A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is
The circuit shown in the figure contains two diodes D1 and D2, each with a forward resistance of 50 ohms and infinite backward resistance. If the battery voltage is 6 V, the current (in amperes) through the 100 ohm resistance is
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An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s2) must be at least:
The truth table given below is for (A and B are the inputs, Y is the output). What type of GATE it will form?
A second pendulum is mounted in a space shuttle. Its period of oscillations will decrease when rocket is:
The difference of speed of light in the two media A and B (vA - vB) is 2.6 × 107 m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: Speed of light in vacuum, c = 3 × 108 ms-1)
An ideal transformer has 500 and the 1000 turns in the primary and the secondary coil. If the DC voltage of 120 V is applied to the primary coil, then the emf produced at the secondary coil will be:
The energy released by the fission of one uranium atom is 200 MeV. The number of fissions required per second to produce 3.2 W of power is
The activity of a radioactive sample falls from 700 s-1 to 500 s-1 in 30 minutes. Its half life is close to:
A cylindrical solid of length L and radius a is having varying resistivity given by ρ = ρ0x where ρ0 is a positive constant and x is measured from the left end of the solid. The cell shown in the figure is having emf V and negligible internal resistance. The electric field as a function of x is best described by:
An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to [Use g = 10 ms-2]
For a gas, the difference between the two specific heats at constant pressure and constant volume is 4150 J kg-1 K-1 and their ratio is 1.4. What is the specific heat of the gas at constant volume in units of J kg-1 k-1?
The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye-piece?
A compound A has molecular formula C₂Cl₃OH. It reduce Fehling's solution and on oxidation gives a monocarboxylic acid B. A is obtained by the action of Cl₂ on ethyl alcohol. A is
The heats of dissociation (k.cals/mole) of methane and ethane are 360 and 620 respectively. From these, C - C bond energy (k.cals/mole) in ethane can be evaluated as
When the densities of the ore particles and gangue particles are different, then the ore is concentrated by
Which of the following reacts rapidly with oxygen in air at ordinary temperature
Propene is reacted with HBr in presence of peroxide, the product is
Let two points be A(1, -1) and B(0, 2). If a point P(x', y') be such that the area of ΔPAB = 5 sq. units and it lies on the line 3x + y - 4λ = 0, then a value of λ is
In a triangle ABC, if then the projection of the vector is equal to:
If c is a point at which Rolle's theorem holds for the function f(x) = loge in the interval [3, 4], where α ∈ R, then f''(c) is equal to
Where [t] denotes greatest integer ≤ t. If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, then the ordered pair (m, n) is
The line y = x + 1 meets the ellipse at two points P and Q. If r is the radius of the circle with PQ as diameter, then (3r)2 is equal to: