steadystate is T.
Two condensers, one of capacity C and other of capacity C/2 are connected to a V  volt battery, as shown in the figure. The work done in charging fully both the condensers is
Two radio antennas radiating waves in phase are located at points A and B, 200 m apart (Figure). The radio waves have a frequency of 6 MHz. A radio receiver is moved out from point BB along a line perpendicular to the line connecting A and B (line BC as shown in the figure). At what distances from B will there be destructive interference?
With the assumption of no slipping, determine the mass mm of the block which must be placed on the top of a 6 kg cart in order that the system period is 0.75 s. What is the minimum coefficient of static friction μS for which the block will not slip relative to the cart if the cart is displaced m50 mm from the equilibrium positions and released? Take (g = 9.8 m s^{2}).
In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric main is 220 V. The minimum capacity of the main fuse of the building will be (Key in the integral value, in Amperes)
The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will be (in ohm)
A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75°C. T (in °C) is given by:
(Given: room temperature = 30°C, specific heat of copper = 0.1 cal/gm°C)
The circuit contains two diodes each with a forward resistance of 50 Ω and with infinite reverse resistance. If the battery voltage is,6 V, the current through the 120 Ω resistance is mA.
The impulse imparted to a ball of mass m, when it strikes a rigid wall with a speed u and rebounds with the same speed is −αmu, what is the value of α?
If 5.08 g of a cupric salt is dissolved in water and excess of KI is added to the solution, and the liberated I_{2} requires 25 ml of M/5 Na_{2}S_{2}O_{3}, where it gets converted into S_{4}O_{6}^{2}, then find the weight percentage of copper in the salt.
A cell utilises the reaction Zn (s) + 2H^{+} (aq) Zn^{2+} (aq) + H_{2} (g). Addition of H_{2}SO_{4} to the cathode compartment will
Which of the following series of reactions correctly represents the chemical relations related to iron and its compound?
Which of the following is formed when NaCl is heated with conc. H_{2}SO_{4} and solid K_{2}Cr_{2}O_{7}?
Which of the following alkenes will react faster with H_{2} under catalytic hydrogenation conditions?
When mchlorobenzaldehyde is treated with 50% KOH solution, the product(s) obtained is/are
Among cellulose, poly(vinylchloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is the weakest is
Name the end product in the following series of reactions
Which of the following does not illustrate the anomalous properties of lithium?
The vapour of Hg absorb some electrons accelerated by a potential difference of 4.5 volts from rest as a result of which light is emitted. If the full energy of a single incident electron is supposed to be converted into light emitted by electron in a single Hg atom, find the wave number (1/λ) of the light
A crystalline hydrated salt on being heated loses 45.6% of its weight. Percentage composition of anhydrous salt is Al  10.5 %, K  15.1 %, S  24.8 %, O  49.6 %. Find molecular formula of salt (hydrated) (M = 948 g/mol for hydrated salt).
Which one of the following ores is best concentrated by froth flotation method?
At 500 K, the half life period of a gaseous reaction at an initial pressure of 80 kPa is 350 s350 s. When the pressure is 40 kPa, the half life period is 175 s; the order of the reaction is :
Consider the following three halides :
(1) CH_{3} − CH_{2} − ClCH_{3}  CH_{2}  Cl
(2) CH_{2} = CH − ClCH_{2} = CH  Cl
(3) C_{6}H_{5} − ClC_{6}H_{5}  Cl
Arrange C − Cl bond length of these compounds in decreasing order 
Ratio of ΔT_{b}/K_{b} of 10 g AB_{2} and 14 g A_{2}B per 100 g of solvent in their respective, solution (AB_{2} and A_{2}B both are nonelectroytes) is 1 mol/kg in both cases. Hence, atomic weight of A and B are respectively :
Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is
The pH of a 0.01 M solution of a weak acid having degree of dissociation 12.5% is ____. (Answer up to 1 decimal place)
For the reaction A → C + D, the initial concentration of A was 0.01 M. After 100 s, the concentration of A becomes 0.001 M. The rate constant of the reaction has the numerical value 9.0. The order of reaction is
The number of stereo isomers possible for a compound of the molecular formula is CH_{3}−CH=CH−CH(NH_{2})−CH_{3} is
Total number of optically inactive stereoisomers of tartaric acid is/are
If the normal at the point (bt_{1}^{2}, 2bt_{1}) on a parabola meets the parabola again at the point (bt_{2}^{2}, 2bt_{2}), then
The differential equation whose solution is Ax^{2} + By^{2} = 1, where A and B are arbitrary constants, is of
The volume of a parallelepiped whose sides are given by = 2i  3j, = i + j  k, = 3i  k is
In an experiment with 15 observations on x, the following results were available.
∑x^{2} = 2830, ∑x = 170
One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance was
The general solution of sin x  3 sin 2x + sin 3x = cos x  3 cos 2x + cos 3x is
If the p^{th} term of an A.P. be q and q^{th} term is p, then its r^{th} term will be
For a random variable X, if E(X) = 5 and Var(X) = 6, then E(X^{2}) is equal to
The area bounded by y = xe^{x} and the lines x = 1, y = 0 is
The integral is equal to (where [.]. denotes the greatest integer function)
A plane passes through (1, 2, 2) and is perpendicular to two planes 2x – 2y + z = 0 and x – y + 2z = 4. Square of the distance of the plane from the point (52, 53, 57) is
If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B are
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is p/q, then p is equal to
^{20}C_{4} + 2.^{20}C_{3} + ^{20}C_{18}  ^{22}C_{18} is equal to
If coefficient of variation of a distribution is 60% and its standard deviation is 18, then its arithmetic mean is
357 docs148 tests

357 docs148 tests
