A point on the hypotenuse of a triangle is at distance a and b from the side of the triangle then minimum length of the hypotenuse is
A wire when connected to 220 V mains supply has power dissipation P1. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is P2. Then what will be P2 : P1 ?
If in the circuit, power dissipation is 150 W, then R is
Which one of the following properties is not shown by NO ?
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(1) It combines with oxygen to form nitrogen dioxide
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(2) It′s bond order is 2.5
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(3) It is diamagnetic in gaseous state
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(4) It is a neutral oxide
When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx2 where a and b are constants. The work done in stretching the unstretched rubber-band by L is :
A block of mass m is placed on a surface with a vertical cross section given by y = 6 . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :
The radiation corresponding to 3 → 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 × 10−4 T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :
Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross- section of each rod = 4 cm2. End of copper rod is maintained at 100 °C where as ends of brass and steel are kept at 0 °C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :
A green light is incident from the water to the air - water interface at the critical angle (θ). Select the correct statement.
(1) The spectrum of visible light whose frequency is more than that of green light will come out to the air
medium.
(2) The entire spectrum of visible light will come out of the water at various angles to the normal.
(3) The entire spectrum of visible light will come out of the water at an angle of 90° to the normal.
(4) The spectrum of visible light whose frequency is less than that of green light will come out to the air
medium.
From a tower of height H, a particle is thrown vertically upwards with a speed U. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is :
One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :
(1) The change in internal energy in the process AB is − 350 R.
(2) The change in internal energy in the process BC is − 500 R.
(3) The change in internal energy in whole cyclic process is 250 R.
(4) The change in internal energy in the process CA is 700 R.
A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
During the propagation of electromagnetic waves in a medium : (1) Electric energy density is equal to the magnetic energy density. (2) Both electric and magnetic energy densities are zero. (3) Electric energy density is double of the magnetic energy density. (4) Electric energy density is half of the magnetic density.
The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 × 103 A m−1. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside
In a large building,there are15 bulbs of 40W,5bulbs of 100W,5 fans of 80W and1heater of1kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :
Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :?
A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it ? (1) A screw gauge having 100 divisions in the circular scale and pitch as 1 mm. (2) A screw gauge having 50 divisions in the circular scale and pitch as 1 mm. (3) A meter scale. (4) A vernier calliper where the 10 divisions in vernier scale matches with 9 division in main scale & main scale has 10 divisions in 1 cm.
A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3*10^4 V/m, the charge density of the positive plate will be close to :
The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is :
(For steel Young’s modulus is 2 × 10^11 N m−2 and coefficient of thermal expansion is 1.1 × 10^−5 K^−1)
Half life of 90Sr is 6.93 years. In a child body 1 
of 90Sr dopped in place of calcium, how many years will it take to reduce its concentration by 90% (Assume no involvement of Sr in metabolism).
Number of chiral centers in chloramphenicol is ?
Cl2 on reaction with hot & conc. NaOH gives two chlorine having products X and Y. On treatment with AgNO3, X gives precipitate. Determine average bond order of Cl and O bond in 'Y' ?
Each of solution A and B of 100 L containing 4 g NaOH and 9.8 g H2SO4. Find pH of solution which is obtain by mixing 40 L solution of A and 10 L solution of B.
Shown in the figure below is a meterbridge set up with null deflection in the galvanometer. The value of the unknown resistance R is
A 5 V battery with internal resistance 2 
and 2 V battery with internal resistance 1 are connected to a 10 resistor as shown in the figure. The current in the 10 resistor is
Consider a block of conducting material of resistivity 
shown in the figure. Current I enters at A and leaves from D. We apply the superposition principle to find voltage 
developed between B and C. The calculation is done in the following steps:
(i) Take current I entering from A and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance r from A by using Ohm’s law 
where j is the current per unit area at r.
(iii) From the r dependence of E(r), obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current I leaving D and superpose results for A and D.
For current entering at A, the electric field at a distance r from A is
Consider a block of conducting material of resistivity shown in the figure. Current I enters at A and leaves from D. We apply the superposition principle to find voltage developed between B and C. The calculation is done in the following steps:
(i) Take current I entering from A and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance r from A by using Ohm’s law where j is the current per unit area at r.
(iii) From the r dependence of E(r), obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current I leaving D and superpose results for A and D.
measured between B and C is
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
A material B has twice the specific resistance of A. A circular wire made of B has twice the diameter of a wire made of A. Then for the two wires to have the same resistance, the ratio lB / lA of their respective lengths must be
The resistance of a bulb filament is 100 
at a temperature of 100º C. If its temperature coefficient of resistance be 0.005 per ºC, its resistance will become 200 at a temperature of
The current I drawn from the 5 volt source will be
In a Wheatstone’s bridge, three resistance P, Q and R connected in the three arms and the fourth arm is formed by two resistance S1 and S2 connected in parallel. The condition for bridge to be balanced will be
The Kirchhoff’s first law 
and second law (), 
where the symbols have their usual meanings, are respectively based on
In a potentiometer experiment, the balancing with a cell is at length 240 cm. On shunting, the cell with a resistance of 
, the balancing length becomes 120 cm. The internal resistance of the cell is
Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are R1 and R2 (R2 > R1). If the potential difference across the source having internal resistance R2 is zero, then
In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, What will be the value of the resistor R?
In a metre bridge experiment null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?
An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3, then what will be the ratio of the currents passing through the wire?
13.4g of a sample of unstable hydrated salt: Na2SO4 . nH2O was found to contain 6.3g of water. Determine the number of water of crystallisation
X ml of H2 gas effuses through a hole in a container in 5 seconds. The time taken for the effusion of the same volume of the gas specified below under identical conditions is :
The behaviour of a real gas is usually depicted by plotting compressibility factor Z versus P at a constant temperature. At high temperature and high pressure, Z is usually more than one. This fact can be explained by van der Waals equation when
The temperature of an ideal gas is increased from 140 K to 560 K. If at 140 K the root mean square velocity of the gas molecule is V, at 560 K it becomes
Amongst LiCl, RbCl, BeCl2 and MgCl2 the compounds with greatest and least ionic character respectively are
In the formation of N2+ from N2 the electron is removed from
The pair having similar geometry is
The species which does not show paramagnetism is
The velocity of electron in the ground state hydrogen atom is 
. Its velocity in the second orbit would be
An electron is moving with a kinetic energy of 
. What will be de Broglie wave length for this electron?
SO2 is angular and CO2 is linear why?
Dipole moment of BF3 is zero.Why?