Maths-
General
Easy

Question

stack l i m with x rightwards arrow 0 below   fraction numerator square root of 1 plus x end root minus square root of 1 minus x end root over denominator sin to the power of negative 1 end exponent invisible function application x end fraction equals

  1. 2    
  2. 1    
  3. –1    
  4. None of these    

The correct answer is: 1


    Related Questions to study

    General
    Physics-

    The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis. The optical path length of ray R will be

    The figure shows a transparent slab of length 1 m placed in air whose refractive index in x direction varies as mu equals 1 plus x to the power of 2 end exponent left parenthesis 0 less than x less than 1 right parenthesis. The optical path length of ray R will be

    Physics-General
    General
    Physics-

    A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from S subscript 1 end subscript and S subscript 2 end subscript. The distance between slits is 1 mm.

    A parallel beam of light 500 nm is incident at an angle 30° with the normal to the slit plane in a young's double slit experiment. The intensity due to each slit is Io. Point O is equidistant from S subscript 1 end subscript and S subscript 2 end subscript. The distance between slits is 1 mm.

    Physics-General
    General
    Physics-

    In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

    In a Young's Double slit experiment, first maxima is observed at a fixed point P on the screen. Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to the intensity at point O (centre of the screen)

    Physics-General
    parallel
    General
    Physics-

    An YDSE is carried out in a liquid of refractive index mu equals 1.3 and a thin film of air is formed in front of the lower slit as shown in the figure. If a maxima of third order is formed at the origin O, find the thickness of the air film. The wavelength of light in air is lambda subscript 0 end subscript equals 0.78 mu m and D/d=1000.

    An YDSE is carried out in a liquid of refractive index mu equals 1.3 and a thin film of air is formed in front of the lower slit as shown in the figure. If a maxima of third order is formed at the origin O, find the thickness of the air film. The wavelength of light in air is lambda subscript 0 end subscript equals 0.78 mu m and D/d=1000.

    Physics-General
    General
    Physics-

    Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

    Two coherent radio point sources that are separated by 2.0 m are radiating in phase with a wavelength of 0.25 m. If a detector moves in a large circle around their midpoint, at how many points will the detector show a maximum signal ?

    Physics-General
    General
    Physics-

    Two coherent narrow slits emitting light of wavelength lambda in the same phase are placed parallel to each other at a small separation of 2 lambda. The light is collected on a screen S which is placed at a distance D left parenthesis much greater-than lambda right parenthesis from the slit S subscript 1 end subscript as shown in figure. Find the finite distance x such that the intensity of P is equal to intensity at O.

    Two coherent narrow slits emitting light of wavelength lambda in the same phase are placed parallel to each other at a small separation of 2 lambda. The light is collected on a screen S which is placed at a distance D left parenthesis much greater-than lambda right parenthesis from the slit S subscript 1 end subscript as shown in figure. Find the finite distance x such that the intensity of P is equal to intensity at O.

    Physics-General
    parallel
    General
    Physics-

    Consider the arrangement shown in figure. By some mechanism, the separation between the slits S subscript 3 end subscript and S subscript 4 end subscript can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of S subscript 1 end subscript S subscript 2 end subscript and S subscript 3 end subscript S subscript 4 end subscript. When z equals fraction numerator D lambda over denominator 2 blank d end fraction, the intensity measured at P is I. Find this intensity when z is equal to

    1) fraction numerator D lambda over denominator d end fraction,
    2) fraction numerator 3 D lambda over denominator 2 blank d end fraction, and
    3) fraction numerator 2 D lambda over denominator d end fraction.

    Consider the arrangement shown in figure. By some mechanism, the separation between the slits S subscript 3 end subscript and S subscript 4 end subscript can be changed. The intensity is measured at the point P which is at the common perpendicular bisector of S subscript 1 end subscript S subscript 2 end subscript and S subscript 3 end subscript S subscript 4 end subscript. When z equals fraction numerator D lambda over denominator 2 blank d end fraction, the intensity measured at P is I. Find this intensity when z is equal to

    1) fraction numerator D lambda over denominator d end fraction,
    2) fraction numerator 3 D lambda over denominator 2 blank d end fraction, and
    3) fraction numerator 2 D lambda over denominator d end fraction.

    Physics-General
    General
    Maths-

    stack l i m with x rightwards arrow pi divided by 2 below   fraction numerator a to the power of cot invisible function application x end exponent minus a to the power of cos invisible function application x end exponent over denominator c o t invisible function application x minus c o s invisible function application x end fraction equals

    stack l i m with x rightwards arrow pi divided by 2 below   fraction numerator a to the power of cot invisible function application x end exponent minus a to the power of cos invisible function application x end exponent over denominator c o t invisible function application x minus c o s invisible function application x end fraction equals

    Maths-General
    General
    Physics-

    In Young's double slit experiment S subscript 1 end subscript and S subscript 2 end subscript are two slits. Films of thicknesses t subscript 1 end subscript and t subscript 2 end subscript and refractive indices m subscript 1 end subscript and m subscript 2 end subscript are placed in front of S subscript 1 end subscript and S subscript 2 end subscript respectively. If m subscript 1 end subscript t subscript 1 end subscript equals m subscript 2 end subscript t subscript 2 end subscript, then the central maximum will :

    In Young's double slit experiment S subscript 1 end subscript and S subscript 2 end subscript are two slits. Films of thicknesses t subscript 1 end subscript and t subscript 2 end subscript and refractive indices m subscript 1 end subscript and m subscript 2 end subscript are placed in front of S subscript 1 end subscript and S subscript 2 end subscript respectively. If m subscript 1 end subscript t subscript 1 end subscript equals m subscript 2 end subscript t subscript 2 end subscript, then the central maximum will :

    Physics-General
    parallel
    General
    Physics-

    Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

    Two coherent sources are placed 0.9 mm apart and the fringes are observed one metre away. The wavelength of monochromatic light used if it produces the second dark fringes at a distance of 10 mm

    Physics-General
    General
    Physics-

    Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

    Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

    Physics-General
    General
    Physics-

    Bright colours exhibited by spider's web, exposed to sunlight are due to

    Bright colours exhibited by spider's web, exposed to sunlight are due to

    Physics-General
    parallel
    General
    Physics-

    Two light beams produce interference pattern to give maxima and minima on the screen. If the intensities of the light beams are in the ratio of 9:4, then the ratio of intensities of maxima and minima is

    Two light beams produce interference pattern to give maxima and minima on the screen. If the intensities of the light beams are in the ratio of 9:4, then the ratio of intensities of maxima and minima is

    Physics-General
    General
    Physics-

    The axes of the polariser and analyser are inclined to each other at 60° If the amplitude of polarised light emergent through analyzer is A The amplitude of unpolarised light incident on polariser is

    The axes of the polariser and analyser are inclined to each other at 60° If the amplitude of polarised light emergent through analyzer is A The amplitude of unpolarised light incident on polariser is

    Physics-General
    General
    Chemistry-

    In open square brackets C r open parentheses H subscript 2 end subscript O close parentheses subscript 6 end subscript close square brackets to the power of 3 plus end exponent ion central metal ion has d-electrons equal to

    In open square brackets C r open parentheses H subscript 2 end subscript O close parentheses subscript 6 end subscript close square brackets to the power of 3 plus end exponent ion central metal ion has d-electrons equal to

    Chemistry-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.