A real valued function f (x) satisfies the functional equation f(x – y) = f (x)f (y) – f(a – x)f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

Anonymous User Maths Set, Relations and Functions 20 May, 2020 64 views

Let f : (–1, 1) B, be a function defined by f(x)  = , then f is both one­-one and onto when B is the interval

Anonymous User Maths Set, Relations and Functions 20 May, 2020 56 views

## What is the domain of the function f(x) = ? What is the domain of the function f(x) = ?

Anonymous User Maths Set, Relations and Functions 20 May, 2020 60 views

## If f : R  R satisfies f (x + y) = f (x) + f (y), for all and f (1) = 7, then  is If f : R R satisfies f (x + y) = f (x) + f (y), for all and f (1) = 7, then is

Anonymous User Maths Set, Relations and Functions 18 May, 2020 64 views

## Domain of definition of the function Domain of definition of the function Anonymous User Maths Set, Relations and Functions 18 May, 2020 67 views

## A function f from the set of natural numbers to integers defined by A function f from the set of natural numbers to integers defined by Anonymous User Maths Set, Relations and Functions 18 May, 2020 60 views

## If f : R  S, defined by f(x) = sin x -  cos x  + 1, is onto, then what will be the interval of S? If f : R S, defined by f(x) = sin x - cos x  + 1, is onto, then what will be the interval of S?

Anonymous User Maths Set, Relations and Functions 18 May, 2020 57 views

## The function  is The function is

Anonymous User Maths Set, Relations and Functions 17 May, 2020 68 views

## What is the domain of ? What is the domain of ?

Anonymous User Maths Set, Relations and Functions 17 May, 2020 60 views

## What is the period of ? What is the period of ?

Anonymous User Maths Set, Relations and Functions 17 May, 2020 50 views

Let T be the rth term of an A.P. whose first term r
is a and common difference is d. If for some positive integers m, n, m 1 n, Tm = 1 , and Tn = 1 , then
a – d equals

Anonymous User Maths Sequences and Series 17 May, 2020 61 views

A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions of the circular scale.

What will be the diameter of wire from the above data?

Anonymous User Physics 15 May, 2020 55 views

A thermally insulated vessel contains an ideal gas of molecular mass M and the ratio of specific heats It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by

Anonymous User Physics Thermodynamics 15 May, 2020 60 views

Direction: The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements.

A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

Statement-1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of p.

Statement-2: The centre of the interference pattern is dark.

Anonymous User Physics Waves and Sound Waves 15 May, 2020 54 views

Two particles are executing simple harmonic motion of the same amplitude A and frequency w along the x-axis. Their mean position is separated by distance X0 (X0 > A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

Anonymous User Physics Oscillation 15 May, 2020 57 views

Let the x–z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of 2 and medium with z < 0 has a refractive index of . A ray of light in medium 1 given by the vector is incident on the plane of separation. What will be the angle of refraction in medium 2?

Anonymous User Physics Ray Optics 15 May, 2020 59 views

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, what will be the angular speed of the disc?

Anonymous User Physics Circular and Rotational Motion 15 May, 2020 55 views

Two bodies of masses m and 4m are placed at a distance r. What will be the gravitational potential at a point on the line joining them where the gravitational field is zero?

Anonymous User Physics Gravitation and Projectile 15 May, 2020 57 views

A fully charged capacitor C with initial charge q0 is connected to a coil of self-inductance L at t = 0. What is the time at which the energy is stored equally between the electric and the magnetic fields?

Anonymous User Physics Electromagnetic Induction & Alternating Current 15 May, 2020 76 views

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them

Anonymous User Physics Electrostatic 15 May, 2020 62 views

Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1, m2 and m3 and the number of molecules are n1, n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is

Anonymous User Physics Thermodynamics 15 May, 2020 59 views

A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m s-1. The speed of the image of the second car as seen in the mirror of the first one is

Anonymous User Physics Ray Optics 15 May, 2020 63 views

The electrostatic potential inside a charged spherical ball is given by where r is the distance from the centre; a, b are constants. Then the charge density inside the ball is

Anonymous User Physics Electrostatic 15 May, 2020 57 views

An object moving with a speed of 6.25 m s-1, is decelerated at a rate given by , where v is the instantaneous speed. What would be the time taken by the object to come to rest?

Anonymous User Physics Laws of Motion and Friction 15 May, 2020 65 views

A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3. Then what will be T1 and T2 ?

Anonymous User Physics Thermodynamics 15 May, 2020 62 views

A current I flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius R. What is the magnitude of the magnetic induction along its axis?

Anonymous User Physics Magnetic Effect of Current 15 May, 2020 90 views

A boat is moving due east in a region where the earth’s magnetic field is 5.0 × 10-5 N A-1m-1due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is 1.50 m s-1, what will be the magnitude of the induced emf in the wire of aerial?

Anonymous User Physics Electromagnetic Induction & Alternating Current 15 May, 2020 56 views

A Carnot engine operating between temperatures T1 and T2 has efficiency 1/6. When T2 is lowered by 62 K, its efficiency increases to 1/3. Then what will be T1 and T2 ?

Anonymous User Physics Thermodynamics 14 May, 2020 56 views

A current I flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius R. What is the magnitude of the magnetic induction along its axis?

Anonymous User Physics Magnetic Effect of Current 14 May, 2020 54 views

A resistor R and 2 capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. (log102.5 = 0.4)

Anonymous User Physics Electromagnetic Induction & Alternating Current 14 May, 2020 55 views

## The transverse displacement y(x,t) of a wave on a string is given by This represents a The transverse displacement y(x,t) of a wave on a string is given by This represents a

Anonymous User Physics Waves and Sound Waves 14 May, 2020 58 views

A mass M, attached to a horizontal spring, executes SHM with an amplitude A1. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2

What is the ratio of ?

Anonymous User Physics Oscillation 14 May, 2020 55 views

The half-life of a radioactive substance is 20 minutes. What will be the approximate time interval (t2 – t1) between the time t2 when 2/3 of it has decayed and time t1 when 1/3 of it had decayed?

Anonymous User Physics Atomic Physics 14 May, 2020 65 views