Maths-
General
Easy
Question
If
then at
is
- continuous if b=0
- discontinuous for any real b
- differentiable for b= ±1
- non-differentiable for any real b
The correct answer is: continuous if b=0
Related Questions to study
chemistry-
In the reaction ![3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖](data:image/png;base64,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)
In the reaction ![3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖](data:image/png;base64,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)
chemistry-General
chemistry-
The product (A) formed can:
The product (A) formed can:
chemistry-General
chemistry-
Which of the following is the strongest oxidising agent?
Which of the following is the strongest oxidising agent?
chemistry-General
Maths-
Two circles with radii
, touch each other externally. If
be the angle between the direct common tangents, then
Two circles with radii
, touch each other externally. If
be the angle between the direct common tangents, then
Maths-General
Maths-
In triangle ABC, medians AD and BE are drawn. If AD=4, and
, then the area of the △ABC is
In triangle ABC, medians AD and BE are drawn. If AD=4, and
, then the area of the △ABC is
Maths-General
physics-
Two coherent sources S1 and S2 are separated by a distance four times the wavelength
of the source. The sources lie along y axis whereas a detector moves along + x-axis. Leaving the origin and far off points the number of points where maxima are observed is
Two coherent sources S1 and S2 are separated by a distance four times the wavelength
of the source. The sources lie along y axis whereas a detector moves along + x-axis. Leaving the origin and far off points the number of points where maxima are observed is
physics-General
physics-
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
physics-General
physics-
A beam with wavelength l falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
A beam with wavelength l falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
physics-General
physics-
Two ideal slits
and
are at a distance d apart and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through
as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,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)
Two ideal slits
and
are at a distance d apart and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through
as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,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)
physics-General
physics-
A monochromatic beam of light falls on YDSE apparatus at some angle (say
) as shown in figure. A thin sheet of glass is inserted in front of the lower slit
. The central bright fringe (path difference = 0) will be obtained
![](data:image/png;base64,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)
A monochromatic beam of light falls on YDSE apparatus at some angle (say
) as shown in figure. A thin sheet of glass is inserted in front of the lower slit
. The central bright fringe (path difference = 0) will be obtained
![](data:image/png;base64,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)
physics-General
maths-
Find the sum of the infinite series ![fraction numerator 1 over denominator 1.3 end fraction plus fraction numerator 1 over denominator 2.5 end fraction plus fraction numerator 1 over denominator 3.7 end fraction plus fraction numerator 1 over denominator 4.9 end fraction plus horizontal ellipsis horizontal ellipsis straight infinity](data:image/png;base64,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)
Find the sum of the infinite series ![fraction numerator 1 over denominator 1.3 end fraction plus fraction numerator 1 over denominator 2.5 end fraction plus fraction numerator 1 over denominator 3.7 end fraction plus fraction numerator 1 over denominator 4.9 end fraction plus horizontal ellipsis horizontal ellipsis straight infinity](data:image/png;base64,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)
maths-General
physics-
In the figure is shown Young’s double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is
, then
will be equal to
![](data:image/png;base64,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)
In the figure is shown Young’s double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is
, then
will be equal to
![](data:image/png;base64,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)
physics-General
physics-
Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by
. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio
![](data:image/png;base64,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)
Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by
. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio
![](data:image/png;base64,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)
physics-General
physics-
In an interference arrangement similar to Young's double slit experiment, the slits
are illuminated with coherent microwave sources each of frequency
. The sources are synchronized to have zero phase difference. The slits are separated by distance d = 150 m. The intensity I
is measured as a function of
, where
is defined as shown. If I0 is maximum intensity, then
for
is given by
![](data:image/png;base64,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)
In an interference arrangement similar to Young's double slit experiment, the slits
are illuminated with coherent microwave sources each of frequency
. The sources are synchronized to have zero phase difference. The slits are separated by distance d = 150 m. The intensity I
is measured as a function of
, where
is defined as shown. If I0 is maximum intensity, then
for
is given by
![](data:image/png;base64,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)
physics-General
physics-
In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on
for constructive interference at P between the ray BP and reflected ray OP
![](data:image/png;base64,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)
In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on
for constructive interference at P between the ray BP and reflected ray OP
![](data:image/png;base64,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)
physics-General