Maths-
General
Easy

Question

In straight triangle A B C comma 4 R straight capital delta sin A over 2 sin invisible function application B over 2 sin invisible function application C over 2 equals

  1. straight capital delta squared
  2. straight capital delta squared over S
  3. straight capital delta squared S
  4. S over straight capital delta squared

The correct answer is: straight capital delta squared over S

Related Questions to study

General
Maths-

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets square root of x squared plus a x plus b end root minus x close square brackets

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets square root of x squared plus a x plus b end root minus x close square brackets
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator open square brackets square root of x squared plus a x plus b end root minus x close square brackets open square brackets square root of x squared plus a x plus b end root plus x close square brackets over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator x squared plus a x plus b minus x squared over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator a x plus b over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction
d i v i d i n g space t h e space n u m e r a t o r space a n d space d e n o m i n a t o r space b y space x comma
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator a plus begin display style b over x end style over denominator open square brackets square root of 1 plus begin display style a over x end style plus begin display style b over x squared end style end root plus 1 close square brackets end fraction
equals fraction numerator a over denominator square root of 1 plus 1 end fraction
equals a over 2

Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets square root of x squared plus a x plus b end root minus x close square brackets

Maths-General
Lt subscript x not stretchy rightwards arrow straight infinity end subscript open square brackets square root of x squared plus a x plus b end root minus x close square brackets
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator open square brackets square root of x squared plus a x plus b end root minus x close square brackets open square brackets square root of x squared plus a x plus b end root plus x close square brackets over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator x squared plus a x plus b minus x squared over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator a x plus b over denominator open square brackets square root of x squared plus a x plus b end root plus x close square brackets end fraction
d i v i d i n g space t h e space n u m e r a t o r space a n d space d e n o m i n a t o r space b y space x comma
equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator a plus begin display style b over x end style over denominator open square brackets square root of 1 plus begin display style a over x end style plus begin display style b over x squared end style end root plus 1 close square brackets end fraction
equals fraction numerator a over denominator square root of 1 plus 1 end fraction
equals a over 2
General
Maths-

L t subscript n not stretchy rightwards arrow straight infinity end subscript sum from n equals 1 to n of   open square brackets fraction numerator 1 over denominator left parenthesis 2 n plus 1 right parenthesis left parenthesis 2 n plus 3 right parenthesis end fraction close square brackets

L t subscript n not stretchy rightwards arrow straight infinity end subscript sum from n equals 1 to n of   open square brackets fraction numerator 1 over denominator left parenthesis 2 n plus 1 right parenthesis left parenthesis 2 n plus 3 right parenthesis end fraction close square brackets
equals limit as n rightwards arrow infinity of fraction numerator 1 over denominator 3.5 end fraction plus fraction numerator 1 over denominator 5.7 end fraction plus fraction numerator 1 over denominator 7.9 end fraction plus....... plus fraction numerator 1 over denominator open parentheses 2 n plus 1 close parentheses left parenthesis 2 n plus 3 right parenthesis end fraction
equals limit as n rightwards arrow infinity of 1 half open parentheses 1 third minus 1 fifth plus 1 fifth minus 1 over 7 plus 1 over 7 minus 1 over 9 plus........ plus fraction numerator 1 over denominator 2 n plus 1 end fraction minus fraction numerator 1 over denominator 2 n plus 3 end fraction close parentheses
equals limit as n rightwards arrow infinity of 1 half open parentheses 1 third minus fraction numerator 1 over denominator 2 n plus 3 end fraction close parentheses
equals 1 half limit as n rightwards arrow infinity of open parentheses fraction numerator 2 n plus 3 minus 3 over denominator 3 left parenthesis 2 n plus 3 right parenthesis end fraction close parentheses
equals 1 half limit as n rightwards arrow infinity of open parentheses fraction numerator 2 n over denominator 6 n plus 9 end fraction close parentheses
u sin g space L space h o s p i t a l space t h e o r e m comma space
equals 1 half limit as n rightwards arrow infinity of open parentheses fraction numerator begin display style fraction numerator d blank over denominator d n end fraction end style 2 n over denominator begin display style fraction numerator d blank over denominator d n end fraction end style 6 n plus 9 end fraction close parentheses
equals 1 half cross times 2 over 6 equals 1 over 6

L t subscript n not stretchy rightwards arrow straight infinity end subscript sum from n equals 1 to n of   open square brackets fraction numerator 1 over denominator left parenthesis 2 n plus 1 right parenthesis left parenthesis 2 n plus 3 right parenthesis end fraction close square brackets

Maths-General
L t subscript n not stretchy rightwards arrow straight infinity end subscript sum from n equals 1 to n of   open square brackets fraction numerator 1 over denominator left parenthesis 2 n plus 1 right parenthesis left parenthesis 2 n plus 3 right parenthesis end fraction close square brackets
equals limit as n rightwards arrow infinity of fraction numerator 1 over denominator 3.5 end fraction plus fraction numerator 1 over denominator 5.7 end fraction plus fraction numerator 1 over denominator 7.9 end fraction plus....... plus fraction numerator 1 over denominator open parentheses 2 n plus 1 close parentheses left parenthesis 2 n plus 3 right parenthesis end fraction
equals limit as n rightwards arrow infinity of 1 half open parentheses 1 third minus 1 fifth plus 1 fifth minus 1 over 7 plus 1 over 7 minus 1 over 9 plus........ plus fraction numerator 1 over denominator 2 n plus 1 end fraction minus fraction numerator 1 over denominator 2 n plus 3 end fraction close parentheses
equals limit as n rightwards arrow infinity of 1 half open parentheses 1 third minus fraction numerator 1 over denominator 2 n plus 3 end fraction close parentheses
equals 1 half limit as n rightwards arrow infinity of open parentheses fraction numerator 2 n plus 3 minus 3 over denominator 3 left parenthesis 2 n plus 3 right parenthesis end fraction close parentheses
equals 1 half limit as n rightwards arrow infinity of open parentheses fraction numerator 2 n over denominator 6 n plus 9 end fraction close parentheses
u sin g space L space h o s p i t a l space t h e o r e m comma space
equals 1 half limit as n rightwards arrow infinity of open parentheses fraction numerator begin display style fraction numerator d blank over denominator d n end fraction end style 2 n over denominator begin display style fraction numerator d blank over denominator d n end fraction end style 6 n plus 9 end fraction close parentheses
equals 1 half cross times 2 over 6 equals 1 over 6
General
Maths-

L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator 1 cubed plus 2 cubed plus 3 cubed plus midline horizontal ellipsis comma plus n cubed over denominator n squared open parentheses n squared plus 1 close parentheses end fraction

L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator 1 cubed plus 2 cubed plus 3 cubed plus midline horizontal ellipsis comma plus n cubed over denominator n squared open parentheses n squared plus 1 close parentheses end fraction
equals L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style 1 fourth end style n squared open parentheses n plus 1 close parentheses squared over denominator n squared open parentheses n squared plus 1 close parentheses end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n squared plus 2 n plus 1 over denominator n squared plus 1 end fraction
u sin g space L space h o s p i t a l space t h e o r e m comma
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style fraction numerator d n squared plus 2 n plus 1 over denominator d n end fraction end style over denominator begin display style fraction numerator d n squared plus 1 over denominator d n end fraction end style end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator 2 n plus 2 over denominator 2 n end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n plus 1 over denominator n end fraction
A g a i n comma space u sin g space L space h o s p i t a l space t h e o r e m comma
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style fraction numerator d n plus 1 over denominator d n end fraction end style over denominator begin display style fraction numerator d n over denominator d n end fraction end style end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript 1 over 1
equals 1 fourth

L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator 1 cubed plus 2 cubed plus 3 cubed plus midline horizontal ellipsis comma plus n cubed over denominator n squared open parentheses n squared plus 1 close parentheses end fraction

Maths-General
L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator 1 cubed plus 2 cubed plus 3 cubed plus midline horizontal ellipsis comma plus n cubed over denominator n squared open parentheses n squared plus 1 close parentheses end fraction
equals L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style 1 fourth end style n squared open parentheses n plus 1 close parentheses squared over denominator n squared open parentheses n squared plus 1 close parentheses end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n squared plus 2 n plus 1 over denominator n squared plus 1 end fraction
u sin g space L space h o s p i t a l space t h e o r e m comma
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style fraction numerator d n squared plus 2 n plus 1 over denominator d n end fraction end style over denominator begin display style fraction numerator d n squared plus 1 over denominator d n end fraction end style end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator 2 n plus 2 over denominator 2 n end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n plus 1 over denominator n end fraction
A g a i n comma space u sin g space L space h o s p i t a l space t h e o r e m comma
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style fraction numerator d n plus 1 over denominator d n end fraction end style over denominator begin display style fraction numerator d n over denominator d n end fraction end style end fraction
equals 1 fourth L t subscript n not stretchy rightwards arrow straight infinity end subscript 1 over 1
equals 1 fourth
parallel
General
physics-

An isosceles prism of angle 1200 has a refractive index of square root of 2 Two parallel monochromatic rays enter the prism parallel to each other in air as shown the rays emerging from the opposite face

An isosceles prism of angle 1200 has a refractive index of square root of 2 Two parallel monochromatic rays enter the prism parallel to each other in air as shown the rays emerging from the opposite face

physics-General
General
physics-

A light beam is travelling from Region I to Region IV (refer figure) The refractive index in Region I, II, III and IV are n subscript 0 end subscript comma fraction numerator n subscript 0 end subscript over denominator 2 end fraction comma fraction numerator n subscript 0 end subscript over denominator 6 end fraction text  and  end text fraction numerator n subscript 0 end subscript over denominator 8 end fraction, respectively The angle of incidence q for which the beam just misses entering Region IV is

A light beam is travelling from Region I to Region IV (refer figure) The refractive index in Region I, II, III and IV are n subscript 0 end subscript comma fraction numerator n subscript 0 end subscript over denominator 2 end fraction comma fraction numerator n subscript 0 end subscript over denominator 6 end fraction text  and  end text fraction numerator n subscript 0 end subscript over denominator 8 end fraction, respectively The angle of incidence q for which the beam just misses entering Region IV is

physics-General
General
physics-

A ray of light, travelling in a medium of refractive index 2, is incident onto the flat surface of a slab, the angle of incidence being 37° The refractive index m of the material of the slab varies with depth (x) from the top surface as mu open parentheses x close parentheses equals R open parentheses 2 minus x close parentheses, where x is in ‘m’ and R is 1 m–1 The maximum depth reached by the ray is text  (take  end text open sin invisible function application 37 to the power of ring operator end exponent almost equal to 0.6 close parentheses

A ray of light, travelling in a medium of refractive index 2, is incident onto the flat surface of a slab, the angle of incidence being 37° The refractive index m of the material of the slab varies with depth (x) from the top surface as mu open parentheses x close parentheses equals R open parentheses 2 minus x close parentheses, where x is in ‘m’ and R is 1 m–1 The maximum depth reached by the ray is text  (take  end text open sin invisible function application 37 to the power of ring operator end exponent almost equal to 0.6 close parentheses

physics-General
parallel
General
physics-

A container is filled with water (m = 1.3(C) upto a height of 33.25 cm A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level The focal length of the mirror is

A container is filled with water (m = 1.3(C) upto a height of 33.25 cm A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level The focal length of the mirror is

physics-General
General
physics-

White light is incident on the interface of glass and air as shown in the figure If green light is just totally internally reflected then the emerging ray in air contains

White light is incident on the interface of glass and air as shown in the figure If green light is just totally internally reflected then the emerging ray in air contains

physics-General
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physics-

A ray of light is incident at the glass-water interface at an angle i it emerges finally parallel to the surface of water, then the value of mg would be

A ray of light is incident at the glass-water interface at an angle i it emerges finally parallel to the surface of water, then the value of mg would be

physics-General
parallel
General
physics-

A ray of light travels from a medium of refractive index m to air Its angle of incidence in the medium is i, measured from the normal to the boundary, and its angle of deviation is d d is plotted against i which of the following best represents the resulting curve

A ray of light travels from a medium of refractive index m to air Its angle of incidence in the medium is i, measured from the normal to the boundary, and its angle of deviation is d d is plotted against i which of the following best represents the resulting curve

physics-General
General
maths-

if blank to the power of straight prime O to the power of straight prime is the Orthocentre of straight triangle A B C t h e n space OA equals

if blank to the power of straight prime O to the power of straight prime is the Orthocentre of straight triangle A B C t h e n space OA equals

maths-General
General
physics-

A cubical block of glass of refractive index n1 is in contact with the surface of water of refractive index n2 A beam of light is incident on vertical face of the block (see figure) After refraction, a total internal reflection at the base and refraction at the opposite vertical face, the ray emerges out at an angle q The value of q is given by :

A cubical block of glass of refractive index n1 is in contact with the surface of water of refractive index n2 A beam of light is incident on vertical face of the block (see figure) After refraction, a total internal reflection at the base and refraction at the opposite vertical face, the ray emerges out at an angle q The value of q is given by :

physics-General
parallel
General
physics-

A diverging beam of light from a point source S having divergence angle a , falls symmetrically on a glass slab as shown the angles of incidence of the two extreme rays are equal If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

A diverging beam of light from a point source S having divergence angle a , falls symmetrically on a glass slab as shown the angles of incidence of the two extreme rays are equal If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

physics-General
General
physics-

A ray of light passes through four transparent media with refractive indices mu subscript 1 end subscript comma mu subscript 2 end subscript comma mu subscript 3 end subscript text  and  end text mu subscript 4 end subscript as shown in the figure, the surfaces of all media are parallel If the emergent ray CD is parallel to the incident ray AB, we must have

A ray of light passes through four transparent media with refractive indices mu subscript 1 end subscript comma mu subscript 2 end subscript comma mu subscript 3 end subscript text  and  end text mu subscript 4 end subscript as shown in the figure, the surfaces of all media are parallel If the emergent ray CD is parallel to the incident ray AB, we must have